Real-Time Optimization of Single Pole Low Pass Filter using Signal-to-Noise Ratio Maximization

In this paper, further studies have been made on improving the output performance optimization of the exponentially weighted moving average filter for real-time system applications. It has been shown in prior research that the filter is an effective, low-cost filtering algorithm; however, its output performance is dependent on the calibration of its gain parameter. As a result, the filter will produce sub-optimal outputs if not calibrated correctly. A method is sought that can provide an appropriate gain parameter for maximizing the signal-to-noise ratio of the filter's resulting output, thereby increasing the effectiveness of the filter for real-time system applications. A trial-and-error experimental approach was used to find the filter's optimal parameter gain that maximizes the filter's output signal to noise ratio for a known signal that is sampled using a Gaussian distribution model. It was found that the output signal performance of the complementary filter is highly dependent on its chosen parameter gain, and using a static parameter gain value is unsuitable. An equation was found that approximates an optimal parameter gain to produce a filtered output with the best signal to noise ratio and applied to a real-world application.

I. Introduction

A single-pole low pass filtering algorithm, commonly known as the exponentially weighted moving average (EMA) filter, is the most basic implementation of a low pass infinite impulse response (IIR) filter. It has been shown that the EMA has superior performance compared to other low-cost filtering algorithms in terms of both iteration speed and computational requirements [1]. The EMA's filtering effectiveness, however, is dependent on its tuning, as is the case with many other filtering algorithms. In order to present the EMA as a filtering algorithm that is ideal in terms of computational performance and filtering effectiveness, a tuning strategy is needed to ensure that the filter is providing an optimal output. In this paper, an automatic tuning method for a signal with Gaussian distributed noise characteristics is experimentally developed for the EMA whereby the algorithm can be tuned in real-time based on measured signal performance metrics.