Abstract
This paper is concerned with the distributed field estimation problem using a sensor network, and the main purpose is to design a local filter for each sensor node to estimate a spatially-distributed physical process using the measurements of the whole network. The finite element method is employed to discretize the infinite dimensional process, which is described by a partial differential equation, and an approximate finite dimensional linear system is established. Due to the sparsity on the spatial distribution of the source function, the -regularized filtering is introduced to solve the estimation problem, which attempts to provide better performance than the classical centralized Kalman filtering. Finally, a numerical example is provided to demonstrate the effectiveness and applicability of the proposed method.
Highlights
Many spatially-distributed physical phenomena are modeled as scalar or vector fields, which are governed by partial differential equations (PDEs), e.g., the distribution of temperature, the concentration of pollutants in atmosphere or water and the dynamics of flows
Due to the constraints on energy and communication bandwidth of a single sensor node, distributed information processing is usually employed in wireless sensor networks
This paper investigated the scalar field estimation problem with the measurements from a sensor network
Summary
Many spatially-distributed physical phenomena are modeled as scalar or vector fields, which are governed by partial differential equations (PDEs), e.g., the distribution of temperature, the concentration of pollutants in atmosphere or water and the dynamics of flows. A distributed high-pass consensus filter was used to fuse local measurements, such that all sensor nodes could track the average measurement of the whole network These algorithms are established based on the information form of Kalman filtering, and analyses of the stability and performance of the Kalman-consensus filter have been provided in [4]. The distributed estimation problems were discussed for mobile sensor networks in [8], and a two-stage extended Kalman-consensus filter algorithm was proposed. In [14], the spatial domain was decomposed into some overlapping subdomains to assign a communication network, and the parallel Schwartz method was employed to form a consensus strategy for the local Kalman filters on each sensor node.
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