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

TL;DR

This paper introduces a scalable, distributed Gaussian process algorithm using Kalman filtering for efficient scalar field estimation in wireless sensor networks, improving convergence speed and accuracy.

Contribution

It proposes a novel Kalman filter-based distributed Gaussian process framework that reduces computational complexity and enhances consensus speed in large-scale sensor networks.

Findings

Rapid consensus convergence demonstrated in simulations

High estimation accuracy achieved in dynamic environments

Scalable approach suitable for large WSNs

Abstract

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.