A = [0 1; 0 0];
B = [0; 1];
C = [1 0];
D = 0;

r0 = 10000; dr0 = -150;     % initial conditions
Sw = 900;                   % spectral density for disturbance
Sv = 3600;                  % spectral density for noise
Sigma_e_0 = [1e6 0; 0 4e5]; % covariance matrix for initial estimation error

[Sigma_e_infinity,V,L] = care(A',C',B*Sw*B',Sv)
L = L';

%% Building Kalman filter as a dynamic system

Ak = (A-L*C);
Bk = [B L];

F = ss(Ak,Bk(:,2),eye(2,2),zeros(2,1))

%% Designing Kalman filter using high level Matlab function KALMAN
G = ss(A,B,C,D);
[K,E,P] = kalman(G,Sw,Sv)
K = K(2:3,:)

%% Setting the simulation parameters

tc = 0.1;
piw = tc*Sw;
piv = tc*Sv;