﻿ 一种考虑GPS信号中断的导航滤波算法<sup>*</sup>
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1. 北京航空航天大学 航空科学与工程学院, 北京 100083;
2. 北京航空航天大学 自动化科学与电气工程学院, 北京 100083

A navigation filtering algorithm considering GPS signal interruption
HE Kanghui1, DONG Chaoyang1, WANG Qing2
1. School of Aeronautic Science and Engineering, Beihang University, Beijing 100083, China;
2. School of Automation Science and Electrical Engineering, Beihang University, Beijing 100083, China
Received: 2019-01-02; Accepted: 2019-04-05; Published online: 2019-04-30 16:05
Foundation item: National Natural Science Foundation of China (61873295)
Corresponding author. DONG Chaoyang, E-mail: dongchaoyang@buaa.edu.cn
Abstract: Aimed at the problem of GPS data interruption in the UAV INS/GPS integrated navigation system, an improved filtering algorithm is designed. Firstly, the kinematics model of UAV navigation is established. Then the traditional extended Kalman filter (EKF) technique and strong tracking filter are combined. A new navigation filtering algorithm is designed by using the membership function in fuzzy theory. The simulation results show that the improved algorithm can quickly adapt to the sudden change of GPS signal. When the GPS signal recovers from the fault state to the normal state, the improved algorithm can converge to the steady state more quickly than the ordinary EKF algorithm, and the flight state is re-completed and estimated. At the same time, compared with the common EKF and strong tracking extended Kalman filter (STEKF) algorithm, the improved algorithm has higher filtering accuracy.
Keywords: extended Kalman filter (EKF)     strong tracking filter     integrated navigation     global positioning system (GPS)     membership function

1 标准离散扩展卡尔曼滤波模型

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2 针对导航的模糊强跟踪扩展卡尔曼滤波器 2.1 强跟踪滤波器

2.2 含次优渐消因子的扩展卡尔曼滤波器

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2.3 模糊强跟踪扩展卡尔曼滤波器

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E(Zk+1*Zk+1*T)为残差的期望，表达式为

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3 仿真实验

3.1 无人机导航运动学模型

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3.2 滤波参数设计

 图 1 3种滤波算法结果(东向) Fig. 1 Results of three filtering algorithms (east)

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 算法 估计误差均方根值/m EKF 6.35 ASTKF [24] 7.54 本文改进的STEKF 5.99

3.3 GPS中断响应测试

 图 2 飞行轨迹变化 Fig. 2 Flight path variation

 图 3 3种滤波算法在北向、东向和地向误差变化 Fig. 3 North, east and ground direction error variation

 算法 GPS中断恢复后收敛速度/s EKF 3.84 ASTKF [24] 0.38 本文改进的STEKF 0.25

4 结论

1) 本文将强跟踪扩展卡尔曼滤波(STEKF)运用到了无人机导航系统中，并对其作出了改进。

2) 改进STEKF算法能够在GPS信号恢复后迅速地进入稳态(0.25 s)，而不是逐渐地收敛。

3) 改进STEKF算法保证了导航滤波精度，误差小于普通的EKF算法和[24]文献中的ASTKF算法。

#### 文章信息

HE Kanghui, DONG Chaoyang, WANG Qing

A navigation filtering algorithm considering GPS signal interruption

Journal of Beijing University of Aeronautics and Astronsutics, 2019, 45(9): 1874-1881
http://dx.doi.org/10.13700/j.bh.1001-5965.2018.0786