Linearized Error Propagation in Odometry

The related fields of mobile robotics and ground vehicle localization lack a linearized theory of odometry error propagation. By contrast, the equivalent Schuler dynamics which apply to inertial guidance have been known and exploited for decades. In this paper, the general solution of linearized propagation dynamics of both systematic and random errors for vehicle odometry is developed and validated. The associated integral transforms are applied to the task of eliciting the major dynamic behaviors of errors for several forms of odometry. Interesting behaviors include path independence, response to symmetric inputs, zeros, extrema, monotonicity and conservation. Applications to systems theory, systems design, and calibration are illustrated.