[Sound source localization] Comparison of sound source localization algorithms based on matlab different spatial spectrum estimation [including Matlab source code 545]

1. Introduction

MUSIC algorithm is a method based on matrix feature space decomposition. From a geometric point of view, the observation space of signal processing can be decomposed into a signal subspace and a noise subspace. Obviously, these two spaces are orthogonal. The signal subspace is composed of eigenvectors corresponding to the signal in the data covariance matrix received by the array, and the noise subspace is composed of eigenvectors corresponding to all the smallest eigenvalues (noise variance) in the covariance matrix.
1 Algorithm principle The
MUSIC algorithm is an important cornerstone of the spatial spectrum estimation direction finding theory. as follows:

(1) Regardless of the shape of the direction-finding antenna array, and regardless of the dimensionality of the incident angle of the incoming wave, assuming that the array is composed of M elements, the matrix form of the array output model can be expressed as: Y(t)=AX (t)+N(t)

Among them, Y is the observed complex vector of array output data; X is the unknown spatial signal complex vector; N is the additive noise in the array output vector; A is the direction matrix of the array; here, the expression of A matrix is determined by the atlas Said.

The processing task of the MUSIC algorithm is to try to estimate the number D of the spatial signal incident on the array, the intensity of the spatial signal source and the direction of the incoming wave.

(2) In actual processing, the data obtained by Y is a limited number of samples (also called snapshots or snapshots) within a limited time period. During this time, it is assumed that the direction of the incoming wave does not change and the noise is the same as the signal Uncorrelated white noise defines the second moment of the array output signal: Ry.

(3) The core of the MUSIC algorithm is to perform eigenvalue decomposition on Ry, and use eigenvectors to construct two orthogonal subspaces, namely the signal subspace and the noise subspace. The characteristic decomposition of Ry is to make the formula in the atlas hold true.

(4) U is a non-negative definite Hermitian matrix, so the eigenvalues obtained by eigendecomposition are all non-negative real numbers, with D large eigenvalues and MD small eigenvalues, composed of eigenvectors corresponding to the large eigenvalues The space Us is the signal subspace, and the space Un formed by the eigenvectors corresponding to the small eigenvalues is the noise subspace.

(5) The noise eigenvector is used as a column vector to form a noise eigenmatrix, which is expanded into an MD-dimensional noise subspace Un, which is orthogonal to the signal subspace. And the column space vector of Us coincides with the signal subspace, so the column vector of Us and the noise subspace are also orthogonal. Therefore, the spatial spectrum function can be constructed.

(6) Obtain the maximum value of the spectral function in the spatial spectral domain, and the angle corresponding to the spectral peak is the estimated value of the direction angle of the incoming wave.

2 Theoretical development and application The
MUSIC (Multiple Signal Classification) algorithm was proposed by the American ROSchmidt in 1979, and it marked that the spatial spectrum estimation direction finding has entered a stage of prosperity. It introduces the concept of "vector space" into the field of spatial spectrum estimation. After thirty years of development, it can be said that its theory has been relatively mature.

Since the 1980s, people have conducted extensive and in-depth research on the super-resolution spatial spectrum estimation algorithm based on eigen-decomposition, and proposed a series of efficient processing methods, the most classic of which is the multi-signal classification (MUSIC) algorithm. The algorithm has to go through a one-dimensional search to find the source of the source, and the computational complexity of multi-dimensional search algorithms such as relative maximum likelihood (ML) and weighted subspace fitting (WSF) has been reduced a lot. The algorithm represented by MUSIC has a shortcoming, that is, it is not ideal for coherent signal processing. Among a series of processing schemes for coherent signal sources, the more classic ones are spatial smoothing techniques, such as spatial smoothing (SS) and modified spatial smoothing (MSS) algorithms. However, the spatial smoothing technique comes at the cost of losing the effective aperture of the array, and it is only suitable for uniformly spaced uniform linear arrays (ULA).

In fact, the spatial spectrum estimation algorithm is calculated under the known number of signal sources, which is impossible in practical applications. The number of sources can only be estimated based on the observation data. In his classic work, ROSchmidt proposed a method to estimate the signal source based on the distribution of the eigenvalues of the array covariance matrix. This method is perfect in theory, at least correct for independent sources and some related sources, but in fact, due to the limited data length, to a large extent, it can only rely on subjective judgment to determine the number of sources.

Second, the source code

clc;
clear all;
close all;
set(0,'defaultaxesfontsize',9);            %设置字体大小
load s.mat;
wnd=256;
inc=128;

[Angle1]=Spectrum_Method('capon',s1,s2,wnd,inc,45);
subplot(311)
plot(Angle1,'*'),axis tight
title('Capon')
xlabel('帧数')
ylabel('角度/度')

[Angle2]=Spectrum_Method('music',s1,s2,wnd,inc,45);
subplot(312)
plot(Angle2,'*'),axis tight
title('Music')
xlabel('帧数')
ylabel('角度/度')
function frameout=enframe(x,win,inc)

nx=length(x(:));            % 取数据长度
nwin=length(win);           % 取窗长
if (nwin == 1)              % 判断窗长是否为1，若为1，即表示没有设窗函数
   len = win;               % 是，帧长=win
else
   len = nwin;              % 否，帧长=窗长
end
if (nargin < 3)             % 如果只有两个参数，设帧inc=帧长
   inc = len;
end
nf = fix((nx-len+inc)/inc); % 计算帧数
frameout=zeros(nf,len);            % 初始化
indf= inc*(0:(nf-1)).';     % 设置每帧在x中的位移量位置
inds = (1:len);             % 每帧数据对应1:len
frameout(:) = x(indf(:,ones(1,len))+inds(ones(nf,1),:));   % 对数据分帧

Three, running results

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Four, remarks