Kalman-Bucy filter for optimum radio-inertial navigation

A seemingly paradoxical situation existed in the Kalman-Bucy formulation of a problem of optimum radio-inertial navigation. The difficulty is traced to the a priori information used in the estimate and variance equations. The reason for the existence of an improved a priori estimate is given. It is shown that with the improved a priori information as initial conditions, the Kalman-Bucy filter gives the same result as that obtained by Peterson originally using the integral equation approach.