Vehicle Dynamics Estimation Using Kalman Filters

This paper deals with the application of stochastic state estimators in vehicle dynamics control. It is often unrealistic to assume that all vehicle states and the disturbances acting on it can be measured. System states that cannot be measured directly, can be estimated by a Kalman Filter. The idea of the Kalman filter is to implement a model of the real system in an on-board computer in parallel with the system itself. This paper will give 3 examples of this principle applied to automotive systems.     

Effect of vehicle model on the estimation of lateral vehicle dynamics

A methodology is presented for estimating vehicle handling dynamics, which are important to control system design and safety measures. The methodology, which is based on an extended Kalman filter (EKF), makes it possible to estimate lateral vehicle states and tire forces on the basis of the results obtained from sinusoidal steering stroke tests that are widely used in the evaluation of vehicle and tire handling performances. This paper investigates the effect of vehicle-road system models on the estimation of lateral vehicle dynamics in the EKF. Various vehicle-road system models are considered in this study: vehicle models (2-DOF, 3-DOF, 4-DOF), tire models (linear, non-linear) and relaxation lengths. Handling tests are performed with a vehicle equipped with sensors that are widely used by vehicle and tire manufacturers for handling maneuvers. The test data are then used in the estimation of the EKF and identification of lateral tire model coefficients. The accuracy of the identified values is validated by comparing the RMS error between experimentally measured states and regenerated states simulated using the identified coefficients. The results show that the relaxation length of the tire model has a notable impact on the estimation of lateral vehicle dynamics.     

Fault detection and isolation for a full-scale railway vehicle suspension with multiple Kalman filters

Reliability and dependability in complex mechanical systems can be improved by fault detection and isolation (FDI) methods. These techniques are key elements for maintenance on demand, which could decrease service cost and time significantly. This paper addresses FDI for a railway vehicle: the mechanical model is described as a multibody system, which is excited randomly due to track irregularities. Various parameters, like masses, spring- and damper-characteristics, influence the dynamics of the vehicle. Often, the exact values of the parameters are unknown and might even change over time. Some of these changes are considered critical with respect to the operation of the system and they require immediate maintenance. The aim of this work is to detect faults in the suspension system of the vehicle. A Kalman filter is used in order to estimate the states. To detect and isolate faults the detection error is minimised with multiple Kalman filters. A full-scale train model with nonlinear wheel/rail contact serves as an example for the described techniques. Numerical results for different test cases are presented. The analysis shows that for the given system it is possible not only to detect a failure of the suspension system from the system's dynamic response, but also to distinguish clearly between different possible causes for the changes in the dynamical behaviour.     

Dual extended Kalman filter for vehicle state and parameter estimation

The article demonstrates the implementation of a model-based vehicle estimator, which can be used for combined estimation of vehicle states and parameters. The estimator is realised using the dual extended Kalman filter (DEKF) technique, which makes use of two Kalman filters running in parallel, thus 'splitting' the state and parameter estimation problems. Note that the two problems cannot be entirely separated due to their inherent interdependencies. This technique provides several advantages, such as the possibility to switch off the parameter estimator, once a sufficiently good set of estimates has been obtained. The estimator is based on a four-wheel vehicle model with four degrees of freedom, which accommodates the dominant modes only, and is designed to make use of several interchangeable tyre models. The paper demonstrates the appropriateness of the DEKF. Results to date indicate that this is an effective approach, which is considered to be of potential benefit to the automotive industry.     

北斗卫星与车载传感器融合的车辆定位

为了改善北斗卫星定位性能,基于卡尔曼滤波设计了北斗卫星与车载传感器的数据融合算法。算法包括车辆方向融合和车辆位置融合两部分,前者融合电子罗盘和陀螺测量得到的北向角及其变化率,估算北向角的真实值;后者首先同步车速矢量与北斗卫星测量得到的车辆位置矢量,再根据融合结果估算车辆定位信息。为了验证数据融合算法,设计了北斗卫星与车辆状态信息采集系统,利用本系统采集的实车数据进行的仿真计算表明,算法能够提高定位频率、减小定位误差,提高北斗卫星定位的性能。     

Customer loads of two-wheeled vehicles

Customer usage profiles are the most unknown influences in vehicle design targets and they play an important role in durability analysis. This publication presents a customer load acquisition system for two-wheeled vehicles that utilises the vehicle's onboard signals. A road slope estimator was developed to reveal the unknown slope resistance force with the help of a linear Kalman filter. Furthermore, an automated mass estimator was developed to consider the correct vehicle loading. The mass estimation is performed by an extended Kalman filter. Finally, a model-based wheel force calculation was derived, which is based on the superposition of forces calculated from measured onboard signals. The calculated wheel forces were validated by measurements with wheel–load transducers through the comparison of rainflow matrices. The calculated wheel forces correspond with the measured wheel forces in terms of both quality and quantity. The proposed methods can be used to gather field data for improved vehicle design loads.     

Lateral controller design for an unmanned vehicle via Kalman filtering

This paper proposes a lateral control system for an unmanned vehicle that is designed to improve the responsiveness of the system with the use of a PD control. The vehicle heading error can be stabilized, and the transient response characteristics can be improved using the proposed controller. A mathematical model of the vehicle dynamics using two degrees of freedom was developed for the controller design. The waypoint tracking method for autonomous navigation was tested with incorporation of the Point-to-Point algorithm with position and heading measurements received from GPS receivers via Kalman filtering. The performance of the designed controller was verified through experiments with a real vehicle.     

Unscented Kalman filter for vehicle state estimation

Vehicle dynamics control (VDC) systems require information about system variables, which cannot be directly measured, e.g. the wheel slip or the vehicle side-slip angle. This paper presents a new concept for the vehicle state estimation under the assumption that the vehicle is equipped with the standard VDC sensors. It is proposed to utilise an unscented Kalman filter for estimation purposes, since it is based on a numerically efficient nonlinear stochastic estimation technique. A planar two-track model is combined with the empiric Magic Formula in order to describe the vehicle and tyre behaviour. Moreover, an advanced vertical tyre load calculation method is developed that additionally considers the vertical tyre stiffness and increases the estimation accuracy. Experimental tests show good accuracy and robustness of the designed vehicle state estimation concept.     

An Extended Adaptive Kalman Filter for Real-time State Estimation of Vehicle Handling Dynamics

This paper considers a method for estimating vehicle handling dynamic states in real-time, using a reduced sensor set; the information is essential for vehicle handling stability control and is also valuable in chassis design evaluation. An extended (nonlinear) Kalman filter is designed to estimate the rapidly varying handling state vector. This employs a low order (4 DOF) handling model which is augmented to include adaptive states (cornering stiffnesses) to compensate for tyre force nonlinearities. The adaptation is driven by steer-induced variations in the longitudinal vehicle acceleration. The observer is compared with an equivalent linear, model-invariant Kalman filter. Both filters are designed and tested against data from a high order source model which simulates six degrees of freedom for the vehicle body, and employs a combined-slip Pacejka tyre model. A performance comparison is presented, which shows promising results for the extended filter, given a sensor set comprising three accelerometers only. The study also presents an insight into the effect of correlated error sources in this application, and it concludes with a discussion of the new observer's practical viability.     

Using GPS with a model-based estimator to estimate critical vehicle states

This paper demonstrates a method to estimate the vehicle states sideslip, yaw rate, and heading using GPS and yaw rate gyroscope measurements in a model-based estimator. The model-based estimator using GPS measurements provides accurate and observable estimates of sideslip, yaw rate, and heading even if the vehicle model is in neutral steer or if the gyro fails. This method also reduces estimation errors introduced by gyroscope errors such as the gyro bias and gyro scale factor. The GPS and Inertial Navigation System measurements are combined using a Kalman filter to generate estimates of the vehicle states. The residuals of the Kalman filter provide insight to determine if the estimator model is correct and therefore providing accurate state estimates. Additionally, a method to predict the estimation error due to errors in the estimator model is presented. The algorithms are tested in simulation with a correct and incorrect model as well as with sensor errors. Finally, the estimation scheme is tested with experimental data using a 2000 Chevrolet Blazer to further validate the algorithms.     

Investigation of automatic path tracking using an extended Kalman filter

This paper proposes a lane marker recognition method that uses the steering angle in addition to image information. A Kalman filter was reconfigured regarding the yaw motion and lateral motion of lane markers, previously treated as a stochastic process, as the states of a vehicle model driven on the basis of the steering angle. Driving tests conducted with an actual vehicle verified that this method provides good tracking at the time of steering input and avoids misrecognition of lane marker candidate points in inclement weather.     

Comparative study of vehicle tyre–road friction coefficient estimation with a novel cost-effective method

This paper qualitatively and quantitatively reviews and compares three typical tyre–road friction coefficient estimation methods, which are the slip slope method, individual tyre force estimation method and extended Kalman filter method, and then presents a new cost-effective tyre–road friction coefficient estimation method. Based on the qualitative analysis and the numerical comparisons, it is found that all of the three typical methods can successfully estimate the tyre force and friction coefficient in most of the test conditions, but the estimation performance is compromised for some of the methods during different simulation scenarios. In addition, all of these three methods need global positioning system (GPS) to measure the absolute velocity of a vehicle. To overcome the above-mentioned problem, a novel cost-effective estimation method is proposed in this paper. This method requires only the inputs of wheel angular velocity, traction/brake torque and longitudinal acceleration, which are all easy to be measured using available sensors installed in passenger vehicles. By using this method, the vehicle absolute velocity and slip ratio can be estimated by an improved nonlinear observer without using GPS, and the friction force and tyre–road friction coefficient can be obtained from the estimated vehicle velocity and slip ratio. Simulations are used to validate the effectiveness of the proposed estimation method.     

基于RFID和IMU技术的室内定位方法研究与应用

针对在室内停车场等GPS信号较差的工况,行驶车辆无法实时获取准确定位的问题,文章结合RFID和IMU两种定位技术,使用卡尔曼滤波器耦合该两组定位系统信号,并将该方法应用在某款车型上,结果表明在室内停车场能够获得实时准确的位置信息。     

基于探测车数据的路段行程时间估计

利用探测车数据进行路段行程时间估计面临着两类误差：采样误差和非采样误差,从而导致估计结果精度不高和可靠性差。在回顾已有估计方法的基础上,有针对性地引入了自适应式卡尔曼滤波,建立了相应的状态方程和观测方程,利用相似时间特征的历史数据标定了状态转移系数,并对滤波进行了求解。以实际数据对估计方法进行了验证,平均相对误差为13.13%。研究表明,自适应式卡尔曼滤波能够应用到基于探测车数据的路段行程时间估计中来,并具有估计精度高、收敛速度快、参数少、对初值不敏感等优点。     

State observer-based sliding mode control for semi-active hydro-pneumatic suspension

This paper proposes an improved virtual reference model for semi-active suspension to coordinate the vehicle ride comfort and handling stability. The reference model combines the virtues of sky-hook with ground-hook control logic, and the hybrid coefficient is tuned according to the longitudinal and lateral acceleration so as to improve the vehicle stability especially in high-speed condition. Suspension state observer based on unscented Kalman filter is designed. A sliding mode controller (SMC) is developed to track the states of the reference model. The stability of the SMC strategy is proven by means of Lyapunov function taking into account the nonlinear damper characteristics and sprung mass variation of the vehicle. Finally, the performance of the controller is demonstrated under three typical working conditions: the random road excitation, speed bump road and sharp acceleration and braking. The simulation results indicated that, compared with the traditional passive suspension, the proposed control algorithm can offer a better coordination between vehicle ride comfort and handling stability. This approach provides a viable alternative to costlier active suspension control systems for commercial vehicles.     

A vehicle ABS adaptive sliding-mode control algorithm based on the vehicle velocity estimation and tyre/road friction coefficient estimations

A sliding-mode observer is designed to estimate the vehicle velocity with the measured vehicle acceleration, the wheel speeds and the braking torques. Based on the Burckhardt tyre model, the extended Kalman filter is designed to estimate the parameters of the Burckhardt model with the estimated vehicle velocity, the measured wheel speeds and the vehicle acceleration. According to the estimated parameters of the Burckhardt tyre model, the tyre/road friction coefficients and the optimal slip ratios are calculated. A vehicle adaptive sliding-mode control (SMC) algorithm is presented with the estimated vehicle velocity, the tyre/road friction coefficients and the optimal slip ratios. And the adjustment method of the sliding-mode gain factors is discussed. Based on the adaptive SMC algorithm, a vehicle's antilock braking system (ABS) control system model is built with the Simulink Toolbox. Under the single-road condition as well as the different road conditions, the performance of the vehicle ABS system is simulated with the vehicle velocity observer, the tyre/road friction coefficient estimator and the adaptive SMC algorithm. The results indicate that the estimated errors of the vehicle velocity and the tyre/road friction coefficients are acceptable and the vehicle ABS adaptive SMC algorithm is effective. So the proposed adaptive SMC algorithm can be used to control the vehicle ABS without the information of the vehicle velocity and the road conditions.     

A model of driver steering control incorporating the driver's sensing of steering torque

Steering feel, or steering torque feedback, is widely regarded as an important aspect of the handling quality of a vehicle. Despite this, there is little theoretical understanding of its role. This paper describes an initial attempt to model the role of steering torque feedback arising from lateral tyre forces. The path-following control of a nonlinear vehicle model is implemented using a time-varying model predictive controller. A series of Kalman filters are used to represent the driver's ability to generate estimates of the system states from noisy sensory measurements, including the steering torque. It is found that under constant road friction conditions, the steering torque feedback reduces path-following errors provided the friction is sufficiently high to prevent frequent saturation of the tyres. When the driver model is extended to allow identification of, and adaptation to, a varying friction condition, it is found that the steering torque assists in the accurate identification of the friction condition. The simulation results give insight into the role of steering torque feedback arising from lateral tyre forces. The paper concludes with recommendations for further work.     

A novel global sensitivity analysis on the observation accuracy of the coupled vehicle model

ABSTRACT

This paper proposes a novel 2-step global sensitivity analysis algorithm to provide an in-depth sensitivity analysis of the vehicle parameters on the system responses. A 9 degree-of-freedom nonlinear vertical–lateral coupled vehicle model is developed, and 12 parameters along with 7 system responses are selected for the sensitivity analysis. In order to reduce the computational effort, the proposed 2-step algorithm calculates the elementary effects and selects 7 influential parameters from these 12, and then uses the Sobol' method to obtain the global sensitivity indexes of these influential parameters. An unscented Kalman filter is finally designed to show the effect and importance of the selected sensitive parameters on the observation accuracy. Simulations with different vehicle types, velocities and tyre models have verified that the proposed algorithm can accurately describe the relationship between the vehicle parameters and system responses, which is of directive significance to improve vehicle controller and observer performances.     

Velocity and normal tyre force estimation for heavy trucks based on vehicle dynamic simulation considering the road slope angle

A precise estimation of vehicle velocities can be valuable for improving the performance of the vehicle dynamics control (VDC) system and this estimation relies heavily upon the accuracy of longitudinal and lateral tyre force calculation governed by the prediction of normal tyre forces. This paper presents a computational method based on the unscented Kalman filter (UKF) method to estimate both longitudinal and lateral velocities and develops a novel quasi-stationary method to predict normal tyre forces of heavy trucks on a sloping road. The vehicle dynamic model is constructed with a planar dynamic model combined with the Pacejka tyre model. The novel quasi-stationary method for predicting normal tyre forces is able to characterise the typical chassis configuration of the heavy trucks. The validation is conducted through comparing the predicted results with those simulated by the TruckSim and it has a good agreement between these results without compromising the convergence speed and stability.     

Effective assessment of tyre–road friction coefficient using a hybrid estimator

Vehicle stability and active safety control depend heavily on tyre forces available on each wheel of a vehicle. Since tyre forces are strongly affected by the tyre–road friction coefficient, it is crucial to optimise the use of the adhesion limits of the tyres. This study presents a hybrid method to identify the road friction limitation; it contributes significantly to active vehicle safety. A hybrid estimator is developed based on the three degrees-of-freedom vehicle model, which considers longitudinal, lateral and yaw motions. The proposed hybrid estimator includes two sub-estimators: one is the vehicle state information estimator using the unscented Kalman filter and another is the integrated road friction estimator. By connecting two sub-estimators simultaneously, the proposed algorithm can effectively estimate the road friction coefficient. The performance of the proposed estimation algorithm is validated in CarSim/Matlab co-simulation environment under three different road conditions (high-μ, low-μ and mixed-μ). Simulation results show that the proposed estimator can assess vehicle states and road friction coefficient with good accuracy.