Vehicle Sideslip Angle Estimation using a Hybrid Approach

Abstract

Accurate and robust vehicle state estimation is important for proper operation of vehicle control systems. For lateral stability control accurate estimation of the Vehicle Sideslip Angle (VSA) is of utmost importance. This thesis aims to develop an accurate and highly robust model to estimate the VSA. Common vehicle sensors such as the Inertial Measurement Unit (IMU), Global Positioning System (GPS) and steering angle sensor are used to provide measurements of vehicle states that are relatively easy to directly measure. Additionally, wheel bearing strains measurements are collected by the Load-­Sensing Bearing (LSB), which can be mapped to the tire forces that are measured by wheel force transducers. Insight regarding the tire forces could be beneficial to VSA estimation. The focus lies upon neural network estimators and hybrid structures, which combine the neural network estimator with an observer model.
A large-­scale experimental dataset composed of standardised vehicle manoeuvres is used to develop and evaluate different estimation architectures. The dataset consists of 216 manoeuvres, which corresponds to approximately two hours of driving time.

Neural network estimators are data-­driven and therefore rely on high quality data. Various neural network architectures exist for the purpose of time series estimation. In this thesis the Feedforward Neural Network (FFNN), Recurrent Neural Network (RNN) and Transformer are examined in detail. The FFNN
and RNN yield similar performance in terms of Root Mean Squared Error (RMSE) and Maximum Error (ME) on the test set. The Transformer is unable to match this performance level due to the absence of a proper positional encoding of the measurements. Due to the simpler structure and lower data requirement, the FFNN is selected for application in the hybrid structures.
To create a hybrid estimator, the uncertainty level of the VSA estimate from the neural network is required. To obtain the uncertainty using a neural network, various methods exist such as Monte Carlo Dropout (MCDO), Monte Carlo Batch Normalisation (MCBN) and the Uncertainty Deep Ensemble (UDE). These methods are compared using three metrics, the RMSE, Predictive Loglikelihood (PLL) and Continuous Ranked Probability Score (CRPS). A combination of these metrics does not only evaluate the estimation accuracy, but also the quality of the corresponding estimated uncertainty level. The UDE consisting of
FFNNs provides the best performance and even outperforms the single FFNN in terms of RMSE by a decrease of 8.6%. Therefore, the UDE is used to develop the different hybrid structures.

The Extended Kalman Filter (EKF) and Unscented Kalman Filter (UKF) are built on a nonlinear bicycle model. Different sets of inputs for the observers, as well as constant or adaptive covariance matrices create different variations. These observer variations are combined with the UDE to form hybrid estimation
models. The different variations show equal performance due to the high accuracy of the UDE on the test set. The high performance of the UDE causes the measurement noise to be tuned to a very low level, which results in the observer ’trusting’ the UDE estimations. Therefore, the performance of the different
hybrid structures is almost equal to that of the original UDE.

To investigate if the observer is actually able to correct neural network estimations, a suboptimal neural network is created. This network is trained only on measurements with an absolute lateral acceleration lower than 5 m/s2. This mimics sparse data of high sideslip angles, a common problem for data­-driven
approaches in this setting. This causes the uncertainty of the neural network estimations to be higher in these operating regions. A linear scaling of the uncertainty level to match the variance of the noise on the other measurements does not yield satisfactory results. However, an exponential scaling of the
uncertainty level causes a higher differentiation between low and high confidence levels. This exponential scaling decreases the RMSE of the hybrid structure with 11.4 %. Furthermore, a method for adapting the process noise based on the quality of the observer model estimation is implemented. This equates to
similar performance in terms of RMSE, but introduces a number of additional parameters to tune.