# Improved noise reduction for nonlinear PMDC motor dead zone and friction model using variants of extended Kalman filter with practical validation

## TL;DR

This paper introduces an improved adaptive extended Kalman filter for reducing noise in nonlinear PMDC motor systems, leading to better state estimation and performance.

## Contribution

The novel contribution is an adaptive EKF variant that adjusts covariance matrices for improved noise reduction and estimation accuracy in PMDC motors.

## Key findings

- The adaptive AEKF achieves smaller root mean square errors in state estimation compared to traditional EKF.
- AEKF improves convergence speed and tolerance to disturbances in PMDC motor applications.

## Abstract

An improved framework for measurement noise reduction of nonlinear PMDC motor using variants of extended Kalman filter (EKF) is presented in this paper. Simulatory as well as experimental testing and validation of presented developments has also been performed. The nonlinearities like hard dead zone and friction have been incorporated in the PMDC motor model. Position as well as velocity measurement scenarios have been considered. Firstly, the noise corrupted measurement is invoked in standard EKF that perform prediction and correction to generate the best possible reduced noise estimate of the true measurement. One drawback standard EKF is that it ignores the effect of noise in the physical system and setting process and measurement covariance values in a vague manner that cause inaccurate estimates. In order to remedy this problem, an adaptive variant of EKF is introduced that utilizes the weighting coefficients and forgetting factor in order to set covariance parameters accurately and hence measurement noise reduction and estimation results get relatively accurate. The propositions are tested for angular position and velocity applications through simulation as well as practical experimentation. The results indicate that the adaptive AEKF provides quantitative improvements over the traditional EKF significantly by adaptively adjusting noise covariance matrices. In addition, it is observed that AEKF produce smaller root mean square errors in state estimation, enhance convergence speed, and demonstrate higher tolerance to unforeseen disturbances. These improvements make AEKF particularly valuable in applications such as PMDC machines, navigation systems, robotics, and sensor fusion, where precise and reliable state estimation is critical.