Combined recurrent neural networks and particle-swarm optimization for sideslip-angle estimation based on a vehicle multibody dynamics model

The active safety system of a vehicle typically relies on real-time monitoring of the sideslip angle and other critical signals, such as the yaw rate. The vehicle sideslip angle cannot be measured directly due to the high cost and impracticality of sensor networks. The vehicle sideslip can be estimated using kinematic, dynamic, or machine-learning models and available vehicle states. This paper combines recurrent neural networks and the particle-swarm optimization (PSO) algorithm to estimate the vehicle sideslip angle accurately. First, a vehicle-dynamics model is constructed to conduct dynamics simulations of vehicles under various driving conditions and road environments for data collection. Secondly, the obtained vehicle states, including velocity, acceleration, yaw rate, and steering, are used to develop machine-learning models that estimate the vehicle sideslip angle. Two machine-learning models are proposed using the long short-term memory neural network (LSTM) and the bidirectional long short-term memory neural network (BiLSTM). Thirdly, the PSO algorithm is employed to optimize the hyperparameters of the LSTM and BilLSTM models for enhanced estimation precision. The Gaussian noise is added to the datasets to evaluate the robustness of the estimation models. The results indicate that the estimation models are capable of accurately predicting the vehicle’s sideslip angle. The $R^2$ $R^{2}$ values of the results are mostly greater than 0.96. The PSO algorithm can improve estimation precision, and the PSO-LSTM model performs the best.