M.7 Converting MS-assisted measurement reports into position estimates

3GPP45.005GSM/EDGE Radio transmission and receptionTS

M.7.1 Introduction

To convert the MS measurement reports in case of MS-assisted mode of A-GPS into position errors, a transformation between the "measurement domain" (code-phases, etc.) into the "state" domain (position estimate) is necessary. Such a transformation procedure is outlined in the following clauses. The details can be found in [ICD-GPS 200], [P. Axelrad, R.G. Brown] and [S.K. Gupta].

M.7.2 MS measurement reports

In case of MS-assisted A-GPS, the measurement parameters are contained in the RRLP GPS MEASUREMENT INFORMATION ELEMENT (subclause A.3.2.5 in 3GPP TS 44.031). The measurement parameters required for calculating the MS position are:

1) Reference Time: The MS has two choices for the Reference Time:

a) "Reference Frame";

b) "GPS TOW ".

2) Measurement Parameters: 1 to <maxSat>:

a) "Satellite ID (SV PRN)";

b) "Whole GPS chips";

c) "Fractional GPS Chips";

d) "Pseudorange RMS Error".

Additional information required at the system simulator:

1) "Reference Location" (subclause A.4.2.4 in 3GPP TS 44.031):
Used for initial approximate receiver coordinates.

2) "Navigation Model" (subclause A.4.2.4 in 3GPP TS 44.031):
Contains the GPS ephemeris and clock correction parameters as specified in [ICD-GPS 200]; used for calculating the satellite positions and clock corrections.

3) "Ionospheric Model" (subclause A.4.2.4 in 3GPP TS 44.031):
Contains the ionospheric parameters which allow the single frequency user to utilize the ionospheric model as specified in [ICD-GPS 200] for computation of the ionospheric delay.

M.7.3 Weighted Least Squares (WLS) position solution

The WLS position solution problem is concerned with the task of solving for four unknowns; xu, yu, zu the receiver coordinates in a suitable frame of reference (usually ECEF) and bu the receiver clock bias. It typically requires the following steps:

Step 1: Formation of pseudo-ranges

The observation of code phase reported by the MS for each satellite SVi is related to the pseudo-range/c modulo 1 ms (the length of the C/A code period). For the formation of pseudo-ranges, the integer number of milliseconds to be added to each code-phase measurement has to be determined first. Since 1 ms corresponds to a travelled distance of 300 km, the number of integer ms can be found with the help of reference location and satellite ephemeris. The distance between the reference location and each satellite SVi is calculated and the integer number of milli-seconds to be added to the MS code phase measurements is obtained.

Step 2: Formation of weighting matrix

The MS reported "Pseudorange RMS Error" values are used to calculate the weighting matrix for the WLS algorithm described in [P. Axelrad, R.G. Brown]. According to 3GPP TS 44.031, the encoding for this field is a 6 bit value that consists of a 3 bit mantissa, Xi and a 3 bit exponent, Yi for each SVi:

The weighting Matrix W is defined as a diagonal matrix containing the estimated variances calculated from the "Pseudorange RMS Error" values:

Step 3: WLS position solution

The WLS position solution is described in [P. Axelrad, R.G. Brown] and usually requires the following steps:

1) Computation of satellite locations at time of transmission using the ephemeris parameters and user algorithms defined in [ICD-GPS 200] section 20.3.3.4.3.

2) Computation of clock correction parameters using the parameters and algorithms as defined in [ICD-GPS 200] section 20.3.3.3.3.1.

3) Computation of atmospheric delay corrections using the parameters and algorithms defined in [ICD-GPS 200] section 20.3.3.5.2.5 for the ionospheric delay, and using the Gupta model defined in [S.K. Gupta] p. 121 equation (2) for the tropospheric delay.

4) The WLS position solution starts with an initial estimate of the user state (position and clock offset). The Reference Location is used as initial position estimate. The following steps are required:

a) Calculate geometric range (corrected for Earth rotation) between initial location estimate and each satellite included in the MS measurement report.

b) Predict pseudo-ranges for each measurement including clock and atmospheric biases as calculated in 1) to 3) above and defined in [ICD-GPS 200] and [P. Axelrad, R.G. Brown].

c) Calculate difference between predicted and measured pseudo-ranges

d) Calculate the "Geometry Matrix" G as defined in [P. Axelrad, R.G. Brown]:

with where rsi is the Satellite position vector for SVi (calculated in 1) above), and is the estimate of the user location.

e) Calculate the WLS solution according to [P. Axelrad, R.G. Brown]:

f) Adding the to the initial state estimate gives an improved estimate of the state vector:

.

5) This new state vector can be used as new initial estimate and the procedure is repeated until the change in is sufficiently small.

Step 4: Transformation from Cartesian coordinate system to Geodetic coordinate system

The state vector calculated in Step 3 contains the MS position in ECEF Cartesian coordinates together with the MS receiver clock bias. Only the user position is of further interest. It is usually desirable to convert from ECEF coordinates xu, yu, zu to geodetic latitude  , longitude  and altitude h on the WGS84 reference ellipsoid.

Step 5: Calculation of "2-D Position Errors"

The latitude  / longitude obtained after Step 4 is used to calculate the 2-D position error.

Annex N (normative):
Reference Test Scenarios for DARP Phase II (MSRD)