Theoretical Performance Bounds of Model-Based Electrocardiogram Parameter Estimation

Abstract

<div>Objective: Clinical parameter estimation from the electrocardiogram (ECG) is a recurrent field of research. It is debated that ECG parameter estimation performed by human experts and machines/algorithms is always model-based (implicitly or explicitly). Therefore, depending on the selected data-model, the adopted estimation scheme (least-squares error, maximum likelihood, or Bayesian), and the prior assumptions on the model parameters and noise distributions, any estimation algorithm used in this context has an upper performance bound, which is not exceedable (for the same model and assumptions).</div><div><br></div><div>Method: 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 bases expansions (including polynomials) and sum of Gaussian functions.</div><div><br></div><div>Results: The developed framework is evaluated over real and synthetic data, for three popular applications: T/R ratio estimation, ST-segment analysis and QT-interval estimation, using the state-of-the-art estimators in each context, and compared with the derived theoretical CRLBs.</div><div>Conclusion and Significance: The proposed framework and the derived CRLBs provide fact-based guidelines for the selection of data-models, sampling frequency (beyond the Nyquist requirements), modeling segment length, the number of beats required for average ECG beat extraction, and other factors that influence the accuracy of ECG-based clinical parameter estimation.</div>