Performance Analysis of Moving Average Filter Using Allan Variance

This work presents the use of the area of Allan VARiance (AVAR) as an alternate measure for Mean Squared Error (MSE) to select an optimal Moving Average (MA) filter that minimizes MSE between noisy and filtered signals. MSE is a standard performance index that quantifies the performance of MA filters. However, for signals with non-white noise characteristics - a category that includes nearly all real-world signals - the calculation of MSE is not quickly done with one but typically requires multiple experiments. This work shows that the area of AVAR estimates noise properties from one iteration of measured data and achieves the same optimization results. While AVAR methods are typically used to analyze the variance of static window averages of data, prior recent work extends this to include moving average calculations. In this work, these results are extended further to illustrate that the time-correlation window in the area of AVAR calculations relates to the window size used in the MA filter. This relationship is then utilized to show that the discrete integration of the AVAR curve yields a performance index that quickly identifies the MSE-optimal filter for input with drift (random walk) corrupted by white noise. AVAR is compared against the MSE to show that both the performance indices give similar results when choosing the optimal MA filter, but with only one iteration of AVAR calculations versus significant iterations (hundreds or more) for MSE calculations.