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In many cases, the error covariance matrix P(nln) will converge to a steady-state value Pas n → ∞. Assume that C, Qw, and Qv are the limiting values of C(n), Qw(n), and Qv(n), respectively.
(a) For A(n) = I, show that if P(n|n) converges to a steady state value P, then the limiting value satisfies the algebraic Ricatti equation PCH(CPCH + Qv)-1 P- Qw = 0
(b) Derive the Ricatti equation for a general state transition matrix A(n) that has a limiting value of A.
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