Abstract
This letter concerns distributed spatial filtering over networked systems, i.e., transforming signal values given for nodes to those with a desired spatial frequency characteristic via a distributed computation. An existing filtering algorithm can achieve only low-pass filter characteristics, which limits its range of applications. To address this limitation, we extend the aforementioned filtering algorithm using an additional design parameter. We then present a characterization of all the realizable filter characteristics as a necessary and sufficient condition for achieving distributed spatial filtering. As a result, it is shown that the extended algorithm increases the range of the realizable filter characteristics. The proposed method is verified not only by simulation but also by denoising experiments for a real sensor network. The results show that the proposed method effectively reduces spatial noise and achieves higher performance than an average consensus algorithm and an average filter.
Highlights
N ETWORKED systems, in which subsystems are interconnected through networks, are of great interest in the field of systems and control
An example of low-pass filtering is illustrated in Fig. 1, where xi is the signal value for node i and we assume that the nodes with close indices
2) We demonstrate the effectiveness of our distributed spatial filtering (DSF) method through experiments, using a real sensor network
Summary
N ETWORKED systems, in which subsystems (i.e., nodes) are interconnected through networks, are of great interest in the field of systems and control. Typical tasks, e.g., consensus [1], [2] and formation [3], [4], have been well studied, whereas here, we consider a different task, namely distributed spatial filtering (DSF). In this task, the nodes obtain signal values with a desired spatial frequency characteristic from given ones only through local communications. When measuring temperature at different locations using a sensor network, spatial low-pass filtering is useful for reducing the measurement noise.
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