Chandrasekhar-type filter using covariance information for white Gaussian plus colored observation noise

Abstract

This paper proposes recursive least-squares (RLS) Chandrasekhar-type filtering equations using the covariance information in the case of white Gaussian plus colored observation noise in linear continuous-time wide-sense stationary stochastic systems. Here, it is assumed that the system matrices in the state-space models for the signal and the colored noise, the cross-variance functions of the state variables for the signal and the colored noise with the observed value, the observation vectors for the signal and the colored noise, the variance of white Gaussian noise and the observed value are known. The number of differential equations included in the current Chandrasekhar-type filter is less than the previous filter using the covariance information. The Chandrasekhar-type equations are derived based on the invariant imbedding method. The Chandrasekhar-type filter brings numerically efficient algorithm in computation time.