💥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
