Adaptive Robust Filtering Algorithm for BDS Medium and Long Baseline Three Carrier Ambiguity Resolution

doi:10.11947/j.JGGS.2020.0206

Abstract

Abstract:

For classical TCAR(three carrier ambiguity resolution) algorithm is affected by ionospheric delay and measurement noise, it is difficult to reliably fix ambiguity at medium and long baselines. An improved TCAR algorithm which takes the influence of ionospheric delay into account and has good adaptive robustness is proposed. On the basis of the non-geometric TCAR model, ionospheric delay is obtained by linearly combining extra-wide-lane with fixed ambiguity, and then wide-lane ambiguity is solved. Solving narrow-lane ambiguity by adaptive robust filtering by constructing optimal combination observation, which can effectively improve the fixed success rate of narrow-lane ambiguity and reduce the adverse effects of gross error. Experimental results show that the improved TCAR algorithm can guarantee a high fixed correct rate of wide-lane ambiguity, effectively improve fixed success rate of narrow-lane ambiguity, and has a good ability to resist gross error.

Key words: adaptive robust filter; Beidou; wide-lane; narrow-lane; ambiguity; TCAR

Yangjun GAO,Zhiwei LV,Pengjin ZHOU,Zhengyang JIA,Lundong ZHANG,Dianwei CONG. Adaptive Robust Filtering Algorithm for BDS Medium and Long Baseline Three Carrier Ambiguity Resolution[J]. Journal of Geodesy and Geoinformation Science, 2020, 3(2): 53-61.

Figures/Tables 13

Tab.1

Tab.2

Fig.1

Tab.3

Fig.2

Fig.3

Fig.4

Fig.5

Fig.6

Fig.7

Tab.4

Tab.5

Tab.6

References 20

[1]	YANG Yuanxi. Progress, contribution and challenges of compass/BeiDou satellite navigation system[J]. Acta Geodaetica et Cartographica Sinica, 2010,39(1):1-6.
[2]	FENG Yanming. GNSS three carrier ambiguity resolution using ionosphere-reduced virtual signals[J]. Journal of Geodesy, 2008,82(12):847-862. doi: 10.1007/s00190-008-0209-x
[3]	FENG Yanming, LI Bofeng. Three carrier ambiguity resolutions:generalised problems, models and solutions[J]. Journal of Global Positioning Systems, 2009,8(2):115-123. doi: 10.5081/jgps
[4]	WANG K, ROTHACHER M. Ambiguity resolution for triple-frequency geometry-free and ionosphere-free combination tested with real data[J]. Journal of Geodesy, 2013,87(6):539-553. doi: 10.1007/s00190-013-0630-7
[5]	TANG Wenming, DENG Chenlong, SHI Chuang, et al. Triple-frequency carrier ambiguity resolution for BeiDou navigation satellite system[J]. GPS Solutions, 2014,18(3):335-344. doi: 10.1007/s10291-013-0333-9
[6]	ZHANG Xiaohong, HE Xiyang. Performance analysis of triple-frequency ambiguity resolution with BeiDouobservations[J]. GPS Solutions, 2016,20(2):269-281. doi: 10.1007/s10291-014-0434-0
[7]	FAN Jianjun, WANG Feixue. A method for GNSS three frequency ambiguity resolution based on short baselines[J]. Acta Geodaetica et Cartographica Sinica, 2007,36(1):43-49.
[8]	LIANG Xiao, HUANG Zhigang, QIN Honglei, et al. Multi-frequency BeiDou differential positioning using combination of wide and narrow Lane for LAMBDA resolution[J]. Journal of Harbin Institute of Technology, 2017,49(11):46-51.
[9]	HENKEL P, GÜNTHER C. Reliable integer ambiguity resolution:multi-frequency code carrier linear combinations and statistical a priori knowledge of attitude[J]. Navigation, 2012,59(1):61-75. doi: 10.1002/navi.v59.1
[10]	XIE Jiantao, HAO Jinming, LIU Weiping, et al. BDS triple frequency linear combination observation optimization for medium-long baseline[J]. Geomatics and Information Science of Wuhan University, 2017,42(12):1779-1784.
[11]	XIE Jiantao, HAO Jinming, HAN Cong, et al. Research of BDS single-epoch and triple-frequency ambiguity resolution using the modified TCAR method[J]. Journal of Geomatics Science and Technology, 2016,33(1):6-10, 15.
[12]	SONG Yulong, LIAN Baowang, TANG Chengkai. BDS/GPS AEKF RTK algorithm utilizing multi-frequency ambiguity resolution for medium baseline[J]. Systems Engineering and Electronics, 2017,39(8):1794-1800.
[13]	LIU Shuo, ZHANG Lei, LI Jian. A modified wide lane bootstrapping ambiguity resolution algorithm[J]. Geomatics and Information Science of Wuhan University, 2018,43(4):637-642.
[14]	ZHAO Qile, DAI Zhigang, HU Zhigang, et al. Three-carrier ambiguity resolution using the modified TCAR method[J]. GPS Solutions, 2015,19(4):589-599. doi: 10.1007/s10291-014-0421-5
[15]	LI Jinlong. BDS/GPS multi-frequency real-time kinematic positioning theory and algorithms[J]. Acta Geodaetica et Cartographica Sinica, 2015,44(11):1927. DOI: 10.11947/j.AGCS.2015.20150254.
[16]	YANG Yuanxi. Adaptively robust least squares estimation[J]. Acta Geodaetica et Cartographica Sinica, 1996,25(3):206-211.
[17]	LOU Yidong, GONG Xiaopeng, GU Shengfeng, et al. Assessment of code bias variations of BDS triple-frequency signals and their impacts on ambiguity resolution for long baselines[J]. GPS Solutions, 2017,21(1):177-186. doi: 10.1007/s10291-016-0514-4
[18]	ZHAO Qile, SUN Binzi, DAI Zhiqiang, et al. Real-time detection and repair of cycle slips in triple-frequency GNSS measurements[J]. GPS Solutions, 2015,19(3):381-391. doi: 10.1007/s10291-014-0396-2
[19]	WANG Xing, LIU Wenxiang, SUN Guangfu. An improved geometry-free three carrier ambiguity resolution method for the BeiDou navigation satellite system[J]. Journal of Navigation, 2016,69(6):1393-1408. doi: 10.1017/S0373463316000163
[20]	YANG Yuanxi, REN Xia, XU Yan. Main progress of adaptively robust filter with applications in navigation[J]. Journal of Navigation and Positioning, 2013,1(1):9-15.

i	j	k	λ₍_i_,_j_,_k₎	μ₍_i_,_j_,_k₎	β₍_i_,_j_,_k₎
0	-1	1	4.884	28.529	-1.591
1	4	-5	6.371	172.614	0.652
1	0	-1	1.025	6.875	-1.231
1	-1	0	0.847	5.575	-1.293
0	1	0	0.248	1.000	1.672
0	0	1	0.236	1.000	1.515
1	0	0	0.192	1.000	1.000

Optimal combination	h₁	h₂	h₃	k₁	k₂	k₃
ΔΔ?_LC₁	0.5669	0.4076	0.0175	0.0005	0.0007	0.0068
ΔΔ?_LC₂	0.5575	0.4030	0.0271	0.0008	0.0010	0.0106

Date of collection	Baseline length	Sampling interval	Observation time	Cutoff height angle
2018-03-12	25km	10s	25000s	15°
2018-03-12	170km	10s	25000s	15°
2018-03-12	350km	10s	25000s	15°

Algorithm	Total epoch/s	Wide-lane fixed epoch/s	Wide-lane fixed correct rate/(%)	Narrow-lane fixed epoch/s	Narrow-lane fixed correct rate/(%)
Classical TCAR	25000	24838	99.35	5325	21.30
MTCAR	25000	25000	100.00	24370	97.48

Algorithm	Total epoch/s	Wide-lane fixed epoch/s	Wide-lane fixed correct rate/(%)	Narrow-lane fixed epoch/s	Narrow-lane fixed correct rate/(%)
Classical TCAR	25000	24470	97.88	4840	19.36
MTCAR	25000	25000	100.00	20990	83.96