Estimation of state transition matrix in the Kalman filter based inverse ECG solution with the help of training sets

Abstract

At this study the main motivation is to solve inverse problem of ECG with Kalman filter. In order to obtain feasible solutions determination of the state transition matrix (STM) correctly is vital. In literature the STM is usually found by using the test data itself which is not a realistic scenario. The major goal of this study is to determine STM without using test data. For that purpose a two stage method is suggested. At the first step the probability density function (pdf) is calculated using training sets and then this pdf is used to find Bayes-MAP solution which uses only spatial information. At the second step, the Bayes-MAP solution is used to find STM and later on, that STM is used in Kalman filter to obtain final results. It is seen that the results obtained with this method are better then normal Bayes-MAP results and the errors are within acceptable limits. So it is concluded that the usage of Bayes-MAP solutions in STM determination is a serious alternative for STM estimation.