Abstract
This work considers the problem of remote estimation of Wiener processes and proposes a sample preprocessing method to ensure the convergence of the estimation distortion. Specifically, 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 exact expression for the convergent mean squared error (MSE) 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 derived MSE, the quantization precision, the sampling interval, and the transmission time of a single piece of update information are optimized individually. We further give two algorithms to obtain two global suboptimal MSEs for practical cases considering low thresholds of quantization precision and sampling interval, following a demonstration of the unsolvability of the joint optimization. The numerical results reveal that dynamic distortion plays a greater role than static distortion due to the fast-varying nature of the Wiener process, which also verifies the effectiveness of the proposed preprocessing method in controlling the quantization error.