Steady-state Kalman Filter

The steady state of continuous_continuous Kalman filter which is equivalent to when time derivative of P(t) goes to zero and reduces the Differential Riccati equation to the Continuous Algebraic Riccati equation (works in Matlab only). The code example is available in matlab_implementation/steady_state/examples/ss_example.m and the code for the filter is in matlab_implementation/steady_state of https://github.com/mannyray/KalmanFilter:

clear all;
addpath('..');
C = [1, 0.1]; %observation matrix to obtain measurement y (y = C*x + noise)
A = [-1,0.2;-0.1,-1]; %(d/dt)x(t) = A*x(t)
R_c = [0.1^2]; %continuous sensor noise
Q_c = [0.001^2,0;0,0.001^2]; %continuous process noise

P_steady = sskf(A,C,Q_c,R_c)

produces

ans = 

1.0e-06 *

 0.504888842491879   0.024508560851831
 0.024508560851831   0.497548868161834