Instant k = 1. RTK Strategy for ambiguity resolution unesp. Cartography Science Post-Graduate Program - São Paulo State - Brazil. Post-processed Strategy.
Motivation Objective
Investigating Multipath Mitigation for Kinematic Applications using Wavelet Techniques Presidente Prudente Sao Paulo State University Brazil
Wavelet Method Experiments/Results
PhD. PhD. Student Eniuce Menezes de Souza PhD. PhD. João F. Galera Monico
Conclusions
Department of Cartography PhD. PhD. Aylton Pagamisse Department of Mathematics
unesp
Motivation
Cartography Science PostPost-Graduate Program - São Paulo State - Brazil
Motivation
GNSS kinematic relative positioning has essential importance and can support several applications
Navigation
For other applications and research
Real time is necessary
Post-processed mode can be useful
unesp
Cartography Science PostPost-Graduate Program - São Paulo State - Brazil
In order to obtain high accuracy, the involved errors have to be mitigated
unesp
Cartography Science PostPost-Graduate Program - São Paulo State - Brazil
Motivation
Objective
Multipath is still one of the major challenges for high precision GPS relative positioning
To investigate multipath reduction by using wavelet methods
It is not attenuated in the DD Atmosphere Orbit
At kinematic applications
Short Baselines - DD
Clocks
To investigate ambiguities resolution using data affect by multipath / RTK and pos-processed
Multipath Multipath errors can even increase unesp
Cartography Science PostPost-Graduate Program - São Paulo State - Brazil
unesp
Cartography Science PostPost-Graduate Program - São Paulo State - Brazil
1
Post-processed Strategy
RTK Strategy
for ambiguity resolution
for ambiguity resolution
k = 1
Instant k = 1
RLS adjustment
k = k+1
RLS adjustment in real time
Ratio >3 ?
Ratio >3 ? no
Processing ended
yes
Fixed N
Reprocess the data with the constrained N
Float N
no unesp
yes
Try to solve N
Fixed N
k = k+1
Float N
Last instant? yes N Constrained? no
Try to solve the ambiguities (N) vector at each instant k yes
no
Cartography Science PostPost-Graduate Program - São Paulo State - Brazil
unesp
Constrain N to fixed or float values Cartography Science PostPost-Graduate Program - São Paulo State - Brazil
Wavelet Method The DD residuals (∆∇v) from RLS can be modeled by:
∆∇v i = f (t i ) + ε i , i = 0, K , n − 1 εi ~N(0,σ2 ) -Desirable Gaussian Function white noise and σDDisResiduals the noise level
Wavelet Method
unesp
1º: Find the Discrete Wavelet Transform (DWT) of ∆∇v to obtain the wavelet coefficients using the pyramidal algorithm (Mallat, 1998)
Cartography Science PostPost-Graduate Program - São Paulo State - Brazil
unesp
A1 A2 A3
D1 D2
D3
A: low-frequency bias D: high-frequency noise
Cartography Science PostPost-Graduate Program - São Paulo State - Brazil
Wavelet Method 2º: Modify the wavelet coefficients by thresholding: Hard Threshold 0, d i < λ TλH (d i ) = d i , d i ≥ λ
Universal Parameter (fast and automatic) λ = σˆ 2 log n
Multipath Detection at kinematic positioning
Noise level σˆ = 3median d J −1,k : 0 ≤ k < n 2 0,6745
{
}
3º: Reconstruct f with the IDWT => => Multipath bias components 4º: DDcorrected = DDoriginal - Multipath bias 5º: RLS is performed again unesp
Cartography Science PostPost-Graduate Program - São Paulo State - Brazil
unesp
Cartography Science PostPost-Graduate Program - São Paulo State - Brazil
2
Multipath Detection
Implementation
Differently of static applications, it is necessary to use data windows to process the observations The proposed approaches were implemented in: GPSeq software FORTRAN/C/C++ languages Under development at UNESP, Presidente Prudente, Sao Paulo, Brazil
The 5 steps presented are performed for each window of data At each instant k, the DD residuals from instant k-τ +1 to instant k are decomposed Pyramidal Algorithm => τ ≥ 4 Data from some previous instants are used in the multipath detection, but just the data from the current instant is corrected unesp Cartography k Science PostPost-Graduate Program - São Paulo State - Brazil
unesp
Cartography Science PostPost-Graduate Program - São Paulo State - Brazil
Experiments – 11/09/2007 Kinematic Mode: Vehicle (small tractor) moved anchored around a pivot Topcon Hipper GGD
Experiments Device fixed in a reinforced concrete base unesp
Cartography Science PostPost-Graduate Program - São Paulo State - Brazil
unesp
Experiments – 11/09/2007
Steel cable linked to a spin axis with minimum attrition
Cartography Science PostPost-Graduate Program - São Paulo State - Brazil
Experiments – 11/09/2007
~15m
unesp
Cartography Science PostPost-Graduate Program - São Paulo State - Brazil
unesp
Cartography Science PostPost-Graduate Program - São Paulo State - Brazil
3
Base
Base Rover: stopped for about 20 min (to try) to solve the ambiguities
unesp
Cartography Science PostPost-Graduate Program - São Paulo State - Brazil
unesp
Cartography Science PostPost-Graduate Program - São Paulo State - Brazil
Ambiguities
RTK unesp
Multipath Mitigation
Ambiguities resolution is affected by multipath Float N
PostProcessed Cartography Science PostPost-Graduate Program - São Paulo State - Brazil
Data processing period: 800 sec Tractor was stopped at firsts 400 sec For each k: the multipath is detected, extracted, and directly applied to the DD to correct it Instantaneously, the RLS is performed again with the corrected DD unesp
Cartography Science PostPost-Graduate Program - São Paulo State - Brazil
Baseline Discrepancies
64 127 190 253 316 379 442 505 568 631 694 757 820 883 946
Instants
2
Post-Processed Float
Coordinate SD
1,5 1 0,5 0 1
unesp
78 155 232 309 386 463 540 617 694 771 848 925
Cartography Science PostPost-Graduate Program Instants- São Paulo State - Brazil
Pseudorange DD observations
Multipath Processing Strategies 1) Standard: no multipath mitigation was applied 2) WAV: the wavelet method was applied
0,9 0,7 0,5 0,3 0,1 -0,1 1 -0,3 -0,5
Post-Processed Float
RTK Float
Standard Deviation (m)
Processing Strategies
Baseline Discrepancies (m)
RTK Float
DD14_03 Highest PRN: 03 (55° - 59°) Less multipath
DD14_18 Lowest PRN: 18 (23° - 18°) More multipath
unesp
Cartography Science PostPost-Graduate Program - São Paulo State - Brazil
4
Carrier-Phase DD Residuals
DD14_03 Highest PRN: 03 (55° - 59°) Less multipath
DD14_03 Highest PRN: 03 (55° - 59°) Less multipath
DD14_18 Lowest PRN: 18 (23° - 18°) More multipath
DD14_18 Lowest PRN: 18 (23° - 18°) More multipath
unesp
Cartography Science PostPost-Graduate Program - São Paulo State - Brazil Instants
715
664
613
562
511
460
409
358
307
256
205
154
103
743
690
637
584
531
478
425
372
319
729
677
625
573
521
469
417
365
313
261
209
105
157
937
885
833
781
729
677
625
573
521
469
417
365
One can verify that after the multipath correction, the results were better than in the standard processing – but we still can see systematic effects
729
673
617
561
505
449
393
337
281
225
169
57
113
WAV
Instants
3 2 1 0 -1 1
313
697
639
581
523
465
407
349
291
233
175
1
59
117
Instants
Standard U - WAV U
261
0,1
209
(m)
0,3
157
Standard N - WAV N
Standard 1 0,8 0,6 0,4 0,2 0 -0,2 -0,4 105
-0,9
1
Baseline Discrepance (m)
-0,7
(m)
1
Known baseline length = Circumference radius
-0,5
-0,1
Multipath was affecting significantly the results
Cartography Science PostPost-Graduate Program - São Paulo State - Brazil
-0,3
Instant s
unesp
0,5 -0,5
Baseline Length Discrepancies
0,1 -0,1
Tractor was stopped just beside the bus
1,5
Instants
unesp
Standard E - WAV E
Largest discrepancies are in the beginning of the data set
WAV U
2,5
53
U coordinate variation was smaller when wavelets were applied
Standard U
U Coordinate (m)
937
865
793
721
649
577
505
433
361
289
217
145
73
Improved significantly after applying the wavelet method to correct multipath, showing that this effect was significantly unesp Cartographyreduced Science PostPost-Graduate Program - São Paulo State - Brazil
Standard – WAV
1
Instants
0 Instants
Local Coordinates Discrepancies
0 -20 266
10 5
WAV N
20
213
20 15
Instants
Standard N
160
WAV Solution: ambiguities could be more reliable fixed
25
-5 -15
107
35 30
WAV E
5
52
Origin in the pivot point
WAV
Standard E 15
1
Standard
Local Coordinates E, N, and U
N Coordinate (m)
40
1
Maximum LOMStandard: 38 Maximum LOMWAV: 4 Mean improvement: 80%
Local Overall Model (LOM)
Observations Quality: Statistic Test LOM Indicative of unmodeled effects
Cartography Science PostPost-Graduate Program - São Paulo State - Brazil
54
Cartography Science PostPost-Graduate Program - São Paulo State - Brazil
53
unesp
E Coordinate (m)
Pseudorange DD Residuals
unesp
Cartography Science PostPost-Graduate Program - São Paulo State - Brazil
5
Baseline Length Discrepancies
Wavelet Method
Known baseline length = Circumference radius
Modifying the wavelet coefficients by thresholding:
Standard
Universal Parameter (fast and automatic) λ = σˆ 2 log n
697
639
581
523
465
407
349
1
291
}
233
{
σˆ = median d J −1,k : 0 ≤ k < n 2 0,6745
175
Noise level
WAV
1 0,8 0,6 0,4 0,2 0 -0,2 117
0, d i < λ TλH (d i ) = d i , d i ≥ λ
59
Hard Threshold
Instants
We decrease the noise level
After multipath correction, the results were better than in the standard processing unesp
Cartography Science PostPost-Graduate Program - São Paulo State - Brazil
Mean and SD Baseline Lenght Discrepancies Standard (m)
WAV (m)
Improvement
Mean
0.136
0.043
70%
SD
0.264
0.032
88%
unesp
Cartography Science PostPost-Graduate Program - São Paulo State - Brazil
unesp
Cartography Science PostPost-Graduate Program - São Paulo State - Brazil
Conclusions Wavelet spectral analysis appears to be a powerful method for mitigating multipath effects in kinematic GNSS applications 9 The multipath trend in the DD residuals was corrected 9 Ambiguities resolution became more reliable 9 LOM statistic test showed good improvement (data quality) 9 Baseline length estimative improved 70% on average However, more experiments are required. Data from a flight test are under analyses. unesp
Cartography Science PostPost-Graduate Program - São Paulo State - Brazil
Thanks for your attention! http://gege.fct.unesp.br unesp
Cartography Science PostPost-Graduate Program - São Paulo State - Brazil
6
