Methods for performing sequential invariant extended kalman filtering in navigation and positioning tasks

Abstract

The present disclosure relates to a method for performing sequential invariant extended Kalman filtering in a navigation and positioning task. The method solves the problem that efficient fusion of observations in different frames is difficult to achieve under an IEKF framework, and geometric consistency of covariance propagation cannot be guaranteed. The method includes: dividing observations of navigation sensors according to different frames; constructing a state vector in a Lie group form; performing modeling an output of an inertial measurement unit; performing state propagation according to Lie group state equations; calculating propagation of a covariance matrix; establishing a left-invariant observation equation and a right-invariant observation equation according to the two types of observations; synchronously updating a state estimation through a left-invariant extended Kalman filter and a right-invariant extended Kalman filter; and mapping a left-invariant covariance matrix and a right-invariant covariance matrix via a common state covariance matrix to complete sequential fusion.

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