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摘要: 针对无迹卡尔曼滤波（Unscented Kalman fllter，UKF）在强非线性系统中估计效果差的问题，提出了双层无迹卡尔曼滤波（Double layer unscented Kalman filter，DLUKF）算法，该算法用带权值的采样点表征先验分布，而后用内层UKF算法对每个采样点进行更新，最后引入外层UKF算法的更新机制得到估计值和估计协方差.仿真结果表明，相比于传统算法，所提的DLUKF算法可以在较低计算负载下获得较高滤波估计精度.
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关键词:
- 状态估计 /
- 采样策略 /
- 无迹卡尔曼滤波 /
- 改进的无迹卡尔曼滤波 /
- 无迹粒子滤波
Abstract: The unscented Kalman filter (UKF) has the problem of the inaccurate estimation in strong nonlinear systems. To solve this problem, the double layer unscented Kalman filter (DLUKF) algorithm is proposed. In the proposed algorithm, the weighted sampling points are used to represent the prior distribution, and then the inner layer UKF algorithm is used to update each sampling point. Finally, the state estimations are obtained by the update mechanism of the outer layer UKF algorithm. Simulation results show that the proposed algorithm not only has a low computational complexity, but also has a very good estimation accuracy, compared with the existing filtering algorithms.1) 本文责任编委 朱纪洪 -
表 1 各算法计算时间及RMSE对比分析表
Table 1 The calculation time and RMSE of each algorithm
算法 运行时间(s) 平均RMSE UKF 0.0002 0.1566 IUKF 0.0014 0.0881 RUEKF 0.0006 0.0378 RUCKF 0.0031 0.0337 高阶UKF 0.0006 0.1434 高阶CKF 0.0006 0.1437 UPF (100) 0.1032 0.1153 UPF (200) 0.2097 0.0714 UPF (300) 0.3200 0.0626 UPF (400) 0.4296 0.0564 UPF (500) 0.5416 0.0476 DLUKF 0.0016 0.0297 
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表 2 仿真参数设置
Table 2 The Simulation parameters
参数 $T$ $q$ ${\sigma _{1r}}$ ${\sigma _{1\varepsilon }}$ ${\sigma _{2r}}$ ${\sigma _{2\varepsilon }}$ $\varepsilon $ 数值 1 1 20 m 0.2$^{o}$ 200 m 0.2$^{o}$ 0.1
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表 3 各个算法的性能
Table 3 The performance of each algorithm
算法 运行时间(s) 平均RMSE UKF 0.0059 99.8709 IUKF 0.0424 85.0107 RUEKF 0.0150 100.2616 RUCKF 0.0397 99.8704 高阶UKF 0.0193 100.4763 高阶CKF 0.0191 99.7558 UPF (300) 3.5953 88.2638 UPF (400) 4.8406 86.5004 UPF (500) 6.0552 85.8206 UPF (600) 7.2596 85.1056 UPF (700) 8.4211 84.6700 UPF (800) 9.6178 83.2706 UPF (900) 10.8389 82.9057 UPF (1 000) 12.0105 82.4258 DLUKF 0.0757 78.5559
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