Theoretical Performance Bounds of Model-Based Electrocardiogram
Parameter Estimation
Abstract
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).
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.
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.
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.