Cramér-Rao Lower Bounds of Model-Based Electrocardiogram Parameter Estimation

Abstract

Clinical parameter estimation from the electrocardiogram (ECG) is a recurrent field of research. It is debated that ECG parameters estimated by human experts and machines/algorithms is always model-based (implicitly or explicitly). Therefore, all estimation algorithm used in this context have performance bounds in terms of the achievable mean squared error, which are not exceedable. These bounds depend on the adopted data-model, the estimation scheme (least-squares error, maximum likelihood, or Bayesian), and prior assumptions on the model parameters and noise distributions. In this research, we develop a comprehensive theoretical framework for ECG parameter estimation and derive the Cramér-Rao lower bounds (CRLBs) for the most popular signal models used in the ECG modeling literature, namely functional expansions (including polynomials) and sum of Gaussian functions. The developed framework is evaluated over real and synthetic data for three popular applications: T-to-R wave ratio estimation, ST-segment analysis and QT-interval estimation, using the state-of-the-art estimators in each context. The proposed framework and the derived CRLBs provide practical guidelines for the selection of data-models, sampling frequency (beyond the Nyquist rate), modeling segment length, number of beats required for ECG beat averaging, and other factors that influence the accuracy of ECG-based clinical parameter estimation.