Distributed Kalman Filter with a Gaussian Process for Machine Learning

Distributed estimation is a fundamental problem of sensor networks, in which each node leverages information from neighboring nodes to calculate estimates while maintaining a consensus on those estimates. Estimates may include both the state of the dynamical system and the parameters defining a model of that system. However, the dynamical model may be unknown, time-varying, or contain errors, prompting the need for an adaptive component to learn the dynamics. Adaptive methods have been scarcely addressed in the context of distributed estimation. The novelty of this paper is formulating a methodology involving state estimation, parameter estimation, and consensus filtering. The chosen components include a recursive form of Gaussian process regression for parameter estimation while a distributed Kalman filter enables the consensus and state estimation. Furthermore, this paper derives the objective function and gradient equations for a gradient-based optimization of the parameters defining the dynamical model. Lastly, a simulation demonstrates the distributed estimation capability with a comparison to a centralized solution.