A robust adaptive filtering algorithm for high-maneuvering hypersonic vehicles

doi:10.23919/JSEE.2025.000131

Abstract

Abstract:

This paper concentrates on addressing the hypersonic glide vehicle (HGV) tracking problem considering the high maneuverability and non-stationary heavy-tailed measurement noise without prior statistics in complicated flight environments. Since the interacting multiple model (IMM) filtering is famous with its ability to cover the movement property of motion models, the problem is formulated as modeling the non-stationary heavy-tailed measurement noise without any prior statistics in the IMM framework. Firstly, without any prior statistics, the Gaussian-inverse Wishart distribution is embedded in the improved Pearson type-VII (PTV) distribution, which can adaptively adjust the parameters to model the non-stationary heavy-tailed measurement noise. Besides, degree of freedom (DOF) parameters are surrogated by the maximization of evidence lower bound (ELBO) in the variational Bayesian optimization framework instead of fixed value to handle uncertain non-Gaussian degrees. Then, this paper analytically derives fusion forms based on the maximum Versoria fusion criterion instead of the moment matching approach, which can provide a precise approximation for the PTV mixture distribution in the mixing and output steps combined with the weight Kullback-Leibler average theory. Simulation results demonstrate the superiority and robustness of the proposed algorithm in typical HGVs tracking when the measurement noise without priori statistics is non-stationary.

Key words: hypersonic vehicle, Pearson type-VII (PTV) distribution, without priori statistics, modeling

Xinru LIANG, Changsheng GAO, Wuxing JING, Ruoming AN. A robust adaptive filtering algorithm for high-maneuvering hypersonic vehicles[J]. Journal of Systems Engineering and Electronics, 2025, 36(5): 1317-1334.

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Parameter	Value	Parameter	Value
The reference area/m²	0.48	Flight duration/s	800
Longitude/(°)	−152	Lift-drag ratio coefficient	3.5
Latitude/(°)	25	Mass of the vehicle/kg	907.2

Filtering algorithm	ARMSE of position/m	ARMSE of velocity/(m/s)	Time/s
VBAKF-PM	365.227	164.937	3.527
VBSTF	341.172	146.109	4.127
PTVCKF	315.411	133.203	3.954
IMVMMSTd	312.046	123.217	10.789
VB-IMM-QR	305.129	80.653	11.556
IMMPVIIKF	317.426	141.366	11.485
The proposed filter	283.354	62.208	11.845

Filtering algorithm	ARMSE of position/m	ARMSE of velocity/(m/s)	Time/s
VBAKF-PM	861.321	301.374	4.157
VBSTF	820.918	273.357	4.574
PTVCKF	760.853	264.495	4.264
IMVMMSTd	742.394	248.064	13.643
VB-IMM-QR	655.784	104.612	13.579
IMMPVIIKF	769.297	268.361	13.593
The proposed filter	591.468	86.598	13.885

Filtering algorithm	ARMSE of position/m	ARMSE of velocity/(m/s)	Time/s
VBAKF-PM	495.172	210.333	4.922
VBSTF	481.323	182.714	5.497
PTVCKF	458.794	171.344	5.166
MVMMSTd	462.231	158.895	14.079
VB-IMM-QR	439.814	92.351	13.947
IMMPVIIKF	456.759	177.421	13.867
The proposed filter	406.005	72.764	14.135

Filtering algorithm	ARMSE of position/m	ARMSE of velocity/(m/s)	Time/s
VBAKF-PM	1227.479	394.199	5.527
VBSTF	1164.347	347.543	6.027
PTVCKF	1094.203	341.537	5.854
MVMMSTd	1091.462	330.274	14.729
VB-IMM-QR	926.278	132.933	14.606
IMMPVIIKF	1101.258	354.058	14.585
The proposed filter	829.630	102.396	14.845