GPS, Galileo and BeiDou inter-system biases estimation in relative positioning with code and phase pseudoranges
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1 GPS, Galileo and BeiDou inter-system biases estimation in relative positioning with code and phase pseudoranges Cecile Deprez and Rene Warnant University of Liege, Belgium
2 Multi-GNSS Many systems : GPS, GLONASS, Galileo, BeiDou, QZSS, IRNSS GPS GLONASS Galileo BeiDou QZSS 2
3 Multi-GNSS Overlapping frequencies : L1 (GPS) E1 (Galileo) B1 (BeiDou Phase III) L1 (QZSS) L5 (GPS) E5a (Galileo) L5 (QZSS) L5 (IRNSS) L2 (GPS) L2 (QZSS) E5b (Galileo) B2 (BeiDou) Upper L-Band Lower L-Band E1 E5a L5 L5 E5b B2 L2 L2 E6 B3 B1 L1 L1 Frequency (Mhz) 3 GLONASS GPS BeiDou Galileo
4 Inter-system biases (ISBs) One way code observation model GPS : P G 1,k = D G 1 + T G 1 + I G 1,k G (G) + M 1,k,m + c. δt 1 δt G + d 1 d G G + ε 1,k,m Galileo : P E 1,k = D E 1 + T E 1 + I E 1,k E (E) + M 1,k,m + c. δt 1 δt E + d 1 d E E + ε 1,k,m + c. (δt 1 (E) δggto δt E ) P 1,k : Pseudo-range δt 1 : Receiver clock errors D 1 : Geometric distance δt : Satellite clock errors T 1 : Tropospheric delay d 1 : Receiver hardware delay I 1,k : Ionospheric delay d : Satellite hardware delay M 1,k,m : Multipath ε 1,k,m : Code noise Galileo to GPS Time Offset = Different Time Systems 4
5 Inter-system biases (ISBs) In a zero baseline case : Single difference : G P 12,k = D G (G) (G) 12 + δt 12 d12 + G ε12,k,m E P 12,k = D E (E) (E) 12 + δt 12 d12 + E ε12,k,m The GGTO term disappears Double difference : P GG 12,k = D GG GG 12 + ε 12,k,m P GE 12,k = D GE (GE) 12 d 12 + GE ε12,k,m Single reference satellite for all observations Differential hardware delay between GPS and Galileo (ISB) 5
6 Equipment Antennae : 2 x TRIMBLE TRM SCIS (chock ring antenna) (ULG0 & ULG1) Receivers : 2 x Trimble NetR9 (TRM 1 & TRM 2) 2 x Septentrio PolaRx4 (Sept1 & Sept2) 1 x Septentrio PolaRxS (Sept 3) 1 x Septentrio PolaRx5 (Sept 4) Splitters : 1 x 2-way splitter 1 x 4-way splitter 6
7 Results CODE PSEUDORANGES 7
8 Code ISBs (m) Code ISBs (m) in zero baseline mode ( ) X5 TR 0,00-4,44-4,44 X4 4, ,06 XS 4,44 0,06 - TR 0,00-4,40-4,44 X4 4,40 0,00-0,04 XS 4,44 0,04 - TR 0,00-4,44-4,49-4,48 X4 4,44 0,00-0,04-0,03 XS 4,49 0, , X5 4,48 0,03 0, VERY STABLE RESULTS Galileo E5a / GPS L5 8 TR-TR X4-XS TR-XS TR-X4
9 Code ISBs (m) Code ISBs (m) in zero baseline mode ( ) TR - -2,82 - TR 0,13-2,92-2,53 TR 0,13-2,82-2,57 X4 2, ,06 X4 2,92 0,02-0,05 X4 2,82 0,02-0,04 XS - 0,06 - XS 2,53 0,05 - XS 2,57 0, TR-TR X4-XS TR-XS TR-X4 VERY STABLE RESULTS Galileo E5b / BeiDou B2
10 Code ISBs (m) Code ISBs (m) Code ISBs (m) in zero baseline mode (2016) TRIMBLE Net R9 - Septentrio X4 Galileo E5a/GPS L5 TRIMBLE Net R9 - Septentrio X4 Galileo E5b/BeiDou B DoY DoY Mean = 4,439 StD = 0,053 Mean = 2,639 StD = 0,046 10
11 Baseline Precision (m) Multi-GNSS positioning Precision of the computed positions with Galileo E5a/ GPS L5 in zero baseline 14 TRIMBLE NetR9 Septentrio X Uncorrected: Mean: 8,11 m Estimated: Mean: 1,60 m Corrected: Mean:1,49 m DoY of 2016 Uncorrected Corrected Estimated 11
12 Trimble multipath filter ON 2016a X5 Septentrio multipath filter ON and OFF does not impact ISBs 2016b X5 TR 0,00-4,44-4,49-4,48 TR - -5,98-6,03-6,03 E5a/L5 X4 4,44 0,00-0,04-0,03 X4 5, ,05-0,04 XS 4,49 0, ,02 XS 6,03 0, ,01 X5 4,48 0,03 0,02 - X5 6,03 0,04 0,01 - E5b/B2 TR 0,13-2,82-2,57 X4 2,82 0,02-0,04 XS 2,57 0,04 - Not influenced by the filter activation TR - -2,87-2,57 X4 2, ,04 XS 2,57 0,04-12
13 Code ISBs (m) Code ISBs (m) in zero baseline mode ( ) X5 TR 0,11-0,49-0,25 X4 0,49-0,00 XS 0,25 0,00 - TR 0,15-0,39-0,14 X4 0,39 0,00 0,00 XS 0,14 0,00 - TR 0,15-0,22-0,16-0,02 X4 0,22 0,00 0,00-0,17 XS 0,16 0, , VARYING RESULTS X5 0,02 0,17 0,17 - Galileo E1 / GPS L1 13 TR-TR X4-XS TR-XS TR-X4
14 Mean ISB (m) Code ISBs (m) in zero baseline with identical receiver-types Analysis over the year TRM1 - TRM Firmware updates? DoY Zero baseline Short baseline 14
15 Mean ISB (m) Mean ISB (m) Code ISBs (m) Code ISBs (m) in zero baseline with different receiver-types TRM2 Septentrio X DOY 0.6 Influence of the temperature? Analysis over year 2015 Galileo E1/GPS L1 TRM1 Septentrio X TRM2 - Septentrio X DoY Analysis over year 2016 Temperature registered inside the receiver s room ISBs removing: on the basis of 5-previous the ISBs! days mean TRM2 seems to be responsible for the observed variations of DOY Short Baseline Zero Baseline Wielob. (Short Baseline)
16 Trimble multipath filter ON 2016a X5 2016b X5 E1/L1 TR 0,15-0,22-0,16-0,02 X4 0,22 0,00 0,00-0,17 XS 0,16 0, ,17 TR - -1,62-1,65-1,80 X4 1,62 0,00 0,00-0,17 XS 1,65 0, ,17 X5 0,02 0,17 0,17 - X5 1,80 0,17 0,17-16
17 Results CARRIER PHASES 17
18 Phase ISBs (cycle) Phase ISBs (cycle) in zero baseline mode ( ) a 2016b TR 0,00-0,24-0,24 TR 0,00-0,24-0,24 TR - -0,24-0,24 X4 0,24 0,00 0,00 X4 0,24 0,00 0,00 X4 0,24-0,00 XS 0,24 0,00 - XS 0,24 0,00 - XS 0,24 0, No firmware update influence Not influenced by the activation of the Trimble multipath filter A 2016B TR-TR X4-XS TR-X4 TR-XS Galileo E5b / BeiDou B2
19 Conclusions and prospects Conclusions Code ISBs Galileo E5a/GPS L5, Galileo E5b/BeiDou B2 show very stable values Galileo E1/GPS L1 ISBs are varying with some receiver models (temperature influence?) The activation of multipath filters might have an impact on ISBs (Galileo E5a/GPS L5, Galileo E1/GPS L1) Identical receivers show close to 0 ISB values Not influenced by firmware updates Phase ISBs Firmware updates of 2015/2016 do not impact Galileo E5b/ BeiDou B2 phase ISB values The activation of multipath filters has also no effect on Galileo E5b/ BeiDou B2 phase ISBs Positioning Prospects Removing mean ISBs on the basis of previous days analysis improve positioning results Compute BeiDou B1 (III)/ Galileo E1/ GPS L1 ISBs Process longer baselines 19
20 Thank you for your attention Cecile Deprez and Rene Warnant University of Liege, Belgium
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