欠测量条件下飞行器编队协同相对导航方法

doi:10.12305/j.issn.1001-506X.2026.01.24

摘要/Abstract

摘要：

针对卫星导航拒止环境中飞行器编队欠测量相对导航难题，提出一种编队成员之间仅测距离或视线角度的协同相对导航方法。首先，以相对位置、航向角差、速度为基础并纳入传感器有色噪声在内，建立了相对运动状态模型。然后，建立了由仅测距或仅测角两种相对测量和飞行器航向、空速测量信息组成的测量模型，在此基础上引入李导数理论对相对导航状态进行了可观测性分析，获得了激励系统状态可观测性的充分条件。接着，以三个飞行器构成编组并建立几何拓扑一致性约束模型，在此基础上设计了基于一致性无味卡尔曼滤波（consensus unscented Kalman filter，CUKF）算法的分布式估计算法。最后，对所提方法进行了Monte Carlo打靶仿真验证，仿真结果表明，飞行器的运动满足可观测性条件时相对导航状态是可观测的，几何拓扑一致性约束的引入确实提升了系统可观测性，三机编队时混合测量方式相比全员仅测距或测角更具优势，相对位置的估计误差不超过5 m/轴（3σ）。

关键词: 飞行器编队, 相对导航, 可观测性分析, 一致性无味卡尔曼滤波

Abstract:

In view of the problem of accurate relative navigation with insufficient measurement between formation aircraft in a satellite navigation-denied environment, a cooperative relative navigation method is proposed in which the formation members only measure distance or line-of-sight angle between each other. First, with the information of relative position, heading angle difference, velocity, the relative motion state model including sensor colored-noise is established. Then, a measurement model consisting of two relative measurements, distance measurement or angle measurement, and the aircraft heading and airspeed measurement information is established, then observability analysis of the main relative states is conducted based on Lie derivative theory, sufficient conditions for the observability of the incentive system state are obtained. A geometric topology consistency constraint model is established for the formation with three aircraft, based on which a consensus unscented Kalman filter （CUKF） algorithm is established, which is a distributed estimation algorithm. Simulation is introduced with the help of the Monte Carlo shooting method. Simulation results show that when the theoretical analysis of observability is satisfied, the relative navigation states can be observed, and the introduction of geometric topological consensus constraints can improve the observability of the system. The hybrid measurement scheme with three aircraft formation has more advantages than the range-only or angle-only measurement scheme. The relative position estimation error on a single axis is within 5 m （3σ）.

Key words: aircraft formation, relative navigation, observability analysis, consensus unscented Kalman filter (CUKF)

中图分类号:

V 249.32

庄智星, 龚柏春, 郝明瑞, 王子文. 欠测量条件下飞行器编队协同相对导航方法[J]. 系统工程与电子技术, 2026, 48(1): 265-277.

Zhixing ZHUANG, Baichun GONG, Mingrui HAO, Ziwen WANG. Cooperative relative navigation method for aircraft formation in under-measurement conditions[J]. Systems Engineering and Electronics, 2026, 48(1): 265-277.

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参数	值
陀螺仪常值误差估计误差/（°/h）	50
航向角差估计误差/（°）	5
加速度计常值误差估计误差/mg	1
相对位置估计误差/m	1
空速管常值误差估计误差/（m/s）	10
速度估计误差/（m/s）	1

参数	值	参数	值	参数	值
陀螺仪常值偏差/（°/h）	50	加速度计常值偏差/mg	1	空速管常值误差/（m/s）	10
陀螺仪随机误差/（°/h）	5	加速度计随机误差/mg	0.1	空速管随机误差/（m/s）	1
航向角测量误差/（°）	5	方位角测量误差/（°）	1	距离测量误差/m	10

参数	坐标轴	均值		标准差
参数	坐标轴	UKF	CUKF	UKF	CUKF
位置/m	x轴	0.040	−0.002	1.711	1.405
位置/m	y轴	0.013	−0.022	2.061	1.652
速度/（m/s）	x轴	0.001	0.001	0.097	0.089
速度/（m/s）	y轴	−0.413	−0.410	0.147	0.129
航向角差/（º）	—	−0.005	−0.004	0.102	0.090
陀螺仪/（º/h）	—	2.562	1.441	4.006	3.049
加速度计/mg	x轴	−0.031	−0.018	0.045	0.035
加速度计/mg	y轴	0.012	0.011	0.007	0.007
空速管/（m/s）	—	0.392	0.390	0.141	0.123

参数	坐标轴	方案A	方案B	方案C	方案D
位置/m	x轴	1.725	1.405	1.380	1.654
位置/m	y轴	1.799	1.652	1.312	1.653
速度/（m/s）	x轴	0.092	0.089	0.089	0.091
速度/（m/s）	y轴	0.134	0.129	0.128	0.132
航向角差/（º）	—	0.108	0.090	0.078	0.064
陀螺仪/（º/h）	—	2.635	3.049	3.689	3.713
加速度计/mg	x轴	0.032	0.035	0.041	0.040
加速度计/mg	y轴	0.007	0.007	0.007	0.007
空速管/（m/s）	—	0.128	0.123	0.122	0.127

参数	位置	速度	航向角	陀螺仪	加速度计	空速管
距离	√	—	√	—	—	√
方位角	√	—	√	—	—	—
航向角	√	—	√	—	—	—
空速管	√	√	—	—	—	√
陀螺仪	√	—	—	√	—	—
加速度计	√	—	—	—	√	—