www.pudn.com > kalmanmatalab.rar > AR_to_SS.m, change:2000-04-24,size:1107b

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)