Online Estimation of Friction Coefficients of Winter Road Surfaces Using the Unscented Kalman Filter

Abstract

An innovation to a previously proposed method for estimating friction coefficients of winter road surfaces was achieved through the introduction of a relatively new algorithm, the unscented Kalman filter. Its use, instead of a generic algorithm, made estimating friction coefficients in real time possible while keeping the core vehicular motion model unchanged. The problem of estimating such coefficients was too complicated to apply conventional feedback techniques, such as an extended Kalman filter, because of the presence of not only a nonlinear algebra equation but also a set of multiple differential equations. The unscented Kalman filter did not require any explicit function of state and observation equations in deriving Kalman gain. This paper describes the usefulness of this new filter in solving the problem and describes numerical experiments that validated the effectiveness of the proposed new method in terms of computational efficiencies. The friction coefficients estimated with the new technique were in fairly good accordance with those measured in the field.

Get full access to this article

View all access options for this article.

References

Nakatsuji

and Kawamura

. Relationship Between Winter Road-Surface Conditions and Vehicular Motion: Measurements by Probe Vehicles Equipped with Global Positioning System. In Transportation Research Record: Journal of the Transportation Research Board, No. 1824, Transportation Research Board of the National Academies, Washington, D.C., 2003, pp. 106–114.

Nakatsuji

Kawamura

and Maeda

. Inverse Estimation of Friction Coefficients of Winter Road Surface with Vehicular Motion Data Measured by GPS-Equipped Probe Vehicles. In Transportation Research Circular E-C063: International Symposium on Snow Removal and Ice Control Technology. Transportation Research Board of the National Academies, Washington, D.C., 2004, pp. 442–454.

Nakatsuji

Hayashi

Kawamura

and Shirakawa

. Inverse Estimation of Friction Coefficients of Winter Road Surfaces: New Considerations of Lateral Movements and Angular Movements. In Transportation Research Record: Journal of the Transportation Research Board, No. 1911, Transportation Research Board of the National Academies, Washington, D.C., 2005, pp. 149–159.

Julier

S. J.

Uhlmann

J. K.

and Durrant-Whyte

H. F.

. A New Approach for Filtering Nonlinear System. Proc., American Control Conference, Seattle, Wash., June 21–23, 1995, pp. 1628–1632.

Wan

E. A.

and van der Merwe

The Unscented Kalman Filter. In Kalman Filtering and Neural Networks ( Haykin

, ed.), John Wiley and Sons, New York, 2001, pp. 221–280.

Arimoto

Kalman Filter (in Japanese). Sangyo Tosyo, Tokyo, 1977.

Katayama

Applied Kalman Filter (in Japanese). Asakura Syoten, Tokyo, 2000.

Sakai

Tire Engineering (in Japanese). Grand Prix Press, Tokyo, 1987.

Moore

D. F.

The Friction of Pneumatic Tyres. Elsevier, New York, 1975.

10.

Masato

Dynamics and Control of Vehicles (in Japanese). Kyoritsu Press, Tokyo, 1979.

11.

Bell

M. G.

and Iida

. Transportation Network Analysis. John Wiley and Sons, New York, 1997.

12.

Simon

and Chia

. Kalman Filtering with State Equality Constraints. IEEE Transactions on Aerospace and Electronic Systems, Vol. 39, No. 1 2002, pp. 128–136.

13.

Simon

and Simon

D. L.

. Kalman Filtering with Inequality Constraints for Turbofan Engine Health Estimation. National Aeronautics and Space Administration, 2003. gltrs.grc.nasa.gov/reports/2003/TM-2003-212111.pdf. Accessed July 2007.

14.

Ranjitkar

and Nakatsuji

. Advances in Microscopic Traffic Data Collection Using Instrumented Vehicles. Traffic Engineering and Control, Vol. 47, No. 4, April 2006, pp. 147–151.

15.

Gurusinghe

G. S.

Nakatsuji

Azuta

Ranjitkar

and Tanaboriboon

. Multiple Car-Following Data with Real-Time Kinematic Global Positioning System. In Transportation Research Record: Journal of the Transportation Research Board, No. 1802, Transportation Research Board of the National Academies, Washington, D.C., 2002, pp. 166–180.