A statistical approach for optimal order adjustment of a moving average filter

The moving average (MA) filter is a smoothing filter well-known in the digital signal processing community. The MA filter has only one configuration parameter, N, which is the order of the filter and is used to adjust the smoothing effect of an MA filter. The MA filtering technique can be effectively used to de-noise signals coming from inertial sensors. One of the drawbacks of the MA filter is that the theory behind digital signal processing does not provide a formal method to determine the value of N. Thus, N is usually chosen based on the previous experience of the MA filter designer. The present work proposes a novel approach to find the optimal value of N. The methodology compares two signals, one coming from a low-cost, MA-filtered inertial sensor, and another coming from a high-end inertial sensor. A statistical significance analysis is done for several orders of an MA filter for a particular low-cost inertial sensor. Finally, N is chosen considering the lowest MA filter order that performs the highest level of de-noising with respect to the high-end inertial sensor. The adjustment methodology is tested on four MEMS IMUs using a real-world trajectory generated by driving a vehicle. As a result, inertial sensors under study experience a noise reduction up to 52% for noisier inertial sensors.