srfaur

square-root algorithm

Calling Sequence

[p,s,t,l,rt,tt]=srfaur(h,f,g,r0,n,p,s,t,l)

Arguments

:h, f, g convenient matrices of the state-space model. : :r0 E(yk*yk’). : :n number of iterations. : :p estimate of the solution after n iterations. : :s, t, l intermediate matrices for successive iterations; : :rt, tt gain matrices of the filter model after n iterations. : :p, s, t, l may be given as input if more than one recursion is

desired (evaluation of intermediate values of p).

:

Description

square-root algorithm for the algebraic Riccati equation.

Examples

//GENERATE SIGNAL
x=%pi/10:%pi/10:102.4*%pi;
`rand`_('seed',0);`rand`_('normal');
y=[1;1]*`sin`_(x)+[`sin`_(2*x);`sin`_(1.9*x)]+`rand`_(2,1024);

//COMPUTE CORRELATIONS
c=[];for j=1:2,for k=1:2,c=[c;`corr`_(y(k,:),y(j,:),64)];end;end
c=`matrix`_(c,2,128);

//FINDING H,F,G with 6 states
hk=`hank`_(20,20,c);
[H,F,G]=`phc`_(hk,2,6);

//SOLVING RICCATI EQN
r0=c(1:2,1:2);
[P,s,t,l,Rt,Tt]=srfaur(H,F,G,r0,200);

//Make covariance matrix exactly symmetric
Rt=(Rt+Rt')/2

See Also

• phc Markovian representation
• faurre filter computation by simple Faurre algorithm
• lindquist Lindquist’s algorithm