Data Denoising of Sensor Network Using Polynomial Graph Filter Designed by Gegenbauer Polynomial

Sensor networks play a crucial role in smart cities, with applications such as remote environmental monitoring and target tracking. A major challenge in data collection is the corruption of measurement data by unwanted noise, necessitating the development of effective data denoising methods. In this paper, the sensor network is modeled as a graph consisting of nodes and edges, allowing the application of graph filtering techniques from graph signal processing to address the denoising problem. The proposed approach involves several key steps: First, the transfer matrix of the graph filter is expressed as a linear combination of Gegenbauer polynomials, which generalize Legendre and Chebyshev polynomials. Second, the filter coefficients are determined by minimizing the integral weighted least squares error between actual and ideal spectral responses. Third, design examples of frequency-selective graph filters are presented. Fourth, an implementation structure for the designed filter is derived using the recurrence relation of Gegenbauer polynomials. Finally, the effectiveness of the proposed method is demonstrated through its application to temperature data denoising in the sensor networks at USA and Taiwan.