Differentiable Moving Horizon Estimation for Vehicle Kinematics via Learning Covariance Matrices

This paper introduces the Differentiable Moving Horizon Estimation (DMHE) as a solution for robustly estimating vehicle kinematics, especially when prior knowledge of the covariance matrices for process and measurement noises is lacking. Traditional moving horizon estimation requires known covariance matrices and employs Sequential Quadratic Programming (SQP) to optimize its cost function. This inherent assumption often limits its real-world applicability. We address this constraint by proposing a method that learns noise covariance matrices through matrix differentials. This innovation ensures DMHE's robust estimation capabilities across various noisy signals. Through comprehensive evaluations on vehicle lateral estimation and adaptive Stanley control, DMHE is benchmarked against established algorithms including moving horizon estimation (MHE), noise adaptive MHE (NMMHE), expectation-maximization MHE (EMMHE), and variational Bayesian MHE (VBMHE). Our experiments consistently highlight DMHE's high performance. Further validations, targeting both side and forward direction observation methods, underscore its potential in practical vehicular kinematics applications. Overall, our research paves the way for advancements in robust and efficient kinematic estimation techniques for vehicles.