A geometry aware particle filter for bearings-only tracking using inferred range estimates

Bearings-only tracking (BOT), which is of significant importance in underwater surveillance applications employing passive sonar systems, involves estimating the dynamic state of a target using only angle (bearing) measurements. In the absence of direct range information, BOT constitutes a nonlinear and partially observable state estimation problem, for which Bayesian particle filters provide a natural framework for inference. However, standard particle filters often suffers from sample impoverishment, also called degeneracy, primarily due to the use of importance proposals that do not adequately align with the underlying measurement geometry. This problem is addressed in the literature using two strategies, (a) sequential importance sampling variants, and (b) range inclusion variants. Yet, these methods still struggle in challenging scenarios when measurements are noisy or when the target is close to the observer, wherein small angular errors cause large position uncertainty. In this paper, we propose a PF scheme that leverages velocity projections along the bearing direction to infer a range for each particle. This inferred range is then used to sample particle positions along the bearing line, aligning the proposal distribution with the likely measurement geometry. This strategy improves sample efficiency and enables more accurate tracking, particularly in challenging scenarios. Theoretical analysis and simulations establish that the proposed method outperforms state-of-the-art in tracking accuracy and tolerance to degeneracy.