New RLS Wiener Smoother for Colored Observation Noise in Linear Discrete-time Stochastic Systems

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In the estimation problems, rather than the white observation noise, there are cases where the observation noise is modeled by the colored noise process. In the observation equation, the observed value ) (k y is given as a sum of the signal ) ( ) ( k Hx k z  and the colored observation noise ) (k vc . In this paper, the observation equation is converted to the new observation equation for the white observation noise. In accordance with the observation equation for the white observation noise, this paper proposes new RLS Wiener estimation algorithms for the fixed-point smoothing and filtering estimates in linear discrete-time wide-sense stationary stochastic systems. The RLS Wiener estimators require the following information: (a) the system matrix for the state vector ) (k x ; (b) the observation matrix H ; (c) the variance of the state vector ) (k x ; (d) the system matrix for the colored observation noise ) (k vc ; (e) the variance of the colored observation noise.