相关噪声下时延估计

最近在相关高斯噪声下的时延估计，，进行仿真实验，需要生成两路相关的高斯白，由于从来没接触过，在MATLAB官网找到一个函数，如下。。求教，查了很多论文，发现直接互相关法在相关噪声背景下几乎是失效的，可是我按照这个函数写的时延估计程序，互相关的方法还能得出很好的结果。另外，做基于四阶累积量与RLS自适应滤波结合估计时延时，误差系数曲线异常，找了很久的资料，也还没解决，，，求各位前辈指教！！！

（Multisynchrosqueezing Transform - File Exchange - MATLAB Central  https://ww2.mathworks.cn/matlabcentral/fileexchange/68571-multisynchrosqueezing-transform）

function [result, sampRpp] = correlatedGaussianNoise(Rpp, nSamp)
%% generates correlated 0-mean Gaussian vector process
%生成相关的0均值高斯向量过程
% inputs: Rpp - correlation matrix. must be positive definite %相关矩阵。必须是正定的  大小决定输出向量
%               and size determines output vector
%         nSamp - number of independent samples of correlated process相关过程的独立样本数量
%
% output: result - matrix of dimension Rpp rows X nSamp cols.  矩阵的尺寸Rpp行X nSamp cols
%
% result has form:
%        < ------ nSamp ------->
%        ------------------------   data is correlated along  数据是相关的
%   |    |                      |   all rows for each column
%   |    |       output         |
%   p    |    data  matrix      |   data is independent along
%   |    |                      |   all columns for a given row给定行的所有列
%   |    |                      |
%        < -------- nSamp ------>
%
% example: use following correlation matrix (output implicitly 3 rows) 示例:使用以下相关矩阵(隐式输出3行)
%          [1    0.2   0.2] 
%          [0.2   1    0.2] 
%          [0.2  0.2    1 ]
% 
% and 1e5 samples to check function
%
%% 
%  n = 3; Rpp = repmat(0.2, [n,n]);  Rpp(1:(n+1):n^2) = 1;
%  disp(Rpp)
%  nSamp = 1e5;
%  [x, sampR] = correlatedGaussianNoise(Rpp, nSamp);
%  disp(sampR)
%
%% -----------------------------------------------------
% michaelB
%

%% algorithm

% check dimenions - add other checking as necessary...
if(ndims(Rpp) ~= 2),
    result = [];
    error('Rpp must be a real-valued symmetric matrix');
    return;
end

% symmeterize the correlation matrix
Rpp = 0.5 .*(double(Rpp) + double(Rpp'));

% eigen decomposition
[V,D] = eig(Rpp);

% check for positive definiteness
if(any(diag(D) <= 0)),
    result = [];
    error('Rpp must be a positive definite');
    return;
end

% form correlating filter
W = V*sqrt(D);

% form white noise dataset
n = randn(size(Rpp,1), nSamp);

% correlated (colored) noise
result = W * n;

% calculate the sample correlation matrix if necessary
if(nargout == 2),
    sampRpp = 0;
    for k1=1:nSamp,
        sampRpp = sampRpp + result(:,k1) * (result(:,k1)');
    end
    
    % unbiased estimate
    sampRpp = sampRpp ./ (nSamp - 1);
end

% % % % 基于四阶累积量与RLS自适应滤波的时延估计方法（FOC-RLS）%%%%%%
clc
clear all
close all
N = 500; 
fs=1000; 
a=-0.5;
nn = 2; Rpp = repmat(0.9, [nn,nn]);  Rpp(1:(nn+1):nn^2) = 1;
disp(Rpp);
nSamp=500;
[result, sampRpp] = correlatedGaussianNoise(Rpp, nSamp);
n1=0.4*result(1,:);  %result为2行矩阵，第一行  为噪声1，第二行  为噪声2
n2=0.4*result(2,:);%%系数调整信噪比的大小
t=linspace(1,10,N);
sin1=exp(a*t);  
sin2=zeros(1,length(sin1));
delay= 100;
sin2((delay+1):length(sin1))=sin1(1:length(sin1)-delay); 

nn1=sin(2*pi*10*t); 
nn2=zeros(1,length(nn1));
nn2((delay+1):length(nn1))=nn1(1:length(nn1)-delay); 

single_1=sin1+n1+nn1;  %single_A
single_2=sin2+n2+nn2;%%single_B
snr1=SNR_singlech(sin1,single_1);
snr2=SNR_singlech(sin2,single_2);
figure,
plot(t,single_1,'color','b');
hold on;
plot(t,single_2,'color','g');
legend(' 信号A','信号B'); 
X1=fft(single_1,2*N-1);
X1J=conj(X1);
X2=fft(single_2,2*N-1);
X2J=conj(X2);
X12=X2.*X1J;
R12=fftshift(real(ifft(X12)));
r12max=max(abs(R12));
R12=R12 / r12max;
lags=-499:499;
figure,
plot(lags,R12,'color','b');title('基本互相关');

xCum4 = cum4est (single_1, 90, 20, 0, 'biased', 10, 10);%自四阶累积  
xCum4Size = size(xCum4);    %返回数组维度
 absmax1=max(abs(xCum4));
 xCum4=xCum4/absmax1;
 xCum4_hu = cum4est (ifft(X12), 90, 20, 0, 'biased', 10,10);%互四阶累积
 xCum4Size_hu = size(xCum4_hu);    %返回数组维度
 absmax=max(abs(xCum4_hu));
 xCum4_hu=xCum4_hu/absmax;
 
 
 figure,
subplot(2,1,1)
plot(xCum4,'color','b') ; title('信号1四阶自累积量运算');  
xlabel('子频带数')
subplot(2,1,2)
plot(xCum4_hu,'color','b') ; title('互四阶累积量运算');  
xlabel('子频带数')

jieguo=xcorr(xCum4,xCum4_hu,'unbiased');    %%频域的累积量互相关
fore=ifft(jieguo);  %%%反变换到时域
figure,
plot(jieguo,'color','b') ; title('四阶累积量互相关');  

[v1,location1]=max(abs(fore));
delaytime_foc=(fix(length(jieguo)/2)-location1)/fs %经过累积计算换算出信号的延迟时间
 [v2,location2]=max(abs(R12));
 location2=lags(location2);
delaytime_cc=location2/fs  %互相关换算出信号的延迟时间

% % % % % % % %  RLS   % % % % % % % % % % % % % % % % 
x1=xCum4;    %产生高斯随机系列
d1=sin1;    % 期望输出

[y1 e1 w1] = RLS(x1, d1, 32);

figure,
subplot(2,1,1)
plot(e1,'color','b') ; title('y1_error');  
subplot(2,1,2)
plot(w1(end,:),'color','b') ; title('y1 滤波器权系数');  


x2=y1'-xCum4_hu;
d2=sin2; 
[y2 e2 w2] = RLS(x2, d2, 32);

figure,
subplot(2,1,1)

plot(e2,'color','b') ; title('误差曲线');xlabel('迭代次数') ; ylabel('输出误差估计') ;  
subplot(2,1,2)
plot(w2(end,:),'color','b') ; title('滤波器权系数');  xlabel('迭代次数') ; ylabel('权矢量的值') ;

[v3,location3]=max(abs(e2));
delaytime_RLS=(location3)/fs %经过累积计算换算出信号的延迟时间