General solution for linearized systematic error propagation in vehicle odometry

Abstract

Vehicle odometry is a nonlinear dynamical system in echelon form. Accordingly, a general solution can be written by solving the nonlinear equations in the correct order. Another implication of this structure is that a completely general solution to the linearized (perturbative) dynamics exists. The associated vector convolution integral is the general relationship between output error and both the input error and reference trajectory. Solutions for errors in individual coordinates are in the form of line integrals in state space. Response to initial conditions and translational scale errors, among others, is path independent and vanishes on all closed trajectories. Response to other errors is path dependent and can be reduced to expressions in error moments of the reference trajectory. These path dependent errors vanish on closed symmetric paths, among others. These theoretical results and the underlying error expressions have many uses in design, calibration, and evaluation of odometry systems.