Modeling of local search for track updates in phased array radar tracking

A distinctive aspect of a phased array radar is that its beam can be positioned repeatedly, if necessary, in an allocation for a track update. When the first beam of the allocation fails to detect a return, a local search process is enforced by successively positioning the beam toward the predicted target position and its neighborhood until a successful track update is made. The local search can be characterized in terms of the events that can occur in the process and the probabilities of those events. In predicting the event probabilities, it is required to evaluate the expectation of a product of target detection probabilities of successive illuminations. In this paper, approximate but analytic and efficient expressions are presented for the expectation of a product of detection probabilities and angular measurement accuracy of detection for repeated beam-positioning.