% example ch13ex12.m
% Illustrates construction of the Kalman filter
clc
echo on

A=[-1 0
   0 -2];
B=[0 0];B=B';
 G=[1
1];
C=[0 1];
D=[0];
Q=[1];R=[1];
[L,P,E]=lqe(A,G,C,Q,R)
[ae,be,ce,de]=estim(A,B,C,D,L)
% This computes the estimator
% Now convert to transfer function form

[num,den]=ss2tf(ae,be,ce,de)
% note that there are three rows corresponding to the three states: x1,x2 and z
% y corresponds to x2. Hence the second row gives the transfer function for the estimator