Target Tracking: Uniformly Directed Motion from a Normally Distributed Position
CENTER FOR NAVAL ANALYSES ALEXANDRIA VA SYSTEMS EVALUATION GROUP
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Following observations of a target position, a set of probabilities, or a position density function, is obtained. If no further information is available, the corresponding probabilities or density function, after a time interval of arbitrary duration, are obtained from the initial probabilities, and an assumed distribution of target course and speed. Point by point computation of the final position probabilities is always possible, but such a procedure is inefficient where all of the distributions may be specified by means of a few parameters. In this case, a preferred approach is to derive the form of the final position density and compute the values of the parameters necessary for a complete specification from the values of the parameters of the initial position density and the assumed distribution of course and speed. In this research contribution, the initial position density is bivariate normal. It is assumed that the distribution of target speed may be approximated by a discrete distribution and that the distribution of target course is independent of speed and uniform on the interval 0 to 2 pi. It is shown that the final position density is expressible as an infinite series of Modified Bessel Functions and that a formal similarity with a well-documented density could be utilized in the computation of its values.
- Statistics and Probability