Comparative analysis of a nonlinear observer and nonlinear Kalman filters for magnetic position estimation

Hamidreza Movahedi, Ali Zemouche, Rajesh Rajamani

Research output: Chapter in Book/Report/Conference proceedingConference contribution


This paper analyzes state estimation for nonlinear systems in the presence of sensor noise and process disturbances. A class of systems involving nonlinear functions of vector arguments in the output equations is considered. A nonlinear observer that satisfies a H∞ disturbance rejection constraint in addition to providing asymptotic stability in the absence of disturbances is developed using Lyapunov analysis. The observer is shown analytically to provide a guaranteed upper bound on the norm of the estimation error. The performance of the nonlinear observer is compared with the performance of two of the most popular and powerful methods for estimation in nonlinear systems - the extended Kalman filter (EKF) and the unscented Kalman filter (UKF). A magnetic position estimation problem is utilized as the real-world application for the evaluation. In the case of the disturbances being gaussian noise, the UKF and the nonlinear observer provide approximately the same level of performance and they both surpass the performance of the EKF. However, in the case of 2-norm-bounded non gaussian noise such as spikes/ pulses, the nonlinear observer is shown to significantly outperform both the UKF and the EKF.

Original languageEnglish (US)
Title of host publication2023 American Control Conference, ACC 2023
PublisherInstitute of Electrical and Electronics Engineers Inc.
Number of pages6
ISBN (Electronic)9798350328066
StatePublished - 2023
Event2023 American Control Conference, ACC 2023 - San Diego, United States
Duration: May 31 2023Jun 2 2023

Publication series

NameProceedings of the American Control Conference
ISSN (Print)0743-1619


Conference2023 American Control Conference, ACC 2023
Country/TerritoryUnited States
CitySan Diego

Bibliographical note

Funding Information:
This research was supported in part by the National Science Foundation through grant NSF CMMI 1562006 and by a University of Minnesota UMII-MnDRIVE fellowship.

Publisher Copyright:
© 2023 American Automatic Control Council.


Dive into the research topics of 'Comparative analysis of a nonlinear observer and nonlinear Kalman filters for magnetic position estimation'. Together they form a unique fingerprint.

Cite this