Optimal federated fusion of multiple maneuvering targets based on multi-Bernoulli filters

Abstract

A federated fusion algorithm of joint multi-Gaussian mixture multi-Bernoulli (JMGM-MB) filters is proposed to achieve optimal fusion tracking of multiple uncertain maneuvering targets in a hierarchical structure. The JMGM-MB filter achieves a higher level of accuracy than the multi-model Gaussian mixture MB (MM-GM-MB) filter by propagating the state density of each potential target in the interactive multi-model (IMM) filtering manner. Within the hierarchical structure, each sensor node performs a local JMGM-MB filter to capture survival, newborn, and vanishing targets. A notable characteristic of our algorithm is a master filter running on the fusion node, which can help identify the origins of state estimates and supplement missed detections. The outputs of all filters are associated into multiple groups of single-target estimates. We rigorously derive the optimal fusion of IMM filters and apply it to merge associated single-target estimates. This optimality is guaranteed by the covariance upper-bounding technique, which can truly eliminate correlations among filters. Simulation results demonstrate that the proposed algorithm outperforms the existing centralized and distributed fusion algorithms in linear and heterogeneous scenarios, and the relative weights of the master and local filters can be adjusted flexibly.

1. Introduction

Decentralized fusion tracking of multiple maneuvering targets aims to estimate multi-target states by integrating the outputs of multiple local filters. The soft decision problem of maneuvering targets’ motion models is generally addressed by local filters (Zhao, 2024).

So far, the joint use of the jump Markov (JM) theory (Balenzuela et al., 2022) and the random finite set (RFS) filtering theory (Mahler, 2014) has been the most successful attempt at tracking multiple maneuvering targets. In the JM theory, multiple model-conditioned tracking filters are performed in parallel, and their filtering results are mutually interacted according to the Markovian chain to resolve the target dynamic model uncertainty. Inspired by the interactive multi-model (IMM) theory (Chang and Athans, 1978), the first genuine JM-RFS filter is the multi-model (MM) implementation of the probability hypothesis density (PHD) filter (Punithakumar et al., 2008), which propagates the first-order moment of the full multi-target density. An MM tracking system is constructed based on the cardinalized PHD (CPHD) filter that simultaneously propagates the multi-target PHD and its cardinality distribution (Georgescu and Willett, 2012). The multi-Bernoulli (MB) filter exhibits superiority over the PHD and CPHD filters in single-model scenarios (Vo et al., 2009; Yi et al., 2020; Hu XL et al., 2022) since it gets closer to the full multi-target density.

The work that is most representative of the MM-MB filter (Dunne and Kirubarajan, 2013; Xie XX et al., 2023) models the state probability density function (PDF) as a function of the state and model variables. Of course, there are some other implementations of the JM-RFS filter (Li WL and Jia, 2011; Wu WH et al., 2021a), such as the straightforward fitting of the dynamical state evolution matrix and the MM-labeled MB (MM-LMB) filter. An alternative to the MB-based MM filter (Wu SY et al., 2019) assigns a model probability vector to the estimate of each potential target. This vector will absorb the differences in measurement likelihoods under different models and favor the true model in combining model-conditioned estimates of the same target. Every MM-RFS filter can be implemented using the Gaussian mixture (GM) method (Dong et al., 2021; Sun YC et al., 2022) and the sequential Monte Carlo (SMC) method (Ouyang et al., 2012; Zhou et al., 2024). We proposed a joint multi-Gaussian mixture multi-Bernoulli (JMGM-MB) filter that outperforms the MM-GM-MB filter in both active and passive tracking scenarios (Xue and Feng, 2024). In this filter, each potential maneuvering target’s state estimate is characterized by a set of parallel model-related Gaussian functions with model probabilities, and a weight quantifies the possibility of this estimate. These model-related parameters are propagated in the full IMM filtering manner and thus can capture unknown target maneuvers adaptively. The JMGM-MB filter maintains the single-model MB filtering form, resulting in a more friendly compressed representation.