Reconstruction Error Estimation of Gaussian Markov Processes with Jitter

Abstract

The reconstruction error estimation of the Gaussian Markov process in the presence of jitter is investigated in this paper, taking into account mainly two samples in the analysis. Two different situations are considered. In the first situation, the position of the first sample does not have jitter, but it exists in the second sample. In the second condition, the two samples have the presence of jitter. The probability density functions of jitter are represented by the uniform and the Erlang distributions. The results are obtained by applying statistical averaging to the conditional mean rule with respect to the random variable of jitter. This rule defines the conditional variance function as reconstruction error function, which allows us to determine the reconstruction error of the Gaussian Markov process on the whole time domain.