Adaptive Real-Time Numerical Differentiation with Variable-Rate Forgetting and Exponential Resetting

TL;DR

This paper introduces an adaptive real-time numerical differentiation method that dynamically adjusts to changing sensor noise characteristics using variable-rate forgetting and exponential resetting, improving robustness in digital PID control.

Contribution

It extends the AISE method with variable-rate forgetting and exponential resetting to better handle time-varying noise in sensor data.

Findings

Enhanced noise adaptability in numerical differentiation

Faster response to changing noise characteristics

Maintains bounded covariance in recursive estimation

Abstract

Digital PID control requires a differencing operation to implement the D gain. In order to suppress the effects of noisy data, the traditional approach is to filter the data, where the frequency response of the filter is adjusted manually based on the characteristics of the sensor noise. The present paper considers the case where the characteristics of the sensor noise change over time in an unknown way. This problem is addressed by applying adaptive real-time numerical differentiation based on adaptive input and state estimation (AISE). The contribution of this paper is to extend AISE to include variable-rate forgetting with exponential resetting, which allows AISE to more rapidly respond to changing noise characteristics while enforcing the boundedness of the covariance matrix used in recursive least squares.