Abstract
This paper is concerned with the problem of multi-input multi-output, infinite time, linear time-invariant optimal coloured-noise discrete-time Kalman filter in frequency domain. A simple new algorithm is given for the solution to the steady state gain of the coloured noise of the optimum filter based on a transfer function approach. The algorithm is based on spectral factorization of the observed spectral density matrix of the filter which generates directly the return-difference matrix of the optimal filter. This leads to the proof of necessary condition of optimality of filter. The method seems to be more direct than by algebraic Riccati equation solution and can easily be implemented on a digital computer.
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