Statistical quantification of least-squares battery state of charge estimation errors

Sergio Mendoza, Ji Liu, Partha Mishra, Hosam K. Fathy

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

4 Scopus citations


This paper derives analytic expressions for both the mean and variance of battery state of charge (SOC) estimation error, assuming a least squares estimation law. The paper examines three sources of estimation error, namely: (i) voltage measurement errors (both bias and noise), (ii) current measurement bias, and (iii) mismatch between the order of the battery model used for estimation and the true order of the battery's dynamics. There is already a rich literature on quantifying battery SOC estimation errors for different estimator designs. The novelty of this paper stems from its extensive examination of both the expected SOC estimation bias and noise, for a least squares estimation algorithm, in the presence of three different fundamental sources of these estimation errors. We show, both analytically and using Monte Carlo simulation, that under reasonable operating conditions, the expected bias in SOC estimation for lithium-ion batteries is dominant compared to the expected estimation variance. This leads to the important insight that quantifying SOC estimation variance using Fisher information furnishes overly optimistic predictions of achievable SOC estimation accuracy.

Original languageEnglish (US)
Title of host publicationAdvances in Control Design Methods, Nonlinear and Optimal Control, Robotics, and Wind Energy Systems; Aerospace Applications; Assistive and Rehabilitation Robotics; Assistive Robotics; Battery and Oil and Gas Systems; Bioengineering Applications; Biomedical and Neural Systems Modeling, Diagnostics and Healthcare; Control and Monitoring of Vibratory Systems; Diagnostics and Detection; Energy Harvesting; Estimation and Identification; Fuel Cells/Energy Storage; Intelligent Transportation
PublisherAmerican Society of Mechanical Engineers
ISBN (Electronic)9780791850695
StatePublished - Jan 1 2016
EventASME 2016 Dynamic Systems and Control Conference, DSCC 2016 - Minneapolis, United States
Duration: Oct 12 2016Oct 14 2016

Publication series

NameASME 2016 Dynamic Systems and Control Conference, DSCC 2016


OtherASME 2016 Dynamic Systems and Control Conference, DSCC 2016
Country/TerritoryUnited States

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Industrial and Manufacturing Engineering
  • Mechanical Engineering


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