k-NN Adaptive IPLF–PMBM Underwater Multi-Target Tracking Algorithm

The Poisson multi-Bernoulli mixture (PMBM) filter performs well in active sonar tracking, but its standard form assumes a single, globally preset clutter intensity, which matches poorly the range-dependent reverberation of the underwater channel. This paper applies the iterated posterior linearization filter (IPLF) within the PMBM recursion and proposes a k-nearest-neighbor (k-NN) estimator of the local clutter intensity, in which the distance to the k-th neighbor of each measurement sets an adaptive bandwidth and the intensity entering the newborn existence probability comes from the measurements rather than from a preset. In batch form the pairwise distance matrix is formed once per frame, at a cost of 0.14 ms per frame for about ninety measurements. In a power-law clutter scenario, the method reaches a generalized optimal sub-pattern assignment (GOSPA) value of 11.13, which is 22.9% below the standard filter at a preset that underestimates the clutter level, with the difference carried by the false-alarm term. A preset sweep shows that the best fixed value, 11.23, is reached only when the preset is tuned after the fact, and the adaptive method matches it without tuning. The result varies by less than 0.07 over neighbor counts from 8 to 90, and a uniform-clutter control shows that the adaptation neither helps nor harms when the clutter has no spatial structure.