Consensus-Based Distributed Nonlinear Filtering With Kernel Mean Embedding

This article proposes a consensus-based distributed nonlinear filter with kernel mean embedding (KME) to fill the gap of kernel-based filters for distributed sensor networks. Specifically, to approximate the posterior distribution, the system state is embedded into a higher dimensional reproducing kernel Hilbert space (RKHS), and then the nonlinear measurement function is linearly represented. As a result, an update rule for the KME of posterior distribution is established in the RKHS. To demonstrate that the proposed distributed filter can achieve centralized estimation accuracy, a centralized filter is first developed by extending the standard Kalman filter in the state space to the RKHS. Then, the proposed distributed filter is proved to be equivalent to the centralized one. Two examples highlight the effectiveness of the developed filters in target tracking scenarios, including a nearly constantly moving target and a turning target, respectively, with range, bearing, and range-rate measurements.