**Author(s): ** Seiichi Nakamori**Journal: ** Journal of Signal and Information Processing ISSN 2159-4465

**Volume: ** 03;

**Issue: ** 03;

**Start page: ** 316;

**Date: ** 2012;

Original page**Keywords: ** Discrete-Time Stochastic System |

RLS Wiener Filte |

RLS Wiener Fixed-Point Smoother |

Colored Observation Noise |

Covariance Information**ABSTRACT**

Almost estimators are designed for the white observation noise. In the estimation problems, rather than the white observation noise, there might be actual cases where the observation noise is modeled by the colored noise process. This paper examines to design a new estimation technique of recursive least-squares (RLS) Wiener fixed-point smoother and filter for colored observation noise in linear discrete-time wide-sense stationary stochastic systems. The observation

*y(k)* is given as the sum of the signal

*z(k)*=

*Hx(k)* and the colored observation noise

*vc(k)*. The RLS Wiener estimators explicitly require the following information: 1) the system matrix for the state vector

*x(k)*; 2) the observation matrix

*H*; 3) the variance of the state vector

*x(k)*; 4) the system matrix for the colored observation noise

*vc(k)*; 5) the variance of the colored observation noise; 6) the input noise variance in the state equation for the colored observation noise.

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