无线传感器网络的时钟同步估计问题（Matlab代码实现）

news2024/12/24 2:47:14

💥1 概述

📚2 运行结果

🎉3 参考文献

👨‍💻4 Matlab代码

💥1 概述

随着无线传感器网络的快速发展,其应用领域也越来越广。在诸多的应用环境中都需要大量已同步的传感器节点通过协同作用执行一个分布式的任务,因此时钟同步成为了无线传感器网络众多应用的基础。

📚2 运行结果

主函数部分代码：

% Code for Clock Synchronization for Wireless Sensor Networks
clc
clear all
close all
load("ClockSync.mat");

tx = tx_timestamps;
rx = rx_timestamps;

% Estimate of phi2 based on the Clock Synchronisation Equation
x = rx - tx - tau;
% (x has a Gaussian noise distribution (contributions from rx & tx measurement errors)

% Phi_2 Scaled as per Data set
phi_2s = phi_2 .* ones(K,trial,6);
phi2 = phi_2 .* ones(10,6);
p = phi_2.* ones(1,6);

% Estimated phi - Mean of timestamps of K messages with trials
phi_mean = squeeze(mean(x,2));
% Standard Deviation for K messages with trials
phi_std  = squeeze(std(x,1,2));
% Bias in Measurements for K messages with trials
phi_bias = (phi_mean - phi2).^2;
% Variance in Measurements for K messages
phi_var = (1/trial) * phi_std.^2;

% Calculated MSE & CRLB for the Dataset (average over K messages)
se = (x - phi_2s).^2 ;% Squared Error
mse_c = mean(squeeze(mean(se,2)));
crlb_c = mean(phi_var);

% Theoretical MSE & CRLB for the Dataset (average over K messages)
mse_t = mean(phi_var + phi_bias);
crlb_t = (1/trial) * noise_var;

% Phi : Estimates and Standard deviations
phi_mm = mean(phi_mean);
phi_sm = mean(phi_std);
 
% Plot of Theoretical & Estimated CRLB vs. Noise Variance 
figure
loglog(noise_var, crlb_t,'Marker', 'o')
%hold on
%loglog(noise_var, crlb_c,'Marker', 'x')
title('CRLB of \phi with noise variance','FontName', 'Times')
xlabel('Noise \sigma^2','FontName', 'Times')
ylabel('CRLB','FontName', 'Times')
legend('Theoretical CRLB') %, 'Calculated CRLB')
saveas(gca,['CRLB_Variance.png']);

% Plot of MSE vs. Noise Variance 
figure
loglog(noise_var, mse_t,'Marker', 'o')
hold on
loglog(noise_var, mse_c,'Marker', 'x')
title('MSE of \phi with noise variance','FontName', 'Times')
xlabel('Noise \sigma^2','FontName', 'Times')
ylabel('MSE','FontName', 'Times')
legend('Theoretical MSE', 'Calculated MSE')
saveas(gca,['MSE_Variance.png']);

% Plot of Phi_Estimate vs. Noise Variance 
figure
semilogx(noise_var, p,'Marker','o')
hold on
semilogx(noise_var, phi_mm,'Marker', 'x')
title('Estimate of \phi with noise variance','FontName', 'Times')
xlabel('Noise \sigma^2','FontName', 'Times')
ylabel('Estimate E[\phi]','FontName', 'Times')
legend('Reference', 'Numerical Estimate')
saveas(gca,['Estimate_Variance.png']);

% Plot of Data Sets with different noise variances
min_x = min(x,[],'all');
max_x = max(x,[],'all');
figure('Renderer', 'painters', 'Position', [10 10 1200 600])
t = tiledlayout(2,3,'TileSpacing','none');
for i = 1 : 6
    nexttile
    x1 = x(:,:,i);
    grid minor
    % pdf distribution for plotting Observed Data
    x_pdf(i,:) = linspace(min_x,max_x,K*trial);
    y_pdf(i,:) = normpdf(x_pdf(i,:), phi_mm(i), phi_sm(i));
    xline(phi_mm(i),'-','Estimate');
    hold on
    histogram(x1(:), 'Normalization', 'pdf', 'EdgeColor','k' ,'FaceColor' , 'none');
    hold on
    plot(x_pdf(i,:), y_pdf(i,:), 'color', 'b' , 'LineWidth',1);
    title(['E[\phi] for 10k MC run; Noise \sigma^2  = ', num2str(phi_sm(i))],'FontName', 'Times');
    xlabel('Distribution','FontName', 'Times');
    ylabel(['PDF'],'FontName', 'Times');
end