﻿ 北斗中长基线三频模糊度解算的自适应抗差滤波算法
 文章快速检索 高级检索

Adaptive robust filtering algorithm for BDS medium and long baseline three carrier ambiguity resolution
GAO Yangjun, LÜ Zhiwei, ZHOU Pengjin, JIA Zhengyang, ZHANG Lundong, CONG Dianwei
Institute of Geospatial Information, Information Engineering University, Zhengzhou 450001, China
Corresponding author: LÜ Zhiwei, E-mail: lvzhiwei@sina.com
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 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 fixed success rate of narrow-lane ambiguity and reduce the adverse effects of gross error. Experimental results show that improved TCAR algorithm can guarantee high fixed correct rate of wide-lane ambiguity, effectively improve fixed success rate of narrow-lane ambiguity, and has good ability to resist gross error.
Key words: adaptive robust filter     Beidou     wide-lane     narrow-lane     ambiguity     TCAR

1 经典TCAR算法 1.1 基本观测量

BDS采用双差观测量实现中长基线相对定位，双差伪距和载波相位观测方程表达式为[2]

(1)
(2)

(3)
(4)

1.2 计算步骤

 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

(1) 超宽巷模糊度解算

(5)

(2) 宽巷模糊度解算

(6)

(3) 窄巷模糊度解算

(7)

(8)
(9)

(10)
(11)
2 改进TCAR算法 2.1 超宽巷模糊度解算

(12)
(13)

(14)
2.2 宽巷模糊度解算

(15)

(16)

(17)

(18)
2.3 窄巷模糊度解算

(19)

(20)
(21)
(22)

 最优组合 h1 h2 h3 k1 k2 k3 ∇ΔφLC1 0.566 9 0.407 6 0.017 5 0.000 5 0.000 7 0.006 8 ∇ΔφLC2 0.557 5 0.403 0 0.027 1 0.000 8 0.001 0 0.010 6

(1) 基本模型

(23)

(24)

(2) 等价权计算

(25)

(26)

(3) 误差判别统计量

(27)

(4) 自适应因子

(28)

 图 1 改进TCAR算法流程 Fig. 1 Flowchart of improved TCAR algorithm

3 试验分析

 采集日期 基线长度/km 采样间隔/s 观测时长/s 截止高度角/(°) 2018-03-12 25 10 25 000 15 2018-03-12 170 10 25 000 15 2018-03-12 350 10 25 000 15

25 km长基线为荥阳-郑州的基线；170 km长基线为平顶山-郑州的基线；350 km长基线为随州-郑州的基线。

 图 2 宽巷模糊度估值误差(25 km, C01-C10) Fig. 2 Wide-lane ambiguity estimation error(25 km, C01-C10)

 图 3 窄巷模糊度估值误差(25 km, C01-C10) Fig. 3 Narrow-lane ambiguity estimation error(25 km, C01-C10)

(1) 25 km基线数据处理结果

(2) 170 km基线数据处理结果

 图 4 宽巷模糊度估值误差(170 km, C01-C10) Fig. 4 Wide-lane ambiguity estimation error(170 km, C01-C10)

 图 5 窄巷模糊度估值误差(170 km, C01-C10) Fig. 5 Narrow-lane ambiguity estimation error(170 km, C01-C10)

(3) 350 km基线数据处理结果

 图 6 宽巷模糊度估值误差(350 km, C01-C06) Fig. 6 Wide-lane ambiguity estimation error(350 km, C01-C06)

 图 7 窄巷模糊度估值误差(350 km, C01-C06) Fig. 7 Narrow-lane ambiguity estimation error(350 km, C01-C06)

 算法 总历元/s 宽巷固定历元/s 宽巷固定正确率/(%) 窄巷固定历元/s 窄巷固定正确率/(%) 经典TCAR 25 000 24 838 99.35 5325 21.30 MTCAR 25 000 25 000 100.00 24 370 97.48

 算法 总历元/s 宽巷固定历元/s 宽巷固定正确率/(%) 窄巷固定历元/s 窄巷固定正确率/(%) 经典TCAR 25 000 24 470 97.88 4840 19.36 MTCAR 25 000 25 000 100.00 20 990 83.96

 算法 总历元/s 宽巷固定历元/s 宽巷固定正确率/(%) 窄巷固定历元/s 窄巷固定正确率/(%) 经典TCAR 25 000 24 430 97.72 2623 10.49 MTCAR 25 000 25 000 100.00 19 825 79.30

4 结论

﻿

 [1] 杨元喜. 北斗卫星导航系统的进展、贡献与挑战[J]. 测绘学报, 2010, 39(1): 1–6. 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 BeiDou observations[J]. GPS Solutions, 2016, 20(2): 269–281. DOI:10.1007/s10291-014-0434-0 [7] 范建军, 王飞雪. 一种短基线GNSS的三频模糊度解算(TCAR)方法[J]. 测绘学报, 2007, 36(1): 43–49. 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. DOI:10.3321/j.issn:1001-1595.2007.01.008 [8] 梁宵, 黄智刚, 秦红磊, 等. 采用宽窄巷结合的LAMBDA解算方法的北斗多频差分定位技术[J]. 哈尔滨工业大学学报, 2017, 49(11): 46–51. 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. DOI:10.11918/j.issn.0367-6234.201612083 [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] 谢建涛, 郝金明, 刘伟平, 等. 中长基线的BDS三频线性组合观测量优化[J]. 武汉大学学报(信息科学版), 2017, 42(12): 1779–1784. 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] 谢建涛, 郝金明, 韩聪, 等. BDS单历元TCAR算法优化研究[J]. 测绘科学技术学报, 2016, 33(1): 6–10, 15. 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] 宋玉龙, 廉保旺, 唐成凯. 基于多频模糊度解算的BDS/GPS中基线AEKF RTK算法[J]. 系统工程与电子技术, 2017, 39(8): 1794–1800. 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] 刘硕, 张磊, 李健. 一种改进的宽巷引导整周模糊度固定算法[J]. 武汉大学学报(信息科学版), 2018, 43(4): 637–642. 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] 李金龙. 北斗/GPS多频实时精密定位理论与算法[J]. 测绘学报, 2015, 44(11): 1927. 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] 杨元喜. 自适应抗差最小二乘估计[J]. 测绘学报, 1996, 25(3): 206–211. YANG Yuanxi. Adaptively robust least squares estimation[J]. Acta Geodaetica et Cartographica Sinica, 1996, 25(3): 206–211. DOI:10.3321/j.issn:1001-1595.1996.03.009 [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] 杨元喜, 任夏, 许艳. 自适应抗差滤波理论及应用的主要进展[J]. 导航定位学报, 2013, 1(1): 9–15. 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. DOI:10.3969/j.issn.2095-4999.2013.01.003
http://dx.doi.org/10.11947/j.AGCS.2019.20180379

0

#### 文章信息

GAO Yangjun, LÜ Zhiwei, ZHOU Pengjin, JIA Zhengyang, ZHANG Lundong, CONG Dianwei

Adaptive robust filtering algorithm for BDS medium and long baseline three carrier ambiguity resolution

Acta Geodaetica et Cartographica Sinica, 2019, 48(3): 295-302
http://dx.doi.org/10.11947/j.AGCS.2019.20180379