Filtering for linear systems with shifted noises

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Abstract
In this paper a method of approximation of a white noise by wide band noises is developed and based on this the complete set of equations of the Kalman type optimal filter for the linear signal-observation system with the signal noise delaying the observation noise is deduced. The respective Riccati equation is found as a system of equations containing partial differential equations. A possible application of the results to navigation and guidance of spacecrafts is discussed.