Nonlinear observer design for a magnetic position estimation technique

Yan Wang, Ryan Madson, Rajesh Rajamani

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

8 Scopus citations


This paper develops an observer for a magnetic field based position sensor. The process model for the magnetic field sensing system is linear while the output equation is highly nonlinear. Previous results on observer design in nonlinear systems have mostly assumed that the output equation is linear, even if the process dynamics are nonlinear. This paper presents a new observer design technique that can rigorously address the presence of nonlinearity in the output equation. The estimation error dynamics of a two degree-of-freedom observer is transformed into a Lure system in which the sector condition for the nonlinearity in the feedback loop is constructed from the element-wise bounds on the Jacobian matrix of the nonlinear measurement equation. The developed observer design technique is applied to non-intrusive estimation of the position of a piston inside a pneumatic cylinder. Experimental results show that the observer can accurately estimate piston position with sub-mm accuracy. The advantages of the nonlinear observer over an extended Kalman Filter are demonstrated. The developed observer has applications in many other problems involving nonlinear output equations.

Original languageEnglish (US)
Title of host publication54rd IEEE Conference on Decision and Control,CDC 2015
PublisherInstitute of Electrical and Electronics Engineers Inc.
Number of pages6
ISBN (Electronic)9781479978861
StatePublished - Feb 8 2015
Event54th IEEE Conference on Decision and Control, CDC 2015 - Osaka, Japan
Duration: Dec 15 2015Dec 18 2015

Publication series

NameProceedings of the IEEE Conference on Decision and Control
Volume54rd IEEE Conference on Decision and Control,CDC 2015
ISSN (Print)0743-1546
ISSN (Electronic)2576-2370


Other54th IEEE Conference on Decision and Control, CDC 2015

Bibliographical note

Publisher Copyright:
© 2015 IEEE.


  • Jacobian matrices
  • Mathematical model
  • Observers
  • Pistons
  • Robot sensing systems


Dive into the research topics of 'Nonlinear observer design for a magnetic position estimation technique'. Together they form a unique fingerprint.

Cite this