Efficient Bayesian ECG denoising using adaptive covariance estimation and nonlinear Kalman Filtering

Abstract

Model-based Bayesian methods for denoising electrocardiogram (ECG) signals have demonstrated promise in preserving ECG morphology and diagnostic properties. These methods are effective for preserving and enhancing the features of ECG signals. However, their performance heavily relies on accurately selecting model parameters, particularly the state and measurement noise covariance matrices. Some of these frameworks also involve computationally intensive computations and loops for state estimation. To address these problems, in this study, we propose a novel approach to improve the performance of several model-based Bayesian frameworks, including the extended Kalman filter/smoother (EKF/EKS), unscented Kalman filter/smoother (UKF/UKS), cubature Kalman filter/smoother (CKF/CKS), and ensemble Kalman filter/smoother (EnKF/EnKS), specifically for ECG denoising tasks. Our methodology dynamically adjusts the state and measurement covariance matrices of the filters using outputs from nonlinear Kalman-based filtering methods. For each filter, we develop a unique approach based on the theoretical foundations of that filter. Additionally, we introduce two distinct strategies for updating these matrices, considering whether the noise in the signals is stationary or nonstationary. Furthermore, we propose a computationally efficient method that significantly reduces the calculation time required for implementing CKF/CKS, UKF/UKS, and EnKF/EnKS frameworks, while maintaining their denoising performance. Our approach can achieve a 50 % reduction in computation time for these frameworks, effectively making them twice as fast as their original implementations We thoroughly evaluated our approach by comparing denoising performance between the original filters and their adaptive versions, as well as against the state-of-the-art marginalized particle extended Kalman filter (MP-EKF). The evaluation utilized various normal ECG segments obtained from different records. The results demonstrate that the adaptive adjustment of covariance matrices significantly improves the denoising performance of nonlinear Kalman-based frameworks in both stationary and non-stationary environments, achieving performance comparable to that of the MP-EKF framework.