Near-Optimal Moving Average Estimation at Characteristic Timescales: An Allan Variance Approach

A major challenge in moving average (MA) estimation is the selection of an appropriate averaging window length or timescale over which measurements remain relevant to the estimation task. Prior works typically perform timescale selection by examining multiple window lengths (or models) before selecting the `optimal' one using heuristics, domain knowledge expertise, goodness-of-fit, or information criterion (e.g., AIC, BIC etc.). In the presented work, we propose an alternative mechanism based on Allan Variance (AVAR) that obviates the need for assessing multiple models and systematically reduces reliance on heuristics or rules-of-thumb. The Allan Variance approach is used to identify the timescale that minimizes bias, thus determining the timescale over which past information remains most relevant. We also introduce an alternative method to obtain AVAR for unevenly spaced timeseries. The results from moving average estimation using an Allan Variance-determined window length are compared to the optimal moving average estimator that minimizes mean square error (MSE) for a variety of signals corrupted with Gaussian white noise. While the relevant timescales determined through AVAR tend to be longer than those associated with minimum MSE (i.e., AVAR-based MA estimation requires more measurements spread over a longer period of time), the AVAR-based moving average approach provides a valuable, systematic technique for near-optimal simple moving average estimation.