WO1997036187A1

WO1997036187A1 - Apparatus and method for differential satellite positioning

Info

Publication number: WO1997036187A1
Application number: PCT/AU1997/000204
Authority: WO
Inventors: Roderick Charles Bryant; Eamonn Patrick Glennon
Original assignee: Sigtec Navigation Pty. Ltd.
Priority date: 1996-03-27
Filing date: 1997-03-27
Publication date: 1997-10-02
Also published as: AUPN896496A0

Abstract

A method and apparatus for positioning one of a set of mobile antennas capable of receiving signals from GPS satellites, each mobile antenna being associated with corresponding mobile user equipment and capable of communicating with a base station, wherein the mobile user equipment receives and decodes signals from each GPS satellite, and communicates to the base station data enabling knowledge of the identity of each satellite and uncorrected mobile antenna position, the base station decodes signals through a base station antenna from each of the set of GPS satellites used by the mobile user equipment, computes an uncorrected range from each satellite to the base station antenna, and compares the uncorrected range from each satellite to the base station antenna with an actual range based on computed satellite positions and a known base antenna position, to provide systematic range errors for each of the set of GPS satellites, and the base station utilises a known relationship between range error and antenna position error to deduce a correction to the mobile antenna position.

Description

APPARATUS AND METHOD FOR DIFFERENTIAI. SATELLITE POSITIONING

Technical Field

This invention relates to differential global positioning satellite systems ("DGPS").

Background Art

Global positioning satellite systems ("GPS") are systems in which a constellation of satellites emitting radio signals is used to determine the position of antennas on or above the earth's surface. Such systems provide facilities to allow user equipment to measure the distance ("range") between the satellite and the antenna of the user equipment. The ranges are obtained by estimating the time of flight of the radio signal between the satellite and the user equipment antenna. The user equipment computes the time of flight using data describing the orbit of each satellite, together with data encoded in the signal representing the time of emission of the signal from the satellite. Using the calculated values of the precise positions of several satellites at the time of emission and the ranges to them, the user equipment is able to compute the user equipment antenna position using triangulation.

In the general case, this form of position estimation is essentially a three dimensional (3D) technique, since the three dimensional location of the antenna is computed. However, if one coordinate of the location of the user equipment is known, then a two dimensional (2D) solution may be obtained. There are two primary benefits of using a 2D solution. First, the number of satellites required to produce the position estimate is one less for a 2D solution compared with the 3D solution. If a number of satellites are obscured from the antenna of the user equipment, a 2D solution may be the only possible calculation which can be performed in certain circumstances. Second, for a given set of satellites the Dilution of Precision (DOP) is also smaller for a 2D solution than for a 3D solution. The DOP is the statistical ratio by which a range error is translated into a position error and hence the use of prior information in the form of one position coordinate leads to a reduction in the position error. The altitude is invariably the position coordinate which is available to be used in this way and this will be the assumed form of 2D positioning in this specification, without limiting the broadest scope of the invention to such altitude-based 2D positioning.

As long as the assumed value of the altitude iβ correct, 2D positioning works well. However, where there is an error in the assumed altitude, this will translate to an error in the computed horizontal position (latitude, longitude) estimated from the satellite ranges. Often the horizontal error thus produced is larger than the altitude error which caused it.

There are many sources of error in GPS systems. These include systematic errors generated in the satellites which deliberately introduce a random element into the ranges measured by all user equipment using the same satellites in the same way, and atmospheric delays experienced by the signals which cause the signals to travel at less than the assumed speed of light in vacuo and which effect the ranges measured by all user equipment in a given geographical region. Often such systematic errors, which affect each user equipment in a given region in the same way, are the dominant sources of error. This has given rise to the development of differential GPS ("DGPS") in which the errors measured at a location of known position (called a reference location) are used to correct measurements or positions estimated at other locations.

Known types of DGPS include; (1) A system in which the range errors measured at the reference location are broadcast to mobile receivers within a given geographical area and used by the user equipment at the mobile locations to correct the locally computed range estimates prior to computing the position of the mobile equipment.

(2) A system in which range errors are measured at several reference sites and transmitted to a central site. At the central site a set of coefficients is computed allowing the appropriate correction for any given location within a large geographical area to be estimated. These coefficients are then broadcast to mobile user equipment within the large geographical area, allowing each user equipment to correct its measured range prior to computing its position.

(3) A system in which ranges measured by mobile user equipment within a given geographical area are reported to a reference location where range errors for all satellites in view are constantly measured. At the reference site the reported ranges are then corrected for the errors measured at the base site prior to computation of the positions of the mobile equipment.

(4) A system in which the position error measured at a reference site is used to correct positions reported from mobile locations within a certain geographical area, without consideration for the particular satellite set used by the base site or by the mobile locations.

(5) A system in which positions and the sets of satellites use to compute those positions are reported to a reference site by mobile user equipment within a given geographical area. The position of the base site is then computed using ranges measured at the base site for the satellites whose IDs were reported by each mobile user equipment. The error in this position estimate is then used to correct the corresponding position report.

(6) A system in which position errors are measured at a reference site and broadcast along with the satellites in the set used to measure that position error to the mobile user equipment. The mobile user equipments then use this information and estimate their own position using the same set of satellites which is subsequently corrected using the broadcast correction or error.

While all of the above systems in principle will operate effectively in a perfect environment where communications are fast and reliable and satellites are not often obscured, in practice a number of problems limit the known options differently: (a) particular satellites are often unable to be received either by the base station or the user equipment, and systems which require the mobile user equipment to use the same satellite set as the base station therefore suffer; (b) there may be bandwidth limitations on communications between the mobile user equipment and the base station, slowing systems in which much data needs to be communicated;

(c) computational inaccuracies can arise in systems which compute corrected positions from corrected ranges, the range error being very small in comparison with the range.

Summary of the Invention

It is an object of the current invention to provide an alternative method and apparatus for DGPS of improved performance.

In accordance with a first broad aspect of the invention there is provided a method of positioning one of a set of one or more mobile antennas capable of receiving signals from GPS satellites, each mobile antenna being associated with corresponding mobile user equipment and capable of communicating with a base station, wherein (i) the mobile user equipment receives and decodes, from each of a set of GPS satellites, signals encoded with a time of signal transmission and communicates to the base station data enabling knowledge of a) the identity of each of the set of GPS satellites, and b) an uncorrected mobile antenna position computable from uncorrected ranges from the mobile antenna to each of the set of GPS satellites, the uncorrected ranges being computable from the time of signal transmission, the actual time of receipt of the signal by the mobile antenna, and predetermined satellite orbit information;

(ii) the base station receives and decodes signals through a base station antenna from each of the set of GPS satellites used by the mobile user equipment, computes an uncorrected range from each satellite to the base station antenna, and compares the uncorrected range from each satellite to the base station antenna with an actual range based on computed satellite positions and a known base antenna position, to provide systematic range errors for each of the set of GPS satellites;

(iii) the base station utilises a known relationship between range error and antenna position error to deduce a correction to the mobile antenna position.

By transforming range error into position error for the satellite set used by the mobile user equipment, computational accuracy is improved while providing flexibility. Preferably, in embodiments where the mobile user equipment is capable of operating in 2D or 3D mode, the mobile user equipment communicates the mode of operation to the base station, and if the mode is 2D then (i) the base station computes a systematic altitude error for the mobile antenna by comparing a known altitude of the mobile antenna with an uncorrected altitude deduced from the communicated data; and

(ii) the systematic altitude error is used together with said range errors in the deduction of corrections to the mobile antenna position.

Thus, use of the transformation between range error and position error allows easy incorporation of 2D modes of operation by including the altitude error as an additional range error in the same computation.

Preferably the method includes positioning by dead reckoning during periods of satellite obscuration.

Thus, in some areas, such as high rise areas of cites, it may be impossible for the receiver to perform a fix for minutes at a time because of satellite obscuration. In many applications it is desirable to continue positioning during these periods by using other sensors to sense the vehicle motion. This technique is usually referred to as Dead Reckoning (DR) .

Preferably the method includes using one or more reference GPS fixes, and correcting GPS-related errors in the dead reckoning position reports.

In cases where DR sensors are used to determine the vehicle position relative to an initial position and heading obtained from a GPS fix, and the DR position reports will involve GPS-related errors, which should thus be corrected. Preferably, the known relationship between position error and range error may be modelled by a relationship of the form

ΔX = P*H^T*INV[H*P*H^T + R]*ΔY, where P is a matrix of error covariances in the uncorrected position of the mobile antenna, R is a matrix of estimates of error covariances in the range errors ΔY, giving a least squares estimate of position error ΔX, and INV is matrix inversion or pseudo-inversion.

Alternatively, the known relationship between position error and range error may be modelled as a linear relationship of the form

ΔX = INV[H] * ΔY, where ΔX is a position error vector,

ΔY is a range error vector,

H is a matrix of direction cosine vectors from the base station antenna towards the satellites, and INV is matrix inversion or pseudo-inversion.

In embodiments where the mobile user equipment is capable of operating in 2D or 3D mode, the altitude error may be included in the vector ΔY of range errors and a corresponding row in the matrix H is a partial derivative of a modelled distance r from the uncorrected mobile antenna position to the centre of the earth with respect to cartesian coordinates x, y, z, where the z axis passes through the poles. The modelled distance may be in the form of an ellipsoid model of the earth's surface of the form r² = x² + y² + z² * a² / b² where a and b are constants defining eccentricity of the earth's shape about the poles.

According to a second broad aspect of the present invention there is provided a method of positioning one of a set of one or more mobile antennas capable of receiving signals from GPS satellites, each mobile antenna being associated with corresponding mobile user equipment, including positioning by dead reckoning during periods of satellite obscuration.

Preferably the method includes positioning by dead reckoning using one or more reference GPS fixes, and correcting GPS-related errors in dead reckoning position reports .

Preferably correcting GPS-related errors in said dead reckoning position reports includes correcting an initial heading error, and said correction of said initial heading error includes: i) computing an initial heading correction from a reference GPS fix, and ii) computing a corrected position for each dead reckoning fix by applying said heading correction to a vector connecting a reference GPS position to a dead reckoning position.

Preferably the method includes defining a first and second reference GPS fix, said first reference GPS fix providing an initial dead reckoning heading, and said second reference GPS fix providing an initial dead reckoning position.

According to a third broad aspect of the present invention there is provided an apparatus for positioning one of a set of one or more mobile antennas capable of receiving signals from GPS satellites, each mobile antenna being associated with corresponding mobile user equipment and capable of communicating with a base station, wherein the apparatus is adapted to perform the method described above, including any of the preferred features of that method. According to a fourth broad aspect of the present invention there is provided an apparatus for positioning one of a set of one or more mobile antennas capable of receiving signals from GPS satellites, each mobile antenna being associated with corresponding mobile user equipment and capable of communicating with a base station, wherein said apparatus comprises a base station adapted:

(i) to receive from the mobile user equipment data enabling knowledge of a) the identity of each of the set of GPS satellites, and b) an uncorrected mobile antenna position computable from uncorrected ranges from the mobile antenna to each of the set of GPS satellites, the uncorrected ranges being computable from time of signal transmission, the actual time of receipt of the signal by the mobile antenna, and predetermined satellite orbit information; (ii) to receive and decode signals from each of the set of GPS satellites used by the mobile user equipment, compute an uncorrected range from each satellite to the base station antenna, and compare the uncorrected range from each satellite to the base station antenna with an actual range based on computed satellite positions and a known base antenna position, to provide systematic range errors for each of the set of GPS satellites; and

(iii) to utilise a known relationship between range error and antenna position error to deduce a correction to the mobile antenna position.

Preferably, where the mobile user equipment is capable of operating in 2D or 3D mode, the base station is adapted to receive a signal indicative of the mode from the mobile user equipment and the base station is adapted to

(i) compute a systematic altitude error for the mobile antenna by comparing a known altitude of the mobile antenna with an uncorrected altitude deduced from the communicated data; and (ii) use the systematic altitude error together with said range errors in the deduction of corrections to the mobile antenna position, if said mode is 2D.

Preferably the base station includes a computer.

Preferably the base station includes a multi-channel receiver.

Preferably the base station includes an antenna.

Brief Description of the Drawings

In order that the invention may be more clearly understood, a preferred embodiment will now be described, by way of example, with reference to the accompanying drawings in which:

Figure 1 shows a schematic diagram of the functional arrangement of the preferred embodiment of the invention;

Figure 2 illustrates a hardware configuration of the base station 4;

Figure 3 is a context diagram for the software which controls the GPS base station computer 21;

Figure 4 is a data flow diagram providing detail of the context diagram of Figure 3; Figure 5 shows further details of process A shown in Figure ; and

Figure 6 illustrates the functional breakdown of process C shown in Figure . Detailed Description of the Preferred Embodiment

Referring now to Figure 1, there is shown a schematic diagram of the functional arrangement of the preferred embodiment of the invention. Mobile user equipment 1 has a mobile antenna 2 associated with it which is adapted to receive signals from GPS satellites orbiting the earth. The mobile user equipment 1 decodes the signal from each of a set of the GPS satellites, the signals being encoded with a time of signal transmission from the corresponding GPS satellite. This time of signal transmission enables the mobile user equipment to calculate using the finite speed of transmission of electromagnetic signals an uncorrected range from the mobile antenna 2 to each of the set of GPS satellites, taking into account predetermined satellite orbit information called ephemeris data held in the mobile user equipment 1. From the uncorrected ranges calculated in the mobile user equipment, an uncorrected mobile antenna position is computable by triangulation. In the embodiment described here, the uncorrected mobile antenna position is computed inside the mobile user equipment 1, and the mobile user equipment is capable of operating in either 2D or 3D mode. Via a mobile communication antenna 3, the mobile user equipment 1 communicates to a base station 4 data enabling knowledge of the identity 7 of each of the set of GPS satellites used in the computation of uncorrected ranges, the mode 8 (2D or 3D) of operation, and an uncorrected mobile antenna position 6 to the base station 4 which receives the signal via a second communication antenna 5. In this embodiment, the data enabling knowledge of the uncorrected mobile antenna position is of the form of a direct communication of the identity of each of the set of GPS satellites and the uncorrected mobile antenna position, but variations may be contemplated such as communication of uncorrected ranges which enable this knowledge to be simply computed at the base station 4.

At the base station 4, a base station antenna 10 and base station suer Equipment 11 are adapted to receive and decode signals from each of the set of GPS satellites used by the mobile user equipment. In the preferred embodiment, the base station is continuously monitoring all satellites which can be received and is computing uncorrected ranges from each such satellite to the base station antenna, in the same manner as the mobile user equipment 1 computes uncorrected ranges from the mobile antenna 2 to each GPS satellite. By virtue of such continuous computation, the base station 4 is continuously updating information which will enable it to calculate a range error 13 by comparing with a known base station antenna position 12 stored at the base station 4. In alternative embodiments, the base station 4 may communicate with each of the set of GPS satellites only on activation by communication from the mobile user equipment 1. In either case, it may be necessary to first adjust the uncorrected range from each satellite to the base station antenna to take account of differing times of signal transmission from the GPS satellite, in order to deduce what would have been the uncorrected range measured by the base station if the measurement were performed in relation to a signal emitted at the same time as the signal received by the mobile user equipment 1.

Utilising an algorithm 14 to be described below, the range error 13 is converted into a mobile antenna position error 15. The mobile antenna position error 15 is then combined with the uncorrected mobile antenna position 6 to produce a corrected mobile antenna position 17. Depending on the use to which the system is put, this corrected mobile antenna position 17 may then be communicated back to the mobile user equipment 1 for display or use of accurate position information, or alternatively retained at that base station for accurate position logging of the mobile user equipment 1. The algorithm 14 may be a linear transformation of the form commonly used in obtaining a position solution. For example, the computation ΔX=INV[H]*ΔY may be used where X is the position vector, Y is the vector of ranges and H is a matrix of direction cosine vectors from the reported position to the satellites such that ΔY=H*Δx. The function INV is a matrix inversion or pseudo- inversion. The direction cosines are equal to the partial derivatives of the elements of range Y with respect to the elements of position X and hence H is a linear transformation matrix between small changes in X (ie Δx) and small changes in Y (ie ΔY) .

More sophisticated algorithms may be used in which an estimate is made of the covariances R of the errors in the range error estimates, and of the covariances P in the errors in reported position, and these are used to weight the error computation so as to provide a least squares estimate of the position error. The position error would then be obtained as

ΔX=P*H^T*INV[H*P*H^T + R]*ΔY. This formula is the same as the well-known Kalman filter update formula.

There are various ways in which P and R may be estimated. R may be established a priori by measurement and analysis. Typically, in this case, R would be a diagonal matrix of equal error variances. Alternatively, it could be estimated inside the base station receiver. The range errors giving rise to the errors in the position, X, may also be estimated a priori . Typically, the covariances matrix, P, would be a diagonal matrix of unequal error variances equal to ε*diag[H^τH] where ε is a scalar estimate of the equal error variances in the range estimates and the function diag[] extracts a leading diagonal matrix from its arguments. For correction of 2D position estimates the altitude error may be simply treated as an error in another range estimate where the "range" concerned is the range from the centre of the earth. In this case the row in the H matrix corresponding to this "range" is the vector of partial derivatives of r with respect to x,y and z where r is the "range", x,y and z are the cartesian coordinates of the reference position and r² = x² + y² +z²*a²/b² where a and b are constants defining the eccentricity of the earth's shape. The z ordinate in this case is along the axis passing through the poles.

There are several ways to obtain the altitude error 16. For example, it may be obtained as the difference between the altitude obtained as part of a recent corrected 3D position and the reported altitude. This assumes that the true altitude of the mobile or roving antenna has not altered since the previous 3D position fix was made. Alternatively it may be obtained by using the reported horizontal position to index a table or file of stored altitude data to obtain a close approximation to the altitude of the mobile or roving antenna and then subtracting the reported altitude. This is the preferred method and gives more accurate results when iterated by using the corrected position to look up the altitude table and perform the correction several times.

For correction of DR reports, the method computes the position correction for the GPS fix with reference to which the mobile equipment performed dead reckoning. The mobile equipment, therefore, reports the reference GPS fix data to the base to permit the corresponding position correction to be computed. This initial position correction may then be used to correct all subsequent DR fixes reported from the same mobile until a new GPS fix is performed at that mobile. However, the GPS-related errors in the DR fix derive from both the initial position error and the initial heading error. The latter may be corrected by:

1. Computing an initial heading correction for the reference GPS fix, and

2. Computing a corrected position for each DR fix by applying the heading correction to the vector connecting the reference GPS position to the DR position. In order to perform step 1 above it is necessary to know the velocity of the mobile at the time of the reference GPS fix. This can be estimated by the GPS receiver and included in the position report, typically in the form of speed and heading. This is not shown in Fig. 1, which illustrates the basic scheme only.

The velocity consists of the true velocity plus a velocity error dominated by systematic velocity errors that may be measured independently at the base. Hence, by estimating the velocity error and subtracting it from the reported velocity it is possible to obtain a better estimate of the true velocity. The heading correction may then be obtained as the difference between the arguments of the two velocity vectors.

The velocity error may be obtained from the systematic range rate errors using the same gain matrix as is used to obtain the position error from the pseudorange errors:

ΔX' = P^*H^T*INV[H^*P^*H^T + R] ^*ΔY'

where H, P and R are the matrices defined previously, ΔY' is the vector of range rate errors obtained as the differences between the measured range rates at the base and those predicted by calculation from the satellite motion. The heading correction may thus be computed as follows :

Δh = Arg(X' - ΔX') - Arg(X')

where X' is the uncorrected velocity vector representing the mobile velocity at the time of the reference GPS fix and the Arg function takes the argument of a vector.

The corrected position for a DR fix is then obtained as:

X_c = X_GPS - ΔX + [X_DR - X_σps]Z(Arg(X_DR - X_GPS)+Δh)

where X_c is the corrected DR position, X_DR is the raw DR position, Δx is the computed correction for the reference GPS fix and X_GPS is the corrected reference GPS position.

One problem with this technique is that Arg(X') is undefined when [X¹] is zero. Hence, if the vehicle is stationary for the reference GPS fix then this technique may not be used. This is of course, consistent with the fact that the heading of the vehicle may only be derived from the vehicle velocity while the vehicle is moving which means that a minimum speed must be set for the heading acquisition in the vehicle in any case. This leads to a situation in which the reference GPS fix may not be the GPS fix from which the heading was acquired. When this is the case then the heading correction should not be applied. Alternatively two separate reference GPS fixes may be defined with one for the initial DR heading and the other for the initial DR position. This is the preferred solution.

Figure 2 illustrates a hardware configuration of the base station 4. The dispatch computer 20 passes position reports to the base station GPS computer 21 and receives corrected position reports from the GPS base station comruter 21 in return. The format of both reports is the same. A GPS base station receiver 22 is connected to one of the serial ports of the base station GPS computer and the base station antenna 10 is connected to the RF input connector of the GPS base station receiver. The base station antenna 10 must be mounted with a clear view of the sky and should be of a type designed to discriminate against multipath interference from below. For example, the multiNAV G4270 ABS base kit supplied by Sigtec Navigation comes equipped with an anti-multipath ground plate designed for this purpose. More expensive alternatives may provide even greater multi-path immunity via the incorporation of choke rings.

The mobile user equipment 1 may be any receiver capable of reporting position (inclusive of altitude), positioning mode (ie, 2D or 3D), time of fix (ie, time of signal transmission) and SV numbers of the satellites used to make the determination of position. It is preferable to use a receiver with a compact message format for communication to the base station incorporating all this data in order to preserve the communication bandwidth. This may be critical for computer aided or automated dispatch applications.

For best performance the mobile user equipment 1 should be configured to perform clean and immediate transitions between error vectors when changes in the set of satellites 7 used to perform the position determination occurs.

Typically, GPS receivers provide smoothed position reports, and when a change occurs to the satellite set, for example as a result of obscuration by trees or structures, the change in the error in the report of position occurs slowly. During this transition period the differential corrections computed at the base station 4 will be inaccurate as they will not account for the smoothing operation. However, if the smoothing is suppressed when set changes occur than the correctability of the errors is preserved. Figure 3 is a context diagram for the software which controls the GPS base station computer 21 for the basic scheme not involving correction of DR reports. The central process, termed "Perform Differential Positioning" controls the GPS base station receiver 22 in order to extract pseudorange correction at one second intervals for all satellites in view. The process also reads an almanac file (which may be in the "Yuma" format) in order to compute the approximate positions of the satellites in view. The almanac file is updated once per day from the GPS base station receiver 22. Using the calculated range error and the uncorrected mobile antenna position it then computes mobile antenna position errors for each position report received from the dispatch computer 20. The base station computer 21 then applies the appropriate corrections and returns corrected mobile antenna position reports to the dispatch computer 20.

The "Perform Differential Positioning" process may be broken down into simpler subprocesses as indicated in Figure 4. The range errors for each satellite in view are stored in a database along with the corresponding times of signal transmission and appropriate entries in that database are selected by process C which utilises those errors to convert uncorrected mobile antenna positions to corrected mobile antenna positions. In selecting appropriate entries, Process C takes account of the satellite set and the time of signal transmission. Process B accepts raw position reports from the dispatch computer, and parses them into the uncorrected mobile positions, the time of signal transmission from the satellite and the satellite set used by the mobile user equipment, and any other fields. In process D, the corrected position and other information is assembled into a corrected position report which is then returned to the dispatch computer 20.

Process E is activated on start up of the base station computer to convert the Almanac data for all satellites in the constellation of GPS satellites into standard Ephemeris data base format used by process C. Process E also runs once per day to convert and store Almanac data extracted from the base station receiver.

Figure 5 shows further details of process A shown in figure 4. Sub process A2 operates as follows:

1. Read initialisation commands from the configuration file (see figure 4) and transmit to GPS base station receiver 22, with a delay of one second between commands.

2. Request Almanac report from GPS base station receiver once per day.

3. Request range errors report at one second intervals from GPS base station receiver 22.

The precise formats of the commands used are specific to the particular GPS base station receiver 22 which is utilised.

Process Al interprets two types of report from the GPS base station receiver 22. One such report is a range corrections report which would usually conform to the specified format of message type 1 of the RTCM-SC104 standard, as set out in RTCM Recommended Standards for Differential Navstar GPS Service, [version 2.1, Radio Technical Commission for Maritime Services, 3 January

1994] . Only this message type is required because it is being received at a high update rate and no interpolation is required between the type 1 messages.

The RTCM message type 17 or the NMEA GPALM message [NMEA 0183, Standard For Interfacing Marine Electronic Devices, version 2.00, National Marine Electronics Association, 1 January 1992] would be used to report the Almanac data. Alternatively the Ephemeris data could be extracted from the GPS baβe station receiver 22 for each satellite being tracked.

Figure 6 illustrates the functional breakdown of process C shown in Figure .

Process Cl computes satellite positions from the Keplerian elements as described in the GPS Interface Control Document [ICD-GPS-200, Navstar GPS Segment /Navigation User Interfaces (Public Release Version) revision B-PR, ARINC Research Corporation, I July 1993] . Procesβ C2 obtains satellite positions from process Cl and the mobile position expressed in cartesian coordinates (x, y, z) is obtained from process C5. These data (in earth-centred earth-fixed (ECEF) cartesian coordinates with units of meters) are used to compute a matrix of direction cosines between the GPS antenna and the satellite set used by the mobile user equipment as follows:

(x^r - x₁)/r₁ (y_r -

(z_r - z₁)/x₁

(x_r - x₂)/r₂ (y_r - y₂)/r₂ (z_r - z₂)/r₂

(x_r - x₃)/r₃ ⁽y_r - y₃ ⁾ r₃ (z_r - z₃)/r₃

(x_r - x₄)/r₄ ⁽y_r - y₄ ⁾/^r4 (z_r - z₄)/r₄

(x_r - x₅)/r₅ <y_r - γ₅)/r₅ (z_r - z₅)/r₅ x_r / r₀ Yr ^r0 a²/b²*z_r/r₀

where x_r denotes the x coordinate of the mobile antenna, x₁ are denotes the range from satellite 1 from the mobile antenna and x, y and z are the directions of the three cartesian coordinate axes. r₀ denotes the "range" from the "centre of the earth" to the mobile antenna computed as

= * ² + y_r ² + z_r * a² / b² where a and b are well known parameters describing the eccentricity of the earth's shape. The number of rows depends on the number of satellites used to obtain the mobile position to be corrected. In the example above five satellites were used in the mobile position solution and six rows are required. In the general case of correcting a 2D fix one more row than the number of satellites is required to accommodate the altitude correction. For correcting a 3D fix this last row is not required.

The above matrix is given the symbol H. Although it is not invertible, it is used in process C3 to compute a weighted pseudo-inverse which is given by:

H^"1 = H*P*H^T* INV[H*P*H^T + R] , where the T denotes transpose, the function INV denotes matrix inversion, the matrix P is the estimated error covariances of the raw position vector and the matrix R is the estimated error covariance of the pseudorange vector. This is a well-known procedure used in Kalman filters.

A simply determined estimate of P that takes into account the satellite geometric is given by:

P=e*e*DIAG(INV[H^τH] )

where e iβ an a priori error factor determined empirically for the mobile receiver used and the function DIAGO produces a diagonal matrix with the same diagonal elements as the input matrix.

R is a diagonal matrix with _Xi equal to the estimated variance of the pseudorange error for the ith satellite. Typically, this is set a priori to the same value for all satellites but could be estimated dynamically using standard techniques. In the 2D case, the entry, R_NN, in the last row is the estimated variance of the error in the altitude and depends on the precision and accuracy of the altitude table, the steepness of the terrain and the number of iterations used to obtain the altitude (see later) .

More sophisticated non-diagonal estimates for P and R could be used but would probably have to be estimated dynamically by the software. In most applications the improvement to be gained would normally be swamped by errors from sources such as multipath distortion.

The matrix, H^_1, is the transformation matrix to be used to transpose the vector of pseudorange errors and altitude error onto a position error. This is also performed by C3. The pseudorange errors must be in the same order as the columns of the Measurement Matrix, H, with, in the 2D case, the altitude error last. The position error is then computed as follows:

ΔX = H^"1 ΔY

where X is a column vector of position in ECEF cartesian coordinates in the same units as the pseudorange column vector, Y. For correction of a 2D position report this calculation is iterated using different values only for the altitude correction as described below.

Process C3 obtains the altitude correction in the first instance as zero. That is to say, the first position correction to be computed using pseudorange corrections only. This is passed to Process C4 which computes the Corrected xyz position.

The corrected xyz position is then used by Process C3 to obtain the corresponding altitude from the Altitude Database. The raw altitude is extracted from the xyz Position and subtracted from the altitude obtained from the Altitude Database to give the Altitude Correction for the second iteration. Third and subsequent iterations are the same as the second. The iterative process terminates when the difference in the altitude obtained in successive iterations is less than a set threshold or when a fixed number of iterations have been processed.

Process C5 transforms from the latitude, longitude and height coordinates of the mobile position report to ECEF cartesian coordinates before the correction can be applied in Process C . Methods for doing this are well known. The ECEF (or xyz) position is also passed to Process C2 for use in computing the Measurement Matrix, H.

The resulting correction vector is simply added to the position vector in Process C4 to give the corrected position vector which is then transformed back into latitude, longitude and height using standard methods in Process C6.

Modifications may be made to the invention as would be apparent to a person skilled in the art of GPS system designs. For example, although the above description has concentrated on the calculation and storage of range errors and position errors, the negative of those values (i.e. range corrections and position corrections) is equivalent data and references in this specification to errors are to be taken to encompass the use of corrections alternatively. These and other modifications may be made without departing from the ambit of the current invention, the nature of which is to be ascertained from the foregoing description and the drawings.

Claims

THE CLAIMS DEFINING THE INVENTION ARE AS FOLLOWS:

1. A method of positioning one of a set of one or more mobile antennas capable of receiving signals from GPS satellites, each mobile antenna being associated with corresponding mobile user equipment and capable of corrvmunicating with a base station, wherein

(i) the mobile user equipment receives and decodes, from each of a set of GPS satellites, signals encoded with a time of signal transmission and communicates to the base station data enabling knowledge of a) the identity of each of the set of GPS satellites, and b) an uncorrected mobile antenna position computable from uncorrected ranges from the mobile antenna to each of the set of GPS satellites, the uncorrected ranges being computable from the time of signal transmission, the actual time of receipt of the signal by the mobile antenna, and predetermined satellite orbit information;

(ii) the base station receives and decodes signals through a base station antenna from each of the set of GPS satellites used by the mobile user equipment, computes an uncorrected range from each satellite to the base station antenna, and compares the uncorrected range from each satellite to the base station antenna with an actual range based on computed satellite positions and a known base antenna position, to provide systematic range errors for each of the set of GPS satellites; (iii) the base station utilises a known relationship between range error and antenna position error to deduce a correction to the mobile antenna position.

2. A method as claimed in claim 1 where the mobile user equipment is capable of operating in 2D or 3D mode, the mobile user equipment communicates the mode of operation to the base station, and if the mode is 2D then (i) the base station computes a systematic altitude error for the mobile antenna by comparing a known altitude of the mobile antenna with an uncorrected altitude deduced from the communicated data; and (ii) the systematic altitude error is used together with said range errors in the deduction of corrections to the mobile antenna position.

3. A method as claimed in either claim 1 or 2, wherein said method includes positioning by dead reckoning during periods of satellite obscuration.

4. A method as claimed in claim 3, including positioning by dead reckoning using one or more reference GPS fixes, and correcting GPS-related errors in dead reckoning position reports.

5. A method as claimed in claim 4, wherein correcting GPS-related errors in said dead reckoning position reports includes correcting an initial heading error, and said correction of said initial heading error includes: i) computing an initial heading correction from a reference GPS fix, and ii) computing a corrected position for each dead reckoning fix by applying said heading correction to a vector connecting a reference GPS position to a dead reckoning position.

6. A method as claimed in claim 5 including defining a first and second reference GPS fix, said first reference GPS fix providing an initial dead reckoning heading, and said second reference GPS fix providing an initial dead reckoning position.

7. A method as claimed in any one of the preceding claims, wherein said known relationship between position error and range error is modelled by a relationship of the form

8. A method as claimed in any one of claims 1 to 6, wherein said known relationship between position error and range error is modelled as a linear relationship of the form ΔX = INV[H]*ΔY, where Δx is a position error vector, ΔY is a range error vector,

H is a matrix of direction cosine vectors from the base station antenna towards the satellites, and

INV is matrix inversion or pseudo-inversion.

9. A method as claimed in claim 8 wherein, when said mobile user equipment is capable of operating in 2D or 3D mode, the altitude error is included in the vector ΔY of range errors and a corresponding row in the matrix H is a partial derivative of a modelled distance r from the uncorrected mobile antenna position to the centre of the earth with respect to cartesian coordinates x, y, z, where the z axis passes through the earth's poles.

10. A method as claimed in claim 9 wherein said modelled distance is in the form of an ellipsoid model of the earth's surface of the form r² = x² + y² + z² * a² / b² where a and b are constants defining eccentricity of the earth's shape about the poles.

11. A method of positior ig one of a set of one or more mobile antennas capable c receiving signals from GPS satellites, each mobile antenna being associated with corresponding mobile user equipment, including positioning by dead reckoning during periods of satellite obscuration.

12. A method as claimed in claim 11, including positioning by dead reckoning using one or more reference GPS fixes, and correcting GPS-related errors in dead reckoning position reports.

13. A method as claimed in claim 12, wherein correcting GPS-related errors in said dead reckoning position reports includes correcting an initial heading error, and said correction of said initial heading error includes: i) computing an initial heading correction from a reference GPS fix, and ii) computing a corrected position for each dead reckoning fix by applying said heading correction to a vector connecting a reference GPS position to a dead reckoning position.

14. A method as claimed in claim 13 including defining a first and second reference GPS fix, said first reference GPS fix providing an initial dead reckoning heading, and said second reference GPS fix providing an initial dead reckoning position.

15. A method as claimed in any one of the preceding claims, employing range corrections and position corrections rather than range errors and position errors, respectively.

16. An apparatus for positioning one of a set of one or more mobile antennas capable of receiving signals from GPS satellites, each mobile antenna being associated with corresponding mobile user equipment and capable of communicating with a base station, wherein said apparatus is adapted to perform the method as claimed in any one of the preceding claims.

17. An apparatus as claimed in claim 16 including a computing device and a multi-channel receiver.

18. An apparatus as claimed in claim 17, wherein said computing device is a computer provided with or running a computer program to perform said method.

19. An apparatus for positioning one of a set of one or more mobile antennas capable of receiving signals from GPS satellites, each mobile antenna being associated with corresponding mobile user equipment and capable of communicating with a base station, wherein said apparatus comprises a computer readable medium on which is recorded a computer program adapted to control an apparatus including a computer to perform the method as claimed in any one of claims 1 to 15.

20. An apparatus for positioning one of a set of one or more mobile antennas capable of receiving signals from GPS satellites, each mobile antenna being associated with corresponding mobile user equipment and capable of communicating with a base station, wherein said apparatus comprises a base station adapted:

21. An apparatus as claimed in claim 20 wherein, where the mobile user equipment is capable of operating in 2D or 3D mode, the base βtation is adapted to receive a signal indicative of the mode from the mobile user equipment and the base station is adapted to

22. An apparatus as claimed in either claim 20 or 21, wherein said apparatus is adapted to perform positioning by dead reckoning during periods of satellite obscuration.

23. An apparatus as claimed in claim 22, wherein said apparatus includes a dead reckoning sensor to perform said dead reckoning.

24. An apparatus as claimed in either claim 22 or 23, wherein said apparatus is adapted to perform positioning by dead reckoning using one or more reference GPS fixes, and to correct GPS-related errors in dead reckoning position reports.

25. An apparatus as claimed in claim 24, wherein said apparatus is adapted to correct GPS-related errors in said dead reckoning position reports by correcting an initial heading error, said correction of said initial heading error being performed by: i) computing an initial heading correction from a reference GPS fix, and ii) computing a corrected position for each dead reckoning fix by applying said heading correction to a vector connecting a reference GPS position to a dead reckoning position.

26. An apparatus as claimed in claim 25, wherein said apparatus is adapted to define a first and second reference GPS fix, said first reference GPS fix to provide an initial dead reckoning heading, and said second reference GPS fix to provide an initial dead reckoning position.

27. An apparatus as claimed in any one of claims 20 to 26, wherein said known relationship between position error and range error is modelled by a relationship of the form

28. An apparatus as claimed in any one of claims 20 to 26, wherein said known relationship between position error and range error is modelled as a linear relationship of the form

ΔX = INV[H]*ΔY, where Δx is a position error vector, AY iβ a range error vector,

29. An apparatus as claimed in any on of claims 20 to

28, wherein said base station includes a computer.

30. An apparatus as claimed in any on of claims 20 to

29, wherein said base station includes a multi-channel receiver.

31. An apparatus as claimed in any on of claims 20 to 30, wherein said base station includes an antenna.