F.3 WLS position solution
25.1713GPPFrequency Division Duplex (FDD)Release 17Requirements for support of Assisted Global Positioning System (A-GPS)TS
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 UE 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 UE code phase measurements is obtained.
Step 2: Formation of weighting matrix
The UE reported "Pseudorange RMS Error" values are used to calculate the weighting matrix for the WLS algorithm [9]. According to 3GPP TS 25.331 [4], 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 reference [9] and usually requires the following steps:
1) Computation of satellite locations at time of transmission using the ephemeris parameters and user algorithms defined in [8] section 20.3.3.4.3.
2) Computation of clock correction parameters using the parameters and algorithms as defined in [8] section 20.3.3.3.3.1.
3) Computation of atmospheric delay corrections using the parameters and algorithms defined in [8] section 20.3.3.5.2.5 for the ionospheric delay, and using the Gupta model in reference [10] 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 UE measurement report.
b) Predict pseudo-ranges for each measurement including clock and atmospheric biases as calculated in 1) to 3) above and defined in [8,9].
c) Calculate difference between predicted and measured pseudo-ranges
d) Calculate the "Geometry Matrix" G as defined in [9]:
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 [9]:
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 UE position in ECEF Cartesian coordinates together with the UE 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 G (informative):
Change History
Table G.1: TS history before approval
|
Date |
Meeting |
Document |
Comment |
Version old |
Version New |
|
RAN WG4 #29 |
R4-031082 |
Document proposed at RAN#29 |
|||
|
RAN WG4 #29 |
R4-031156 |
Comments added inline with discussion at RAN#29 |
|||
|
Dec 2003 |
Comment on R4-031156 |
||||
|
Jan 2004 |
RAN WG4 #30 |
R4-040104 |
Comments added after Ad-hoc 29/1/04 |
||
|
Jan 2004 |
RAN WG4 #29 |
R4-040169 |
Revised version of R4-040104 to allow printing |
||
|
May 2004 |
RAN WG4 #31 |
R4-040362 |
Revised version of R4-040233 |
||
|
May 2004 |
RAN WG4 #31 |
R4-040387 |
Approved version at RAN#31 |
||
|
May 2004 |
RAN WG4 #31 |
V0.0.0 produced based on R4-040387 |
0.0.0 |
||
|
May 2004 |
V0.1.0 with input from R4-040364 |
0.0.0 |
0.1.0 |
||
|
Aug 2004 |
Conference call on Aug 5, 2004 |
V0.1.0 with approved CRs: R4-04043, R4-04048, R4AH-04049, R4AH-04050 and R4AH-04052 |
0.1.0 |
0.2.0 |
|
|
Aug 2004 |
RAN WG4 #32 |
R4-040465 |
V0.2.0 for approval at RAN WG4 #32 |
||
|
Aug 2004 |
RAN WG4 #32 |
R4-040564 |
V0.3.0 for approval at RAN WG4 #32, inclusion of changes in R4-040535 |
0.2.0 |
0.3.0 |
|
Sep 2004 |
RAN #25 |
RP-040341 |
Submit for approval |
0.3.0 |
1.0.0 |
|
Sep 2004 |
RAN #25 |
Approved at RAN#24 |
1.0.0 |
6.0.0 |
Table G.2: Release 6 CR approved at TSG RAN #26
|
RAN Tdoc |
Spec |
CR |
R |
Ph |
Title |
Cat |
Curr |
New |
Work Item |
|
RP-040413 |
25.171 |
001 |
2 |
Rel-6 |
Removal of inconsistencies in TS 25.171 |
F |
6.0.0 |
6.1.0 |
LCS-UEPos-AGPSPerf |
Table G.3: Release 6 CR approved at TSG RAN #29
|
RAN Tdoc |
Spec |
CR |
R |
Ph |
Title |
Cat |
Curr |
New |
Work Item |
|
RP-050499 |
25.171 |
0003 |
1 |
Rel-6 |
Changes to GPS scenarios |
F |
6.1.0 |
6.2.0 |
LCS-UEPos-AGPSPerf |
Table G.4: Creation of Release 7
|
RAN Tdoc |
Spec |
CR |
R |
Ph |
Title |
Cat |
Curr |
New |
Work Item |
|
25.171 |
Rel-7 |
Release 7 created following decision at RAN#31 |
6.1.0 |
7.0.0 |
Table G.4: Release 7 CRs approved at TSG RAN #32
|
RAN Tdoc |
Spec |
CR |
R |
Ph |
Title |
Cat |
Curr |
New |
Work Item |
|
RP-060305 |
25.171 |
0005 |
Rel-7 |
Horizontal Accuracy IE change for nominal accuracy requirement |
A |
7.0.0 |
7.1.0 |
TEI6 |
|
|
RP-060305 |
25.171 |
0007 |
Rel-7 |
Change to altitude of simulated UE position |
A |
7.0.0 |
7.1.0 |
TEI6 |
Table G.5: Release 8
|
RAN Meeting |
RAN Tdoc |
CR |
R |
Title |
Cat |
Curr |
New |
Work Item |
|
SP-42 |
Upgrade unchanged from Rel 7 |
8.0.0 |
||||||
|
SP-46 |
Upgrade unchanged from Rel 8 |
9.0.0 |
||||||
|
SP-51 |
Upgraded unchanged from Rel-9 |
9.0.0 |
10.0.0 |
|||||
|
SP-57 |
– |
– |
– |
Update to Rel-11 version (MCC) |
– |
10.0.0 |
11.0.0 |
– |
|
SP-65 |
– |
– |
– |
Update to Rel-12 version (MCC) |
– |
11.0.0 |
12.0.0 |
|
|
SP-70 |
– |
– |
– |
Update to Rel-13 version (MCC) |
– |
12.0.0 |
13.0.0 |
|
|
RP-75 |
– |
– |
– |
Update to Rel-14 version (MCC) |
– |
13.0.0 |
14.0.0 |
|
Change history |
|||||||
|
Date |
Meeting |
TDoc |
CR |
Rev |
Cat |
Subject/Comment |
New version |
|
2018-06 |
SA#80 |
– |
– |
– |
– |
Update to Rel-15 version (MCC) |
15.0.0 |
|
2020-06 |
SA#88 |
– |
– |
– |
– |
Update to Rel-16 version (MCC) |
16.0.0 |
|
2022-03 |
SA#95 |
Update to Rel-17 version (MCC) |
17.0.0 |
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