Diffusion Field Estimation Using Decentralized Kernel Kalman Filter with Parameter Learning Over Hierarchical Sensor Networks

In this paper, a task is addressed to track a nonlinear time-varying diffusion field based on data collected by sensor networks. By exploiting kernel methods, the nonlinear field function is approximated by a linear combination of kernel functions in a reproducing kernel Hilbert space (RKHS). To capture the dynamical property of a diffusion field and the relation of system input and output data, a state-space model on weights of these kernel functions is constructed with unknown process noise. Thus, the nonlinear tracking problem is transformed into a linear state estimation solved by Kalman filter. Further, this kernel Kalman filter (KKF) is decomposed into a decentralized fashion in a way to collect sensor data efficiently over a hierarchical network structure with different clusters. To adapt the algorithm to unknown process noise, a decentralized variational Bayesian KKF is proposed to learn the distributions of system unknown variables.