<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>The noises associated with MEMS measurements can significantly impact their accuracy. The noises characterised by random walk and bias instability errors strictly depend on temperature effects that are difficult to specify during direct measurements. Therefore, the paper aims to estimate the fractional noise dynamics of the stationary MEMS gyroscope based on finite length triple estimation algorithm (FLTEA). The paper deals with the state, order and parameter estimation of fractional order noises originating from the MEMS gyroscope, being part of the popular Inertial Measurement Unit denoted as SparkFun MPU9250. The noise measurements from <italic>x</italic>, <italic>y</italic> and <italic>z</italic> gyroscope axes are identified using a modified triple estimation algorithm (TEA) with finite approximation length. The TEA allows a simultaneous estimation of the state, order and parameter of fractional order systems. Moreover, as it is well-known that the number of samples in fractional difference approximations plays a key role, we try to show the influence of applying the TEA with various approximation length constraints on final estimation results. The validation of finite length TEA in the noise estimation process coming from MEMS gyroscope has been conducted for implementation length reduction achieving 50% of samples needed to estimate the noise with no implementation losses. Additionally, the capabilities of modified TEA in the analysis of fractional constant and variable order systems are confirmed in several numerical examples.</p>
</abstract>

The noises associated with MEMS measurements can significantly impact their accuracy. The noises characterised by random walk and bias instability errors strictly depend on temperature effects that are difficult to specify during direct measurements. Therefore, the paper aims to estimate the fractional noise dynamics of the stationary MEMS gyroscope based on finite length triple estimation algorithm (FLTEA). The paper deals with the state, order and parameter estimation of fractional order noises originating from the MEMS gyroscope, being part of the popular Inertial Measurement Unit denoted as SparkFun MPU9250. The noise measurements from x, y and z gyroscope axes are identified using a modified triple estimation algorithm (TEA) with finite approximation length. The TEA allows a simultaneous estimation of the state, order and parameter of fractional order systems. Moreover, as it is well-known that the number of samples in fractional difference approximations plays a key role, we try to show the influence of applying the TEA with various approximation length constraints on final estimation results. The validation of finite length TEA in the noise estimation process coming from MEMS gyroscope has been conducted for implementation length reduction achieving 50% of samples needed to estimate the noise with no implementation losses. Additionally, the capabilities of modified TEA in the analysis of fractional constant and variable order systems are confirmed in several numerical examples.

Finite Length Triple Estimation Algorithm and its Application to Gyroscope MEMS Noise Identification

Acta Mechanica et Automatica

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

The noises associated with MEMS measurements can significantly impact their accuracy. The noises characterised by random walk and bias instability errors...

Finite Length Triple Estimation Algorithm and its Application to Gyroscope MEMS Noise Identification

Published Online: Apr 25, 2023

Page range: 219 - 229

Received: Oct 31, 2022

Accepted: Jan 04, 2023

DOI: https://doi.org/10.2478/ama-2023-0025

Keywords
fractional calculus, fractional Kalman filter, estimation of fractional order systems, fractional order noise

© 2023 Michal Macias et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Finite Length Triple Estimation Algorithm and its Application to Gyroscope MEMS Noise Identification

Published Online: Apr 25, 2023

Page range: 219 - 229

Received: Oct 31, 2022

Accepted: Jan 04, 2023

DOI: https://doi.org/10.2478/ama-2023-0025

Keywordsfractional calculus, fractional Kalman filter, estimation of fractional order systems, fractional order noise

© 2023 Michal Macias et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
fractional calculus, fractional Kalman filter, estimation of fractional order systems, fractional order noise