Kalman Filter-Based Distributed Gaussian Process for Unknown Scalar Field Estimation in Wireless Sensor Networks

In this letter, we propose an online scalar field estimation algorithm of unknown environments using a distributed Gaussian process (DGP) framework in wireless sensor networks (WSNs). While the kernel-based Gaussian process (GP) has been widely employed for estimating unknown scalar fields, its centralized nature is not well-suited for handling a large amount of data from WSNs. To overcome the limitations of the kernel-based GP, recent advancements in GP research focus on approximating kernel functions as products of E-dimensional nonlinear basis functions, which can handle large WSNs more efficiently in a distributed manner. However, this approach requires a large number of basis functions for accurate approximation, leading to increased computational and communication complexities. To address these complexity issues, the paper proposes a distributed GP framework by incorporating a Kalman filter scheme (termed as K-DGP), which scales linearly with the number of nonlinear basis functions. Moreover, we propose a new consensus protocol designed to handle the unique data transmission requirement residing in the proposed K-DGP framework. This protocol preserves the inherent elements in the form of a certain column in the nonlinear function matrix of the communicated message; it enables wireless sensors to cooperatively estimate the environment and reach the global consensus through distributed learning with faster convergence than the widely-used average consensus protocol. Simulation results demonstrate rapid consensus convergence and outstanding estimation accuracy achieved by the proposed K-DGP algorithm. The scalability and efficiency of the proposed approach are further demonstrated by online dynamic environment estimation using WSNs.