comparison toolboxes/FullBNT-1.0.7/Kalman/learning_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).
+% Generate data from this process, and try to learn the dynamics back.
+
+% 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 = 1;
+rand('state', seed);
+randn('state', seed);
+T = 100;
+[x,y] = sample_lds(F, H, Q, R, initx, T);
+
+% Initializing the params to sensible values is crucial.
+% Here, we use the true values for everything except F and H,
+% which we initialize randomly (bad idea!)
+% Lack of identifiability means the learned params. are often far from the true ones.
+% All that EM guarantees is that the likelihood will increase.
+F1 = randn(ss,ss);
+H1 = randn(os,ss);
+Q1 = Q;
+R1 = R;
+initx1 = initx;
+initV1 = initV;
+max_iter = 10;
+[F2, H2, Q2, R2, initx2, initV2, LL] =  learn_kalman(y, F1, H1, Q1, R1, initx1, initV1, max_iter);
+