双重因子图与模糊度优化的双动态载体定位算法

doi:10.7527/S1000-6893.2024.31332

Abstract

Abstract:

With the rapid development of unmanned systems， autonomous driving， and other related fields， dual dynamic carrier relative positioning technology has become increasingly important for achieving high-precision real-time positioning and adapting to complex environments. To improve the accuracy and reliability of the existing relative positioning algorithm for dual dynamic carrier， this paper proposes a dual dynamic carrier relative positioning algorithm based on Double Factor graph and Ambiguity Resolution optimization （DF-AR）， incorporating reference station processing， ambiguity resolution， and mobile station resolution optimization methods. To improve relative positioning accuracy， a factor graph optimization model integrating multi-frequency and multi-system Kalman filtering is used to suppress single-point positioning errors at the reference station. Using baseline constraints along with data quality weighting， an improved data and model-driven partial ambiguity resolution strategy is constructed. The ambiguity subset with higher reliability is selected to improve the success rate of ambiguity fixation and the reliability of the relative positioning solution. Based on these improvements， a sliding window is introduced in the factor graph optimization model to dynamically adjust the data amount. The positioning solution of the mobile station is reoptimized to achieve more robust relative positioning results. Static evaluation experiments， dual-vehicle and UAV/vehicle dynamic relative positioning experiments were carried out. The experimental results show that in different experimental scenarios， the baseline solution error of the DF-AR relative positioning algorithm has an error reduction of 69.72%， 94.89%， and 68.03% compared to the RTKLIB algorithm. The baseline solution accuracy has been improved from meter level to decimeter level， effectively enhancing the reliability and accuracy of relative positioning.

Key words: navigation systems, dual dynamic carrier, relative positioning, ambiguity resolution, factor graph optimization, baseline constraint

CLC Number:

V324.2⁺4

Ershen WANG, Zexin LIU, Deyan WANG, Tengli YU, Fanchen MENG, Yayi LIU, Song XU. Dual dynamic carrier positioning algorithm based on double factor graph and ambiguity optimization[J]. Acta Aeronautica et Astronautica Sinica, 2025, 46(13): 531332.

Figures/Tables 27

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References 31

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算法	参考站处理	模糊度固定策略	移动站优化
WLK	WLS	LAMBDA	KF
KLK	KF	LAMBDA	KF
FLK	FGO-KF	LAMBDA	KF
WLPK	WLS	LDM-PAR	KF
WBPK	WLS	BDM-PAR	KF
FBPK	FGO-KF	BDM-PAR	KF
DF-AR	FGO-KF	BDM-PAR	SFGO

项目	策略
观测数据	BDS/GPS多频数据
星历	广播星历
截止高度角/（°）	15
截止信噪比/dBHz	20
速度约束	GNSS多普勒测速
随机模型	高度角模型

算法	E向误差/m		N向误差/m		U向误差/m		RMSE/m
算法	最大	平均	最大	平均	最大	平均	RMSE/m
WLK	1.636 1	1.446 9	0.828 0	0.598 9	0.889 2	0.573 3	1.677 0
KLK	1.620 9	1.417 8	0.815 8	0.567 0	0.874 2	0.548 6	1.632 5
FLK	1.610 3	1.285 8	0.812 3	0.471 5	0.859 5	0.474 1	1.465 9

算法	相对定位误差/m				基线误差/m
算法	E向	N向	U向	RMSE	最大	平均
WLK	1.446 9	0.598 9	0.573 3	1.677 9	0.181 4	0.010 9
FBPK	1.185 7	0.374 7	0.409 6	1.339 3	0.013 1	0.003 6
DF-AR	0.338 4	0.327 3	0.398 4	0.808 9	0.166 2	0.003 3

计算结果			算法
计算结果			WLK	KLK	FLK	WLPK	WBPK	FBPK	DF-AR
定位误差/m	E向	最大	6.392 0	6.094 6	6.245 9	6.792 0	5.967 2	5.997 4	3.257 9
		平均	1.429 6	1.427 6	1.304 9	1.442 3	1.373 6	1.186 1	0.590 0
		RMSE	1.467 2	1.443 6	1.330 4	1.479 3	1.388 5	1.218 9	0.689 5
	N向	最大	1.406 4	1.320 5	1.266 3	1.336 4	1.211 8	1.179 2	1.127 2
		平均	0.701 0	0.673 8	0.560 8	0.630 9	0.608 1	0.468 0	0.325 0
		RMSE	0.765 4	0.678 4	0.571 1	0.699 3	0.614 4	0.488 8	0.423 9
	U向	最大	8.556 4	11.433 5	8.405 4	11.474 3	11.515 1	8.999 2	4.890 0
		平均	0.916 3	0.914 5	0.881 1	0.890 4	0.885 6	0.776 4	0.644 9
		RMSE	0.974 2	0.995 5	0.966 1	0.981 7	0.979 0	0.880 1	0.851 6
	总RMSE		1.920 3	1.880 2	1.740 6	1.908 2	1.850 0	1.580 9	1.174 9
	总STD		0.398 5	0.367 7	0.391 2	0.455 4	0.460 9	0.430 4	0.504 5
速度误差/（m·s^-1）		最大	8.779 0	11.435 7	8.894 8	11.466 6	11.506 7	8.952 0	4.390 8
速度误差/（m·s^-1）		平均	0.045 3	0.062 2	0.131 2	0.074 8	0.089 3	0.191 9	0.243 6
加速度误差/（m·s^-2）		最大	19.887 5	23.465 8	19.535 6	23.505 2	23.602 0	19.972 5	5.375 5
加速度误差/（m·s^-2）		平均	0.151 0	0.178 6	0.367 4	0.200 2	0.237 1	0.541 3	0.876 2
固定率/%			55.34	30.02	55.17	99.07	96.13	95.16	99.26

Dual dynamic carrier positioning algorithm based on double factor graph and ambiguity optimization

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算法	基线误差/m				相对速度误差/（m·s^-1）
算法	最大	平均	RMSE	STD	最大	平均
WLK	1.243 7	0.213 1	0.322 2	0.241 7	1.061 3	0.047 6
KLK	3.378 2	0.221 6	0.334 6	0.250 8	3.383 5	0.050 5
FLK	1.286 6	0.217 5	0.323 7	0.239 8	1.214 1	0.048 6
WLPK	3.431 7	0.211 0	0.333 1	0.257 9	3.305 6	0.049 5
WBPK	3.456 8	0.210 9	0.333 5	0.258 4	3.331 0	0.049 9
FBPK	1.253 9	0.202 4	0.307 6	0.231 8	1.390 9	0.060 9
DF-AR	0.197 8	0.010 9	0.027 7	0.025 5	0.205 7	0.005 7

计算结果			算法
计算结果			WLK	KLK	FLK	WLPK	WBPK	FBPK	DF-AR
定位误差/m	E向	最大	5.708 3	5.576 9	5.586 1	5.317 3	5.190 0	5.172 0	1.623 2
		平均	1.969 4	1.894 8	1.810 2	1.654 0	1.492 0	1.648 9	0.794 2
		RMSE	2.147 1	2.075 5	1.974 4	1.844 2	1.694 8	1.809 5	0.855 6
	N向	最大	6.212 4	6.125 3	5.027 9	6.018 1	5.986 5	4.671 7	2.121 2
		平均	2.468 5	2.373 0	2.346 3	2.286 6	2.254 8	2.219 5	0.303 2
		RMSE	2.549 4	2.459 2	2.407 0	2.373 7	2.343 3	2.281 7	0.399 0
	U向	最大	11.316 9	11.338 8	9.578 7	11.468 7	11.635 1	9.636 3	4.826 7
		平均	4.086 1	4.032 3	4.261 9	3.935 3	3.826 0	4.200 4	2.241 5
		RMSE	4.386 4	4.335 8	4.549 0	4.245 8	4.145 1	4.504 4	2.383 0
	总RMSE		5.509 1	5.399 5	5.512 3	5.202 1	5.054 2	5.363 8	2.563 2
	总STD		1.410 9	1.417 7	1.443 2	1.420 8	1.423 1	1.450 5	0.711 2
速度误差/（m·s^-1）		最大	3.527 0	3.444 0	3.479 2	3.418 8	3.402 9	3.515 6	1.918 3
速度误差/（m·s^-1）		平均	0.123 2	0.141 4	0.176 7	0.235 8	0.322 8	0.226 7	0.075 0
加速度误差/（m·s^-2）		最大	7.735 9	7.571 8	7.599 6	7.504 0	7.399 8	7.600 1	3.837 9
加速度误差/（m·s^-2）		平均	0.416 1	0.466 1	0.565 7	0.653 1	0.844 2	0.693 6	0.195 9
固定率%			55.34	54.25	14.09	97.92	93.64	94.56	94.34

算法	基线误差/m				相对速度误差/（m·s^-1）
算法	最大	平均	RMSE	STD	最大	平均
WLK	6.724 0	2.097 6	2.568 1	2.534 3	5.137 6	0.270 1
KLK	6.726 9	2.099 9	2.570 2	2.536 5	5.137 1	0.269 7
FLK	7.009 1	2.066 3	2.543 2	2.500 3	5.141 2	0.314 7
WLPK	6.809 2	2.100 5	2.574 6	2.535 8	5.131 3	0.269 6
WBPK	6.688 8	2.074 3	2.543 4	2.509 1	5.118 8	0.283 2
FBPK	6.756 4	1.768 4	2.328 9	2.408 9	5.167 9	0.335 5
DF-AR	2.402 5	0.670 7	0.830 3	0.887 1	1.949 7	0.129 1