General Solution for Linearized Error Propagation in Vehicle Odometry

Abstract

Although odometry is nonlinear, it yields sufficiently to linearized analysis to produce a closed-form transition matrix and a symbolic general solution for both deterministic and stochastic error propagation. Accordingly, error propa- gation in vehicle odometry can be understood at a level of theoretical rigor equivalent to the well-known Schuler dynamics of inertial navigation. While response to initial conditions is path-independent, response to input errors can be related to path functionals. These trajectory moments are integral transforms which function like the moment of inertia or the Laplace transform - enabling many error propagation calculations to be performed by hand in closed-form.