Spectral Graph Filtering for Noisy Signals Using the Kalman filter

Noise is unwanted electrical or electromagnetic radiation that degrades the quality of the signal and the data. It can be difficult to denoise a signal that has been acquired in a noisy environment, but doing so may be necessary in a number of signal processing applications. This paper extends the issue of signal denoising from signals with regular structures, which are affected by noise, to signals with irregular structures by applying the graph signal processing (GSP) technique and a very wellknown filter, the standard Kalman filter, after adjusting it. When the modified Kalman filter is compared to the standard Kalman filter, the modified one performs better in situations where there are uncertain observations and/or processing noise and shows the best results. Also, the modified Kalman filter showed a higher efficiency when we compared it with other filters for different types of noise, which are not only standard Gaussian noises but also uniform distribution noise across two intervals for uncertain observation noise.