Processing of Signals Received From Sensors Using the Extended Kalman Filter and the RLS Filter
Abstract
To improve the accuracy of measurements in smart home heating systems, this article presents digital signal processing methods using the extended Kalman filter (EKF) and the recursive least squares method (RLS). The main focus is on processing temperature and water level signals, which are often subject to noise and distortion. A comparative mathematical assessment of the quality of the signals before and after filtering was performed, including the analysis of the root-mean-square error (MSE), mean absolute error (MAE) and resistance to external interference. The analysis showed that EKF can significantly improve the accuracy of filtering, reducing errors by 4 times. The RLS method demonstrates high adaptability, but is inferior to EKF in accuracy. The implementation of the proposed methods ensures a reduction in thermal energy losses by <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$20-30 \%$</tex>. The considered approach can be effectively used to optimize heating systems in smart homes, especially in regions with harsh climatic conditions.