Analyzing Uncertainty in the Spatial Representation of the Kinematic Bicycle Model

Estimating a vehicle’s pose in uncertain environments is a key challenge in autonomous navigation due to noisy sensor data and the nonlinear nature of kinematic models. This study focuses on computing the evolving covariance matrix for a rear-wheel bicycle model under uncertainty in wheel displacement and steering angle. By linearizing trigonometric terms using Taylor series, we derive accurate closed-form expectations that closely match Monte Carlo simulations. To our knowledge, this is the first complete and precise closed-form derivation for this model, addressing limitations in prior work.