Departmental Bulletin Paper Recursive Least-Squares Wiener Fixed-Point Smoother with Uncertain Observations for Colored Observation Noise in Linear Discrete-Time Stochastic Systems


This paper proposes recursive least-squares (RLS) Wiener fixed-point smoothing and filtering algorithms with uncertain observations for colored observation noise in linear discrete-time stochastic systems. The observation equation is given by y(k) = γ(k)z(k) + v_c(k), z(k) = Hx(k), where {γ(k)} is a binary switching sequence with conditional probability, which satisfies (3). The estimators require the following information. (1) The system matrix φ for the state vector x(k). (2) The observation matrix H. (3) The variance K(k, k) of the state vector x(k). (4) The variance K_c(k, k) of the colored observation noise. (5) The system matrix φ_c for the colored observation noise v_c(k). (6) The probability p(k) = P{γ(k) = 1} that the signal exists in the uncertain observation equation and the (2,2) element [P(k
j)]_2,2 of the conditional probability of γ(k), given γ(j), 1 ≤ j < k.

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