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State Estimation of Vehicle’s Dynamic Stability Based on the Nonlinear Kalman Filter

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Abstract

An accurate estimation of a vehicle’s state of motion is the basis of dynamic stability control. Two different nonlinear Kalman filters are adopted for the estimation of the vehicle’s lateral/rollover stability state. First, the overall structure of the state estimation with four inputs and four outputs is introduced. After determining tire-cornering stiffness using a recursive least-squares (RLS) method, the equations of state and of observation for the nonlinear Kalman filter are established based on a vehicle model with four degrees of freedom including planar and rollover dynamics. Then, the specific steps of real-time state estimation using the extended Kalman filter (EKF) and unscented Kalman filter (UKF) are both given. In a co-simulation, we find that the RLS algorithm estimates tire-cornering stiffness accurately and quickly, and the UKF improves the effect of state estimation compared with EKF. In addition, the UKF is verified against data from vehicle tests. The results show the proposed method is reliable and practical in estimating vehicle states.

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Abbreviations

EKF:

Extended Kalman filter

UKF:

Unscented Kalman filter

RLS:

Recursive least squares

DOF:

Degree of freedom

G(k):

Gain matrix

P(k):

Covariance matrix

I :

Unit matrix

x(t):

State variable

u(t):

Control variable

y(t):

Observed variable

w(t):

Process noise

v(t):

Measure noise

T :

Sampling time

\( \xi \) :

Sigma sampling point

ω i :

Weight value

β :

Vehicle sideslip angle

a x :

Longitudinal acceleration

a y :

Lateral acceleration

c :

Roll damping coefficient

k :

Roll stiffness coefficient

\( \phi \) :

Roll angle

h :

Height of mass center

m :

Vehicle mass

m s :

Sprung mass

ω r :

Yaw rate

L :

Wheelbase

a :

Distance of center to the front axle

b :

Distance of center to the rear axle

δ :

Front wheel angle

v x :

Longitudinal speed

v y :

Lateral speed

I x :

Moment of inertia around the x-axis

I z :

Moment of inertia around the z-axis

k 1 :

Cornering stiffness of the front tire

k 2 :

Cornering stiffness of the rear tire

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Acknowledgements

This work was supported in part by the 111 Project (Grant No. B17034) and National Natural Science Foundation of the People’s Republic of China (Grant No. 51505354).

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Authors and Affiliations

  1. School of Automotive Engineering, Wuhan University of Technology, Wuhan, 430070, China

    Xiaofei Pei, Xu Hu, Zhenfu Chen & Bo Yang

  2. Wanxiang Qianchao Corporation, Hangzhou, 311215, China

    Wei Liu

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  1. Xiaofei Pei
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  2. Xu Hu
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  3. Wei Liu
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  4. Zhenfu Chen
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  5. Bo Yang
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Correspondence to Xiaofei Pei.

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Pei, X., Hu, X., Liu, W. et al. State Estimation of Vehicle’s Dynamic Stability Based on the Nonlinear Kalman Filter. Automot. Innov. 1, 281–289 (2018). https://doi.org/10.1007/s42154-018-0028-6

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  • DOI: https://doi.org/10.1007/s42154-018-0028-6

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