一种基于加性潜变量的扩维卡尔曼滤波方法

doi:10.16180/j.cnki.issn1007-7820.2023.05.008

摘要/Abstract

摘要：

现有面对非线性系统所设计的卡尔曼滤波器的性能常随着非线性程度的增强而逐步退化。为了弥补扩展卡尔曼滤波和无迹卡尔曼滤波在线性化过程中的不足之处,文中针对一类由线性项和非线性项累加组成的强非线性系统,建立了一种基于潜变量的扩维卡尔曼滤波方法。该方法将非线性项定义为原始系统的潜变量,并建立了关于潜变量的线性动态关联模型,将潜变量扩维到系统原始的状态变量中,从而建立以原始变量和潜变量为基础的线性系统模型。最后设计出该类系统的高阶扩维卡尔曼滤波器,并经过MATLAB仿真验证了新设计滤波器的有效性与准确性。

关键词: 非线性, 扩展卡尔曼滤波器, 无迹卡尔曼滤波器, 线性化, 潜变量, 动态关联模型, 扩维, 状态变量

Abstract:

The performance of Kalman filters designed for nonlinear systems often degrades with the increase of nonlinear degree. In order to make up for the shortcomings of extended Kalman filter and unscented Kalman filter in the online process, this study proposes an extended dimension Kalman filter method based on hidden variable for a class of strongly nonlinear systems composed of the accumulation of linear and non-linear terms. In this method, the nonlinear term is defined as the hidden variable of the original system, and the linear dynamic correlation model about the hidden variable is established. The hidden variable is extended to the original state variable of the system, so as to establish the linear system model based on the original variable and hidden variable. Finally, the high-order extended dimension Kalman filter of this kind of system is designed. Through MATLAB simulation, the effectiveness and accuracy of the performance of the designed filter are verified.

Key words: nonlinearity, extended Kalman filter, unscented Kalman filter, linearization, hidden variable, dynamic correlation model, dimension expansion, state variable

中图分类号:

TP273

林志鹏,孙晓辉,文成林. 一种基于加性潜变量的扩维卡尔曼滤波方法[J]. 电子科技, 2023, 36(5): 47-54.

LIN Zhipeng,SUN Xiaohui,WEN Chenglin. An Extended Dimension Kalman Filter Method Based on Additive Hidden Variables[J]. Electronic Science and Technology, 2023, 36(5): 47-54.

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	EKF	STF	HV-KF			HV-STF
	EKF	STF	HV-KF	VSEKF	VS STF	HV-STF	VS EKF	VS STF
情况1	7.819 7×10^-4	5.105 1×10^-4	5.059 1×10^-4	35.30%	0.59%	5.025 9×10^-4	35.73%	1.02%
情况2	8.532 7×10^-4	4.497 5×10^-4	4.401 1×10^-4	48.42%	1.13%	4.389 8×10^-4	48.55%	1.26%
情况3	9.407 4×10^-4	5.586 6×10^-4	5.527 0×10^-4	41.24%	0.63%	5.437 5×10^-4	42.20%	1.59%
情况4	10.000 0×10^-4	6.161 5×10^-4	6.022 6×10^-4	39.77%	1.38%	6.009 5×10^-4	39.91%	1.52%

	EKF	STF	HV-KF			HV-STF
	EKF	STF	HV-KF	VSEKF	VS STF	HV-STF	VS EKF	VS STF
情况1	6.561 1×10^-4	7.678 0×10^-5	7.675 8×10^-5	88.30%	0.01%	7.673 0×10^-5	88.31%	0.02%
情况2	8.064 8×10^-4	1.131 0×10^-4	1.128 9×10^-4	86.00%	0.02%	1.117 2×10^-4	86.15%	0.17%
情况3	7.204 9×10^-4	1.057 4×10^-4	1.032 2×10^-4	85.67%	0.35%	1.028 9×10^-4	85.72%	0.40%
情况4	7.355 0×10^-4	8.720 0×10^-5	8.590 1×10^-5	88.32%	0.18%	8.476 8×10^-5	88.47%	0.33%

	EKF	STF	HV-KF			HV-STF
	EKF	STF	HV-KF	VSEKF	VS STF	HV-STF	VS EKF	VS STF
情况1	7.4835×10^-4	1.2812×10^-4	1.1800×10^-4	84.23%	1.35%	1.0142×10^-4	86.44%	3.56%
情况2	7.3689×10^-4	9.8964×10^-5	9.7096×10^-5	86.82%	0.25%	9.6632×10^-5	86.89%	0.32%
情况3	7.2325×10^-4	8.9620×10^-5	8.7261×10^-5	87.93%	0.33%	8.6009×10^-5	88.11%	0.51%
情况4	8.7152×10^-4	1.4497×10^-4	1.1473×10^-4	86.84%	3.47%	1.0415×10^-4	88.05%	4.68%

	EKF	本文算法
动态关联模型	0	4n³-n²
状态一步预测	2n²-n	2N²-N
一步预测协方差	4n³-n²	4N³-N²
增益矩阵	7n³-n²	7N³-N²
新息序列	2nm-n+m	2NM-N+M
状态估计	2nm+n-m	2NM+N-M
估计误差协方差	2n³-2nm²	2N³-2NM²
总和	13n³+2nm²-n²+4nm-n	13N³+2NM²-N²+4NM-N+4n³-n²