Kalman filter has been applied in literature to inverse electrocardiography problem as a spatio-temporal method. However, there is still an open question of how the essential parameters in the state-space representation are found without claiming strong assumptions. In this study, we proposed a maximum likelihood (ML) estimation based method which incorporates multiple body surface measurements to estimate the parameters that are essential to use Kalman filter. Our proposed approach, Maximum Likelihood Inference & Filtering (MLIF), was compared with zero order Tikhonov regularization and Bayesian maximum a posteriori estimation (BMAP) by using three different training sets under two different measurement noise levels. The results showed that mean correlation coefficient (CC) for Tikhonov regularization is 0.60, and mean CC ranges 0.64 to 0.82, and 0.66 to 0.99 for Bayesian MAP and MLIF under 30 dB SNR measurement noise, respectively. Under 10 dB SNR, mean CC is 0.37 for Tikhonov regularization, and mean CC ranges 0.53 to 0.78, and 0.53 to 0.98 for Bayesian MAP and MLIF, respectively.
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机译：卡尔曼滤波器已在文献中应用于逆心电图问题作为一种时空方法。但是，仍然存在如何发现状态空间表示中的基本参数的开放问题，而不会索取强烈的假设。在这项研究中，我们提出了一种基于最大可能性（ML）估计的方法，该方法包括多个体表测量来估计必须使用Kalman滤波器必不可少的参数。我们所提出的方法，最大似然推理和过滤（MLIF）与零阶Tikhonov正规化和贝叶斯最大的后验估计（BMAP）进行了比较，并在两个不同的测量噪声水平下使用三种不同的训练集。结果表明，Tikhonov正规的平均相关系数（CC）为0.60，平均CC为0.64至0.82，分别为30dB SNR测量噪声的MLIF 0.66至0.99。在10 dB SNR下，Tikhonov规则化的平均cc为0.37，分别为贝叶斯地图和MLIF的平均CC为0.53至0.78，以及0.53至0.98。
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