Methods in Vehicle Mass and Road Grade Estimation

Narayanan Kidambi, R. L. Harne, Yuji Fujii, Gregory M. Pietron, K. W. Wang

Research output: Contribution to journalArticlepeer-review

34 Scopus citations


Dynamic vehicle loads play critical roles for automotive controls including battery management, transmission shift scheduling, distance-to-empty predictions, and various active safety systems. Accurate real-time estimation of vehicle loads such as those due to vehicle mass and road grade can thus improve safety, efficiency, and performance. While several estimation methods have been proposed in literature, none have seen widespread adoption in current vehicle technologies despite their potential to significantly improve automotive controls. To understand and bridge the gap between research development and wider adoption of real-time load estimation, this paper assesses the accuracy and performance of four estimation methods that predict vehicle mass and/or road grade. These include recursive least squares (RLS) with multiple forgetting factors; extended Kalman filtering (EKF); a dynamic grade observer (DGO); and a method developed by this research: parallel mass and grade (PMG) estimation using a longitudinal accelerometer. The estimation methods and models were constructed, numerous vehicle tests were performed, and data was evaluated off-line by the estimation approaches. It is found that RLS and EKF yield estimates within 5% of their actual values if provided initial values close to true initial states. To improve estimation when inaccurate initial values are provided, a mass selection algorithm is proposed that determines mass based on converged values from concurrently-operating EKF estimators. Its potential for accurate mass and grade estimation is demonstrated. PMG estimation provides the most reliable and accurate results, and demonstrates the greatest potential for successful real-time implementation to advance the performance, economy, and reliability of future vehicle controls.

Original languageEnglish (US)
Pages (from-to)981-991
Number of pages11
JournalSAE International Journal of Passenger Cars - Mechanical Systems
Issue number3
StatePublished - Sep 2014

All Science Journal Classification (ASJC) codes

  • Modeling and Simulation
  • Automotive Engineering
  • Safety, Risk, Reliability and Quality
  • Mechanical Engineering


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