鲁棒无范围定位算法 （RRGA）（Matlab代码实现）
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目录
1 概述
2 运行结果
3 参考文献
4 Matlab代码实现
1 概述
估值的抗异常误差能力可以用影响函数定量分析.影响函数反映了不同位置上的异常数据对估值造成的相对影响,其绝对值越小,抗差能力越强[11].式(11)所示的广义M估计准则的影响函数为：
2 运行结果
部分代码：
scatter3(data(:,1), data(:,2), data(:,3), 5, data(:,3), 'filled');
colormap(gray);
% Calculate the eigenvectors and eigenvalues
covariance = cov(data);
tt1=data(:,1)-avg(1);tt2=data(:,2)-avg(2);tt3=data(:,3)-avg(3);
tt=[tt1 tt2 tt3];
cc=1/333*(transpose(tt)*tt);
[eigenvec, eigenval ] = eig(covariance);
% Get the index of the largest eigenvector
largest_eigenvec = eigenvec(:, 3);
largest_eigenval = eigenval(3,3);
medium_eigenvec = eigenvec(:, 2);
medium_eigenval = eigenval(2,2);
smallest_eigenvec = eigenvec(:, 1);
smallest_eigenval = eigenval(1,1);
% Plot the eigenvectors
hold on;
quiver3(X0, Y0, Z0, largest_eigenvec(1)*sqrt(largest_eigenval), largest_eigenvec(2)*sqrt(largest_eigenval), largest_eigenvec(3)*sqrt(largest_eigenval), '-m', 'LineWidth',3);
quiver3(X0, Y0, Z0, medium_eigenvec(1)*sqrt(medium_eigenval), medium_eigenvec(2)*sqrt(medium_eigenval), medium_eigenvec(3)*sqrt(medium_eigenval), '-g', 'LineWidth',3);
quiver3(X0, Y0, Z0, smallest_eigenvec(1)*sqrt(smallest_eigenval), smallest_eigenvec(2)*sqrt(smallest_eigenval), smallest_eigenvec(3)*sqrt(smallest_eigenval), '-r', 'LineWidth',3);
hold on;
% Set the axis labels
hXLabel = xlabel('x');
hYLabel = ylabel('y');
hZLabel = zlabel('z');
xlim([-10,10]);
ylim([-10,10]);
zlim([-10,10]);
title('Original 3D data');
%%%%%%%%%%%%% CENTER THE DATA %%%%%%%%%%%
data = data-repmat(avg, size(data, 1), 1);
%%%%%%%%%%%%% NORMALIZE THE DATA %%%%%%%%%%%
stdev = sqrt(diag(covariance));
data = data./repmat(stdev', size(data, 1), 1);
%%%%%%%%%%%%% DECORRELATE THE DATA %%%%%%%%%%%
decorrelateddata = (data*eigenvec);
% Plot the decorrelated data
figure;
scatter3(decorrelateddata(:,1), decorrelateddata(:,2), decorrelateddata(:,3), 5, decorrelateddata(:,3), 'filled');
colormap(gray);
% Plot the eigenvectors (which are now the axes (0,0,1), (0,1,0), (1,0,0)
% and the mean of the centered data is at (0,0,0)
hold on;
quiver3(0, 0, 0, 0, 0, 1*sqrt(largest_eigenval), '-m', 'LineWidth',3);
quiver3(0, 0, 0, 0, 1*sqrt(medium_eigenval), 0, '-g', 'LineWidth',3);
quiver3(0, 0, 0, 1*sqrt(smallest_eigenval), 0, 0, '-r', 'LineWidth',3);
hold on;
% Set the axis labels
hXLabel = xlabel('x');
hYLabel = ylabel('y');
hZLabel = zlabel('z');
xlim([-5,5]);
ylim([-5,5]);
zlim([-5,5]);
title('Decorrelated 3D data');
%%%%%%%%%%%%% PROJECT THE DATA ONTO THE 2 LARGEST EIGENVECTORS %%%%%%%%%%%
eigenvec_2d=eigenvec(:,2:3);
data_2d = data*eigenvec_2d;
% Plot the 2D data
figure;
scatter(data_2d(:,1), data_2d(:,2), 5, data(:,3), 'filled');
colormap(gray);
% Plot the eigenvectors
hold on;
quiver(0, 0, 0*sqrt(largest_eigenval), 1*sqrt(largest_eigenval), '-m', 'LineWidth',3);
quiver(0, 0, 1*sqrt(medium_eigenval), 0*sqrt(medium_eigenval), '-g', 'LineWidth',3);
hold on;
% Set the axis labels
hxLabel = xlabel('x');
hyLabel = ylabel('y');
ylim([-5,5]);
ylim([-5,5]);
title('Projected 2D data');
grid on;
%%%%%%%%%%%%% PROJECT THE DATA ONTO THE LARGEST EIGENVECTOR %%%%%%%%%%%
eigenvec_1d=eigenvec(:,3);
data_1d = data*eigenvec_1d;
% Plot the 1D data
figure;
scatter(repmat(0, size(data_1d,1), 1), data_1d, 5, data(:,3), 'filled');
colormap(gray);
% Plot the eigenvector
hold on;
quiver(0, 0, 0*sqrt(largest_eigenval), 1*sqrt(largest_eigenval), '-m', 'LineWidth',3);
hold on;
% Set the axis labels
hXLabel = xlabel('x');
hYLabel = ylabel('y');
xlim([-5,5]);
ylim([-5,5]);
title('Projected 1D data');
grid on;
3 参考文献
部分理论来源于网络，如有侵权请联系删除。
[1][seyed saber banihashemian (2022). robust range-free localization algorithm (RRGA)
[2]武二永,项志宇,刘济林.鲁棒的机器人蒙特卡洛定位算法[J].自动化学报,2008,34(8):907-911
[3]吴昊,陈树新,侯志强,霍辰杰.一种鲁棒的约束总体最小二乘无源定位算法[J].上海交通大学学报,2013,47(7):1114-1118