Distributed SMC-PHD Fusion for Partial, Arithmetic Average Consensus

We propose an average consensus approach for distributed SMC-PHD (sequential Monte Carlo-probability hypothesis density) fusion, in which local filters extract Gaussian mixtures (GMs) from their respective particle posteriors, share them (iteratively) with their neighbors and finally use the disseminated GM to update the particle weight. The resulting particle distribution is the arithmetic average of the disseminated GM-posteriors. There are two distinguishable features of our approach compared to exiting approaches. First, a computationally efficient particles-to-GM (P2GM) conversion scheme is developed based on the unique structure of the SMC-PHD updater in which the particle weight can be exactly decomposed with regard to the measurements and misdetection. Only significant components of higher weight are utilized for parameterization and so the disseminated information is only a part of that of local posteriors. The consensus, conditioned on partial information dissemination over the network, is called “partial consensus”. Second, importance sampling (IS) is employed to re-weight the local particles for integrating the received GM information, without changing the states of the particles. By this, the local prior PHD and likelihood calculation can be carried out in parallel to the dissemination & fusion procedure. To assess the effectiveness of the proposed P2GM parameterization approach and IS approach, two relevant yet new distributed SMC-PHD fusion protocols are introduced for comparison. One uses the same P2GM conversion and GM dissemination schemes as our approach but local particles are regenerated from the disseminated GMs at each filtering iteration in place of the IS approach. This performs similar to our IS approach (as expected) but prevents any parallelization as addressed above. The other is disseminating the particles between neighbors in place of the P2GM conversion. This avoids parameterization but is communicatively costly. This protocol, essentially seeking complete (posterior) consensus, however, does not perform better than the GM-dissemination based partial consensus. Different to these arithmetic average consensus approaches, the state-of-theart exponential mixture density approach that seeks geometric average consensus is also realized for comparison.