集成先验的低复杂度Nyström-MUSIC方法

doi:10.7527/S1000-6893.2023.29226

Abstract

Abstract:

The traditional Multiple Signal Classification （MUSIC） method has high angle resolution and estimation accuracy， but the high computation complexity and poor real-timeliness involved in using the method for subspace decomposition and spectral peak search greatly limit its practical application in array radar systems. To address the problem that the angle estimation performance of array radar is limited when the computing power is limited， a low-complexity Nyström-MUSIC method based on prior information is proposed. The Nyström approximation is successively exploited to decrease the dimension of the covariance matrix and the prior angle information to determine the spectral peak search in a small area. The matrix size of the subspace decomposition and the time of spectral search are reduced， and finally the computation complexity of MUSIC method is effectively reduced. Simulation results illustrate that compared with the traditional MUSIC method， the low-complexity Nyström-MUSIC method based on prior information reduces the computation complexity by 8 times and cuts the running time by more than 80% under the condition of comparable resolution performance and estimation accuracy. It is verified that the method proposed can realize fast and high-precision estimation of the target azimuth.

Key words: angle estimation, low complexity, prior information, Nystr?m approximation, multiple signal classification (MUSIC)

CLC Number:

V243.2

Qiuyu LIU, Yanwen JIANG, Hongqi FAN, Hongfei LIAN. Low-complexity Nyström-MUSIC method based on prior information[J]. Acta Aeronautica et Astronautica Sinica, 2023, 44(22): 629226-629226.

Figures/Tables 13

Fig.1

Fig.2

Fig.3

Table 1

Comparison of computational complexity

方法	传统MUSIC方法	集成先验的Nyström-MUSIC方法
子空间分解	$O (N M 2 + M 3)$	$O (N M e 2 + M e 3 + (N + K) M M e)$
谱峰搜索	$O (J F O V (M + 1) (M - K))$	$O (K M 2 + J p r i o r M (M + 1))$
总复杂度	$O (N M 2 + M 3 + J F O V (M + 1) (M - K))$	$O (N M e 2 + M e 3 + (N + K) M M e + K M 2 + J p r i o r M (M + 1))$
定量分析	假设 $M = 64 、 M e = 16 、 N = 100 、 K = 1 、 J F O V = 1 001 、 J p r i o r = 101$
子空间分解	$671 744 ≈ 6.7 × 105$	$133 120 ≈ 1.3 × 105$
谱峰搜索	$4 099 095 ≈ 4.1 × 106$	$424 254 ≈ 4.2 × 105$
对比	$M U S I C 本文方法 ≈ 4.8 × 106 5.6 × 105 ≈ 8$

Table 1

Table 2

Parameter settings of multi-target DOA estimation

参数	MUSIC	本文方法
阵元数	64	64
抽取阵元数		16/32/48/64
快拍数	100	100
阵元间距	半波长	半波长
信噪比/dB	10	10
信号角度/（°）	$0, 10, 11.5$	$0, 10, 11.5$
搜索范围/（°）	$- 50 ~ 50$	$- 5 ~ 20$
搜索步长/（°）	0.1	0.1

Table 2

Fig.4

Fig.5

Table 3

Parameter settings of Experiment 1

参数	MUSIC	本文方法
信噪比/dB	$- 10 ~ 15$	$- 10 ~ 15$
信号角度/（°）	随机	随机
搜索范围/（°）	$- 50 ~ 50$	$0 ~ 10$
搜索步长/（°）	1	0.1

Table 3

Fig.6

Fig.7

Fig.8

Table 4

Average running time and running time reduction degree of the two methods

抽取阵元数	16	32	48	64
$T p r o p o s e d$ /s	0.002 6	0.002 8	0.002 9	0.003
$T F F T + p r o p o s e d$ /s	0.002 9	0.003 1	0.003 2	0.003 4
$T M U S I C$ /s	0.016	0.016	0.016	0.016
$T s + F F T$ /%	81.7	80.8	80	79
$T s$ /%	83.7	82.7	81.8	81.1

Table 4

Fig.9

References 27

1	JIANG Y W， QIN Y L， WANG H Q， et al. A side-lobe suppression method based on coherence factor for terahertz array imaging［J］. IEEE Access， 2018， 6： 5584-5588.
2	连红飞，蒋彦雯，范红旗. 汽车雷达多域联合调制波形［J/OL］. 系统工程与电子技术，（2022-11-08）［2023-06-18］..
	LIAN H F， JIANG Y W， FAN H Q. Multi domainjoint modulation waveform for automotive radar［J/OL］. Systems Engineering and Electronics，（2022-11-08）［2023-06-18］..
3	SHI J P， WEN F Q， LIU T P. Nested MIMO radar： Coarrays， tensor modeling， and angle estimation［J］. IEEE Transactions on Aerospace and Electronic Systems， 2021， 57（1）： 573-585.
4	黄倩兰，蔡飞，范红旗，等. 密集假信号存在下单脉冲雷达未分辨目标DOA估计［J］. 系统工程与电子技术， 2023， 45（9）： 2727-2734.
	HUANG Q L， CAI F， FAN H Q， et al. DOA estimation of unresolved targets in the presense of dense false signals with monopulse radar［J］. Systems Engineering and Electronics， 2023， 45（9）： 2727-2734 （in Chinese）.
5	SCHMIDT R. Multiple emitter location and signal parameter estimation［J］. IEEE Transactions on Antennas and Propagation， 1986， 34（3）： 276-280.
6	TANG B， TANG J， ZHANG Y， et al. Maximum likelihood estimation of DOD and DOA for bistatic MIMO radar［J］. Signal Processing， 2013， 93（5）： 1349-1357.
7	VIBERG M， OTTERSTEN B. Sensor array processing based on subspace fitting［J］. IEEE Transactions on Signal Processing， 1991， 39（5）： 1110-1121.
8	QIAN C. A simple modification of ESPRIT［J］. IEEE Signal Processing Letters， 2018， 25（8）： 1256-1260.
9	DAKULAGI V. A new approach to achieve a trade-off between direction-of-arrival estimation performance and computational complexity［J］. IEEE Communications Letters， 2021， 25（4）： 1183-1186.
10	KIM B S， JIN Y， LEE J， et al. Low-complexity MUSIC-based direction-of-arrival detection algorithm for frequency-modulated continuous-wave vital radar［J］. Sensors， 2020， 20（15）： 4295.
11	闫锋刚，沈毅，刘帅，等. 高效超分辨波达方向估计算法综述［J］. 系统工程与电子技术， 2015， 37（7）： 1465-1475.
	YAN F G， SHEN Y， LIU S， et al. Overview of efficient algorithms for super-resolution DOA estimates［J］. Systems Engineering and Electronics， 2015， 37（7）： 1465-1475 （in Chinese）.
12	LIN Y C， LEE T S. Max-MUSIC： A low-complexity high-resolution direction finding method for sparse MIMO radars［J］. IEEE Sensors Journal， 2020， 20（24）： 14914-14923.
13	XU G H， KAILATH T. Fast subspace decomposition［J］. IEEE Transactions on Signal Processing， 1994， 42（3）： 539-551.
14	LI B， WANG S S， ZHANG J， et al. Ultra-fast accurate AoA estimation via automotive massive-MIMO radar［J］. IEEE Transactions on Vehicular Technology， 2022， 71（2）： 1172-1186.
15	XIN J M， SANO A. Computationally efficient subspace-based method for direction-of-arrival estimation without eigendecomposition［J］. IEEE Transactions on Signal Processing， 2004， 52（4）： 876-893.
16	MENG X T， XUE J H， YAN F G， et al. Real-valued propagator method for fast DOA estimation via polynomial rooting［J］. The Journal of Engineering， 2019， 2019（21）： 7792-7795.
17	ROY R， KAILATH T. ESPRIT-estimation of signal parameters via rotational invariance techniques［J］. IEEE Transactions on Acoustics， Speech， and Signal Processing， 1989， 37（7）： 984-995.
18	佘黎煌，刘平凡，张石，等. 一种高精度低复杂度的改进Root-MUSIC算法［J］. 东北大学学报（自然科学版）， 2022， 43（4）： 457-462， 469.
	SHE L H， LIU P F， ZHANG S， et al. An improved root-MUSIC algorithm with high precision and low complexity［J］. Journal of Northeastern University （Natural Science）， 2022， 43（4）： 457-462， 469 （in Chinese）.
19	YAN F G， JIN M， QIAO X L. Low-complexity DOA estimation based on compressed MUSIC and its performance analysis［J］. IEEE Transactions on Signal Processing， 2013， 61（8）： 1915-1930.
20	WILLIAMS C K I， SEEGER M. Using the Nyström method to speed up kernel machines［C］∥ Proceedings of the 13th International Conference on Neural Information Processing Systems. New York： ACM， 2000： 661-667.
21	陈林秀，杨翔宇，张航，等. 基于主动雷达/红外信息融合的复合制导方法［J］. 航空学报， 2022， 43（S1）： 727058.
	CHEN L X， YANG X Y， ZHANG H， et al. Composite guidance technology based on active radar/infrared information fusion［J］. Acta Aeronautica et Astronautica Sinica， 2022， 43（S1）： 727058 （in Chinese）.
22	张哲璇，龙腾，徐广通，等. 重访机制驱动的多无人机协同动目标搜索方法［J］. 航空学报， 2020， 41（5）： 323314.
	ZHANG Z X， LONG T， XU G T， et al. Revisit mechanism driven multi-UAV cooperative search planning method for moving targets［J］. Acta Aeronautica et Astronautica Sinica， 2020， 41（5）： 323314 （in Chinese）.
23	GAO F， CAI Y Y， DENG F， et al. Prior area searching for energy-based sound source localization［J］. Science China Information Sciences， 2022， 65（12）： 1-12.
24	NYSTRÖM E J. Über die praktische auflösung von integralgleichungen mit anwendungen auf randwertaufgaben［J］. Acta Mathematica， 1930， 54： 185-204.
25	LIN M， WANG F， ZHANG C S. Large-scale eigenvector approximation via Hilbert space embedding nyström［J］. Pattern Recognition， 2015， 48（5）： 1904-1912.
26	XU G H， CHO Y， KAILATH T. Application of fast subspace decomposition to signal processing and communication problems［J］. IEEE Transactions on Signal Processing， 1994， 42（6）： 1453-1461.
27	ZHANG Y， NG B P. MUSIC-like DOA estimation without estimating the number of sources［J］. IEEE Transactions on Signal Processing， 2010， 58（3）： 1668-1676.

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Low-complexity Nyström-MUSIC method based on prior information

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