Azimuth-dimensional RCS prediction method based on physical model priors

doi:10.23919/JSEE.2023.000167

Journal of Systems Engineering and Electronics ›› 2025, Vol. 36 ›› Issue (1): 1-14.doi: 10.23919/JSEE.2023.000167

• ELECTRONICS TECHNOLOGY •

Azimuth-dimensional RCS prediction method based on physical model priors

Jiaqi TAN(), Tianpeng LIU(), Weidong JIANG(), Yongxiang LIU(), Yun CHENG()

College of Electronic Science and Technology, National University of Defense Technology, Changsha 410073, China

Received:2022-08-15 Accepted:2023-12-15 Online:2025-02-18 Published:2025-03-18
Contact: Tianpeng LIU E-mail:tanjiaqi17@sina.com;everliutianpeng@sina.cn;jwd2232@vip.163.com;lyx_bible@sina.com;moraincy@126.com
About author:
TAN Jiaqi was born in 1998. She received her B.Eng. degree from Ningbo University, Zhejiang, China, in 2020. She is currently pursuing her Ph.D. degree with the College of Electronic Science and Technology, National University of Defense Technology, Changsha, China. Her research interests are intelligent perception and countermeasure. E-mail: tanjiaqi17@sina.com

LIU Tianpeng was born in 1985. He received his B.Eng., M.Eng, and Ph.D. degrees from the National University of Defense Technology (NUDT), Changsha, China, in 2008, 2011 and 2016 respectively. He is currently an associate professor of the College of Electronic Science and Technology, NUDT. His main research interests are radar signal processing, electronic countermeasure, and cross-eye jamming. E-mail: everliutianpeng@sina.cn

JIANG Weidong was born in 1968. He received his B.S., M.S., and Ph.D. degrees from National University of Defense Technology (NUDT), Changsha, China, in 1991, 1997, and 2001, respectively. He is currently a research fellow with the Research Institute of Space Electronics Information Technology, College of Electronics Science and Technology, NUDT. He is a member of the IEEE. His research interests include target recognition and radar signal processing. E-mail: jwd2232@vip.163.com

LIU Yongxiang was born in 1976. He received his B.S. and Ph.D. degrees from National University of Defense Technology, Changsha, China, in 1999 and 2004, respectively. Currently, he is a professor at National University of Defense Technology. His research interest mainly includes micro-motion characteristics. E-mail: lyx_bible@sina.com

CHENG Yun was born in 1995. He received his B.S. degree from the National University of Defense Technology (NUDT), Changsha, China, in 2018. He is currently pursuing his Ph.D. degree with the College of Electronic Science and Technology, NUDT. His primary research interests are array signal processing and electronic countermeasure. E-mail: moraincy@126.com
Supported by:
This work was supported by the National Natural Science Foundation of China (61921001; 62201588; 62022091).

Abstract

Abstract:

The acquisition, analysis, and prediction of the radar cross section (RCS) of a target have extremely important strategic significance in the military. However, the RCS values at all azimuths are hardly accessible for non-cooperative targets, due to the limitations of radar observation azimuth and detection resources. Despite their efforts to predict the azimuth-dimensional RCS value, traditional methods based on statistical theory fails to achieve the desired results because of the azimuth sensitivity of the target RCS. To address this problem, an improved neural basis expansion analysis for interpretable time series forecasting (N-BEATS) network considering the physical model prior is proposed to predict the azimuth-dimensional RCS value accurately. Concretely, physical model-based constraints are imposed on the network by constructing a scattering-center module based on the target scattering-center model. Besides, a superimposed seasonality module is involved to better capture high-frequency information, and augmenting the training set provides complementary information for learning predictions. Extensive simulations and experimental results are provided to validate the effectiveness of the proposed method.

Key words: azimuth-dimensional radar cross section (RCS), improved neural basis expansion analysis for interpretable time series forecasting (N-BEATS) network, physical model, scattering center model

Jiaqi TAN, Tianpeng LIU, Weidong JIANG, Yongxiang LIU, Yun CHENG. Azimuth-dimensional RCS prediction method based on physical model priors[J]. Journal of Systems Engineering and Electronics, 2025, 36(1): 1-14.

Figures/Tables 16

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Modules stack	Parameters	Value
Scattering-center modules stack	Number of scattering-center modules	4
	Shared FC layers	4
	FC layer size	512
	Order of fractional polynomials	$ {\boldsymbol{M}} = \left[ {0,4,5,5} \right] $, $ {\boldsymbol{N}} = \left[ {3,12,12,12} \right] $
Seasonality modules stack	Number of seasonality modules	2
	Shared FC layers	4
	FC layer size	256
	Harmonic number	1

Predicted azimuth/(°)	Network
Predicted azimuth/(°)	Improved N-BEATS	N-BEATS	LSTM	Season N-BEATS
0.1	1.7411	1.7861	1.5403	1.7561
0.2	2.0014	1.9358	2.0094	2.0381
0.3	1.9534	2.0528	2.2412	2.3324
0.4	2.0068	2.1642	2.2501	2.4176
0.5	2.0106	2.2897	2.4374	2.5103
0.6	2.1460	2.3301	2.4438	2.5665
0.7	2.2175	2.3525	2.4342	2.6209
0.8	2.2197	2.3981	2.4937	2.6727
0.9	2.2201	2.3480	2.4976	2.7116
1.0	2.2677	2.5407	2.5112	2.7463
1.1	2.3088	2.5974	2.5497	2.8176
1.2	2.4171	2.5922	2.5727	2.8915
1.3	2.4548	2.5222	2.6381	2.9481
1.4	2.4565	2.5511	2.6563	3.0084
1.5	2.5012	2.5430	2.7047	3.0746
1.6	2.5195	2.5856	2.7714	3.1578
1.7	2.5228	2.5328	2.8162	3.2391
1.8	2.5409	2.5901	2.8881	3.2943
1.9	2.5875	2.5976	2.9263	3.3375
2.0	2.5870	2.5831	2.9378	3.3964
2.1	2.5903	2.6880	2.9405	3.4682
2.2	2.5862	2.7515	2.9340	3.8951
2.3	2.5982	2.6928	2.9413	3.9271
2.4	2.6476	2.7084	2.9651	3.9736
2.5	2.6487	2.8014	2.8833	4.0547
2.6	2.7480	2.8020	2.9094	4.1064
2.7	2.7964	2.9014	2.8978	4.1678
2.8	2.8053	2.9331	2.9403	4.2319
2.9	2.9194	3.0218	3.0458	4.2388
3.0	2.9987	3.0538	3.1617	4.3175

Predicted azimuth/(°)	Network
Predicted azimuth/(°)	Improved N-BEATS	N-BEATS	LSTM	Season N-BEATS
0.1	0.9155	0.9189	0.9204	0.9084
0.2	0.9046	0.8928	0.9189	0.8992
0.3	0.9029	0.8959	0.9092	0.8842
0.4	0.8956	0.8801	0.9096	0.8778
0.5	0.8957	0.8712	0.8911	0.8657
0.6	0.8757	0.8707	0.8852	0.8572
0.7	0.8688	0.8672	0.8842	0.8555
0.8	0.8682	0.8596	0.8765	0.8462
0.9	0.8681	0.8495	0.8612	0.8376
1.0	0.8640	0.8443	0.8595	0.8263
1.1	0.8586	0.8461	0.8503	0.8237
1.2	0.8560	0.8551	0.8465	0.8119
1.3	0.8518	0.8467	0.8439	0.8001
1.4	0.8517	0.8454	0.8396	0.7947
1.5	0.8510	0.8467	0.8323	0.7910
1.6	0.8555	0.8449	0.8314	0.7886
1.7	0.8516	0.8416	0.8293	0.7842
1.8	0.8478	0.8332	0.8234	0.7791
1.9	0.8430	0.8358	0.8185	0.7714
2.0	0.8421	0.8351	0.8076	0.7685
2.1	0.8398	0.8322	0.8088	0.7609
2.2	0.8301	0.8212	0.8133	0.7589
2.3	0.8303	0.8174	0.8076	0.7546
2.4	0.8194	0.8166	0.8030	0.7513
2.5	0.8155	0.8104	0.8064	0.7496
2.6	0.8090	0.8042	0.8026	0.7472
2.7	0.8059	0.7980	0.8041	0.7418
2.8	0.8024	0.7965	0.7988	0.7389
2.9	0.8037	0.7915	0.7921	0.7358
3.0	0.7932	0.7731	0.7809	0.7331

Physical dimension	Target type
Physical dimension	Cone with multiple grooves	Flat cone	Round cone
Bottom diameter/(°)	0.5/0.8/1.2	0.6/0.7/0.8	0.6/0.7
Overall height/(°)	1.8/2.1/3.5	2/2.5/3	2/2.5
Cone angle/(°)	16/16/20	16/15/14	16/15

Predicted azimuth/(°)	Cone
Predicted azimuth/(°)	Cone 1	Cone 2	Cone 3	Cone 4	Cone 5	Cone 6	Cone 7	Cone 8
0.1	1.1974	1.2151	1.3147	1.3361	1.4037	1.3504	1.4198	1.5079
0.3	1.2049	1.3019	1.3681	1.3825	1.4456	1.8249	1.7642	1.7169
0.5	1.2127	1.3276	1.3995	1.4152	1.4982	1.8655	1.8479	1.8384
0.7	1.2150	1.3358	1.4127	1.4354	1.4762	1.9519	1.9132	1.9003
0.9	1.2187	1.3731	1.4361	1.4637	1.5114	2.0864	1.9956	1.9945
1.1	1.2201	1.4046	1.4682	1.4884	1.5278	2.1473	2.0134	2.0079
1.3	1.2234	1.4423	1.4973	1.5092	1.5691	2.2461	2.1739	2.1246
1.5	1.2291	1.4579	1.5277	1.5674	1.5982	2.3031	2.2648	2.2874
1.7	1.2546	1.4862	1.5562	1.5938	1.6289	2.4633	2.3376	2.3415
1.9	1.2875	1.5147	1.5976	1.6248	1.6737	2.4894	2.4281	2.3976
2.1	1.3670	1.5703	1.6491	1.6621	1.7344	2.5091	2.4961	2.4359
2.3	1.5475	1.6347	1.6899	1.7073	1.8152	2.5163	2.5374	2.5273
2.5	1.5581	1.6991	1.7543	1.7825	1.8968	2.6091	2.5918	2.6484
2.7	1.6165	1.7535	1.8008	1.8649	1.9046	2.6126	2.6364	2.7669
2.9	1.8797	1.8976	1.9013	2.0326	1.9724	2.7786	2.7491	2.8183

Azimuth-dimensional RCS prediction method based on physical model priors

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Predicted azimuth/($ ^\circ $)	Target
Predicted azimuth/($ ^\circ $)	Cone 1	Cone 2	Cone 3	Cone 4	Cone 5	Cone 6	Cone 7	Cone 8
0.1	0.9848	0.9805	0.9789	0.9710	0.9684	0.9710	0.9680	0.9648
0.3	0.9821	0.9753	0.9762	0.9761	0.9672	0.9454	0.9513	0.9461
0.5	0.9839	0.9730	09705	0.9692	0.9605	0.9467	0.9477	0.9403
0.7	0.9817	0.9711	0.9684	0.9686	0.9576	0.9375	0.9319	0.9362
0.9	0.9812	0.9684	0.9633	0.9602	0.9541	0.9239	0.9227	0.9231
1.1	0.9805	0.9647	0.9604	0.9599	0.9502	0.9180	0.9194	0.9254
1.3	0.9799	0.9602	0.9582	0.9576	0.9483	0.9143	0.9083	0.9097
1.5	0.9784	0.9598	0.9541	0.9488	0.9462	0.9081	0.9104	0.8946
1.7	0.9782	0.9543	0.9496	0.9385	0.9388	0.8996	0.8973	0.8911
1.9	0.9730	0.9512	0.9417	0.9357	0.9347	0.8990	0.8915	0.8862
2.1	0.9792	0.9488	0.9377	0.9304	0.9300	0.8972	0.8874	0.8743
2.3	0.9697	0.9427	0.9314	0.9271	0.9275	0.8903	0.8801	0.8628
2.5	0.9606	0.9418	0.9268	0.9122	0.9186	0.8823	0.8751	0.8579
2.7	0.9586	0.9386	0.9205	0.9035	0.9124	0.8801	0.8662	0.8496
2.9	0.9428	0.9315	0.9144	0.8905	0.9046	0.8738	0.8583	0.8314