Multivariable frequency response methods for colored-noise optimal Kalman filter

A simple characterization of the optimal stationary continuous-time Kalman filter with colored-measurement noise is obtained in terms of the return-difference matrix for the associated feedback system in the frequency domain. The spectral factorization of the observation spectral density matrix is developed from the algebraic Riccati equation for a colored-noise optimal filter. This leads to proof of a necessary condition of optimality of a colored noise filter. A straightforward algorithm is presented for the calculation of Kalman gain matrix in the frequency domain. The algorithm is illustrated by an example