Joint State Equality Constraint Identification and Recursive Filtering Based on Deep Learning

doi:10.12382/bgxb.2024.0578

Abstract

Abstract:

The state estimation problem of equality constraint-based target tracking where multiple constraints coexist and the current constraint information is unknown is presented.A joint state equality constraint identification and recursive filtering based on deep learning algorithm is proposed.The gated recurrent units are used to construct a constraint discriminant network,and the current state constraint is identified online by using the radar measurement.A filtering gain learning network based on cascaded gated recurrent units is built in the framework of recursive filtering to adaptively estimate the target state with the help of joint probabilistic modeling and data learning.The final high-precision filtered estimate which meets the real state equality constraint at current sampling instant is obtained based on filtering projection,which combines the state estimate obtained by the gain learning network with the state equality constraint identified by the constraint discriminant network.Experimental results of multi-target tracking example demonstrate that the proposed algorithm outperforms Kalman filtering,interacting multiple model (based on different motion modes/different state equality constraints) and KalmanNet algorithm in terms of estimation accuracy and robustness,with different levels of measurement noises.

Key words: target tracking, equality constraint, linear stochastic system, state estimation, deep learning

CLC Number:

TN953

QIN Yuemei, CHEN Zhong, YANG Yanbo, LI Shuying. Joint State Equality Constraint Identification and Recursive Filtering Based on Deep Learning[J]. Acta Armamentarii, 2025, 46(6): 240578-.

Figures/Tables 18

Fig.1 Overall block diagram of DCIF

Table 1 Network parameters of CDNet

网络	输入层	隐含层	输出层
Input	n	16n²	8n²
GRU	8n²	4n
Output	4n	8n²	l

Fig.2 Internal DNN structure diagram of GLNet

Table 2 Internal DNN network parameters of GLNet

网络	输入层	隐含层	输出层
MLP1	2m²	16m²	2m²
MLP2	m	4m	16m
$P^k \| k - 1$ GRU	2m²+16m	m²
MLP3	m²+n²	8(m²+n²)	m²+n²
MLP4	n	4n	16n
$S^k \| k - 1$ GRU	m²+n²+16n	n²
MLP5	m²+n²	16(m²+n²)	mn
MLP6	mn+m²+n²	16(m²+n²)	2m²

Table 2 Internal DNN network parameters of GLNet

网络	输入层	隐含层	输出层
MLP1	2m²	16m²	2m²
MLP2	m	4m	16m
$P^k \| k - 1$ GRU	2m²+16m	m²
MLP3	m²+n²	8(m²+n²)	m²+n²
MLP4	n	4n	16n
$S^k \| k - 1$ GRU	m²+n²+16n	n²
MLP5	m²+n²	16(m²+n²)	mn
MLP6	mn+m²+n²	16(m²+n²)	2m²

Fig.3 Flowchart of DCIF algorithm

Fig.4 Vehicle motion scenario under multiple road constraints

Fig.5 Loss curves of CDNet

Fig.6 Loss curves of GLNet

Fig.7 Accuracy curve of CDNet identifying test set

Fig.8 1000 Monte Carlo simulations of ξ axis position

Fig.9 1000 Monte Carlo simulations of η axis position

Fig.10 1000 Monte Carlo simulations of ξ axis velocity

Fig.11 1000 Monte Carlo simulations of η axis velocity

Table 3 ARMSEs of comparative algorithms

对比算法	ξ	η	$ξ ·$	$η ·$
KF	8.45	9.24	3.08	3.61
IMM	8.48	8.47	3.79	4.04
IMM-I	12.17	12.19	3.04	3.22
IMM-P	11.94	12.21	3.09	3.29
KNet	7.73	7.91	2.84	3.18
GLNet	7.23	7.08	2.66	2.83
CD-CF	6.41	5.95	2.40	2.46
CFEC	6.20	5.70	2.21	2.04
DCIF	6.13	5.66	2.32	2.37

Table 3 ARMSEs of comparative algorithms

对比算法	ξ	η	$ξ ·$	$η ·$
KF	8.45	9.24	3.08	3.61
IMM	8.48	8.47	3.79	4.04
IMM-I	12.17	12.19	3.04	3.22
IMM-P	11.94	12.21	3.09	3.29
KNet	7.73	7.91	2.84	3.18
GLNet	7.23	7.08	2.66	2.83
CD-CF	6.41	5.95	2.40	2.46
CFEC	6.20	5.70	2.21	2.04
DCIF	6.13	5.66	2.32	2.37

Fig.12 ARMSEs at different r positions along ξ axis

Fig.13 ARMSEs at different r positions along η axis

VFig.14 ARMSEs at different r velocities along ξ axis

Fig.15 ARMSEs at different r velocities along η axis

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