基于路径和算法的飞行器集群分布式相对定位

doi:10.7527/S1000-6893.2023.28735

Abstract

Abstract:

According to the inertial measurement of each node in the aircraft group and the relative distance measurement given by the data link between nodes， the relative positioning including the estimation of the relative position and relative attitude between node pairs can be realized by using the centralized Kalman filter. The centralized algorithm gathers all the data in the group into the central node for centralized processing， and the scalability and reliability of the system are restricted. The distributed relative positioning algorithm such as belief propagation can realize global estimation of the relative position and relative attitude through the processing of local information by each node of the cluster and the information interaction between adjacent nodes. However， in the problem of group relative positioning， the data link topology contains a large number of ring structures， and the belief propagation algorithm has a convergence problem in such case. This paper proposes a distributed exact inference method for relative positioning， which can be applied to any group topology. Under the Gaussian standard and canonical descriptions， the distributed time update and measurement update algorithms for the error states of each node are designed. The distributed algorithms for standard and normative parameters conversion are given based on paths-sum principles. Under the linear Gaussian model assumption， the method in this paper is equivalent to the centralized Kalman filter， which can achieve the optimal estimation of relative positioning. A distributed approximate inference algorithm is proposed based on group decomposition to improve the speed of the algorithm. Results on the six-degree-of-freedom long-duration simulation data show that the relative positioning accuracy of the distributed approximate inference based on the path-sum is close to that of the centralized Kalman filter， and significantly outperforms the existing distributed Gaussian belief propagation algorithm.

Key words: distributed inference, relative positioning, belief propagation, path-Sum, navigation system

CLC Number:

V211.71

Weiqing LAI, Jiuqing WAN. Distributed relative positioning of aircraft group based on path⁃sum algorithm[J]. Acta Aeronautica et Astronautica Sinica, 2024, 45(4): 328735-328735.

Figures/Tables 11

Fig.1

Fig.2

Fig.3

Fig.4

Table 1

Initial state error

初始误差	失准角/（′）	速度误差/（ $m ∙ s - 1$ ）	位置误差/m
东向	0.5	0.1	1
北向	0.5	0.1	1
天向	20	0.1	3

Table 1

Table 2

Parameters of each sensor

传感器	加速度计（100 Hz）		陀螺仪（100 Hz）		数据链（10 Hz）
传感器	加计常值偏值/μg	速度随机游走/ （μg· $H z - 12$ ）	陀螺常值漂移/（（°）·h^-1）	角度随机游走/（（°）· $h - 12$ ）	距离观测误差/m
参数	50	10	0.01°	0.001°	10

Table 2

Fig.5

Fig.6

Table 3

Table 4

Table 5

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算法	相对位置总均方根误差均值/m			相对位置总均方根误差标准差/m
算法	x轴方向	y轴方向	z轴方向	x轴方向	y轴方向	z轴方向
ESKF	2.021 3	4.046 7	5.382 6	0.101 1	0.224 3	0.516 6
GBP	126.834 3	203.776 2	288.133 1	9.126 9	11.968 4	23.673 7
STGBP	56.025 0	101.642 9	145.815 1	6.588 8	7.909 8	13.898 0
路径和	3.559 1	7.807 4	9.566 6	0.429 7	0.880 9	1.665 4

算法	相对姿态总均方根误差均值/（′）			相对姿态总均方根误差标准差/（′）
算法	x轴方向	y轴方向	z轴方向	x轴方向	y轴方向	z轴方向
ESKF	4.604 6	0.253 5	3.344 2	0.120 8	0.062 7	0.260 2
GBP	7.816 0	2.015 0	41.197 7	0.090 5	0.137 4	1.242 5
STGBP	6.180 7	1.019 5	37.131 0	0.723 3	0.466 1	9.181 2
路径和	4.687 7	0.597 9	4.422 7	0.066 3	0.156 4	0.587 5

算法	惯导更新/ ms	时间更新/ ms	量测更新/ ms	总耗时/s
ESKF	0.33	0.20	11.23	413.25
GBP	0.33	0.09	4.33	213.26
STGBP	0.33	0.09	8.77	324.25
路径和	0.33	0.13	6.05	303.75

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Distributed relative positioning of aircraft group based on path⁃sum algorithm

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