Navigating with highly precise odometry and noisy GPS: a case study

Abstract

Abstract: For linear systems, the Kalman filter perfectly handles rank deficiencies in the process noise covariance matrix, i.e., deterministic information. Yet, in a nonlinear setting this poses great challenges to the extended Kalman filter (EKF). In this paper we consider a simplified nonlinear car model with deterministic dynamics, i.e., perfect odometry, and noisy position measurements. Simulations evidence the EKF, when used as a nonlinear observer, 1- fails to correctly encode the physical implications of the deterministic dynamics 2- fails to converge even for arbitrarily small initial estimation errors. On the other hand, the invariant (I)EKF, a variant of the EKF that accounts for the symmetries of the problem 1- correctly encodes the physical implications of the deterministic information 2-is mathematically proved to (almost) globally converge, with explicit convergence rates, whereas the EKF does not even locally converge in our simulations. This study more generally suggests the IEKF is way more natural than the EKF, for high precision navigation purposes.