Vehicle Sideslip Estimation for Four-Wheel-Steering Vehicles Using a Particle Filter

  • Basilio LenzoEmail author
  • Ricardo De Castro
Conference paper
Part of the Lecture Notes in Mechanical Engineering book series (LNME)


The availability of the most relevant vehicle states is crucial for the development of advanced vehicle control systems and driver assistance systems. Specifically the vehicle sideslip angle plays a key role, yet this state is unpractical to measure and still not straightforward to estimate. This paper investigates a particle filter approach to estimate the chassis sideslip angle of road vehicles. The filter relies on a physical model of the vehicle and on measurements available from cheap and widespread sensors including inertial measurement unit and steering wheel angle sensor(s). The approach is validated using experimental data collected with the research platform RoboMobil (RoMo), a by-wire electric vehicle with wheel-individual traction and steering actuators. Results show that the performance of the proposed particle filter is satisfactory, and indicate directions for further improvement.


Sideslip angle Particle filter Electric vehicles Estimation Rear wheel steering Experiments 

List of Symbols

\( a_{y} \)

vehicle lateral acceleration (m/s2)

\( a_{y}^{*} \)

vehicle lateral acceleration with roll angle correction (m/s2)

\( C_{y1} \)

cornering stiffness of the front axle (N/rad)

\( C_{y2} \)

cornering stiffness of the rear axle (N/rad)

\( c \)

input vector

\( e_{i} \)

difference in measurement between actual one and i-th particle prediction

\( F_{x1} \)

longitudinal force at front axle (N)

\( F_{x2} \)

longitudinal force at rear axle (N)

\( F_{y1} \)

lateral force at front axle (N)

\( F_{y2} \)

lateral force at rear axle (N)

\( F_{z1,0} \)

static vertical load on front axle (N)

\( F_{z2,0} \)

static vertical load on rear axle (N)

\( f \)

function describing the model propagation

\( g \)

gravity acceleration (m/s2)

\( h \)

function relating the measurements to the state vector \( x \)

\( J_{z} \)

vehicle yaw mass moment of inertia (kg m2)

\( k \)

time step

\( m \)

vehicle mass (kg)

\( N \)

number of samples

\( n_{p} \)

number of particles of the particle filter

\( n_{x} \)

process noise

\( n_{y} \)

measurement noise

\( q \)

exogenous input vector

\( r \)

vehicle yaw rate (rad/s)

\( u \)

vehicle longitudinal velocity (m/s)

\( v \)

vehicle lateral velocity (m/s)

\( W_{{a_{y} }} \)

weight on the lateral acceleration error

\( W_{i} \)

weight for the i-th particle

\( W_{r} \)

weight on the yaw rate error

\( w_{1} \)

front semi-wheelbase (m)

\( w_{2} \)

rear semi-wheelbase (m)

\( x \)

state vector

\( \widehat{x} \)

estimated state vector

\( y \)

measurement vector

\( \alpha_{1} \)

front tire slip angle (rad)

\( \alpha_{2} \)

rear tire slip angle (rad)

\( \beta \)

sideslip angle at the centre of mass (rad)

\( \widehat{\beta } \)

estimated sideslip angle at the centre of mass (rad)

\( \beta_{1} \)

front sideslip angle (rad)

\( \beta_{2} \)

rear sideslip angle (rad)

\( \Delta t \)

time step (s)

\( \delta_{1} \)

front steering angle (rad)

\( \delta_{2} \)

rear steering angle (rad)

\( \varphi \)

estimated roll angle (rad)

\( \mu \)

average tire-road friction coefficient

\( \phi_{i} \)

predicted measurement for i-th particle

\( \chi_{i} \)

i-th particle



The authors wish to thank the German Academic Exchange Service (Deutscher Akademischer Austauschdienst, DAAD) for supporting this work.


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Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Sheffield Vehicle Dynamics Research Group, Department of Engineering and MathematicsSheffield Hallam UniversitySheffieldUK
  2. 2.Institute of System Dynamics and ControlGerman Aerospace Center (DLR)WeßlingGermany

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