www.gusucode.com > KF和EKF和UKF介绍matlab源码程序 > EKF_UKF_PF1.m
% EKF UKF PF 的三个算法 clear; % tic; x = 0.1; % 初始状态 x_estimate = 1;%状态的估计 e_x_estimate = x_estimate; %EKF的初始估计 u_x_estimate = x_estimate; %UKF的初始估计 p_x_estimate = x_estimate; %PF的初始估计 Q = 10;%input('请输入过程噪声方差Q的值: '); % 过程状态协方差 R = 1;%input('请输入测量噪声方差R的值: '); % 测量噪声协方差 P =5;%初始估计方差 e_P = P; %EKF方差 u_P = P;%UKF方差 pf_P = P;%PF方差 tf = 50; % 模拟长度 x_array = [x];%真实值数组 e_x_estimate_array = [e_x_estimate];%EKF最优估计值数组 u_x_estimate_array = [u_x_estimate];%UKF最优估计值数组 p_x_estimate_array = [p_x_estimate];%PF最优估计值数组 u_k = 1; %微调参数 u_symmetry_number = 4; % 对称的点的个数 u_total_number = 2 * u_symmetry_number + 1; %总的采样点的个数 linear = 0.5; N = 500; %粒子滤波的粒子数 close all; %粒子滤波初始 N 个粒子 for i = 1 : N p_xpart(i) = p_x_estimate + sqrt(pf_P) * randn; end for k = 1 : tf % 模拟系统 x = linear * x + (25 * x / (1 + x^2)) + 8 * cos(1.2*(k-1)) + sqrt(Q) * randn; %状态值 y = (x^2 / 20) + sqrt(R) * randn; %观测值 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%扩展卡尔曼滤波器%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %进行估计 第一阶段的估计 e_x_estimate_1 = linear * e_x_estimate + 25 * e_x_estimate /(1+e_x_estimate^2) + 8 * cos(1.2*(k-1)); e_y_estimate = (e_x_estimate_1)^2/20; %这是根据k=1时估计值为1得到的观测值;只是这个由我估计得到的 第24行的y也是观测值 不过是由加了噪声的真实值得到的 %相关矩阵 e_A = linear + 25 * (1-e_x_estimate^2)/((1+e_x_estimate^2)^2);%传递矩阵 e_H = e_x_estimate_1/10; %观测矩阵 %估计的误差 e_p_estimate = e_A * e_P * e_A' + Q; %扩展卡尔曼增益 e_K = e_p_estimate * e_H'/(e_H * e_p_estimate * e_H' + R); %进行估计值的更新 第二阶段 e_x_estimate_2 = e_x_estimate_1 + e_K * (y - e_y_estimate); %更新后的估计值的误差 e_p_estimate_update = e_p_estimate - e_K * e_H * e_p_estimate; %进入下一次迭代的参数变化 e_P = e_p_estimate_update; e_x_estimate = e_x_estimate_2; %%%%%%%%%%%%%%%%%%%%%%%%%%%粒子滤波器%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% for i = 1 : N p_xpartminus(i) = 0.5 * p_xpart(i) + 25 * p_xpart(i) / (1 + p_xpart(i)^2) + 8 * cos(1.2*(k-1)) + sqrt(Q) * randn; %这个式子比下面一行的效果好 % xpartminus(i) = 0.5 * xpart(i) + 25 * xpart(i) / (1 + xpart(i)^2) + 8 * cos(1.2*(k-1)); p_ypart = p_xpartminus(i)^2 / 20; %预测值 p_vhat = y - p_ypart;% 观测和预测的差 p_q(i) = (1 / sqrt(R) / sqrt(2*pi)) * exp(-p_vhat^2 / 2 / R); %各个粒子的权值 end % 平均每一个估计的可能性 p_qsum = sum(p_q); for i = 1 : N p_q(i) = p_q(i) / p_qsum;%各个粒子进行权值归一化 end % 重采样 权重大的粒子多采点,权重小的粒子少采点, 相当于每一次都进行重采样; for i = 1 : N p_u = rand; p_qtempsum = 0; for j = 1 : N p_qtempsum = p_qtempsum + p_q(j); if p_qtempsum >= p_u p_xpart(i) = p_xpartminus(j); %在这里 xpart(i) 实现循环赋值;终于找到了这里!!! break; end end end p_x_estimate = mean(p_xpart); % p_x_estimate = 0; % for i = 1 : N % p_x_estimate =p_x_estimate + p_q(i)*p_xpart(i); % end %%%%%%%%%%%%%%%%%%%%%%%%%%%%不敏卡尔曼滤波器%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %采样点的选取 存在x(i) u_x_par = u_x_estimate; for i = 2 : (u_symmetry_number+1) u_x_par(i,:) = u_x_estimate + sqrt((u_symmetry_number+u_k) * u_P); end for i = (u_symmetry_number+2) : u_total_number u_x_par(i,:) = u_x_estimate - sqrt((u_symmetry_number+u_k) * u_P); end %计算权值 u_w_1 = u_k/(u_symmetry_number+u_k); u_w_N1 = 1/(2 * (u_symmetry_number+u_k)); %把这些粒子通过传递方程 得到下一个状态 for i = 1: u_total_number u_x_par(i) = 0.5 * u_x_par(i) + 25 * u_x_par(i)/(1+u_x_par(i)^2) + 8 * cos(1.2*(k-1)); end %传递后的均值和方差 u_x_next = u_w_1 * u_x_par(1); for i = 2 : u_total_number u_x_next = u_x_next + u_w_N1 * u_x_par(i); end u_p_next = Q + u_w_1 * (u_x_par(1)-u_x_next) * (u_x_par(1)-u_x_next)'; for i = 2 : u_total_number u_p_next = u_p_next + u_w_N1 * (u_x_par(i)-u_x_next) * (u_x_par(i)-u_x_next)'; end % %对传递后的均值和方差进行采样 产生粒子 存在y(i) % u_y_2obser(1) = u_x_next; % for i = 2 : (u_symmetry_number+1) % u_y_2obser(i,:) = u_x_next + sqrt((u_symmetry_number+k) * u_p_next); % end % for i = (u_symmetry_number + 2) : u_total_number % u_y_2obser(i,:) = u_x_next - sqrt((u_symmetry_number+u_k) * u_p_next); % end %另外存在y_2obser(i) 中; for i = 1 :u_total_number u_y_2obser(i,:) = u_x_par(i); end %通过观测方程 得到一系列的粒子 for i = 1: u_total_number u_y_2obser(i) = u_y_2obser(i)^2/20; end %通过观测方程后的均值 y_obse u_y_obse = u_w_1 * u_y_2obser(1); for i = 2 : u_total_number u_y_obse = u_y_obse + u_w_N1 * u_y_2obser(i); end %Pzz测量方差矩阵 u_pzz = R + u_w_1 * (u_y_2obser(1)-u_y_obse)*(u_y_2obser(1)-u_y_obse)'; for i = 2 : u_total_number u_pzz = u_pzz + u_w_N1 * (u_y_2obser(i) - u_y_obse)*(u_y_2obser(i) - u_y_obse)'; end %Pxz状态向量与测量值的协方差矩阵 u_pxz = u_w_1 * (u_x_par(1) - u_x_next)* (u_y_2obser(1)-u_y_obse)'; for i = 2 : u_total_number u_pxz = u_pxz + u_w_N1 * (u_x_par(i) - u_x_next) * (u_y_2obser(i)- u_y_obse)'; end %卡尔曼增益 u_K = u_pxz/u_pzz; %估计量的更新 u_x_next_optimal = u_x_next + u_K * (y - u_y_obse);%第一步的估计值 + 修正值; u_x_estimate = u_x_next_optimal; %方差的更新 u_p_next_update = u_p_next - u_K * u_pzz * u_K'; u_P = u_p_next_update; %进行画图程序 x_array = [x_array,x]; e_x_estimate_array = [e_x_estimate_array,e_x_estimate]; p_x_estimate_array = [p_x_estimate_array,p_x_estimate]; u_x_estimate_array = [u_x_estimate_array,u_x_estimate]; e_error(k,:) = abs(x_array(k)-e_x_estimate_array(k)); p_error(k,:) = abs(x_array(k)-p_x_estimate_array(k)); u_error(k,:) = abs(x_array(k)-u_x_estimate_array(k)); end t = 0 : tf; figure; plot(t,x_array,'k.',t,e_x_estimate_array,'r-',t,p_x_estimate_array,'g--',t,u_x_estimate_array,'b:'); set(gca,'FontSize',10); set(gcf,'color','White'); xlabel('时间步长');% lable --->label 我的神 ylabel('状态'); legend('真实值','EKF估计值','PF估计值','UKF估计值'); figure; plot(t,x_array,'k.',t,p_x_estimate_array,'g--', t, p_x_estimate_array-1.96*sqrt(P), 'r:', t, p_x_estimate_array+1.96*sqrt(P), 'r:'); set(gca,'FontSize',10); set(gcf,'color','White'); xlabel('时间步长');% lable --->label 我的神 ylabel('状态'); legend('真实值','PF估计值', '95% 置信区间'); %root mean square 平均值的平方根 e_xrms = sqrt((norm(x_array-e_x_estimate_array)^2)/tf); disp(['EKF估计误差均方值=',num2str(e_xrms)]); p_xrms = sqrt((norm(x_array-p_x_estimate_array)^2)/tf); disp(['PF估计误差均方值=',num2str(p_xrms)]); u_xrms = sqrt((norm(x_array-u_x_estimate_array)^2)/tf); disp(['UKF估计误差均方值=',num2str(u_xrms)]); % plot(t,e_error,'r-',t,p_error,'g--',t,u_error,'b:'); % legend('EKF估计值误差','PF估计值误差','UKF估计值误差'); t = 1 : tf; figure; plot(t,e_error,'r-',t,p_error,'g--',t,u_error,'b:'); set(gca,'FontSize',10); set(gcf,'color','White'); xlabel('时间步长');% lable --->label 我的神 ylabel('状态'); legend('EKF估计值误差','PF估计值误差','UKF估计值误差'); % toc;