Retrodiction of Data Association Probabilities via Convex Optimization

In a surveillance environment with high clutter, finding the correct measurement to track associations becomes extremely important for efficient target tracking. This study offers a novel algorithm to retrodict the data association probabilities at any past time instant, when the batch set of measurements is kept in memory. For the retrodiction procedure, the batch association cost is first written explicitly as a binary integer optimization problem with a quadratic cost function and it is shown that the relaxed form of the problem is convex. From the relaxed problem, a lower bound for the optimal association cost is derived, and this lower bound is used as the data association probabilities pertaining to that selected time instant in the past. Due to its consideration of the batch set of data in a retrospective manner, we will call this algorithm as Retrodictive Probabilistic Data Association, RPDA. For simplification of the mathematical analysis, a single point target with no missing measurements, i.e. P
_D
= 1, is taken into account.