Navigation under Abrupt Motion Disturbances: A Convex Programming Perspective

Abstract

An approach to account for sparse and abrupt motion disturbances in navigation applications is presented. Large impulsive disturbances force us to abandon the conventional Gaussian noise assumption in process noise modeling for dynamic systems. The non-Gaussian modeling approach taken in this research can estimate sparse motion outliers much more accurately than the classic Gaussian paradigm. The proposed estimation scheme is framed as a convex optimization problem. This allows for greater flexibility in problem formulation by enabling any finite number of domain dependent convex constraints to be included if desired. Illustration of the method is done for a discrete-time linear state space model for vehicle navigation. The results show that, ℓ1 method, which considers heavy-tailed process noise models, has significant advantages over the classical ℓ2/Gaussian method. ℓ2 method corresponds to the well known Kalman filter. Near perfect recovery of disturbance signals and improved kinematic state estimation is possible with the approach presented. Accurate disturbance recovery has benefits in enabling fault estimation and diagnosis for robust navigation applications. A simulation study is conducted to validate the proposed scheme.