Fusion Strategies in Multiple Particle Filtering in the Presence of Shared Unknown Static Parameters

The multiple particle filter (MPF) was proposed as a way to tackle online hidden states estimation for high-dimensional scenarios, where traditional PFs fail due to the curse of dimensionality. MPF works by partitioning the state into substates and assigning a separate PF to track each substate, while maintaining mutual communication between the employed filters. Like standard PFs, a common problem in MPFs is dealing with unknown static parameters in the model. However, unlike in standard PFs, estimation of these parameters in MPF requires more caution as the parameters can be shared across partitions. Such a scenario calls for fusion of information between partitions and problem becomes even more challenging when the observations in the model are interacting, i.e., when at least one measured data point is a function of more than one hidden state. In this work, we propose general fusion approaches in MPF for the estimation of static parameters shared across partitions. The proposed strategies use weights to quantify the contribution of each partition to the final estimation and can be applied to the general case with interacting observations. We demonstrate the performance of the proposed method on simulated data and showcase its benefits over several competing approaches.