Remote Online Estimation of the Wiener Process: A Preprocessing Method to Ensure Distortion Convergence

In this paper, we consider the problem of remote estimation of Wiener processes and propose a sample preprocessing method to ensure the convergence of estimation distortion. The autocorrelation of the Wiener process is exploited to counteract the effect of strong quantization noise arising from the linearly increasing variance over time. We first derive the convergent expression for the mean squared error without considering transmission outages to explain the proposed preprocessing method. Then, the analysis is extended to more complex and general scenarios with outages. Based on the analyses, the quantization precision and the sampling interval are optimized individually.