Optimal averaging time for improving observer accuracy of stochastic dynamical systems

In the problem of remote estimation by a centralized observer, improvements to the accuracy of observer estimates come at a cost of higher communication bandwidth and energy consumption. In this article we improve observer estimation accuracy by reducing the measurement variance on the sensor node before its transmission to the centralized observer node. The main contribution is to show that measurement variance is a trade-off between dynamical system variance and sensor variance. As a result there is an optimal averaging time that minimizes measurement variance, providing more accurate measurement to the observer. The optimal averaging time is computable by solving a univariate optimization problem.