The probabilities of track initiation and loss using a sliding window for track acquisition

An analytical model is provided which describes the tracking process that evolves from a sequence of detection opportunities. We assume a sliding window of length N, with M (M ≤ N) detections required for track acquisition, and L consecutive misses required for loss of track. We provide a recursive solution for the probabilities of acquisition, loss, and being in track, and then define the distributions of the times of acquisition, loss, and duration for each track and gap that can develop. There are no restrictions on M, N, L, or on a varying sequence of associated detection probabilities. Numerical results are provided for typical cases.