適用于二維陣列的無(wú)格稀疏波達(dá)方向估計(jì)算法

王劍書; 樊養(yǎng)余; 杜瑞; 呂國(guó)云

doi:10.11999/JEIT180340

適用于二維陣列的無(wú)格稀疏波達(dá)方向估計(jì)算法

doi: 10.11999/JEIT180340

西北工業(yè)大學(xué)電子信息學(xué)院 ??西安 ??710129

基金項(xiàng)目: 水聲對(duì)抗重點(diǎn)實(shí)驗(yàn)室基金(kmb5494)

詳細(xì)信息

作者簡(jiǎn)介:
王劍書：男，1989年生，博士生，研究方向?yàn)殛嚵行盘?hào)處理、DOA估計(jì)和波束形成等

樊養(yǎng)余：男，1960年生，教授，主要研究方向?yàn)閿?shù)字圖像處理、數(shù)字信號(hào)處理理論與應(yīng)用、無(wú)線光通信技術(shù)和虛擬現(xiàn)實(shí)技術(shù)等

杜瑞：男，1988年生，博士生，研究方向?yàn)槔走_(dá)信號(hào)處理和模式識(shí)別等

呂國(guó)云：男，1975年生，副教授，主要研究方向?yàn)樾盘?hào)與信息處理、語(yǔ)音和圖像處理、虛擬現(xiàn)實(shí)和嵌入式系統(tǒng)和高速信號(hào)處理等

通訊作者:
王劍書　wangjs123@mail.nwpu.edu.cn

中圖分類號(hào): TN911.7
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- 被引次數(shù): 0
出版歷程
- 收稿日期: 2018-04-12
- 修回日期: 2018-09-04
- 網(wǎng)絡(luò)出版日期: 2018-09-12
- 刊出日期: 2019-02-01

Gridless Sparse Method for Direction of Arrival Estimation for Two-dimensional Array

School of Electronics and Information, Northwestern Polytechnical University, Xi’an 710129, China

Funds: The Foundation of Key Laboratory of Underwater Acoustic Countermeasure (kmb5494)

摘要

摘要:
針對(duì)現(xiàn)有的適用于2維陣列的無(wú)格稀疏波達(dá)方向(DOA)估計(jì)方法性能不足的問(wèn)題，該文提出一種新的方法。對(duì)2維陣列，從原子L0范數(shù)出發(fā)，證明其值等于一個(gè)以矩陣秩為目標(biāo)函數(shù)的半定規(guī)劃(SDP)問(wèn)題的最優(yōu)解。對(duì)該矩陣使用第1類有限階貝塞爾函數(shù)近似表達(dá)，構(gòu)造新的秩優(yōu)化SDP問(wèn)題。根據(jù)低秩矩陣恢復(fù)理論，對(duì)該SDP問(wèn)題的目標(biāo)函數(shù)使用log-det函數(shù)方法平滑替代，然后使用優(yōu)化最小(MM)算法求解，最后通過(guò)(半)正定Toeplitz矩陣的范德蒙分解方法實(shí)現(xiàn)無(wú)格DOA估計(jì)。在MM算法求解模型時(shí)，使用樣本協(xié)方差矩陣構(gòu)造初始優(yōu)化問(wèn)題，減少算法迭代。仿真實(shí)驗(yàn)結(jié)果表明，相較于基于網(wǎng)格的MUSIC和其他無(wú)格DOA估計(jì)方法，該文方法具有更好的均方根誤差(RMSE)性能與對(duì)相鄰源的分辨能力；在快拍數(shù)充足且信噪比(SNR)較高時(shí)，適當(dāng)?shù)牡?類貝塞爾函數(shù)階數(shù)選擇可以實(shí)現(xiàn)與較大階數(shù)接近的RMSE性能，同時(shí)能減少運(yùn)行時(shí)間。
- 波達(dá)方向估計(jì) /
- 無(wú)格 /
- 2維陣列 /
- 半定規(guī)劃 /
- 范德蒙分解
Abstract:
For the fact that current gridless Direction Of Arrival (DOA) estimation methods with two-dimensional array suffer from unsatisfactory performance, a novel girdless DOA estimation method is proposed in this paper. For two-dimensional array, the atomic L0-norm is proved to be the solution of a Semi-Definite Programming (SDP) problem, whose cost function is the rank of a Hermitian matrix, which is constructed by finite order of Bessel functions of the first kind. According to low rank matrix recovery theorems, the cost function of the SDP problem is replaced by the log-det function, and the SDP problem is solved by Majorization-Minimization (MM) method. At last, the gridless DOA estimation is achieved by Vandermonde decomposition method of semidefinite Toeplitz matrix built by the solutions of above SDP problem. Sample covariance matrix is used to form the initial optimization problem in MM method, which can reduce the iterations. Simulation results show that, compared with on-grid MUSIC and other gridless methods, the proposed method has better Root-Mean-Square Error (RMSE) performance and identifiability to adjacent sources; When snapshots are enough and Signal-Noise-Ratio (SNR) is high, proper choice of the order of Bessel functions of the first kind can achieve approximate RMSE performance as that of higher order ones, and can reduce the running time.
- Direction Of Arrival (DOA) estimation /
- Gridless /
- Two-dimensional array /
- Semi-Definite Programming (SDP) /
- Vandermonde decomposition

HTML全文

圖 1 RMSE仿真實(shí)驗(yàn)結(jié)果

下載: 全尺寸圖片幻燈片

圖 2 相鄰源RMSE仿真實(shí)驗(yàn)結(jié)果

下載: 全尺寸圖片幻燈片

圖 3 不同貝塞爾函數(shù)階數(shù)的本文方法仿真實(shí)驗(yàn)結(jié)果

下載: 全尺寸圖片幻燈片

表 1 不同貝塞爾函數(shù)階數(shù)的本文方法平均運(yùn)行時(shí)間(s)

N 20 40 60 80

運(yùn)行時(shí)間 0.7453 1.7536 4.0365 8.0497

下載: 導(dǎo)出CSV

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