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

Abstract

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

CLC Number:

TP273

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.

Figures/Tables 7

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Table 1.

Figure 2.

Table 2.

Table 3.

Figure 3.

Table 4.

References 20

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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

An Extended Dimension Kalman Filter Method Based on Additive Hidden Variables

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