WO2000036520A1

WO2000036520A1 - System and method for measuring movement of objects

Info

Publication number: WO2000036520A1
Application number: PCT/US1999/029719
Authority: WO
Inventors: Lawrence J. Hutchings; Richard Gross; Stephen Jarpe
Original assignee: Acceleron Technologies, Llc.
Priority date: 1998-12-16
Filing date: 1999-12-15
Publication date: 2000-06-22
Also published as: US6305221B1; US6122960A; AU2480200A; WO2000036520A9

Abstract

A device (10) that measures the distance traveled, speed, and height jumped of a person while running or walking. Accelerometers and rotational sensors are placed in the sole of one shoe along with an electronic circuit that performs mathematical calculations to determine the distance and height of each step. A radio frequency transmitter (12) sends the distance and height information to a wristwatch or other central receiving unit. A radio frequency receiver (14) in the wristwatch or other unit is coupled to a microprocessor that calculates an output speed based upon step-distance and elapsed time, and the distance traveled of the runner from the sum of all previous step distances. The output of the microprocessor is coupled to a display (18) that shows the distance traveled, speed, or height jumped of the runner or walker.

Description

SYSTEM AND METHOD FOR MEASURING MOVEMENT OF OBJECTS

FIELD OF THE INVENTION

This invention relates generally to the field of motion analysis and is

particularly directed to a system and method for determining the speed, distance and

height traversed by a person or an object while in motion, for navigation, and for

three-dimensional tracking and analyzing the motion of moving objects.

BACKGROUND OF THE INVENTION

In recent years many individuals have turned to their own fitness

program of regular jogging. As used herein, jogging is also intended to include

running and walking and the words are used interchangeably. Jogging has long been

recognized for its therapeutic effects on the body. It purportedly increases

cardiopulmonary fitness, helps to lower blood pressure, decreases cholesterol and

triglycerides associated with heart disease and reduces weight. Jogging is also one of

the easiest exercises to do. It requires no athletic ability and can be done almost any

time and any place with a minimum of equipment and without assistance. In more

recent times, jogging has also gained acceptance for its recreational value as well and

is recognized as a positive factor in promoting psychological well being.

The popularity of jogging today is well documented by the large

numbers of products and literature available to the public. As in many exercise and

sporting endeavors, there exists in the prior art a wide variety of devices for aiding

those who jog. Many people who run, jog or walk regularly desire to know their progress over time. Therefore, it is desirable to know the accurate distance and speed

traveled during an exercise session. This information allows a jogger to monitor his

or her progress and accordingly pursue a regular course of exercise designed to

enhance performance.

Further, it has become desirable to accurately measure the speed of

amateur and professional runners, both in training and during competition. In the prior

art, such measurements were made with a stopwatch timing the runner over a known

distance. Heretofore, it has not been possible to obtain accurate instantaneous speeds

of runners or height ascended or descended using the measuring devices currently

known in the prior art.

The simplest jogging aids for measuring movements are basic pacing

timers such as those disclosed in U.S. Pat. No. 3,540,344 to Veech and U.S. Pat. No.

3,882,480 to Greber. Pacing timers generate a repetitive audio tone signal at selected

intervals for pacing the strides of the jogging, where the length of the interval between

tones is adjusted to suit the pace of the individual jogger.

There are other running aids known in the prior art such as pedometers

as disclosed in U.S. Pat. No. 4,053,755 to Sherrill. These devices usually count the

number of steps taken and for a particular stride length, the approximate distance

traversed can be determined.

Human speedometers and odometers that measure the speed and

distance traveled by a person include devices that utilize ultrasound to measure the

distance between each foot such as disclosed in U.S. Pat. No. 4,736,312 to Dassler.

Also used is a device that measures the elapsed time of shoe in contact with the ground and converts this to the length of step and speed as disclosed In U.S. Pat. No.

4,578,769 to Frederick.

While pacing timers, pedometers, ultra sound, and elapsed foot-time-

distance devices are useful to the runner and walker, they are deficient in several

areas. For example, while ultra sound devices can measure the distance between two

feet, this is not equivalent to the length of a step or a stride, which is defined as the

distance traveled by the same foot from the beginning of a stride till the end of the

same stride. For example, the difference between (1) separation between feet, as

measured by the ultra sound device, and (2) stride length, is different for each person

and will vary for different speeds of running.

Furthermore, devices that employ elapsed-foot-contact-time

measurements, have significant errors in measuring stride length. It is known that

above a certain speed, stride length begins to increase as speed increases, and the

relationship of stride length to speed is not directly proportional, and moreover, is

different for each runner. In addition, most of the devices mentioned above require

calibration, which may prove to be a difficult task. For example, many of these

devices need to be calibrated by the manufacturer or by specially designed equipment.

It is, therefore, a difficult task to determine the correct stride length for

an individual runner at various speeds. Thus, pacing timers can provide no more than

a constant running pace, and pedometer measurements are only useful as an

approximation of distance traversed. Also, ultra sound and elapsed-foot-time-distance

devices provide only a rough approximation of actual distance traveled and speed of

the person. Also, none of the prior art includes a measurement of height jumped. Running and walking aids known in the prior art are often deficient and cumbersome

to use and they often add weight to the runner or walker while providing only

marginal utility in terms of the amount of information available and its accuracy.

The need to track the movement of objects extends to many

applications such as any object moving in a 1-, 2-, or 3 -dimensional environment.

This includes objects such as vehicles, animals, robots, machine parts,

limbs/extremities. It may also include other objects where the motion analysis

capabilities of this invention may be applied to measure and analyze data captured

such as speed, distance, acceleration, velocity, angle of rotation, number of cycles of

rotational movement, position relative to a known reference frame, and direction of

movement.

With the foregoing in mind, there is a desire for an improved tracking

device that should: be light in weight; serve a number of useful functions; be

inexpensive; be relatively small in size; be wearable or easily insertable or attachable;

provide measurements that are readily available to the user; be reliable and easy to

use; and provide accurate measurements of speed, distance traversed, height jumped,

and other useful information relating to a motion of an object.

OBJECT OF THE INVENTION

It is the overall objective of this invention to provide a new and

improved motion analysis measuring system, which overcomes the disadvantages of

the prior art devices and substantially increases the amount and accuracy of

information available to users such as joggers. A specific objective of this invention is to provide a new and improved

running and walking measuring system, in which the speed of the runner can be easily

and accurately determined.

A further specific objective of this invention is to provide a new and

improved running and walking measuring system, in which the distance traversed by a

runner can be easily and accurately determined.

Another specific objective of this invention is to provide a new and

improved running measuring system, in which the height jumped by a runner or a

jogger can be easily determined.

Another specific objective of this invention is to provide a new and

improved running measuring system, in which the elevation change by a runner or

jogger can be easily determined.

Another specific objective of this invention is to utilize magnetometers

to provide the direction of travel relative to magnetic north.

In accordance with another aspect of the invention, the measuring

system can utilize magnetometers along with gravity measurements to determine the

rotation of the device.

Another specific objective of this invention is to utilize magnetometers

along with rotation sensors and linear accelerometers that provide signals, which are

low passed filtered to obtain gravity tilt measurements, along with unfϊltered signals

provided by linear accelerometers to configure a system that has up to twelve-degrees

of freedom resulting in multiple measurement information and improved accuracy.

Another specific objective of this invention is to provide a new and improved running measuring system that can be utilized for navigation of a person or

an object within an earth (or local global) coordinate system.

Another specific objective of this invention is to couple it with a

Global Positioning Systems (GPS) to determine the location on the earth of a person,

animal or object.

Another specific objective of this mvention is to couple it with radar to

identify the location of objects relative to the device, and to navigate around the

objects.

Another specific objective of this invention is to utilize radar to

identify whether objects along a potential path of travel path are metallic, wood, or

flesh.

Another specific object of the invention is to couple it with a synthetic

voice system to communicate this to the user with a voice synthesis system or an

alarm.

Another specific objective of this invention is to provide a new and

improved three-dimensional tracking and motion measuring system of persons,

extremities, limbs, or objects, in which the path, direction and position data captured

by the sensors and associated with the motion measured can be graphically presented

in real-time or stored for later display and analysis.

Another specific objective of this invention is to provide a new and

improved accuracy of a measuring system by employing clusters of measuring

devices, so that the information gathered can be deemed redundant and random errors are averaged out.

Another specific objective of this invention is to provide a new and

improved accuracy of a measuring system by employing neural -networks.

A still further objective of this invention is to provide a new and

improved running and walking and general motion measuring system having the

above advantages which is light in weight, relatively inexpensive and convenient to

use.

SUMMARY OF THE INVENTION

In accordance with one aspect of the invention, a device for measuring

the performance of people or objects utilizes accelerometers and rotational sensors to

measure the speed, distance traveled, and height ascended or descended. It may be

attached to the sole of a shoe to measure the length of each step, and the sum of steps

can be used to calculate the distance traveled. The sum distance of a number of

previous steps divided by the elapsed time is used to calculate the velocity. In another

aspect of the invention, it may be attached to any part of the body or object and

information signals may be transmitted to the user's watch or other means for display.

In order to alleviate the measurement errors caused by employing the

measuring system, the system sets a reference frame coordinate system that maintains

the same orientation during a cycle. A cycle is a period of time over which a discrete

measurement is made, such as a step. A translation coordinate system moves with the

device and is aligned with the sensors. One set of three-component linear

accelerometers and one set of three-component rotational sensors record motions in the translation coordinate system. Magnetometers may also be employed as described

below. An indication signal may be configured to identify the beginning and end of a

cycle. Accelerations recorded in the translation coordinate system are transformed to

the reference frame coordinate system. Time is incorporated in the device so that

accelerations may be integrated. The length of travel during a cycle is obtained by

integrating twice. Once the length of motion during a cycle is determined, the elapsed

time is used to obtain the speed of the person or object. The maximum value of the

vertical displacement is used to determine the height ascended, or jumped, or

descended during a cycle. The sum length of several cycles is used to obtain the

distance traveled and the total elevation change.

Preferably, in order to alleviate the effects of gravitational field on the

accelerometers, the system initiates a new cycle at a time when the velocity of the user

is constant and the measured acceleration is influenced substantially by gravity.

Gravity measurements obtained at the beginning of a cycle are utilized to correct for

the effect of gravity in the reference frame during the cycle.

Another specific aspect of this invention is to utilize magnetometers to

provide the direction of travel relative to magnetic north within a global coordinate

system. A global coordinate system is one that does not change over time, such as an

earth coordinate system or a grid within a city or a golf course. At a time when the

reference frame coordinate system is oriented such that one axis is parallel with the

gravity vector, the other two magnetometers aligned along the other two axes provide

a signal that corresponds to a compass direction of declination from magnetic north.

The third magnetometer aligned along the gravity vector provides a value to calculate the inclination, or the angle of the magnetic field with the earth's surface. The

declination can be utilized to provide a direction of travel relative to the earth's

magnetic north or to another global coordinate system.

In accordance with another aspect of the invention, the measuring

rotation of the device. In situations where the apparent acceleration of the device is

primarily due to the affect of tilt in the gravity field or the rate of tilt is at a lower

frequency than the changes in linear accelerations of the device, then the linear

acceleration signals can be low pass filtered such that the accelerations due to tilt in

the gravity field are primarily measured. In situations where the rate of tilt is much

slower than the rate of change of linear accelerations and the amplitude of acceleration

due to tilt is also much larger than that due to linear accelerations of the device, errors

in using accelerations signals to calculate rotation are minimal.

In accordance with another embodiment of the invention, rotation rate

sensors or rotational accelerometers are also utilized along with linear accelerometers

and magnetometers, leading to a system with 9 degrees of freedom. If the linear

acceleration signals are low passed filtered for gravity tilt measurements and linear

accelerations due to the device are utilized separately, then the system utilizes six

degrees of acceleration signal and constitutes a twelve degree of freedom system.

Another specific aspect of this invention is to provide a new and

improved measuring system that can be utilized for navigation of a person or an

object. Navigation begins at an initiation point where the location of the person or

objet is known within a global coordinate system. The basic approach to navigation is to use the device to calculate the distance and direction of travel and keep track of

location within the global coordinate system. Accuracy is improved by measuring

position over segments of movement. At the initiation of a cycle of measurement the

reference frame coordinate system is transformed to a global coordinate system. At

the end of each cycle, the vector solution in the global coordinates system is

determined and new position in the global coordinate system is calculated.

Another specific aspect of this invention is to couple a measuring

system in accordance with one embodiment of the invention with a Global Positioning

Systems (GPS) to determine the location on the earth of a person, animal or object. At

the beginning of navigation the position within an earth coordinates system is

determined, and at the end of each cycle, the vector solution in the earth's coordinates

system is determined and the new position in the global coordinate system is

calculated. Periodically, at the beginning of a cycle, a new position within the earth's

coordinate system is determined from a GPS and the accuracy is improved by

updating the navigation position determined by the device.

Another specific aspect of this invention is to couple a measuring

system in accordance with one embodiment of the invention with radar to navigate

around objects. A radar system is adjusted for aperture and distance range to identify

the location of objects relative to the device along a potential path of travel, and the

device can be used to navigate around them. Further, radar signal recognition can be

utilized to identify whether the object is metallic, wood, or flesh from radar signals.

Another specific aspect of the invention is to couple it with a synthetic

voice system. A synthetic voice system can sound the alarm if one approaches an object, or can identify the type of object identified in radar signals.

Another specific aspect of this invention is to provide a new and

improved three-dimensional tracking system of persons, extremities, or objects that

can be stored for detailed analysis.

Acceleration, velocity, and displacement is known as a function of time

within a specified global or reference frame coordinates system. Typically the entire

path of a running or walking excursion within a global coordinate system, or a golf

swing, running stride, or swimming stroke within a reference frame coordinate system

can be stored by the device.

Another specific objective of this invention is to provide a new and

improved accuracy by employing clusters of the device, so that the information

gathered is redundant and random errors that occur due to sensor inaccuracies can be

reduced.

Another specific aspect of this invention is to provide a new and

improved accuracy by employing neural-networks. For this invention, neural

networks may be used to increase the accuracy of the computed distance or location

by providing corrections based on characteristics of the measured sensor inputs. A

neural network is a form of non-linear filter that can have its coefficients determined

by a "training set" of empirical data. The training set is a collection of input data that

produce known outcomes. The training set is used to produce a nonlinear network of

filter coefficients that can determine the correct outcome from new input data. The

exact nature of the corrections and the relationship of the corrections to the input data would be determined by training a neural network with empirical data having a known outcome.

A still further objective of this invention is to provide a new and

improved running and walking and general motion measuring system having the

use.

BRIEF DESCRIPTION OF THE DRAWINGS

The subject matter regarded as the invention is particularly pointed out

and distinctly claimed in the concluding portion of the specification. The invention,

however, both as to organization and method of operation, together with features,

objects, and advantages thereof may best be understood by reference to the following

detailed description when read with the accompanying drawings in which:

Fig. 1 illustrates one embodiment of the invention as employed by a

user.

Fig. 2 illustrates the location of the system's components in the sole of

the shoe, in accordance with an embodiment of the invention.

Fig. 3 is a coordinate system for the reference frame of the stationary

ground, and the vectors of linear and rotational motion that are necessary to determine

motion of the foot in accordance with one embodiment of the invention.

Fig. 4 is a side view diagram of the foot during running, illustrating

information employed to resolve step length in two dimensions in accordance with

one embodiment of the invention. Fig. 5 is a vector diagram illustrating output acceleration, velocity and

displacement of one embodiment of the invention during running.

Fig. 6 illustrates the reference frame and a plot of the path of the

motion of a wrist during walking or jogging, and the measurement of the distance

traveled in accordance with one embodiment of the invention.

Fig. 7 illustrates a plot that explains possible errors caused by locating

the measuring system in the wrist of a user.

Fig. 8 illustrates the coordinate system utilized to measure the distance

traveled by a user employing the measuring system in the wrist or other areas of the

body.

Fig. 9 illustrates how the reference frame coordinate system can be

transformed to a gravity aligned reference frame.

Fig. 10 illustrates how the measuring system may be used for

navigation.

Fig. 11 illustrates how the measuring system may be used to navigate

around objects.

Fig. 12 illustrates how the measuring system may be used to analyze

the movement of objects in three dimensions.

Fig. 13 illustrates how the magnetometers are used along with

accelerometers that are low-pass filtered to obtain tilt measurements of gravity to

calculate the rotation of the device.

Fig. 14 illustrates how several devices are employed to provide

redundant information and random errors can be averaged out. Fig. 15 illustrates how neural networks can be employed to improve accuracy.

Fig.16 is a block diagram of the electronic units necessary to solve

equations for step length in accordance with the invention.

DETAILED DESCRIPTION OF THE INVENTION

Fig.l shows an embodiment of a measuring system 10 as employed by

a user, although the invention is not limited in scope to the location of different

components of the system as illustrated herein. For example, the components of the

measuring system may be located at other parts of the body, such as the wrist and the

waist area. In accordance with the embodiment illustrated in Fig. 1, the shoe of the

user may include interrelated elements such as linear accelerometers; rotational

sensors; a microprocessor to calculate the distance and height of each step; a foot

impact switch; battery; and a radio transmitter 12, as will be explained in more detail

below.

As shown in Fig.l, the user may wear a hand display having a radio

receiver 14. The radio receiver may alternately be located at a remote site so that the

performance of the runner can be monitored by another person. Incorporated into the

receiving unit may be a microprocessor for processing the received signals into the

speed of the runner, the distance traversed and the height jumped. The processed

information may be selectively displayed on display 18. The hand display may also

perform other functions; for example, it may selectively display normal watch functions, such as time of day, date, alarm and stop watch signals.

Fig. 2 shows one possible location of different components of the

measuring system in the sole of the user's shoe. However, the invention is not limited

in scope in this respect, and various components of the system in accordance with the

present invention may be implemented in a variety of arrangements. Accelerometers

2, rotational sensors 4 and a contact switch 8 are preferably placed in the ball-of-the-

foot portion of the sole of the shoe so that they may come in contact with the ground

for each step during either walking or running. As it will explained in more detail

below, the measuring system in accordance with the present invention may also

operate without contact switch 8. Measuring system 10 may include three rotational

sensors 4, each configured to measure the angle of the user's foot with respect to a

reference frame as will be explained in more detail below. Rotational sensors 4 are

well known, such as those provided by AMP model numbers ACH-04-08. Each

rotational sensor converts the measured angle into a corresponding signal, which is

employed by a microprocessor 6 to calculate information related to the user's

movements, such as user's speed, distance traveled and the height jumped. It will be

appreciated that the present invention is not limited in scope to the components

illustrated in Fig. 2. For example, instead of contact switch 8, other means may be

employed so as to generate a signal to indicate the beginning of each step.

Measuring system 10 preferably includes three accelerometers 2, each

configured to measure the acceleration of the user's foot with respect to a reference frame as will be explained in more detail below. The accelerometers may also be

located in the sole of the user's shoe. Accelerometers 2 are well known, such as those

provided by Analog Devices model ADXL05. Each accelerometer may convert the

measured acceleration into a corresponding signal, which may be preferably employed

by microprocessor 6 to accomplish movement measurements.

Also, other components may be separated and placed in another

portion of the shoe. For example, the measuring system may be placed at another

location of the shoe or another location in the body of the user.

Fig. 3 illustrates a plot of the coordinate systems necessary to resolve

step length and height. In the present context, a first coordinate system, such as (x, y,

z) 22, is referred to as the reference frame coordinate system of the stationary ground.

(γ_x, γ_y, γ_z) are the rotational coordinates about the x, y and z axes of the reference

frame. In one embodiment of the invention, rotation about the z axis may not be

measured. These values advantageously indicate the slope of the ground at the

beginning of the step. Preferably, the reference frame coordinate system is reset at the

initiation of a new step and remains stationary throughout the time the same foot

leaves and touches the ground again. The orientation of the reference frame

coordinate system with respect to the foot is arbitrary, but it is preferably selected so

that at the beginning of the step the positive x direction may be aligned with the axis

of the sole of the shoe, the positive y axis may be in the same plane as the sole and at

right angles to the x axis, and the positive z axis may be normal to the plane of the sole of the shoe. The arrows in Fig. 3 indicate the direction of positive motion. The

length and height of each step with respect to this coordinate system may be measured

in accordance with the present invention as explained in more detail hereinafter. The

reference frame coordinate system changes within each cycle.

Fig. 3 also illustrates a second coordinate system, such as (X, Y, Z) 24,

referred to as the translational coordinate system of the linear accelerometers. This

coordinate system moves with the foot and may be centered at the location of the

sensors. Fig. 3 further illustrates rotational coordinates, such as (θ_x , θ_y, θ_z) about

the axes X, Y and Z. These rotational coordinates may be employed advantageously

to keep track of the orientation of the (X, Y, Z) coordinate system relative to the (x, y,

z) coordinate system, as will be explained below, and to resolve the accelerations

along the reference frame.

In Fig.3, an exemplary foot is shown part way through a step that

moves along a trajectory r such as 25. The orientation of the translational coordinate

system with respect to the foot is the same as described for the reference frame, but

moves with the foot. Preferably, the reference and translational coordinate systems

may be aligned together every time a new step is initiated. Furthermore, in

accordance with another embodiment of the invention as explained in reference with

Figs. 7 - 9, the orientation of the reference frame and the translational coordinate

system may be aligned at a beginning of a cycle which may comprise more than one

step. Further, in accordance with another embodiment of the invention as explained in reference with Figures 10 - 12, the orientation of the reference frame coordinate

with respect to the global coordinate system will be determined and absolute motion

in the global reference frame is calculated, in accordance with another embodiment of

the invention.

Fig. 4 illustrates an example of a motion of the foot and how the length

of the step is resolved for a motion in one plane, along two dimensions (here, the

plane of the paper), and for a step along a horizontal surface. The reference frame

coordinate system 26 is that described as 22 in Fig. 3, and the translational coordinate

system 28 is that described as 24 in Fig. 3. The foot is shown part way through a step

having moved along trajectory r such as 29. The translational coordinate system is

moving along trajectory r 29, as described in Fig. 3.

Fig. 4 also illustrates acceleration vectors (A_x, A_z) in the translational

coordinate system. These accelerations are represented by arrows aligned along the X

and Z axes of the translation coordinate system, respectively. The length of the arrows

represent the amount of acceleration for each component (30 and 32, respectively).

The angle of rotation about the y axis relative to the reference frame coordinate

system is θ_y. From these components of motion the acceleration relative to the

reference frame coordinate system can be resolved. This is shown as a_x and a_z in the

reference frame (34 and 36, respectively).

The amount of acceleration and its direction (a vector solution) is preferably employed to keep track of forward and reverse motions of the foot. For

example, if motion remains in the (z, x) plane and the surface is horizontal (Fig. 4), then

a_x = A_x cosθ_y + A_z sinθ_y (1)

a_z = -A_x sinθ_y + A_z cosθ_y - g (2)

Where g is the acceleration due to gravity, which is preferably considered as a factor

due to the use of accelerometers; this follows because typically the accelerometers

that may be employed by the measuring system are of the type that are affected by

gravity. However, the invention is not limited in that scope. For example, if an

accelerometer that is not influenced by gravity is employed then the g factor in

equation (2) may be omitted. Gravity may be assumed to be a constant as explained in

more detail below. Here, acceleration a_z is assumed to be vertical and aligned with the

orientation of gravity. However, the invention is not limited in that scope. For

example, acceleration d^ may be aligned at an angle from the direction of gravity, such

as on a hill, as explained in more detail below. The -g factor added to the a_z

component of equation (2) is to balance the effect of gravity on the inertial

accelerometers. For example, if the user of the system is standing still, θ_y = 0 and

A_z= +g, then a_z = 0. If the user is moving up at g, A_z will read 2g, and a_z = g. If the

user moves down at g and θ_y = 180, A_z = 0, and a_z =-g. For forward horizontal

motion, with, for example, θ_y = 45°, A_z and A_x would be positive and substantially equal from motion, but there would be an added positive component g cos θ_y added to

A_z and an added negative g sinθ_y component added to A_x, and their sum would be

such that a_z = 0. The length of the step is obtained by integration as discussed in

reference with Fig. 5.

Fig. 5 shows the elements that may be employed to obtain a complete

solution of motion of the foot in three dimensions for an embodiment in or on the

shoe. The reference frame is established from the foot contact at the beginning of a

step 40. However the invention is not limited in scope in that respect, and in

accordance with other embodiments of the invention, the reference frame may be

established in other manners as explained in more detail below and in reference with

Figs. 6-8.

The reference frame z axis may be chosen such that it is not aligned

with gravity. For example, the reference frame z axis may not be aligned with the

direction of gravity if the ground (x, y plane) is not horizontal. In that event γ_y 42 is

the angle of the x axis in reference with a horizontal plane, and γ_x 44 is the angle of

the y axis in reference with the horizontal plane. These values are unknown, as they

depend on the orientation of the reference frame in relation to the gravity, such as for

example, the slope of the ground at the beginning of each step, and are calculated by

measuring system 10, as explained below. At any point along the trajectory r, the

components of motion in the reference frame can be determined from the linear

accelerometers and rotational sensors in the translational coordinate system 46. a_x = C, A_x + C₂A_y + C₃A_Z - g sinγ_x (3)

a_y = C₄A_X + C₅A_y + C₆A_Z - g sinγ_y (4)

a_z = C₇A_X + C₈Ay + C₉A_Z - g cosγ_xcosγ_y (5)

where the C] - C₉ are transformation coefficients that are determined from the output

signals generated by rotation sensors. These signals represent, for example, the angles

or incremental changes of the angles that are shown in Fig. 5. The angles may be

determined from rotation sensors that provide signals corresponding to rotation angles

of the embodiment. These rotation sensors may comprise rotation accelerometers or

rotation rate sensors. In accordance with another embodiment of the invention,

rotation angles are measured by magnetic field sensors, also referred to as

magnetometers, operating in conjunction with gravity tilt sensors as explained later

with reference to Fig. 13 and 16.

Since linear accelerometers also record gravity, it is necessary to keep

track of the contribution of gravity to the accelerometers and remove it from

measurements. The values for γ_x and γ_y may be determined at the initiation of each

step, and are substantially equal to zero for a substantially horizontal surface. At this

time the proportion of gravity recorded by the accelerometers is related, among other

things, to the angle from the vertical coordinate (as resolved by an accelerometer such

as the ADXL05, from Analog Devices).

γ_y = Sm '(A_y/g) (7)

It is not necessary to know the values of γ_x and γ_y to determine the

contribution of gravity. Since the reference and translational coordinate systems are

aligned at the initiation of a cycle, the component of gravity at the initiation of a cycle

is just the value of the accelerometer readings at that time, A°_x, A°_y, A°_Z. These terms

involving gravity g can be used to correct for the effect of gravity on the linear

accelerometers, and will be described further below.

There are several methods established in prior art to determine the

values of the coefficients C_t - C₉, such as described by , Titterton, D.H. and Weston,

J.L. Strapdown Inertial Navigation Technology. Peter Peregrins Ltd publisher, 1997;

Britting, Kenneth R. Inertial Navigation Systems Analysis, Wiley-Interscience, a

Division of John Wiley & Sons, Inc. (1971 Library of Congress no. 70-168635) and

incorporated herein by reference; Goldstein, Herbert Classical Mechanics, ch. 4,

Addison Wesley Publishing, Reading Massachusetts (1956) Van Bronkhorst, A. Euler

Angle Strapped-Down Computer, Advisory Group for Aerospace Research and

Development (AGARD), Inertial Navigation Systems and Components, North

Atlantic Treaty Organization (May 1968).

In accordance with one embodiment of the invention, one solution for

the coefficients C_] - C₉ is obtained from incremental rotations dθ, as described here.

Since rotation is not a vector quantity, it is necessary to develop a solution for θθ's,

in accordance with one embodiment of the invention, which act as a vector quantity. As explained hereinafter, the order of rotation for a measuring system

that measures relatively larger angles can provide more than one solution. For

example, the rotations individually about the three axes of a left-hand coordinate

system shown in Figure 5 is explained more fully below. To this end, the

transformation to the reference frame after a rotation about the Z axis is:

cosθ_z -sinθ_z 0 z-' = ssiinnθ θ_z, ccoossθ θ_z, 0 (8)

0 0 1

Where Z^"1 is referred to as a transformation matrix that transfers the coordinates from

the translational frame to the reference frame. The transformation to the reference

frame after a rotation about the Y axis is:

COSθy 0 sinθ_y

0 1 0 (9)

-sinθ_v 0 cosθ

Where Y^"1 is referred to as a transformation matrix that transfers the coordinates from

frame after a rotation about the X axis is:

1 0 0 X^'1 = 0 cosθ_x -sinθ_x (10)

0 sinθ_x cosθ_x

Where X"¹ is referred to as a transformation matrix that transfers the coordinates from

the translational frame to the reference frame. In order to transfer the coordinates of an

object's movement in a 3D space, to a reference frame, it is necessary to multiply the transformation matrices described in reference with equations (8), (9), and (10).

However, the order of rotation matters and the multiplication of the transformation

matrices in different order will result in a different transformation matrix. Therefore a

unique solution to the problem cannot be obtained by using whole angles in this

manner.

For instance, for transforming acceleration measurements using an

order of transformation defined by [Z^{~ l} Y^"1 X^"1^ will result in a 3 x 3 transformation

from the translational frame to transform acceleration signals (A_x A_y A_z) to the

acceleration signals (a_x a_y a_z) in the reference frame.

In that case, equations (3), (4) and (5) can be written as

[a_{x ,} a_y aj ^τ = Z^"1 Y^"1 X^"1 [A_x A_y A_z] ^τ - [A°_{x ,} A°_{y ,} A°_z] ^τ (11)

where,

|cosθ_y cosθ_z -cosθ_x sinθ_z +sinθ_x sinθ_y cosθ_z sinθ_x sinθ_z +cosθ_x sinθ_y cosθ_z|

|cosθ_y sinθ_z cosθ_x cosθ₂ +sinθ_x sinθ_y sinθ_z -sinθ_x cosθ_z +cosθ_x sinθ_y sinθ_z| (12) I -sinθ

Preferably, if a small angle approximation is made such that

cos dθ = 1 and sin(dθ)=dθ and, (dθxdθ)^O, (I)

then the equations for acceleration in the reference frame obtained from accelerations

in the translational frame can be expressed as: A_v - A_yaθ₂ + A,ae, A°_v (13)

a, = A_xaθ_z + A_y - A_Z3Θ_X - A°_y (14)

a. = -A_x3θ_y + A_ydθ_x + A_z - A°_z (15)

It is noted that any transformation order for multiplying the rotation

matrices will result in the same incremental rotation matrix, so that the rotations of the

transformation matrix act as a vector quantity and the solution is unique. The

recorded values A⁰ are used to correct for gravity as described above.

Advantageously, the computational steps start with the initiation of a

cycle. In order to measure only the gravitational field the accelerometers may be

substantially influenced by gravity and not by acceleration due to motion. Preferably,

the initiation of a cycle is a time when the velocity of the sensors is constant. In the

shoe embodiment, the shoe is stationary on the ground between each step and the

velocity is zero. An additional constraint can be imposed:

A°_x ² + A°_y ² + A°_Z ² = g² (16)

Thus, in accordance with one embodiment of the invention the

measuring system measures incremental changes of angels in a series of small time

steps, such as 1/50th of a second as long as condition (I) is sufficiently met. If the

transformation matrix from a translational coordinate to a reference coordinate, for

rotation for the initial time step is referred to as B^"1 (obtained from the rows and

columns of equations 13 - 15), then the acceleration vector in the reference frame is

given by [a] ^τ = B^A] ^1" - [A°] ^τ (17)

wherein [ ]^τ denotes a transpose matrix , and transformation matrix B^{" 1} is defined as

l -aθ_z aθ_y B-¹ = ae_z l -aθ_x (i s) -ae_y aθ_x i

In accordance with one embodiment of the invention, there are at least

three ways to determine the incremental angles dθ's. For example, the incremental

angles in one embodiment are derived based on, among other things, gravity and

magnetic field sensors or magnetometers as described below. In the alternative the

incremental angles are derived based among other things from rotation rate sensors

(such as Hitachi HGA-V). The incremental angles can also be derived from rotation

accelerometers (such as AMP model numbers ACH-04-08).

The measuring system in accordance with one embodiment of the

invention continuously measures an incremental transformation matrix as a new set of

incremental angles dθ's are measured. To this end, the initial transformation matrix

B^"1 is preserved and renamed

C^"1 for the next time step, and a new transformation matrix B^"1 is calculated. To

transform back to the reference frame for the second time step the system calculates

acceleration values in the reference frame as given by

[a] -^T = C¹B ¹[A] -^T - [A°r^τ (19)

For the following incremental angles, C 'B^"1 is preserved and renamed C^"1 for the next time step, and a new B^"1 is calculated for the next time step. At the

end of the next time step the new C 'B^"1 is preserved and renamed C^"1 for the

following time step. This is repeated for the entire measurement cycle.

In accordance with another embodiment of the invention, in order to

assure accurate measurements, the accelerometers employed in the present invention

are desired to be properly calibrated. The embodiments described herein may be

conveniently calibrated in accordance with the present invention. This follows

because gravity g only varies by less than 0.3% throughout the surface of the earth,

and provides a substantially constant value in a direction substantially aligned towards

the center of the earth. Therefore, the vertical component of accelerometer employed

in accordance with the present invention must generate an acceleration signal

substantially equal to gravity g when the device is stationary or moving at a constant

velocity within the earth's global coordinate system. It will be appreciated that an

embodiment in accordance with the present invention may be configured so as to

advantageously reset the value generated by the accelerometers to substantially

represent gravity g at that time. As such, the accelerometers employed in accordance

with the present invention may remain substantially calibrated at all times.

Since the accelerometers and rotation sensors are connected to a timing

device, their values may be known as a function of time. The horizontal and vertical

displacement may then be obtained by integrating by time as they traverse the path:

L_y = J J a_y(t)dt² (21)

L_z = I I a_z(t)dt² (22)

The integration is performed twice to obtain L_x, L_y, L_z shown in the

equations, where the constant of integration is zero if the foot is stationary at the

beginning and end of a cycle. Here, these values can be used for navigation since their

orientation is known with the global reference frame. L_z would be zero if the ground

remained at the slope of the beginning of the step, and would be significant if a

person, for example, climbed a step. To obtain the length of the step or

The maximum height H ascended is,

H = max(L_z) (24)

If L_z is not aligned with the vertical axis, the height ascended can be obtained by

resolving its component in the direction of gravity, as described above.

Fig. 6 illustrates the reference frame and a plot of the path of the

traveled in accordance with one embodiment of the invention. A reference coordinate

frame 120 is set at the initiation of a cycle, and remains fixed for the duration of the

cycle. For the purposes of the present embodiment, a cycle is the period during which a new reference frame is defined and remains fixed. Preferably, the system measures

the distance traveled during each cycle. As such, a cycle does not need to be related

to the steps of the user or a significant distance traversed, and can include several

steps. This reference frame may have a given orientation that is not necessary aligned

along the gravitational field.

The motion of the wrist during a couple of cycles is traced by a thin

line 122. The linear distance traveled by the wrist at the end of the first cycle is

shown as a straight arrow 124. A new cycle is initiated at the same instant, with a

new reference coordinate system 126. The linear distance to the position of the wrist

at the end of the second cycle is shown as a straight aπow 128. The total distance

traveled is the sum of distances for all cycles. The velocity of travel is the distance of

the cycle, or several cycles, divided by the time it takes to travel this distance. The

height jumped is not obtainable with the wrist embodiment because it is not possible

to differentiate between the height jumped by the person and the vertical movement of

wrist. However, in the embodiment where the measuring system is employed at the

waist of the user, the height jumped is also measurable.

Fig. 7 illustrates possible errors caused by locating the measuring

system in the wrist of a user. The movement of the wrist may cause a systematic error

due to the fact that the position of the measuring system at the beginning of a cycle

may not be the same as its position at the end of a cycle. For example, if the wrist is

moving in a circular, sideways, or up and down manner, the measuring system may exhibit an error as illustrated in Fig. 7. As illustrated, when the cycle starts with the

wrist in position 140, and ends with the wrist in position 142, when it should have

been in position 143, then the error is the difference between the distance A and A'. If

during the following cycle the wrist ends in position 144, then there is another error

caused by the difference between the length B and B'. However, this error is

negligible for most applications. For example, if the typical distance between position

142 and 143 is 12 inches, and the lateral distance of a cycle is 200 inches, then the

difference between A and A' is 1.1 inches, which is approximately a 0.5% error.

The error caused by erratic motions of the wrist is systematic as the

distance between A' is always longer than or equal to A, or B' is always longer than

or equal to B. The error depends upon the number of steps taken during a cycle.

A random error may occur due to the fact that a cycle begins or ends

such that the wrist is forward or behind the person. In such a circumstance the error

may be averaged out in following cycles. Thus, a series of cycles is used to calculate

overall distance in order to average out random errors. As a result it is desirable to

determine the length of a cycle that minimizes systematic errors yet allows enough

cycles to average out random error. In one embodiment of the invention, this length is

obtained by testing.

Fig. 8 shows an exemplary coordinate systems employed to obtain a

solution for the distance traveled by a person who employs the measuring system of the present invention at a wrist or a waist. As illustrated, Fig. 8 represents the same

parameters as discussed with reference to Fig. 5, except that the distance traveled is

measured from the wrist or the waist of the user rather than the shoe of the user. At

the initiation of a cycle the reference frame is set along a given orientation. The

reference frame remains fixed for the entire period of a cycle.

As mentioned before, a new reference frame is defined at the beginning

of each cycle. Preferably, each new cycle begins when the accelerometers are

substantially influenced by gravity and not by the acceleration of the measuring

device itself. To this end, the components of gravity acting on the three

accelerometers of the measuring device at the initiation of each cycle is

advantageously the value of the accelerometer readings A°_x , A°_y , and A°_z are due to

gravity, such that

It is noted that the system takes into account the effects of gravity at

the beginning of each cycle as set forth by equation (25) due to the fact that the

accelerometers employed in a preferred embodiment of the invention are forced

balance accelerometers that operate based on inertial mass effects. Thus, preferably a

distinction is made between the acceleration of the user and outside acceleration due

to an external force, such as gravity, acting upon the user. A forced balance

accelerometer considers an external force that pulls on the inertial mass in a particular direction as if the user is accelerating in the opposite direction. As a result, the effects

of gravity may be considered as if the user is accelerating with the same acceleration

substantially equal to effects of gravity.

Furthermore, preferably the velocity of the measuring device at the

beginning of each cycle is a constant, which indicates that the acceleration of the

measuring device itself is substantially zero, so that the accelerometers are influenced

substantially by the gravity and not by the acceleration of the measuring device.

Thus, in accordance with one embodiment of the present invention, the system

initiates a new cycle, whenever a predetermined number of velocity samples remain

constant. At this time, the orientation of gravity can be determined and used to

calculate the height jumped by a person.

As a result the acceleration of the measuring device along a reference

frame coordinate system 76 may be obtained as follows:

a_x = C₁A_x + C₂A_y + C₃A_z - A°_x (26)

a_y = C₄A_X + C₅A_X + C₆A_Z - A°_y (27)

a_z = C₇A_X + C₈Ay + C₉A_Z - A°_z (28)

Where the C, - C₉ are transformation coefficients that are determined

from the output signals as discussed above for Figure 5. The translational coordinate

system moves with the measuring system, such as the watch 78, and provides a value

of A_x , A_y , A_z and θ_x , θ_y , θ_z for determining the coefficients. The calculation of the length of travel during a cycle follows the description above in reference with Figure

5. The length traversed by the measuring system is obtained by integrating twice to

obtain Lx, Ly, and Lz:

L_x = II a_x(t)dt² + Tv°_x (29)

L_y = 11 a_y(t)dt² + Tv°_y (30)

L_z = I I a_z(t)dt² + Tv°_z (31)

where V°_x, V°_y and V°_z are the values of velocity of the sensors at the initiation of a

cycle and T is the time of the cycle. Trigger is set for a time interval, after which time

when V(t)_x, V(t)_y V(t)_z are constant a new cycle is started. These terms will naturally

be included in the integration. So, that at the completion of the first integral the

velocity at time t = 0, V°will be added to the integral. Performing the second integral

will result in displacement plus the velocity at time t = 0 times the time interval T. It

will be appreciated that at the beginning of the very first cycle, the device must be

stationary so that the initial values will be known, which will be zero. To obtain the

length of movement during a cycle,

L={L X ² ₊L y² ₊L x²

(32)

The maximum height H jumped is,

(33) H = max(L_z)

where, L_z is the unit vector aligned with gravity. In accordance with another embodiment of the invention, the

measuring system can be employed as a navigation system. It is noted that in a

navigation system, the movement of an object is measured along a global coordinate

system. Therefore, in addition to the reference frame and the translational frame

disclosed above, the navigation system keeps track of movement within this global

coordinate system. One example of a global coordinate system is the one that its z

axis is aligned with gravity and further includes an x,y axis with known orientation to

the magnetic North field. Thus, the translation to this global coordinate system

involves a two step process. First, the reference frame of the measuring device is

transformed to a gravity aligned coordinate system, such that the vertical axes is

aligned with gravity. The orientation of the horizontal axes is then determined in

relation with the magnetic North field. The measuring system for navigation

application includes three magnetometers aligned along the same axis as linear

accelerometers (Fig. 16).

Figure 9 shows the components necessary to transform from the

reference frame coordinate system to a gravity aligned coordinate system. It is

advantageous to align the coordinate system to gravity for navigation purposes. A

transformation to the gravity aligned coordinate system can be achieved by

multiplying the results obtained in equations (26), (27), (28) or equation (11) by a

gravity aligned transformation matrix H^"1. If this is done after the first time step, it is

not necessary to do it again until the cycle is restarted. At the initiation of a cycle,

when A°_x, A°_y> A°_z are measured, the transformation matrix to a coordinate system that has one axis aligned along the gravity field can be calculated. The values of A°_x, A°_y

A°_z must also be transformed, which should equal (0,0,g).

From Figure 5, the reference frame coordinate system (x,y,z) 80 shares

the origin with a gravity aligned coordinate system (x^g,y^g,x^g) 82, but the z axis is

rotated from the gravity axis. Here, gravity is shown as positive up, since an inertial

accelerometer will show positive g up when standing still. In the following, the first

index is from (x,y,z) relative to the second index (x ,y^g,z ). Figure 9 shows angles for

which several direction cosines are calculated, h, ,, h₂₂, h₃₃, h₂₁, h₃₂, h₁₃, but not all

nine. The direction cosine is the cosine of the angle. The direction cosine

transformation matrix can be constructed from the following constraints:

g² = A°_x ² + A°_y ² + A°_z ² (34)

h₃₃ = A g (35)

z^g, x^g, and x are in the same plane, then

h₁₂ = 0 (36)

the transformation matrix is scew symmetric, therefore

h₁₃ = -h₃₁; -h₁₂ = h₂,; and -h₂₃ = h₃₂ (37)

h₁₃ = A_x/g (38)

from orthogonality conditions: h, ,² + h₁₂ ² + h₁₃ ² = 1; h₂₁ ² + h₂₂ ² + h₂₃ ² = 1; and h₃₁ ² + h₃₂ ² + h₃₃ ² = 1

h, , h₁₂ + h_n h₁₃ + h₁₂ h, , + h₁₂ h₁₃ + h₁₃ h„ + h₁₃ h₁₂ = 0

h₂₁ h₂₂ + h₂₁ h₂₃ + h₂₂ h, + h₂₂ h₂₃ + h₂₃ h₂₁ + h₂₃ h₂₂ = 0

h₃₁ h₃₂ + h₃₁ h₃₃ + h₃₂ h₃, + h₃₂ h₃₃ + h₃₃ h₃₁ + h₃₃ h₃₂ = 0

Then, the direction cosines to transfer from inertial to gravity reference frame is H^"

h^ sqrttl -A- g²] (39) h₁₂ = 0 (40) h,₃ = A°_x/g (41) h₂₁ = 0 (42) h₂₂ = sqrt[l - A°² _y/g²] (43) h₂₃ = A°_y/g (44) h₃₁ = -A°_x/g (45) h₃₂ = -A°_y/g (46) h₃₃ = A°_z/g (47)

So, that in reference with discussions relating equation (19) ,for the initial time step:

C¹ = H B ' (48)

and

[A⁰] ^g = H^"1 [A⁰] (49)

wherein [ ] ^g denotes values in the global coordinate system. Transformation to

gravity aligned frame only needs to be carried out for the first time step in each new

cycle. Furthermore, in the gravity aligned coordinate system the height of one cycle,

i.e. height ascended, or the overall elevation achieved can be calculated. Fig. 10 illustrates how the measuring device is used for navigation in

accordance with one embodiment of the present invention. A global coordinate system

is utilized that remains fixed over time and never changes, such as an earth coordinate

system or a grid within a golf course or a city. A grid with values in one direction of

xl, x2, x3, x4, x5, and x6, and values in an orthogonal direction of yl, y2, y3, y4, y5

and y6 is shown 168. The third component of motion is aligned along an axis

perpendicular to fig. 10 and is discussed below. Also, for convenience, the third

component of direction is assumed to be in the direction of gravity, so that

transformations as described for equations 48-49 above have occurred. If a global

coordinate system is used that is not aligned with the earth's, then its orientation with

respect to the earth needs to be known and a transformation such as for equations 48

and 49 needs to be made.

At the beginning of a navigation session the position of the device is

determined within the global coordinate system 170 and a reference frame coordinate

system 172 is established for the first cycle. The orientation of the reference frame

coordinate system is initially unknown and can be any orientation. As discussed

before, for this system, magnetometers are utilized . The horizontal components of

the magnetometers provide the angle θ_z 176 from magnetic north N^M 174. To this

end, θ₂ is given by

θ_z = arctan(M_x/ M_y) (50)

where, M is the strength of the magnetic field in the horizontal plane and equation 50

is used to obtain a transformation to the global coordinate orientation aligned with the magnetic field.

If it is desired to navigate within a global coordinate system not

aligned with the magnetic field, it is necessary to know the orientation of the new

global coordinate system. For example, when the global coordinate system is defined

as an earth coordinate system, a correction to the angle from the earth's North

coordinate θ_e, or to a grid can be made if the angle between this and the magnetic

field orientation is known. Then, θ'_z - θ_e + θ_z . The initial location within the global

coordinate system may be determined from a GPS system, obtained from a radio

transmission, or entered in directly by hand.

Then,

[A⁰]' = Z 'H ' [A°] (51)

where Z^"1 is referred to as a transformation matrix that transforms the gravity aligned

reference frame to the global coordinate system, H ' is referred to as a transformation

matrix that transforms the reference frame to the gravity aligned reference frame.

And after the initial time step: _c-ι _{= Z}-ι_H-ι_B-ι (52)

After the initial time step, the system continues as described previously for equations

26-31, utilizing [A⁰]'. The position vector after completion of the first cycle L¹ 176 is

shown. Each additional cycle will provide a position vector from the absolute

determined at the end of the previous cycle. Results from two additional cycles L²

178 and L³ 180 are shown.

In accordance with one embodiment of the invention, the measuring system employs a GPS receive to indicate the location when the user has begun

navigation. In the alternative, the measuring system operates with a GPS system to

update GPS readings. The Global Positioning System (GPS) receivers are not able to

obtain satellite signals when direct line-of-sight is blocked, such as by trees,

mountains, buildings, or indoor. The periods when signals are lost, called dropouts,

do not allow for accurate navigation. Further, GPS is specified to be accurate within

100 meters 90% of the time. This level of accuracy is insufficient for identifying

details of navigation, such as the path an individual takes throughout a city. However,

if GPS is coupled with the device, then coordinate position on the earth can be

obtained by GPS and the device can obtain details of navigation; periodic updates of

coordinates can be obtained with the GPS.

The full navigation sequence is now described:

1) Initialize the device: For this step, the measuring system has to be

stationary, V°_x, V°_yN°_z are zero, and the values of A°_x, A°_y A°_z are preserved. The

orientation of gravity is determined and the gravity transformation matrix H^"1 from the

reference frame is computed. The transformation matrix Z^"1 for the global coordinate

system is also computed. The position on the earth is obtained by GPS, or

programmed into the device.

2) After the first time increment of the cycle a matrix B^"1 is calculated for

rotations during that increment, wherein B^"1 is a transformation matrix for

transforming translational coordinate systems to the reference coordinate system, and

acceleration values in the global coordinate system is calculated as a(t,) = H(t₀)-' ZCtoV'BCt,)^-1 A(t.) - H^'ZOo)^"1 A°(t₀)

The matrix C(t,)^~' = H^o)^"^^)^"^^,)^"1 is stored for the next time step, and A°(t₀)' =

H(t₀)^"1Z(t₀)^"1 A°(t₀) and renamed as A°(t₀) for convenience.

3) After the second time step a new matrix B^"1 is calculated for rotations

during that increment, and acceleration values for the second time increment is

calculated as

a(t₂) =C(t₁)-^,B(t₂)-¹A(t₂) - A°(t₀)

A new matrix C(t₂) ^"' = C(t₁)^"1B(t₂)^"1 is preserved for the next time step. This is

repeated for all the time increments of each cycle.

4) The process continues until the trigger time is reached, and the search for a

trigger opportunity starts. For example, when some number of successive samples of

V(t)_x, V(t)_y, and V(t)_z are constant, trigger occurs and a new cycle is initiated. The

values of A°_x, A°_y, and A°_z and V°_x, V⁰ _y> and V°_z at that time are preserved for the next

cycle. The time interval of the last cycle, T, is recorded. Equations as described for

Figure 8 are calculated for the length traveled during the cycle and the height jumped.

The velocity is the L/T or the sum of L's/T's of some number of previous cycles.

Cycles are short enough that only L is only approximately 0.5 to 2.0 meters. A

straight-line travel between increments is assumed. It is noted that for each new

cycle, transformation matrix H^"1 and Z^"1 is recalculated.

5) The x and y component give the direction of travel. The navigational

position is obtained by keeping track of the change of position in the earth's

coordinate system or a grid system, such as within a city. 6) The direction of travel relative to the magnetic field is obtained from the

magnetic sensor reading in the earth's coordinate system.

7) This process continues and the path of a person, animal, or object is

calculated. Periodic updates with GPS can be utilized to improve the accuracy of

position within the earth's coordinate system or a local grid system.

8) The details of navigation can be stored in memory to be downloaded into a

computer for display or analysis.

9) The overall distance traveled, velocity at any time, elevation change, or

height of any one cycle can be determined and displayed.

Fig. 11 illustrates how the measuring system can use radar 360 (Fig.

16) to navigate around objects. A radar system such as the Micropower Impulse Radar

System ("Radar on a Chip") MIRS is adjusted for aperture range and distance range to

identify objects along a potential path of travel. For example, the MIRS can be set to

identify objects within in an aperture range of 10° and a distance range of 10 feet.

Analysis of signals from the MIRS can be used to identify whether an object is wood,

metallic, or flesh. The same global coordinate system 180 as for Figure 10 is used

here. The MIRS is oriented in the direction of travel of a person or object, and its

orientation with respect to the reference coordinate system 182 is known. The position

184 of the device at some time during travel is shown. An object 186 identified as

metallic is located by radar at an angle range of +/- 5 degrees and at a distance range of less than 5 to 15 feet. The absolute position of the object in the global coordinate

system is determined. Either, a synthetic voice via a voice synthesizer 364, announces

the position of the object, so that a person can move around the object; or, a robot or

other device is given internal instructions to move in a direction around the object.

Simultaneously, other objects are searched for by radar. In another embodiment the

location of the object is measured in relation to the reference frame.

Fig. 12 illustrates how the measuring system may be used to analyze

the movement of objects in three dimensions. For example, in accordance with

another embodiment of the invention, the motion of swimmer's hand (wrist) during

one swimming stroke is shown. The device is located on a swimmer's wrist 190.

Motions of the wrist are measured by the translational coordinate system 192 as

described above (the reference frame coordinate system for the cycle is not shown)

and are transformed to a global coordinate system 194 as described above for Figure

10. Motions of the wrist are further transformed to a coordinate system 196 that is

moving with the person at a constant velocity, with an origin at the shoulder, and

aligned with the global coordinate system. The velocity of the person, and thus

coordinate system 196, is determined from the velocity of the person in the global

coordinate system as described above; so, transformation is a subtraction of the

velocity 198 of the coordinate system times the time of the measurement. Thus, the

position, velocity, or acceleration of the device is known at any time throughout the

cycle in coordinate system 196. Motions in this coordinate system are used to analyze

the swimming stroke. The motion of the arm about the pivot point is shown as trajectory 200.

Figure 13 illustrates how the small angle change or increments derived

for equation 18, can be determined from the magnetic and gravity fields as measured,

by keeping track of gravity and navigation fields, employing magnetometers and

linear accelerometers that provide signals that are low pass filtered at around 1Hz.

Either field alone provides insufficient information for a solution. This is because

rotation about the axis of a vector has no solution for rotation angles, and any rotation

(except an orientation perpendicular to the vector) has a component of its rotation

along the axis of the vector. However, there is a unique solution if both fields are used

simultaneously. Consider (m_x,m_y,m_z) to be the magnetic field values before a rotation

of an incremental angle at time t and (M_x,M_y,M_z) to be the magnetic field values after

an incremental change in rotation, say one time step t+At. Similarly, consider

(g_x,g_y,g_z) to be the gravity field values before a rotation of an incremental angle and

(G_x,G_y,G_z) to be the magnetic field values after an incremental change in rotation.

m_x = M_x - M_yδθ_z + M_zδθ_y (53)

m_y = M_xδθ_z + M_y - M_zδθ_x (54)

m_z = -M_xδθ_y + M_yδθ_x + M_z (55)

g_x = G_x - G_yδθ_z + G_zδθ_y (56)

g_y = G_xδθ_z + G_y - G_zδθ_x (57)

g_z = -G_xδθ_y + G_yδθ_x + G_Z (58)

If one simply combines similar equations (i.e. equations 53 and 56, 54 and 57, and 55 and 58), then one obtains a scew symetric matrix operator for the δθ's,

and one should be able to solve directly for the δθ's. However, the matrix is

indeterminate and a direct solution is not possible.

These six equations with three unknowns, however, can be solved by

linear least squares inversion, yielding the best average fit to all the observations. The

equations can be expressed in matrix form as:

(59) [B]c = d

where, B is the matrix of coefficients for the dθ's, C is the vector of δθ's and d is

their product. This is expressed as:

0 M_z/M "M_y M δθ_x (m_x-M_x)/M

-M_z/M 0 M_x/M δθ_y (m_y-M_y)/M

M_y/M -M_x/M 0 δθ_z (m_z-M_z)/M

60) 0 G_z/G "G_y/G (g_x-G_x)/G

-G_z/G 0 G_x/G (g_y-G_y)/G

G_y/G -G_x/G 0 (g_y-G_y)/G

Where G and M are the total magnetic and gravity fields, respectively, which are

calculated as the square root of the sum of their corresponding componenets squared.

They normalize the equations and remove the bias due to the two different fields.

These equations have the classic solution as described in Menke, William

"Geophysical Data Analysis: Discrete Inverse Theory", Academic Press, 1984 and

incorporated herein by reference:

C = [B^τB] ^lB^τd (61)

where, superscript T indicates transpose and superscript -1 indicates an inverse

matrix. Now, it is advantageous to have the flexibility to give different weights to the magnetic and gravity portions of the solution, so that equation 61 can be expressed as:

c = [B^lwB] ^lB^τwd (62)

wherein W is a weighting factor. In computations W_x are weights for magnetic field

values and W₂ are weights for gravity field values. Further, it is advantageous to

minimize the over determined portion of the solution and maximize the under

determined portion. This is achieved by a damped least-squares solution:

c = [B^ΎWB + e²I\^ΛB^Jwd (63)

where / is the identity matrix, and e is the damping factor.

Then,

b, b", b u₃₃

(64) B^τwB + e²I = b₂

b, = w,(M_z/M)² + w,(M_y/M)² + w₂(G_z/G)² + w₂(G_y/G)² + e² b₂ = -w,M_xM_y/M² - W₂G_xG_y/G² b₃ = -w,M_xM_z/M² - w₂G_xG_z/G² b₄ = w,(M_z/M)² + w,(M_x/M)² + w₂(G_z/G)² + w₂(G_x/G)² + e² b₅ -w^M_yMJM¹ w₂G_yG_z/G² b₆ = W,(M_y/M)² + w,(M_x/M)² + w₂(G /G)² + w₂(G_x/Gγ + e^z

Now,

-bub^/b^ + b₁₂ b₉b_π b₇b₁₃ +b₂/b, b₇ -b„ b₁₃ [B^τwB+ e²I\^Λ -b₈b₁₄ b₇b₁₃ - b₂/bjb₇ b₈b«/b² ₂bι₃ + l b₇ -b₈ b₇

where,

b₇ = b₄ - b² ₂/b, b₈ = b₅ - b₂b₃/b, b₉ = b₆ - b² ₃/b, b,₀ = b₃ b, - b₈b₂/b,b₇ b„ = b₉-b² ₈/b₇ b₁₂ = 1 b, +b² ₂/b²,b₇ b₁₃ =b₁₂+ b² ₁₀/b_n b₁₄ =-b₂ b,b₇+ b₈b₁₀b₇b₁, b₁₅ = -b₁₀ b„ b,₆ = l b₇+b² ₈ b² ₇b„ b₁₇ =-b₈/b₇b_n Also,

(66) B^Jwd= b 20

'21

where,

-w₂G_z(g_y-G_y)/G + W₂G_y(g_z-G_z)/G

+ w₂G_z(g_x-G_x)/G - w₂G_x(g_z-G_z)/G b₂₁ = -W,M_y(m_x-M_x)/M +w,M_x(m_y-M_y)/M - w₂G_y(g_x-G_x)/G - w₂G_x(g_y-G_y)/G

finally,

c = \B^[wB + e^lI\'Bwd, (67) so that δθ_x = b₁₃b₁₉ + b₁₄b₂₀ + b₁₅b₂₁ (68) δθ_y = b₁₄b₁₉ + b₁₆b₂₀ + b₁₇b₂₁ (69) δθ_z =b₁₅b₁₉ + b₁₇b₂₀+b₁₈b₂₁ (70)

Fig.14 illustrates how several devices are employed to provide

redundant information and random errors can be averaged out. A cluster of devices

144 all wired to the same algorithm for calculating the distance, speed, height, position, or three dimensional tracking can be used to average out random errors. In

accordance with one embodiment of the invention, each device 144 comprises the

arrangement of components illustrated in Fig. 16. Random errors are reduced by a

factor of l/sqrt(N), where N is the number of devices. It is noted that this

embodiment is most applicable to situations where the apparent acceleration of the

device is primarily due to the affect of tilt in the gravity field or the rate of tilt is at a

lower frequency than the changes in linear accelerations of the device. Further,

preferably the rate of tilt is much slower than the rate of change of linear accelerations

and the amplitude of acceleration due to tilt is also much larger than that due to linear

accelerations of the device.

Fig. 15 illustrates how neural networks can be employed to improve

accuracy. Fig. 15 shows a neural network 322 that increases the accuracy of the

computed distance or location by providing corrections input signals from the sensors

320, based on characteristics of the measured sensor inputs. The output of the nueral-

net provides input into the micro-processor that calculates the distance, speed, height,

position, or three dimensional tracking 324.

Fig. 16 is a block diagram of the components employed to solve the

equations, although the invention is not limited in scope in this respect. Therefore,

any hardware or software system configured to solve the above equations to measure

the length of each cycle and the height ascended or descended may be employed.

Unit 48 may preferably contain three magnetometers that can be employed to measure the magnetic field strength in three directions Mx, My, Mz, and determine direction of travel and compute angular rotations.

Unit 49 may preferably contain three linear accelerometers employed

to measure accelerations Ax, Ay and Az. Unit 50 may preferably contain three

rotational sensors employed to measure angular rotations γ_x, γ_y and γ_z. These

components are configured to measure in three dimensions as shown for figures 5 and

8. Specifically, unit 50 contains three rotational rate sensors. In the alternative, the

rotational accelorometers provide angular rotational signs.

The output terminals of units 48, 49, and 50 are coupled to input

terminals of a processor 52 and analog filters 53. The filters may be employed to

remove high frequency signals that interfere with accuracy. In addition, the linear

accelerometer signals may be separated into six channels: three low passed filtered at

a range, say 40 Hz, to remove high frequency noise, and three low pass filtered at a

range, say 1 Hz, to provide a signal that is commensurate with tilt of the device. This

results in a twelve degree of freedom system. Processor 52 may be employed to make

the calculations necessary to control the removal of instrument constants from the

signals and to direct them to the analog to digital converter 54. In accordance with

another embodiment of the invention, processor 52 may process the analog signals for

calculating equations 23-25 and 49-50

Microprocessor 56 is coupled to a GPS device 362, a voice synthesis and alarm device 364, a radar chip 360, and a neural network 366. As discussed

above, microprocessor 56 operates the algorithm for navigation, three dimensional

tracking and computes speed and distance. It receives signals from various units such

as 360, 362, 364 and 366 to perform its calculation steps. Furthermore,

microprocessor 56 contain algorithms to solve the equations described above and

further prepare signals for the transmitter 58.

Microprocessor 56 is preferably configured to measure the distance L

traversed during each cycle and the maximum height H ascended or descended during

that cycle. Unit 56 decides when to restart the calculation for the next step. It will be

appreciated that these measurements may be employed in either analog or digital

format.

The transmitter includes a means for encoding the output of unit 54

into a transmitted signal. The transmitter may operate on any frequency selected from

1 to 27 MHz or 49 band using amplitude or frequency modulation. The battery

supplies power to the transmitter. The transmitted signal is received and decoded by

the receiver. The receiver may also be selectively tuned to receive the signals of

several different transmitters operating on different frequencies so that the

performance of several runners may be monitored from a remote location

Unit 60 is the remote device, which may be located in the user's

wristwatch, and contains a receiver 62, a microprocessor 64, a mode select switch 66 and a display 68. Transmitter 58 includes a means for encoding the output signals

provided by a microprocessor 56 into a transmitted signal. Transmitter 58 may also

be of the type already known in the art such as the RF Monolithics model HX2000.

Transmitter 58 may operate on any frequency selected and use amplitude or frequency

modulation. The transmitted signal from transmitter 58 is received and decoded by

receiver 62. Receiver 62 may also be of the type known in the prior art such as the RF

Monolithics model RX2010. Receiver 62 may also be selectively tuned to receive the

signals of several different transmitters operating on different frequencies so that the

performance of several runners may be monitored from a remote location.

Microprocessor 64 may be selected from various microprocessors known in the prior

art, such as Motorola model MC68HC05L1.

A typical run mode sequence will now be described with reference to

Fig. 13. Mode select unit 66 is employed at the start of the run or movement

excursion by depressing an appropriate switch, not shown, which is coupled to

microprocessor 64 through an input switch control logic interface. As the cycle

begins, a first output signal is generated by sensors contained in units 48, 49, and 50.

The device is at rest for the beginning of an excursion, then the initial accelerations

will be zero and the initial velocity will be zero, equations 23-27. Units 52 and 53

prepare the signals and they are passed through unit 54 to microprocessor 56. begins

to calculate the initial orientation of the device along the reference coordinates in

accordance with equations. Thereafter unit 48 generates acceleration signals along the translational

coordinates. Rotational sensors contained in unit 50 begin to track the rotation of the

user's foot along the translational coordinate system. Thereafter, unit 52 measures

instantaneous acceleration of the foot along the reference coordinates as the foot

travels in the air and contacts the surface again. Unit 54 receives these acceleration

signals and unit 56 calculates the length of each step by integrating the acceleration

signals. Unit 56 also calculates the height jumped by obtaining the maximum length

measured along the z axis of the reference coordinate system. The output signals are

coupled to RF transmitter 58 and transmitted to receiver 62. The signals received by

receiver 62 are coupled to microprocessor 64. The microprocessor interface converts

the output of a microprocessor to signals suitable to drive display 68.

Speed is continuously calculated by measuring the distance of each

step and is instantaneously available for display. Microprocessor 64 also maintains

running elapsed time. Microprocessor 64 may be configured to calculate distance

traversed by summing the length of all steps taken. It may further be configured to

calculate the instantaneous and the average speed of the user. The running elapsed

time, the distance traversed and the speed may be selectively displayed on display 68.

These values may also be stored in a non-volatile memory (not shown) associated

with microprocessor 64 for virtually an indefinite period of time.

For calibration purposes, microprocessor 56 may be desirably

configured to monitor the value of signals provided by accelerometers of unit 48. Whenever it is determined that the user's foot is on the running surface, the value of

these signals may correspond to gravity, g. If, however, the value of the these signals

does not correspond to gravity, g, microprocessor 56 may provide a feedback signal so

as to reset the values of the accelerometers to provide a desired signal representing

gravity, g.

In the watch mode, microprocessor 64 selectively provides to display

68, normal watch functions such as time of day, date, an alarm signal when a

preselected time occurs. Obviously, many modifications and variations of the above

prefeπed embodiment of the invention will become apparent to those skilled in the art

from a reading of this disclosure. For example, a less expensive embodiment may be

implemented where all electronic components are disposed on the shoe. In that case,

there may be no desire for a transmitter and a receiver circuit. It may also be possible

to combine the functions performed by microprocessors 56 and 64 into one

microprocessor, such as a Motorola model MC68HC05L. In the alternative it is also

possible to combine the functions performed by signal processor 52, and

microprocessors 56 and 64 into one such microprocessor.

Obviously, many modifications and variations of the above prefeπed

embodiment of the invention will become apparent to those skilled in the art from a

reading of this disclosure. It should be realized that the invention is not limited to the

particular embodiment disclosed, but its scope is intended to be governed only by the

scope of the appended claims. It should be realized that the invention is not limited to the particular embodiment disclosed, but its scope is intended to be governed only by

the scope of the appended claims.

It will be appreciated by those skilled in the art, that the measuring

system in accordance with the present invention, may be employed in a variety of

applications beyond the use for walking and jogging. For example a measuring

system may be implemented for medical and biomedical applications. As such, a

measuring system in accordance with the present invention is used in an orthopedic or

a prosthetic device to track the durability of the device over a total distance traveled

by the user. For example, in a prefeπed embodiment patients that undergo hip

replacement surgery, employ a measuring system, either internally, for example

adjacent to the replaced hip or externally, so as to measure the total distance traveled

by a replaced hip. This allows physicians and engineers to collect valuable data

relating to the durability and performance of the artificial hips based on the type of

material used, various artificial hip designs employed or various surgical techniques

used.

In accordance with another embodiment of the invention, instead of

accelerometers velocity sensors may be employed. For a measuring system that

employs a velocity sensor the condition set forth by equation (16) becomes

unnecessary. Thus a new cycle may advantageously begin at any time the velocity of

the user is constant. In accordance with another embodiment of the invention, measuring

systems that operate based on the principles of the present invention are placed on any

limb or extremity of a patient to detect and diagnose range of movements of the

patient, or range of motion, and compare with normal benchmarks.

In accordance with yet another embodiment of the invention a

measuring device is placed in an object, such as a golf ball, in order to conveniently

measure the distance and the height traversed by the ball. In another embodiment of

the invention, a plurality of measuring devices may be employed within a moving

object so as to measure various movements relating to each measuring device. Values

measured by each measuring device may then be combined by a central processor so

as to determine the movements of the measuring devices in relation to each other. For

example, measuring devices may be attached to a clothing article to create a "smart"

clothing article. A user advantageously wears the clothing article. Each measuring

device in the clothing article tracks movement, acceleration, distance and speed for

further calculations.

In another embodiment of the invention a plurality of measuring

devices may be employed by a plurality of persons or objects. Each measuring device

transmits information relating to its movement, acceleration, distance and speed to a

centralized location so that the movement of a group of persons or objects is

advantageously monitored. In addition, when it is necessary to monitor the

movement of a group of animals, each measuring device is attached to an animal for further monitoring. Such a system may be advantageous for wild life preservation

purposes, or in the alternative, for commercial purposes, such as cattle grazing and so forth.

In another embodiment of the invention, a measuring device operating

in accordance with the principles of the present invention may be used for

navigational purposes. For example, at the initiation of the system, the user's location

coordinates are entered into the measuring device. The measuring device thereafter

tracks the location of the movement of the user in relation to the user's initial location.

Specific uses may include attaching the device to moving objects to

measure and track their movements in order to be digitized for animation, or tracking

recreation devices such as golf balls or baseballs. It may also be used to measure

range of motion for physical therapy and other medical measurements. It may also

include navigation of a person or an object, tracking virtual movements for graphic

positioning and display, analyzing motion of an instrument/tool/limb in order to

evaluate performance over time and performance relative to a benchmark motion of

another similar instrument/tool/limb, and other such uses.

Claims

CLAIMS:

1. A system for measuring movement characteristics of a moving

object over a plurality of measurement cycles, said system comprising:

an accelerometer unit attached to said object, said accelerometers configured

so as to provide acceleration signals coπesponding to accelerations associated with a

movement of said object during said plurality of measurement cycles;

a magnetometer unit attached to said object and configured so as to provide

signals coπesponding to magnetic field values within which said moving object is

located;

a processing system coupled to process sets of signals provided by said

magnetometer unit and sets of signals coπesponding to gravity field values within

which said moving object is located based on signals provided by said accelerometer

unit each said set of signals provided before and after an incremental change in

rotation of said moving object within each one of said measurement cycles, said

processing system being configured to calculate based on said gravity and magnetic

field values, incremental rotation angles dθ about an axis of a three dimensional

coordinate system associated with said incremental changes in rotation.

2. The system in accordance with claim 1 wherein said processing

system is further adapted to process said acceleration signals and said rotation angles

dθ so as to measure a distance traversed and the speed of said object during each of

said measurement cycles, wherein each measurement cycle begins when said object has a constant velocity.

3. The system in accordance with claim 1 wherein said processor

applies a plurality of variable weighting factors to said magnetic and gravity field

values.

4. The system in accordance with claim 2 wherein at initiation of

each one of said cycles said acceleration signals coπespond substantially to effects of

gravity and during each one of said measurement cycles said system substantially

subtracts acceleration signals received at initiation of each one of said cycles so as to

eliminate eπors caused by influence of gravity on said measuring system.

5. The system in accordance with claim 4, wherein said

processing system further generates a plurality of incremental transformation matrices

so as to transform characteristics of motion of said object in a translation frame

system to a reference frame coordinate system.

6. The measuring system in accordance with claim 1 , further

comprising a GPS system coupled to said measuring system, wherein an initial

location of said object is provided by said GPS system.

7. The measuring system in accordance with claim 1, further

comprising a radar system for locating objects in the vicinity of said moving object.

8. A method for measuring motion characteristics of a moving object over a plurality of measurement cycles comprising the steps of:

measuring magnetic field values associated with movement of said object;

measuring gravity field values within which said moving object is located;

processing sets of signals coπesponding to said gravity field values and

said magnetic field values, wherein said sets of signals are provided before and after an incremental change in rotation of said moving object within each of said

measurement cycles, so as to calculate incremental rotation angles dθ about an axis of a three dimensional translational coordinate system associated with said incremental

changes in rotation.

9. The method in accordance with claim 8 wherein said step of

measuring gravity field values further comprises the steps of measuring acceleration

signals associated with movement of said object along said translational coordinate

system.

10. The method in accordance with claim 9 wherein said processing

step further comprises the step of applying a plurality of variable weighting factors to

said magnetic and gravity field values.

11. A system for measuring a speed and distance of a moving object over a plurality of measurement cycles, said system comprising:

a plurality of accelerometers and rotational sensors disposed in said

object, said accelerometers configured so as to provide acceleration signals

coπesponding to accelerations associated with a movement of said object during said plurality of measurement cycles, said rotational sensors configured so as to provide

substantially small angular signals coπesponding to substantially small incremental

angles dθoϊ said object about an axis of a three dimensional coordinate system

wherein Cos dθis substantially equal to unity and Sin dθis substantially equal to dθ ; and

a processing system coupled to said accelerometers and said rotational

sensors configured so as to receive said acceleration signals and said angular signals

coπesponding to said substantially small incremental angles dθ , said processing

system adapted to measure a distance traversed and the speed of said object during each of said measurement cycles, wherein each measurement cycle begins when said

object has a constant velocity.

12. The measuring system in accordance with claim 11 wherein at

initiation of each one of said cycles said acceleration signals coπespond substantially

to effects of gravity and during each one of said measurement cycles said system

substantially subtracts acceleration signals received at initiation of each one of said

cycles so as to eliminate eπors caused by influence of gravity on said measuring

system.

13. The measuring system in accordance with claim 12, wherein said processing measuring system further generates a plurality of incremental

transformation matrices so as to transform characteristics of motion of said object in a translation frame coordinate system to a reference frame coordinate system.

14. The measuring system in accordance with claim 13 wherein said

accelerometers further comprise a calibration aπangement so as to reset the value

generated by said accelerometers to gravity g when said measuring system is either

moving at substantially constant velocity and when said measuring system is stationary.

15. The measuring system in accordance with claim 11, further comprising

a GPS system coupled to said measuring system, wherein an initial location of said

object is provided by said GPS system.

16. The measuring system in accordance with claim 11, further comprising

a radar system for locating objects in the vicinity of said moving object.

17. A method for measuring motion characteristics of a moving

object over a plurality of measurement cycles comprising the steps of: measuring acceleration signals associated with movement of said

object along a translational coordinate system defined by the movement of said object;

measuring incremental angles of rotation dθoi said object about each

axis of said translational coordinate system, such that Cos dθis substantially equal to

unity and Sin dθis substantially equal to dθ, and calculating instantaneous accelerations of said moving object with

respect to a reference coordinate that is defined by said moving object at the beginning of each one of said cycles, wherein each one of said measurement cycles begin when

velocity of said moving object is a constant.

18. The method in accordance with claim 17, further comprise the step of performing said acceleration measuring step and said incremental angle

measuring step over a plurality of time increments defined within each of said measuring cycles.

19. The method in accordance with claim 18, wherein said step of measuring incremental angles dθ further comprise the step of providing signals coπesponding to said incremental angles by a plurality of rotational sensors.

20. The method in accordance with claim 19, wherein said

calculating step further comprises the steps of:

(a) generating an incremental transformation matrix [B^"1] when a new

set of said incremental angles are measured so as to transform said acceleration

signals measured in said translational coordinate system to acceleration signals

measured in said reference frame coordinate system;

(b) multiplying said incremental transformation matrix [B^"1] with a

prior incremental transformation matrix measured in a previous time increment so as

to generate an updated incremental transformation matrix;

(c) performing a transformation from said translational coordinate system to said rotational coordinate system by employing said updated incremental transformation matrix; and

(d) repeating said steps (a) through (c) for all time increments defined within each one of said measurement cycles.

21. A navigation method for tracking motion characteristics of a moving object over a plurality of measurement cycles comprising the steps of:

measuring, over a plurality of time increments, acceleration signals

associated with movement of said object along a translational coordinate system defined by the movement of said object;

measuring for each of said time increments, incremental angles of

rotation dθoϊ said object about each axis of said translational coordinate system, such that Cos dθis substantially equal to unity and Sin dθis substantially equal to dθ; and transforming by an incremental transformation matrix [B ¹]

instantaneous accelerations of said moving object from said translational coordinate

system to a reference coordinate that is defined by said moving object at the beginning

of each one of said cycles, wherein each one of said measurement cycles begin when

velocity of said moving object is a constant; transforming by a gravity aligned transformation matrix [H^"1]

instantaneous accelerations of said moving object from said reference frame

coordinate system to a gravity aligned coordinate system; and transforming by a global transformation matrix [Z^"1] instantaneous

acceleration of said moving object from said gravity aligned coordinate system to a

global coordinate system.

22. The method in accordance with claim 21 , further comprising

the step of subtracting acceleration signals measured at initiation of each cycle so as to

eliminate eπors caused by influence of gravity on said navigation system.

23. The method in accordance with claim 22, further comprising

the steps of providing by a GPS system, the initial location of said moving object with

respect to said global coordinate system.