Maximum likelihood cardiac conduction velocity estimation in the presence of ambiguities in the locations and activation times of the recording points

The cardiac conduction velocity vector (CCVV) provides valuable information that is used to distinguish/treat various heart diseases. The CCVV can be estimated using the intracardiac electrograms; i.e., the activation times (ATs) and locations of the recording catheter's electrodes are used for the VV estimation. In practice, the ATs and locations of the electrodes are estimated, and if their estimation errors are not taken into consideration, they may significantly degrade the quality of the velocity estimation. Thus, in this paper, we assume that the locations and the ATs of the catheter's electrodes are contaminated with white Gaussian noise with known variances, and we derive the maximum likelihood (ML) cardiac velocity estimator for the planar wavefront. We further calculate the ML estimate of the AT that the planar wavefront reaches at any given location. Our simulation results show the efficiency of the proposed ML estimators for the velocity and AT, and they also confirm the validity of the derived relations for the covariance of the error of the estimators.