comparison toolboxes/FullBNT-1.0.7/Kalman/tracking_demo.m @ 0:e9a9cd732c1e tip

first hg version after svn

+% Make a point move in the 2D plane
+% State = (x y xdot ydot). We only observe (x y).
+
+% This code was used to generate Figure 15.9 of "Artificial Intelligence: a Modern Approach",
+% Russell and Norvig, 2nd edition, Prentice Hall, 2003.
+
+% X(t+1) = F X(t) + noise(Q)
+% Y(t) = H X(t) + noise(R)
+
+ss = 4; % state size
+os = 2; % observation size
+F = [1 0 1 0; 0 1 0 1; 0 0 1 0; 0 0 0 1]; 
+H = [1 0 0 0; 0 1 0 0];
+Q = 0.1*eye(ss);
+R = 1*eye(os);
+initx = [10 10 1 0]';
+initV = 10*eye(ss);
+
+seed = 9;
+rand('state', seed);
+randn('state', seed);
+T = 15;
+[x,y] = sample_lds(F, H, Q, R, initx, T);
+
+[xfilt, Vfilt, VVfilt, loglik] = kalman_filter(y, F, H, Q, R, initx, initV);
+[xsmooth, Vsmooth] = kalman_smoother(y, F, H, Q, R, initx, initV);
+
+dfilt = x([1 2],:) - xfilt([1 2],:);
+mse_filt = sqrt(sum(sum(dfilt.^2)))
+
+dsmooth = x([1 2],:) - xsmooth([1 2],:);
+mse_smooth = sqrt(sum(sum(dsmooth.^2)))
+
+
+figure(1)
+clf
+%subplot(2,1,1)
+hold on
+plot(x(1,:), x(2,:), 'ks-');
+plot(y(1,:), y(2,:), 'g*');
+plot(xfilt(1,:), xfilt(2,:), 'rx:');
+for t=1:T, plotgauss2d(xfilt(1:2,t), Vfilt(1:2, 1:2, t)); end
+hold off
+legend('true', 'observed', 'filtered', 3)
+xlabel('x')
+ylabel('y')
+
+
+
+% 3x3 inches
+set(gcf,'units','inches');
+set(gcf,'PaperPosition',[0 0 3 3])  
+%print(gcf,'-depsc','/home/eecs/murphyk/public_html/Bayes/Figures/aima_filtered.eps');
+%print(gcf,'-djpeg','-r100', '/home/eecs/murphyk/public_html/Bayes/Figures/aima_filtered.jpg');
+
+
+figure(2)
+%subplot(2,1,2)
+hold on
+plot(x(1,:), x(2,:), 'ks-');
+plot(y(1,:), y(2,:), 'g*');
+plot(xsmooth(1,:), xsmooth(2,:), 'rx:');
+for t=1:T, plotgauss2d(xsmooth(1:2,t), Vsmooth(1:2, 1:2, t)); end
+hold off
+legend('true', 'observed', 'smoothed', 3)
+xlabel('x')
+ylabel('y')
+
+
+% 3x3 inches
+set(gcf,'units','inches');
+set(gcf,'PaperPosition',[0 0 3 3])  
+%print(gcf,'-djpeg','-r100', '/home/eecs/murphyk/public_html/Bayes/Figures/aima_smoothed.jpg');
+%print(gcf,'-depsc','/home/eecs/murphyk/public_html/Bayes/Figures/aima_smoothed.eps');