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

3GPP45.005GSM/EDGE Radio transmission and receptionTS

Tools: ARFCN - Frequency Conversion for 5G NR/LTE/UMTS/GSM

O.7.1 Introduction

To convert the MS measurement reports in case of MS-assisted mode of A-GANSS 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 [IS-GPS-200], [IS-GPS-705], [IS-GPS-800], [SBAS], [IS-QZSS], [GLONASS ‑ICD],[Galileo-ICD],[P. Axelrad, R.G. Brown], [S.K. Gupta] and [BDS-ICD].

O.7.2 MS measurement reports

In case of MS-assisted A-GANSS, the measurement parameters are contained in the RRLP GANSS MEASUREMENT INFORMATION ELEMENT (subclause A.3.2.10 in 3GPP TS 44.031). In case the MS provides also measurements on the GPS L1 C/A signal, 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) "GANSS TOD" and/or "GPS TOW" if GPS L1 C/A signal measurements are also provided.

Note: It is not expected that an MS will ever report both a GANSS TOD and a GPS TOW. However if two time stamps are provided and they derive from different user times, be aware that no compensation is made for this difference and this could affect the location accuracy.

2) Measurement Parameters for each GANSS and GANSS Signal: 1 to <maxSat>:

a) "SV ID"; mapping according to Table A.10.14 in 3GPP TS 44.031;

b) "Code Phase";

c) "Integer Code Phase";

d) "Code Phase RMS Error";

3) Additional Measurement Parameters in case of GPS L1 C/A signal measurements are also provided: 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 or A.4.2.6.1 in 3GPP TS 44.031):
Used for initial approximate receiver coordinates.

2) "GANSS Navigation Model" (subclause A.4.2.6.2 in 3GPP TS 44.031):
Contains the ephemeris and clock correction parameters as specified in the relevant ICD of each supported GANSS; used for calculating the satellite positions and clock corrections.

3) "GANSS Ionospheric Model" (subclause A.4.2.6.1 in 3GPP TS 44.031):
Contains the ionospheric parameters which allow the single frequency user to utilize the ionospheric model as specified in [Galileo-ICD] for computation of the ionospheric delay.

4) "GANSS Additional Ionospheric Model" (subclause A.4.2.6.1 in 3GPP TS 44.031):
Contains the ionospheric parameters which allow the single frequency user to utilize the ionospheric model as specified in [QZSS-ICD] and [BDS-ICD] for computation of the ionospheric delay.

5) "GANSS Time Model" (subclause A.4.2.6.2 in 3GPP TS 44.031):
Contains the GNSS-GNSS Time Offset for each supported GANSS. Note, that "GANSS Time Model" IE contains only the sub-ms part of the offset. Any potential integer seconds offset may be obtained from "UTC Model" (subclause A.4.2.4 in 3GPP TS 44.031), "GANSS UTC Model" (subclause A.4.2.6.2 in 3GPP TS 44.031), or "GANSS Additional UTC Model" (subclause A.4.2.6.2 in 3GPP TS 44.031).

6) "Navigation Model" (subclause A.4.2.4 in 3GPP TS 44.031):
Contains the GPS ephemeris and clock correction parameters as specified in [IS-GPS-200]; used for calculating the GPS satellite positions and clock corrections in case of GPS L1 C/A signal measurements are the only GPS measurements provided in addition to GANSS measurements.

7) "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 [IS-GPS 200] for computation of the ionospheric delay.

O.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 relative to the selected GNSS specific system time. 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 the "GANSS Code Phase Ambiguity", or modulo 1 ms (the length of the C/A code period) in case of GPS L1 C/A signal measurements. 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 at the time of measurement is calculated, and the integer number of milliseconds to be added to the MS code phase measurements is obtained.

Step 2: Correction of pseudo-ranges for the GNSS-GNSS time offsets

In case the MS reports measurements for more than a single GNSS, the pseudo-ranges are corrected for the time offsets between the GNSSs relative to the selected reference time using the GNSS-GNSS time offsets available at the system simulator:

where is the measured pseudo-range of satellite i of GNSS_m. The system time of GNSS_k is the reference time frame, andis the available GNSS-GNSS time offset, and c is the speed of light.

Step 3: Formation of weighting matrix

The MS reported "Code Phase RMS Error" and/or "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 these fields is a 6 bit value that consists of a 3 bit mantissa, Xi and a 3 bit exponent, Yi for each SVi of GNSS_j:

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

Step 4: WLS position solution

The WLS position solution is described in e.g., [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 the relevant ICD of the particular GNSS. The satellite locations are transformed into WGS-84 reference frame, if needed.

2) Computation of clock correction parameters using the parameters and algorithms as defined in the relevant ICD of the particular GNSS.

3) Computation of atmospheric delay corrections using the parameters and algorithms defined in the relevant ICD of the particular GNSS for the ionospheric delay, and using the Gupta model defined in [S.K. Gupta] p. 121 equation (2) for the tropospheric delay. For GNSSs which do not natively provide ionospheric correction models (e.g., GLONASS), the ionospheric delay is determined using the available ionospheric model (see subclause O.7.2) adapted to the particular GNSS frequency.

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 the relevant ICD of the particular GNSS 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 rs_GNSS_m,i is the satellite position vector for SVi of GNSS_m (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 5: Transformation from Cartesian coordinate system to Geodetic coordinate system

The state vector calculated in Step 4 contains the MS position in ECEF Cartesian coordinates together with the MS receiver clock bias relative to the selected GNSS system time. 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 6: Calculation of "2-D Position Errors"

The latitude  / longitude obtained after Step 5 is used to calculate the 2-D position error.

Annex P (normative):
Minimum receiver performance requirements for MSR BS

This annex defines the minimum receiver performance requirements that shall be fulfilled for GSM carrier in MSR BS when referenced from the 3GPP TS 37.104 [33].