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

2025-02-09

AI Summary

Existing distributed Gaussian process (DGP) methods for online, distributed estimation of unknown scalar fields in wireless sensor networks (WSNs) suffer from high computational and communication overheads, as well as slow consensus convergence. Method: This paper proposes a Kalman-filter-enhanced DGP (K-DGP) framework—the first to integrate Kalman filtering into the DGP architecture—combined with nonlinear basis function approximation and a column-preserving consensus protocol. Contribution/Results: K-DGP significantly reduces per-node computational complexity and communication load. Theoretical analysis and simulations demonstrate that K-DGP maintains estimation accuracy while accelerating consensus convergence by over 50%, enabling real-time field modeling in dynamic environments. It exhibits strong scalability and robustness, establishing a novel low-overhead, high-accuracy paradigm for collaborative field estimation in large-scale WSNs.

Technology Category

• Intelligent Robots: State Estimation
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Search and Optimization: Distributed Search

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

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.

Problem

• Estimates unknown scalar fields in WSNs.
• Reduces computational and communication complexities.
• Enhances consensus convergence and estimation accuracy.

Innovation

• Kalman filter in distributed Gaussian process
• New consensus protocol for data transmission
• Linear scalability with basis functions