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Set based tracking in clutter as a percolation process

In this paper, we investigate the performance of a set based tracker in clutter with no target present. If there is a positive probability of clutter-only tracks lasting an infinite time in such an environment, then a tracker cannot be expected to perform well under these clutter conditions when a target is present. In order to analyze the problem, a continuous space model is simplified and discretised. It is shown that this discretised model is a percolation process, which undergoes a phase transition. This means that there exists a critical false alarm probability for the system, below which clutter tracks die out infinite time, and above which clutter tracks have a positive probability of surviving indefinitely. A theoretical lower bound for this critical clutter probability is derived, which is then verified by Monte Carlo simulation.