Multiple Detection Bernoulli Filter Based on Forward and Backward Frame Association

‍ ‍The Bernoulli filter is the sole single-target tracking filter in the random finite set （RFS） framework. It is theoretically the optimal filter for single target tracking achieved by propagating the complete Probability Density Function （PDF） of the target during the recursive process. The classical Bernoulli filter assumes that the target generates at most one measurement from the measurement model at each moment. Therefore， when a single target generates multiple detections， the classical Bernoulli filter tends to produce incorrect target state estimation and trajectory. To effectively address tracking challenges in scenarios where a solitary target results in multiple detections， scholars have introduced several iterations of the Bernoulli filter concept. These multiple detection Bernoulli filters were designed to handle the complexities introduced by a single target potentially generating numerous detection results. Despite the effectiveness of the multiple detection Bernoulli filter handling multiple detections for a single target， the high computational load of calculating all possible subsets of the measurement set remains a major challenge. To overcome this， a variety of partitioning algorithms were developed， which optimize the process by working with part of the subset rather than the entirety of the measurement collection. However， many of these partitioning strategies predominantly focus on the current measurements， neglecting the integration of valuable motion dynamics captured during the recursive steps of the Bernoulli filter operation. To address the computational complexity of the filter， the Hungarian algorithm is innovatively incorporated into the multiple detection Bernoulli filter design in this work. The Hungarian algorithm， which is widely used in video multi-target tracking algorithms， is used to complete the association between the observation set and the prediction target set， achieving good results. This integration led to the development of a novel multiple detection Bernoulli filter based on forward and backward frame association on the basis of the Hungarian algorithm. This state-of-the-art filter harnesses the estimated target state from the preceding frame and the measurement data of the subsequent frame to perform correlations. The correlated outcomes then guide the selection of the most appropriate measurement subset for the filter update or correction phase. By leveraging the dynamic information contained within sequential frames， the algorithm could pinpoint and utilize the measurement cluster that most accurately reflects the actual position of the target. This strategic approach substantially curtails the computational demands of the multiple detection Bernoulli filter while maintaining its tracking performance fidelity. To illustrate the performance of the proposed algorithm， this study adopts the Over-the-horizon Radar （OTHR） measurement model as the multiple detection target measurement model during the simulation. Comprehensive simulations have demonstrated that the new methodology substantially reduces computational complexity without compromising tracking efficacy. Compared to traditional multiple detection Bernoulli filters， which exhaustively process all subsets or part of the subset of the measurement set， this refined method promises enhanced efficiency. Its capacity to maintain stable performance even under reduced computational loads makes it an attractive solution for target tracking applications that demand high-speed， real-time responses.