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盲源分离简单的来讲就是在不明确系统的传输特性的前提下，从系统的源信号估计出观测信号的传输信道。

假设n个未知的源信号，各传感器接收到m个混合的观测信号，为混入的加性噪声，混合系统A为未知的混合矩阵。经过分离系统W后分离出近似与源信号的估计向，盲源分离的数学模型可以表达为：

要想分离出源信号S(t)的估计向量Y(t)主要是要求分解离矩阵W，Y(t)的分离系统过程表达式如下：

盲信号分离的原理框图如图所示，由于混合系统A和源信号S(t)都是未知的，所以对于分离出的估计向量Y(t)可能在幅度大小和排列次序存在不确定性，但是信号的信息存在于信号的波形中，所以并不影响对信号的分离。

``` %----------------------------------------------------------------

clc

clear all

%% --------------------------------- Set Parameters

N = 1; %The number of observed mixtures

Ns = 2; %The number of independent sources

Ls = 1000; %Sample size, i.e.: number of observations

finalTime = 40*pi; %Final sample time (s)

initialTime = 0; %Initial sample time (s)

%% --------------------------------- Generating Data for SSA-ICA

Amix = rand(N,Ns); %Amix is a random N x Ns mixing matrix

timeVector = initialTime:(finalTime-initialTime)/(Ls-1):finalTime; %Vector of time coordinates

source1 = sin(1.1*timeVector); %Independent source component 1, sin(a * t)

source2 = cos(0.25*timeVector); %Independent source component 2, cos(b * t)

S = [source1;source2]; %Source Matrix

figure

plot(timeVector,source1) %Plotting the N independent sources vs. time

xlabel('time (s)')

ylabel('Signal Amplitude')

legend('source 1')

figure

plot(timeVector,source2) %Plotting the N independent sources vs. time

xlabel('time (s)')

ylabel('Signal Amplitude')

legend('source 2')

Yobs = Amix*S; %Matrix consisting of M samples of N observed mixtures

figure

plot(timeVector,Yobs) %Plotting the observed signal vs. time

xlabel('time (s)')

ylabel('Signal Amplitude')

legend('observed signal')

%% --------------------------------- Call SSA-ICA algorithm

M = 200;

Sest = SSA_ICA(Yobs,Ns,M);

%% --------------------------------- Show results

figure

plot(timeVector, Sest(1,:))

xlabel('time (s)')

ylabel('Signal Amplitude')

legend('Source Estimation 1')

figure

plot(timeVector, Sest(2,:))

xlabel('time (s)')

ylabel('Signal Amplitude')

legend('Source Estimation 2') ```

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