Bayesian Approach for Parameter Estimation in Vehicle Lateral Dynamics

Fabien Lionti, Nicolas Gutowski, Sébastien Aubin, Philippe Martinet

Abstract: Estimating parameters for nonlinear dynamic systems is a significant challenge across numerous research areas and practical applications. This paper introduces a novel two-step approach for estimating parameters that control the lateral dynamics of a vehicle, acknowledging the limitations and noise within the data. The methodology merges spline smoothing of system observations with a Bayesian framework for parameter estimation. The initial phase involves applying spline smoothing to the system state variable observations, effectively filtering out noise and achieving precise estimates of the state variables’ derivatives. Consequently, this technique allows for the direct estimation of parameters from the differential equations characterizing the system’s dynamics, bypassing the need for labor-intensive integration procedures. The subsequent phase focuses on parameter estimation from the differential equation residuals, utilizing a Bayesian method known as likelihood-free ABC-SMC. This Bayesian strategy offers multiple advantages: it mitigates the impact of data scarcity by incorporating prior knowledge regarding the vehicle’s physical properties and enhances interpretability through the provision of a posterior distribution for the parameters likely responsible for the observed data. Employing this innovative method facilitates the robust estimation of parameters governing vehicle lateral dynamics, even in the presence of limited and noisy data.