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

first hg version after svn

+function [F,H,Q,R,initx, initV] = AR_to_SS(coef, C, y)
+%
+% Convert a vector auto-regressive model of order k to state-space form.
+% [F,H,Q,R] = AR_to_SS(coef, C, y)
+% 
+% X(i) = A(1) X(i-1) + ... + A(k) X(i-k+1) + v, where v ~ N(0, C)
+% and A(i) = coef(:,:,i) is the weight matrix for i steps ago.
+% We initialize the state vector with [y(:,k)' ... y(:,1)']', since
+% the state vector stores [X(i) ... X(i-k+1)]' in order.
+
+[s s2 k] = size(coef); % s is the size of the state vector
+bs = s * ones(1,k); % size of each block
+
+F = zeros(s*k);
+for i=1:k
+   F(block(1,bs), block(i,bs)) = coef(:,:,i);
+end
+for i=1:k-1
+  F(block(i+1,bs), block(i,bs)) = eye(s);
+end
+
+H = zeros(1*s, k*s);
+% we get to see the most recent component of the state vector 
+H(block(1,bs), block(1,bs)) = eye(s); 
+%for i=1:k
+%  H(block(1,bs), block(i,bs)) = eye(s);
+%end
+
+Q = zeros(k*s);
+Q(block(1,bs), block(1,bs)) = C;
+
+R = zeros(s);
+
+initx = zeros(k*s, 1);
+for i=1:k
+  initx(block(i,bs)) = y(:, k-i+1); % concatenate the first k observation vectors
+end
+
+initV = zeros(k*s); % no uncertainty about the state (since perfectly observable)