International Journal of Automotive Technology

, Volume 19, Issue 4, pp 669–676 | Cite as

Tire Lateral Force Estimation Using Kalman Filter



As for the tire analysis, lateral tire force is a fundamental factor that describes the stability of vehicle handling. Attempts to analyze the vehicle stability have been made based on various objective test methods and some specific factors such as yaw, lateral acceleration and roll angle. However, the problem to identify which axle is lack of the tire grip at a certain situation still remains. Since indoor tire force measurement system cannot represent a real road and vehicle conditions, tire force measurement through a real vehicle test is inevitable. Due to the high price of the tire force measurement device, tire force estimator can be an alternative toward cost reduction and device failure. In this paper, nonlinear planar full car model combined with tire model is proposed. Then, using discrete-time extended Kalman-Bucy filter (EKBF), individual tire lateral force are estimated with modified relaxation length model.

Key Words

Kalman filter Relaxation length Tire force estimation Planar full car model Cornering stiffness model 




longitudinal velocity, m/s


lateral velocity, m/s


yaw rate, rad/s


vehicle mass, kg


moment of inertia about yaw axis, kg m2


left wheel steer angle, rad


right wheel steer angle, rad


half of vehicle track width, m


distance from front axle to the center of gravity, m


distance from rear axle to the center of gravity, m


density of air, kg/m3


drag coefficient, -


vehicle front cross sectional area, m2


roll angle, rad


front roll steer compliance, -


rear roll steer compliance, -


wheel base length, m


height from ground to center of gravity, m


front roll stiffness, nm/rad


rear roll stiffness, nm/rad


distance from cg to roll axis, m


rolling resistance, -


effective radius, m


road friction coefficient, -


relaxation length, m


cornering stiffness, N/rad


lateral stiffness, N/m


distortion stiffness, Nm/rad


fl, fr, rl, rr

front left, front right, rear left, rear right


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Copyright information

© The Korean Society of Automotive Engineers and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Hankook Tire R&D CenterDaejeonKorea
  2. 2.Mechanical Engineering DepartmentKAISTDaejeonKorea

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