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Reduced-power GPS-based system for tracking multiple objects from a central location    

Custom CD of patents similar to US5752218 : Reduced-power GPS-based system for tracking multiple objects from a central location - $19.95
United States Patent5752218   
Link to this pagehttp://www.wikipatents.com/5752218.html
Inventor(s)Harrison; Daniel David (Delanson, NY), Pradeep; Anantha Krishnan (Clifton Park, NY), Brooksby; Glen William (Glenville, NY), Hladik; Stephen Michael (Albany, NY)
AbstractLocation of an object to be tracked is determined by measuring, at a receiver situated at the object, the propagation time differences between the signals from a plurality of GPS satellites, each of which is received by the receiver situated at the object. The measured propagation time difference values are transmitted to a central station where the location of the object to be tracked is calculated based upon the propagation time differences of the signals transmitted from the satellites and data derived from a receiver apart from the object but also receiving signals from the satellites.
   














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Drawing from US Patent 5752218
Reduced-power GPS-based system for tracking multiple objects from a
     central location - US Patent 5752218 Drawing
Reduced-power GPS-based system for tracking multiple objects from a central location
Inventor     Harrison; Daniel David (Delanson, NY) , Pradeep; Anantha Krishnan (Clifton Park, NY) , Brooksby; Glen William (Glenville, NY) , Hladik; Stephen Michael (Albany, NY)
Owner/Assignee     General Electric Company (Schenectady, NY)
Patent assignment
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Publication Date     May 12, 1998
Application Number     08/924,478
PAIR File History     Application Data   Transaction History
Image File Wrapper   Patent Term   Fees
Litigation
Filing Date     August 25, 1997
US Classification     701/207 342/357.07 342/457 701/213 701/215 701/300
Int'l Classification    
Examiner     Nguyen; Tan Q.
Assistant Examiner    
Attorney/Law Firm     Stoner; Douglas E. Snyder; Marvin
Address
Parent Case     This application is a continuation of application Ser. No. 08/456,229 filed May 31, 1995 now abandoned.
Priority Data    
USPTO Field of Search     701/207 701/213 701/214 701/215 701/216 701/223 701/300 342/357 342/356 342/358 342/450 342/457
Patent Tags     reduced-power gps-based tracking multiple objects a central location
   
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5430657
Kyrtsos
701/226
Jul,1995

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5379224
Brown
701/215
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Ishikawa
342/357.03
Sep,1994

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Brown
342/357.09
Jul,1993

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Nov,1992

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Greenspun
342/451
Sep,1992

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Jun,1992

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Apr,1991

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342/457
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What is claimed is:

1. A method for identifying location of an object to be tracked, comprising:

measuring data related to propagation time differences between signals transmitted from a plurality of GPS satellites and received at said object to be tracked, said data comprising code word phase measurements .mu..sub.i for a satellite at a time t.sub.R, where .mu..sub.1 =.gamma..sub.i /T.sub.i.sup.C, and defined as time elapsed to time t.sub.R from the beginning of a code word in the signal from satellite i in which t.sub.R falls, T.sub.i.sup.C being defined as the code period for satellite i at time t.sub.R in the signal received from satellite i, said code word phase measurements being simultaneously derived from the signals transmitted from said plurality of satellites and received at the object to be tracked;

transmitting said data to a central station; and

calculating at said central station the location of said object to be tracked based upon the transmitted data and data derived from at least one receiver apart from said object to be tracked receiving said signals from said plurality of satellites.

2. The method of claim 1 wherein the data transmitted to the central station includes satellite identification data so that the step of calculating the location of said object to be tracked is thereupon based further upon the satellite identification data.

3. The method of claim 1 wherein the step of calculating the location of said object comprises calculating a point of intersection of curves defined by said propagation time differences.

4. The method of claim 1 including the step of transmitting time signals to said object to be tracked over a separate channel so as to maintain clock accuracy at said object to be tracked.

5. A method for identifying location of an object to be tracked comprising:

measuring data related to propagation time differences between signals transmitted from a plurality of GPS satellites and received at said object to be tracked, said data comprising bit phase measurements .mu..sub.i for a satellite i at a time t.sub.R, where .mu..sub.i =.beta..sub.i /T.sub.i.sup.B, .beta..sub.i being the receiver bit-time offset for satellite i and defined as time elapsed to time t.sub.R from the beginning of a code word in the signal from satellite i in which t.sub.R falls, T.sub.i.sup.B being defined as the bit period for satellite i at time t.sub.R in the signal received from satellite i, said bit phase measurements being simultaneously derived from the signals transmitted from said plurality of satellites and received at the object to be tracked;

transmitting said data to a central station; and

calculating at said central station the location of said object to be tracked based upon the transmitted data and data derived from at least one receiver apart from said object to be tracked receiving said signals from said plurality of satellites.

6. The method of claim 5 and further including:

recording, at said object, the time at which the data are simultaneously derived; and

transmitting the recorded time to said central station.

7. The method of claim 5 and further including:

measuring, at said object to be tracked, delay between the time at which the data are recorded and the time when the data are transmitted to the central station; and

transmitting the measured delay to said central station.

8. The method of claim 5 wherein the data transmitted to the central station includes satellite identification data and the step of calculating the location of said object to be tracked is additionally based upon the satellite identification data.

9. The method of claim 5 wherein the step of calculating the location of said object comprises calculating a point of intersection of curves defined by said propagation time differences.

10. The method of claim 5 wherein the signals from said GPS satellites are received at said object to be tracked, and including the step of transmitting time signals to said object to be tracked over a separate channel so as to maintain clock accuracy at said object to be tracked.

11. A method for identifying location of an object to be tracked comprising:

measuring data related to propagation time differences between signals transmitted from a plurality of satellites and received at said object to be tracked, said data comprising receiver code-time offsets for a satellite i and defined as time elapsed to a time t.sub.R from the beginning of a code word in the signal from satellite i in which t.sub.R falls, and code periods in the signal received from satellite i in which time t.sub.R falls, said plurality of satellites comprising GPS satellites, and including the additional step of simultaneously deriving said receiver code-time offsets and code periods from signals received from the plurality of satellites at said object to be tracked;

transmitting said data to a central station; and

calculating at said central station the location of said object to be tracked based upon the transmitted data and data derived from at least one receiver apart from said object to be tracked receiving said signals from said plurality of satellites.

12. A method for identifying location of an object to be tracked, comprising:

measuring data related to propagation time differences between signals transmitted from at least four GPS satellites and received at said object to be tracked, said data related to propagation time differences comprising bit phase measurements simultaneously derived from said signals;

transmitting said data, including satellite identification data, to a central station;

measuring, at said object to be tracked, delay between the time at which the data are recorded and the time when the data are transmitted to the central station;

transmitting the measured delay to said central station; and

calculating at said central station the location of said object to be tracked based upon the transmitted data, the satellite identification data, and data derived from at least one receiver apart from said object to be tracked receiving said signals from said plurality of satellites, the calculating step comprising:

assuming a feasible value for a communication time delay required for a signal transmitted from said object to be tracked to reach the central station;

calculating the location of said object to be tracked based upon the satellite identification data and the assumed value of said communication time delay;

calculating a new value for said communication time delay based upon the calculated location of said object to be tracked; and

calculating a corrected location of said object to be tracked based upon the calculated new value for said communication time delay.

13. The method of claim 12 including the additional step of:

iteratively repeating the calculating steps until little change in location of said object to be tracked is observable.

14. A system for identifying location of an object to be tracked, comprising:

means for measuring data related to propagation time differences between signals transmitted from a plurality of GPS satellites and received at said object to be tracked, each of said signals identifying an associated satellite, said object to be tracked including:

receiver means for receiving signals from at least four GPS satellites; and

first processor means for processing data from the receiver means at predetermined time intervals in synchronism with received signal events, said data being related to propagation time differences for said signals;

receiver means apart from said object for receiving said signals transmitted from said plurality of satellites;

a central station for calculating the location of said object based upon the measured data, data derived from said receiver means apart from said object, and the satellite identification data; and

transmission means for transmitting the processed data to said central station;

said system further including:

second processor means at said central station for determining the location of said object based on the data received from said transmission means and data derived from said receiver means apart from said object.

15. The system of claim 14 wherein said signal events comprise a telemetry-word preamble signal event in a GPS signal.

16. The system of claim 15 wherein said first processor means further comprises means for decoding a satellite time stamp from a predetermined one of the received GPS signals, based upon the telemetry-word preamble signal event.

17. A method for identifying location of an object to be tracked comprising:

means for measuring data related to propagation time differences between signals transmitted from a plurality of GPS satellites and received at said object to be tracked, each of said signals identifying an associated satellite, said object to be tracked including:

receiver means for receiving signals from at least four GPS satellites; and

first processor means for calculating a receiver bit phase for each of said satellites, said bit phase for any satellite i at a time t.sub.R being defined as .beta..sub.i /T.sub.i.sup.B, .beta..sub.i being the receiver bit-time offset for satellite i and defined as time elapsed to time t.sub.R from the beginning of a code word in the signal from satellite i in which t.sub.R falls, and T.sub.i.sup.B being defined as the bit period for satellite i at time t.sub.g in the signal received from satellite i;

receiver means apart from said object for receiving said signals from said plurality of satellites;

a central station; and

transmission means for transmitting the calculated bit phases to said central station;

said system further including:

second processor means at said central station for determining signal propagation times between said plurality of satellites and said object and for determining location of said object based upon the bit phases transmitted by said transmission means and data derived from said receiver means apart from said object.

18. A system for identifying location of an object to be tracked, comprising:

means for measuring data related to propagation time differences between signals transmitted from a plurality of GPS satellites and received at said object to be tracked, each of said signals identifying an associated satellite, said object to be tracked including:

receiver means for receiving signals from at least four GPS satellites, and

first processor means for calculating a bit-time offset for each of said satellites and for determining a bit period for each signal received from said satellites, said bit-time offset for a satellite i being defined as time elapsed to a time t.sub.R from the beginning of a code word in the signal from satellite i in which t.sub.R falls, said bit period for satellite i being determined at time t.sub.R in the signal from satellite i;

receiver means apart from said object for receiving said signals from said plurality of satellites;

a central station; and

transmission means for transmitting time stamps, the calculated bit-time offsets and bit periods, and satellite identification data, to said central station;

said system further including:

second processor means at said central station for determining signal propagation times between said plurality of satellites and said object and for determining location of said object based upon the bit-time offsets and periods, time stamps, satellite identification data transmitted by said transmission means, and data derived from said receiver means apart from said object.
 Description Submit all comments and votes
 


FIELD OF THE INVENTION

This invention relates to object tracking systems used to locate and track multiple terrestrial (including water-based) objects and, more particularly, to power efficient object tracking systems based upon information obtained from satellites.

BACKGROUND OF THE INVENTION

The tracking and location of assets such as railcars, shipping or cargo containers, trucks, truck trailers, automobiles, etc. can be highly advantageous in commerce. Precise tracking of such vehicles and objects can facilitate their being allocated and positioned in an efficient manner, and can provide for immediate, accurate localization of lost, delayed or damaged assets. The space-based global positioning system (GPS) implemented by the United States Department of Defense constitutes a convenient instrumentality for determining geographical position in real time.

The GPS is a multiple satellite-based radio positioning system in which each satellite transmits data that allows precise measurement of the distance from selected ones of the GPS satellites to the antenna of a user's receiver so as to enable the user to compute position, velocity and time parameters through known triangulation techniques. The signals provided by the GPS can be received both globally and continuously.

The GPS comprises three major segments known as the space, control and user segments. The space segment consists of 21 operational satellites and three spare satellites. The satellites are positioned in a constellation such that typically seven satellites, but a minimum of four, are observable by a user anywhere on or near the earth's surface. Each satellite transmits signals on two frequencies known as L1 (1575.42 MHz) and L2 (1227.6 MHz), using spread spectrum techniques that employ two types of spreading functions.

C/A (or coarse/acquisition code) and P (or precise) pseudo random noise (PRN) codes are transmitted on frequency L1, and P code only is transmitted on frequency L2. The C/A is available to any user, military or civilian, but the P code is only available to authorized military and civilian users. Both P and C/A codes contain data that enable a receiver to determine the range between a satellite and the user.

Superimposed on both the P and C/A codes is a navigation (NAV) message. A NAV message contains the GPS signal transmission time; a handover word used in connection with the transition from C/A to P code tracking; ephemeris data for the particular satellites being tracked; and almanac data for all of the satellites in the constellation, including information regarding satellite health, coefficients for the ionospheric delay model for C/A code users, and coefficients used to calculate universal coordinated time (UCT).

The control segment comprises a master control station (MCS) and a number of monitor stations. The monitor stations passively track all GPS satellites in view, collecting ranging data and satellite clock data from each satellite. This information is passed on to the MCS where the satellite's future ephemeris and clock drift are predicted. Updated ephemeris and clock data are uploaded to each satellite for retransmission in each satellite's navigation message. The purpose of the control segment is to ensure that the information transmitted from the satellites is as accurate as possible.

The GPS is intended to be used in a wide variety of applications, including space, air, sea and land vehicle navigation, precise positioning, time transfer, altitude referencing and surveying. A typical GPS receiver comprises a number of subsystems, including an antenna assembly, an RF (radio frequency) assembly, and a GPS processor assembly. The antenna assembly receives the L-band GPS signal and amplifies it prior to insertion into the RF assembly. A significant factor affecting accuracy of the computed position, velocity or time parameters is the positional geometry of the satellite selected for measurement of ranges. Generally, a best position solution is obtained using satellites having wide angles of separation. Considerable emphasis has therefore been placed on designing antenna systems to receive, with uniform gain, signals from any point on the hemisphere.

The RF assembly mixes the L-band GPS signal down to a convenient IF (intermediate frequency) signal. Using various known techniques, the PRN code modulating the L-band signal is tracked through code-correlation at the receiver. This provides the processing gain needed to achieve a signal-to-noise ratio (SNR) sufficient for demodulating the navigation data and signal transmission time. The Doppler shift of the received L-band signal is also measured through a carrier tracking loop. The code correlation and carrier tracking function can be performed using either analog or digital signal processing.

By differencing the signal transmission time with the time of reception, as determined by the clock of the receiver, the pseudo range between the receiver and the satellite being tracked may be determined. The pseudo range includes both the range to the satellite and the offset of the clock from the GPS master time reference. The pseudo range and Doppler measurements (and the navigation data) from four satellites are used to compute a three dimensional position and velocity fix, which calibrates the receiver's clock offset and provides an indication of GPS time.

In some known receivers, the receiver processor controller (RPC) functions are performed using a computer separate from that on which the navigation functions are performed. In other known receivers, both types of functions are performed by a single computer. The RPC processing and memory functions performed by a typical GPS receiver include monitoring channel status and control, signal acquisition and reacquisition, code and carrier tracking loops, computing pseudo range (PR) and delta range (DR) measurements, determining data edge timing, acquisition and storage of almanac and ephemeris data broadcast by the satellites, processor control and timing, address and command decoding, timed interrupt generation, interrupt acknowledgment control and GPS timing.

U.S. Pat. No. 5,225,842 describes an apparatus and method for computing the position and velocity of multiple low cost vehicle-mounted sensors, monitored and tracked by a central control station. The receiver processor functions are physically separated from the navigation functions and the low rate data interfaces provided between the computers that perform these functions, thus achieving cost saving in the GPS sensor that is employed on board each vehicle.

One type of known GPS receiver is described in U.S. Pat. No. 4,114,155, wherein the position of a receiver responsive to C/A signals derived from multiple, orbiting spacecrafts is determined to an accuracy better than 300 meters. Each of the C/A signals has the same carrier frequency and a different, predetermined Gold code sequence that normally prevents position determination from being more accurate than to within 300 meters. C/A signals transmitted to the receiver are separately detected by cross-correlating received Gold code sequences with plural locally derived Gold code sequences. Four of the detected C/A signals are combined to compute receiver position to an accuracy of 300 meters. To determine receiver position to an accuracy better than 300 meters, the relative phase of internally-derived Gold code sequences is varied over the interval of one chip (i.e., pulse) of each sequence, to derive second cross-correlation values indicative of received and locally-derived Gold code sequences.

The basic approach followed most recently is to receive and process the signals from several of the GPS satellites in order to determine range to each satellite (and relative velocity). With perfect knowledge of range to only three of the GPS satellites, exact receiver position can be determined from the intersection of the three "spheres" induced by the known satellite positions and the derived receiver ranges. With receiver noise and imperfect knowledge of satellite positions, the receiver-satellite ranges can only be estimated. Typically, errors from receiver noise are reduced by (effectively) averaging many range calculations.

In the above most recent approach, the range from a particular satellite is estimated by reading a time stamp from the satellite's data stream (the transmission instant), subtracting this from the reception time, and multiplying the time difference by the speed of light. Any error in satellite and receiver clock synchronization leads to proportional range errors. Because the same clock is used in receiving from all satellites, there is only one unknown receiver clock "bias". By using a fourth (or more) satellite, the clock bias and ranges can be jointly estimated.

At the receiver, the reception time is determined by performing a cross-correlation of the received data with a local replica of the known satellite Gold code, and noting the time of a chosen correlation peak, and its position relative to the time stamp. The satellite signal structures use Code Division Multiple Access (CDMA) so that the above cross correlation is part of the standard GPS receiver processing.

The above-described system that follows the most recent basic approach assumes that each receiver must determine its own position. In the system of the invention, there is a central facility or station that needs the receiver positions and can communicate with the receivers. Each tracked object (e.g., a railcar) carries a GPS-based receiver that processes data from several of the visible GPS satellites. However, the full position determination is not made at the railcar. Instead, only partial processing is done at the railcar and intermediate results are transmitted to the central station. The forms of both the partial processing and intermediate results are chosen to minimize the complexity and energy requirements at the railcars.

The standard GPS system requires that the transmit-time stamps, satellite ephemeris and other correction data be decoded from each satellite's data stream at the tracked object. The receiver is thus required to process data from each satellite long enough (between six and 150 seconds) to synchronize with, and decode, these data. This consumes significant power.

SUMMARY OF THE INVENTION

Briefly, in accordance with a preferred embodiment of the invention, a method for identifying location of an asset or object to be tracked comprises measuring data related to propagation time differences between signals transmitted from a plurality of satellites and received at the object to be tracked, transmitting the data to a central station, and calculating, at the central station, the location of the object to be tracked based upon the transmitted data. The data received at the object to be tracked may include data identifying a respective associated satellite by, for example, a satellite identification number, such that the step of calculating the location of the object to be tracked is thereupon based further upon the satellite identification numbers.

In another preferred embodiment, a reduced-power GPS-based system for tracking location of an asset or object from a central location comprises a central station at the central location, and an object to be tracked which includes means for receiving signals from at least four GPS satellites, first processor means for processing data from the receiver means propagation time differences for the signals, and transmission means for transmitting the processed data to the central station. Second processor means situated at the central station determine location of the object based upon the data received from the transmission means.

In still another preferred embodiment, a reduced-power GPS-based system for tracking multiple objects from a central location comprises a central station at the central location, and a plurality of objects to be tracked. Each of the objects includes receiver means containing an antenna for receiving signals including data related to the propagation time differences of the signals from at least four GPS satellites, first processor means for calculating a receiver code word phase for each of the satellites based upon the signals received by the receiver means, and transmission means for transmitting the code word phase to the central station. Second processor means are provided at the central station for determining the signal propagation times between the plurality of satellites and each of the tracked objects based on the receiver code word phase transmitted by the respective object and for determining from the signal propagation times the location of each respective one of the objects.

In another preferred embodiment, a reduced-power GPS-based system for tracking location of multiple objects from a central location comprises a central station at the central location, and an object to be tracked which includes means for receiving signals including data related to propagation time differences of said signals from at least four GPS satellites, first processor means for calculating a receiver code-time offset for each of the satellite signals and for determining the receiver code period for each signal, and for determining identification numbers of the at least four GPS satellites, and transmission means for transmitting the receiver code-time offsets, code periods, and identification numbers to the central station. Second processor means at the central station determine the signal propagation times between the plurality of satellites and the tracked object and determine location of the object based upon the receiver code-time offsets, code period, and satellite identification numbers transmitted by the transmission means.

In still a further preferred embodiment, a reduced-power GPS-based system for tracking location of an object from a central location comprises a central station at the central location, and an object to be tracked which includes means for receiving transmission signals from at least four GPS satellites, first processor means for calculating a receiver bit phase for each of the satellite signals based upon the signals received by the receiver means, means for keeping track of time at the object, and transmission means for transmitting the bit phase signals and time signals to the central station. Second processor means are provided at the central station for determining the signal propagation times between the plurality of satellites and the object and for determining location of the object based upon the bit phase and time signals transmitted by the transmission means.

Utilizing the present invention, power consumption and calculation complexity at the tracked object are reduced relative to that for a standard GPS receiver. Arrival time differences between satellite signals are measured at the tracked object and this information is relayed to the central station via the separate communications link. Satellite data streams need not be decoded at the tracked object.

The central station thereby necessarily determines the location of the object to be tracked. Because the receiver front end and data processor use significant power only when processing, the receiver power can be dramatically reduced by being "active" only long enough to get accurate time-difference measurements. This can be less than one second and requires no GPS data-frame synchronization because of the nature of the signals. For example, assuming that the tracked object is a railcar, new railcar locations typically are needed only as frequently as 15 minutes. Thus the receiver energy used is reduced in direct proportion to the reduction of "active" receiver time. Moreover, receiver complexity and cost can be reduced by replacing the advanced microprocessor employed in current GPS receivers with a simpler one that is matched to the arrival-time differencing tasks.

In accordance with the invention, one object is is to provide a GPS-based asset tracking system in which processing is performed at a location remote from the tracked assets and based upon specific recognizable variables.

Another object is to provide a GPS-based asset tracking system which requires minimal energy at the tracked assets.

BRIEF DESCRIPTION OF THE FIGURES

The features of the invention believed to be novel are set forth in the appended claims. The invention, however, together with further objects and advantages thereof, may best be understood by reference to the following description taken in conjunction with the accompanying drawing(s) in which:

FIG. 1 is a block diagram of a remote tracking system in accordance with the present invention;

FIG. 1A is a block diagram of a railcar tracking unit on an object to be tracked in accordance with the invention;

FIG. 1B is a block diagram of the transmitter at the central station of the remote tracking system of the invention;

FIG. 2 illustrates the long time-scale data frame relationship between a GPS standard time mark and two satellite data frames in accordance with the present invention;

FIG. 3 illustrates a typical Gold-code correlation output signal on a short time scale when the proper code replica is used at the local station receiver;

FIG. 4 illustrates the time delay relationships of the transmitted and received signals;

FIG. 5 illustrates a plurality of intersecting time-difference solution regions on the surface of the earth;

FIG. 6 illustrates tracked object message timing diagrams in accordance with the present invention;

FIG. 7 illustrates tracked object location-dependent communication delay; and

FIG. 8 is a block diagram of a system for evaluating GPS algorithms in accordance with the present invention.

DETAILED DESCRIPTION

The present invention is directed to a system and method for reducing the power and complexity requirements of a local GPS receiver, which can be carried by a railcar, by effectively requiring only measurement of arrival-time differences between a plurality of GPS satellite signals. Data related to these time differences are transmitted to a central station where the majority of calculations required to determine the receiver (railcar) location are performed. In the preferred embodiments, a standard CDMA receiver is employed with radio frequency/intermediate frequency (RF/IF) front end and Gold-code cross correlators.

In FIG. 1, the invention is shown as comprising a plurality of GPS satellites 12, an object to be tracked, such as a railcar carrying a tracking unit 14, and a central station 16. Although the invention is herein described in the context of a railcar, the teachings of the invention are applicable to a variety of objects which may be tracked by a GPS or satellite-based system. With respect to the GPS signal format, accurate timing of GPS signals is critical and is monitored by central station 16.

Each satellite 12 includes its own set of clock correction parameters within its data stream. These allow a receiver to ascertain the absolute transmission timing for each satellite with respect to a common GPS standard time. A particular satellite's clock may drift relative to those of other satellites. The GPS system control monitors these offsets and periodically includes them in the satellite's data stream. The clock time offsets are not needed at the individual receivers and can be determined at central station 16 by utilizing a standard GPS receiver there or at a remotely controlled site.

As shown in FIG. 1A, railcar tracking unit 14 is actually comprised of a railcar receiver 2 responsive to the signals from GPS satellites 12, a processor 3, and a transmitter 4. The received signals are processed in processor 3 to ascertain and utilize propagation time differences among the signals received from GPS satellites 12. The processed signals are furnished to transmitter 4 from whence they are transmitted, as reduced order parameters, to central station 16.

As shown in FIG. 1B, central station 16 includes a receiver 7 responsive to signals from transmitter 4 of tracking unit 14 (FIG. 1A) and a processor 8 responsive to receiver 7 for determining location of tracking unit 14.

In the long time scale data frame shown in FIG. 2, a.sub.i is the frame time offset for satellite i. A value a.sub.j -a.sub.i is the time offset between transmitted signals from two satellites, i and j.

A Gold-code correlator output waveform r.sub.i (.tau.) for satellite i is illustrated in FIG. 3 from the perspective of the railcar receiver. Each correlation-peak location respectively marks the beginning of a new Gold code cycle in the received waveform. Each Gold code cycle is 1 ms long and comprises 1023 binary Gold code "chips". Furthermore, there are 20 code cycles for each encoded navigation data bit. FIG. 3 also illustrates, by a dotted line, a typical bit-boundary position.

With respect to a particular time t.sub.R at a railcar receiver, the receiver code-time offset for satellite i is .gamma..sub.i. The receiver code-time offset is the time elapsed to a time t.sub.R from the beginning of the code word (cycle) in which t.sub.R falls. Similarly, the receiver bit-time offset .beta..sub.i is the time elapsed to time t.sub.R from the beginning of the bit in which t.sub.R falls. The satellite-railcar radial velocity component varies for different satellites and this results in a relative waveform expansion or compression (Doppler) at the railcar. Thus the observed code and bit periods are satellite dependent. The code and bit periods observed at the railcar for satellite i are designated as T.sub.i.sup.C and T.sub.i.sup.B, respectively.

Frequently, the railcar receiver will use satellite signals that are not visible from (i.e., cannot be received by) the central station. This presents no problem because the satellite clocks drift slowly (less than five nanoseconds error per hour). If, at the railcar receiver, time differences are calculated using a satellite that is not visible at the central station, then, at the central station, the last calculated clock offset for that satellite can be used (or extrapolated, based on past drift rate) until that satellite is again visible. As an alternative, central station 16 (FIG. 1) could communicate with standard GPS receivers strategically situated to guarantee satellite visibility.

A key feature of the present invention is the provision of a method for determining location of the object (here, a railcar) to be tracked. In a first method ("method 1"), the object's location is accurately determined from propagation time differences between at least five satellites' signals received at the tracked object. This metho