基于原子范数的波达方向与时延联合估计方法

Joint DOA-delay estimation approach based on atomic norm

为了解决水声通信环境下自主式水下机器人定位难的问题,提出了一种基于原子范数的波达方向(DOA)与时延联合估计方法。首先,基于水声多径多普勒效应的特点建立信道冲激响应公式,将接收信号用矩阵形式表示并对参数进行归一化处理。然后,针对水听器阵列的几何结构和多普勒效应带来的相位误差建立一个新的原子集合,考虑到水声信号在空间域的稀疏性,利用原子范数最小化求解相应的原子。最后,针对由任意线阵带来半正定矩阵中的子矩阵为非Toeplitz矩阵结构而无法进行Vandermonde分解的问题,定义了一个有关水听器几何结构的Hermitian集合,利用长椭球波函数进行半正定规划求解,获得DOA和时延的联合估计。实验结果表明,所提方法在信噪比为20 dB时,DOA估计的均方根误差低至0.2°,在DOA间隔低至3°时仍有77.98%的估计成功概率,估计时延与实际时延的误差可以达到微秒级。

To address the difficult problem of localizing autonomous underwater vehicle in underwater acoustic communication environments,a joint DOA-delay estimation approach based on atomic norm was proposed.Firstly,a channel impulse response formula was established based on the characteristics of underwater acoustic multipath and Doppler effects,and the received signal was represented in a matrix form with normalized parameters.After that,a new set of atoms was established based on the geometric structure of the hydrophone array and the phase error caused by the Doppler effects.Considering the sparsity of the underwater acoustic signal in the spatial domain,the corresponding atoms were solved using atomic norm minimization.Finally,in order to solve the problem that the sub-matrix in the positive semidefinite matrix caused by arbitrary linear arrays was a non-Toeplitz matrix structure and could not be decomposed by Vandermonde,a Hermitian set about the geometric structure of the hydrophone was defined,and the prolate spheroidal wave functions were used to solve the semi-definite programming problem to obtain a joint estimate of DOA and delay.The experimental results show that the root mean square error(RMSE)of the proposed approach is as low as 0.2°when the signal-to-noise ratio(SNR)is 20 dB,and there is still a 77.98%estimation success probability when the DOA interval is as low as 3°.The error between the estimation delay and the actual delay can reach the microsecond level.