TSI-Aided Real-Time Monitoring of Brownian Motions: A Rate-Latency-Distortion Perspective

Real-time monitoring of the Brownian motion or Wiener process has received considerable attention because of its potential in autonomous driving, smart grids, and factory automation. However, conventional periodic sampling-based monitoring may induce error accumulation, which will lead to an infinite distortion as the monitoring time increases. To overcome this, we present a threshold-based sampling policy for the remote reconstruction of Brownian motions. With the aid of timing side information (TSI), the sampling time information can be efficiently compressed. To provide greater insight, we present the real-time and non-real-time reconstruction errors as functions of data rate and transmission delay. Finally, a multi-threshold sampling method is presented to further reduce the transmission rate in remote monitoring with reservation-based multiple access.