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Archive of Mechanical Engineering

The Journal of Committee on Machine Building of Polish Academy of Sciences

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Real-Time Parameter Estimation Study for Inertia Properties of Ground Vehicles

Jeremy Kolansky
  • Mechanical Engineering Department AVDL, Virginia Tech 9L Randolph Hall, Blacksburg, VA 24061
  • :
/ Corina Sandu
  • Mechanical Engineering Department AVDL, Virginia Tech 104 Randolph Hall, Blacksburg, VA 24061
  • :
Published Online: 2013-03-27 | DOI: https://doi.org/10.2478/meceng-2013-0001

Vehicle parameters have a significant impact on handling, stability, and rollover propensity. This study demonstrates two methods that estimate the inertia values of a ground vehicle in real-time.

Through the use of the Generalized Polynomial Chaos (gPC) technique for propagating the uncertainties, the uncertain vehicle model outputs a probability density function for each of the variables. These probability density functions (PDFs) can be used to estimate the values of the parameters through several statistical methods. The method used here is the Maximum A-Posteriori (MAP) estimate. The MAP estimate maximizes the distribution of P(β | z) where β is the vector of the PDFs of the parameters and z is the measurable sensor comparison.

An alternative method is the application of an adaptive filtering method. The Kalman Filter is an example of an adaptive filter. This method, when blended with the gPC theory is capable at each time step of updating the PDFs of the parameter distributions. These PDF’s have their median values shifted by the filter to approximate the actual values.


Parametry pojazdu maja znaczny wpływ na jego własciwosci, takie jak sterowalnosc, stabilnosc i odpornosc na wywrócenie. W pracy przedstawiono dwie metody estymacji parametrów inercyjnych pojazdu terenowego w czasie rzeczywistym.

W modelu pojazdu z niepewnosciami wyznacza sie funkcje gestosci prawdopodobienstwa (PDF) dla kazdej wielkosci opisujac propagacje niepewnosci przez zastosowanie techniki uogólnionego chaosu wielomianowego (gPC). Funkcje te moga byc uzyte do estymacji wartosci parametrów przy wykorzystaniu róznych metod statystycznych. W pracy zastosowano metode maksymalnego estymatora a posteriori (MAP). Estymator MAP maksymalizuje funkcje rozkładu P(β | z), gdzie β jest wektorem funkcji gestosci prawdopodobienstwa parametrów, a z jest wielkoscia mierzalna, otrzymana z porównania wyjsc czujników.

Metoda alternatywna jest zastosowanie filtru adaptacyjnego, którego przykładem jest filtr Kalmana. Metoda ta, w połaczeniu z technika uogólnionego chaosu wielomianowego (gPC), umozliwia, w kazdym kroku adaptacji, uaktualnianie funkcji gestosci prawdopodobienstwa (PDF) parametrów systemu. Działanie filtru powoduje, ze mediany tych funkcji zmieniaja sie dazac do rzeczywistych wartosci poszukiwanych parametrów.

Keywords : Parameter Estimation; EKF; Polynomial Chaos; Bayesian Statistics

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Published Online: 2013-03-27

Published in Print: 2013-03-01

Citation Information: Archive of Mechanical Engineering. Volume 60, Issue 1, Pages 7–21, ISSN (Print) 0004-0738, DOI: https://doi.org/10.2478/meceng-2013-0001, March 2013

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