收稿日期: 2017-03-02
修回日期: 2017-06-29
网络出版日期: 2017-06-29
基金资助
国家自然科学基金（61671453）；安徽省自然科学基金（1608085MF123）
DOA estimation algorithm based on maximum likelihood estimation for nested array
Received date: 2017-03-02
Revised date: 2017-06-29
Online published: 2017-06-29
Supported by
National Natural Science Foundation of China (61671453); Natural Science Foundation of Anhui Province (1608085MF123)
针对在辐射源个数未知的条件下嵌套阵列难以估计多个辐射源角度的问题，提出了基于最大似然估计（MLE）的嵌套阵列角度估计算法。算法在嵌套阵列模型的基础上，首先通过推导阵列截获多辐射源信号的最大似然函数及其梯度，利用最速下降法估计出空域中所有潜在辐射源的角度；然后，通过多元假设检验，利用最大似然比与门限进行比较，确定出空域中所有潜在辐射源中某一时刻发射信号的活跃辐射源角度，排除其余噪声形成的虚假辐射源角度，解决了在辐射源个数未知条件下嵌套阵列对多个辐射源角度估计问题。仿真结果表明：与传统多重信号分类（MUSIC）算法相比，该算法在辐射源数目未知、存在相干信号、低信噪比（SNR）、低快拍数条件下，均具有较好的角度估计精度，并且算法形成的虚拟阵列自由度是空间平滑MUSIC算法的2倍；多元假设检验法比传统信源数目估计算法在低信噪比条件下和处理相干信号方面具有明显优势。
陈璐 , 毕大平 , 崔瑞 , 韩佳辉 . 嵌套阵列最大似然估计测向算法[J]. 航空学报, 2017 , 38(11) : 321212 -321212 . DOI: 10.7527/S1000-6893.2017.321212
To estimate the angles of multiple radiation sources with unknown numbers of signals, this paper presents an algorithm for angle estimation of the nested array based on Maximum Likelihood Estimation (MLE). Based on the nested array model, the maximum likelihood function and its gradient of the multiple signals intercepted by the nested array are derived. The angles of all radiation sources in the airspace are estimated by the steepest descent method. Using the method of multiple hypothesis testing, the maximum likelihood ratio and the threshold are compared to determine the active radiation source angle of the transmitted signal at a certain time and exclude false source angles. The problem of DOA estimation of multiple radiation sources with unknown number of signals by the nested array is thus solved. The simulation results show that under the conditions of unknown number of the radiation source, existing coherent signal, low Signal to Noise Ratio (SNR), and low sampling number, the proposed algorithm has better performance in angle estimation than traditional MUltiple SIgnal Classification (MUSIC) algorithm. The method of multiple hypothesis testing has more advantages than traditional source number estimation algorithms under the condition of low SNR and in the processing of coherent signals.
[1] LIU H Q, ZHAO L M, LI Y, et al. A sparse-based approach for DOA estimation and array calibration in uniform linear array[J]. IEEE Sensors Journal, 2016, 16(15):6018-6027.
[2] LIAO B, WEN J, HUANG L, et al. Direction finding with partly calibrated uniform linear arrays in nonuniform noise[J]. IEEE Sensors Journal, 2016, 16(12):4882-4890.
[3] MOFFET A. Minimum-redundancy linear arrays[J]. IEEE Transactions on Antennas and Propagation, 1968,16(2):172-175.
[4] ELIE B D, AHMAD F, MOENESS G A. Sparsity-based direction finding of coherent and uncorrelated targets using active nonuniform arrays[J]. IEEE Signal Processing Letters, 2015, 22(10):1628-1632.
[5] BHARGAV A, GUPTA N. Multiobjective genetic optimization of nonuniform linear array with low sidelobes and beamwidth[J]. IEEE Antennas and Wireless Propagation Letters, 2013, 12(2):1547-1549.
[6] MIKAEL S, LIEVEN D L. Multiple invariance ESPRIT for nonuniform linear arrays:A coupled canonical polyadic decomposition approach[J]. IEEE Transactions on Signal Processing, 2016, 64(14):3693-3704.
[7] PILLAI S U, BARNESS Y, HABER F. A new approach to array geometry for improved spatial spectrum estimation[J]. Proceedings of the IEEE,1985, 73(10):1522-1524.
[8] PILLAI S, HABER F. Statistical analysis of a high resolution spatial spectrum estimator utilizing an augmented covariance matrix[J]. IEEE Transactions on Acoustics, Speech, and Signal Processing, 1987, 35(11):1517-1523.
[9] HBRAMOVICH Y I, GRAY D A, GOROKHOV A Y, et al. Positive-definite Toeplitz completion in DOA estimation for nonuniform linear antenna arrays. Ⅰ. Fully augmentable arrays[J]. IEEE Transactions on Signal Processing, 1998, 46(9):2458-2471.
[10] HBRAMOVICH Y I, SPENCER N K, GOROKHOV A Y. Positive-definite Toeplitz completion in DOA estimation for nonuniform linear antenna arrays. Ⅱ. Partially augmentable arrays[J]. IEEE Transactions on Signal Processing, 1999, 47(6):1502-1521.
[11] MA W K, HSIEH T H, CHI C Y. DOA estimation of quasi-stationary signals via Khatri-Rao subspace[C]//IEEE International Conference on Acoustics, Speech and Signal Processing. Piscataway, NJ:IEEE Computer Society, 2009:2165-2168.
[12] PAL P, VAIDYANATHAN P P. Nested arrays:A novel approach to array processing with enhanced degrees of freedom[J]. IEEE Transactions on Signal Processing, 2010, 58(8):4167-4181.
[13] MA X R, DONG X H, XIE Y F. An improved spatial differencing method for DOA estimation with the coexistence of uncorrelated and coherent signals[J]. IEEE Sensors Journal, 2016,16(10):3719-3723.
[14] FANG W H, LEE Y C, CHEN Y T. Maximum likelihood 2-D DOA estimation via signal separation and importance sampling[J].IEEE Antennas and Wireless Propagation Letters, 2016, 15(2):746-749.
[15] YANG X P, LI S, HU X N, et al. Improved MDL method for estimation of source number at subarray level[J]. Electronics Letters, 2016, 52(1):85-86.
[16] HAN K Y, NEHORAI A. Improved source number detection and direction estimation with nested arrays and ULAs using jackknifing[J]. IEEE Transactions on Signal Processing, 2013, 61(23):6118-6128.
[17] 齐崇英, 张永顺, 陈西宏, 等. 一种未知信源数的高分辨DOA估计算法[J].通信学报, 2006, 26(3):58-63. QI C Y, ZHANG Y S, CHEN X H, et al. Algorithm on high resolution DOA estimation under condition of unknown number of signal sources[J]. Journal on Communications,2006, 26(3):58-63(in Chinese).
[18] MANIKAS A N, TURNOR L F. Adaptive signal parameter estimation and classification technique[J].IEE Proceedings F-Radar and Signal Processing, 1991, 138(3):267-277.
[19] 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.
[20] LIU C L, VAIDYANATHAN P P. Super nested arrays:Linear sparse arrays with reduced mutual coupling-Part Ⅰ:Fundamentals[J]. IEEE Transactions on Signal Processing, 2016, 64(15):3997-4012.
[21] LIU C L, VAIDYANATHAN P P. Super nested arrays:Linear sparse arrays with reduced mutual coupling-Part Ⅱ:High-order extensions[J]. IEEE Transactions on Signal Processing, 2016, 65(16):4203-4217.
[22] NIU C, ZHANG Y S, GUO J R. Interlaced double-precision 2-D angle estimation algorithm using L-shaped nested arrays[J]. IEEE Signal Processing Letters, 2016, 23(4):522-526.
[23] HAN K Y, NEHORAI A. Wideband Gaussian source processing using a linear nested array[J]. IEEE Signal Processing Letters, 2013,20(11):1110-1113.
[24] CHUNG P J. A max-search approach for DOA estimation with unknown number of signals[J]. IEEE Journal of Selected Topics in Signal Processing, 2010, 4(3):612-619.
/
| 〈 |
|
〉 |
CJA