Distribution of the zero-effort miss distance estimation error in interception problems

In interception problems subject to noise corrupted measurements and random bounded target maneuvers, the miss distance is a random variable with an a-priori unknown distribution. In previous works, such a miss distance distribution could be obtained by a computational approach, assuming that the distribution of the zero-effort miss distance estimation error is known as a function of time. In this paper, this assumption is replaced by an analytical approach based on the knowledge of the measurement error distribution, the estimator structure and the (possibly non-linear) guidance law. For this purpose the shaping filter technique is used, considering that the excitation noise due to the random target maneuvers, as well as the observation noise, are Gaussian white noises. This analytical approach is illustrated by numerical examples.