Nonlinear Observer for Tightly Coupled Integration of Pseudorange and Inertial Measurements

Abstract

A global nonlinear algebraic transform of nonlinear pseudorange measurement equations enables navigation solutions based on a globally valid linear time-varying measurement model. Using an interconnection of a nonlinear attitude observer and a translational motion observer based on pseudorange and range–range measurements, a tightly coupled integrated aided inertial navigation system is designed. The attitude observer uses a proper acceleration estimate from the translational motion observer as a reference vector for the accelerometer measurement. This leads to a feedback interconnection that is shown to be globally exponentially stable under some conditions on the tuning parameters. The model transformation has eliminated the information about a certain nonlinear relationship that exists among the measurements. While this enables the global solution to be found, it also leads to loss of estimation accuracy when there is measurement noise. In order to recover close-to-optimal (minimum variance) estimates, the observer estimates are only used to generate a locally linearized time-varying model that is subsequently employed by a Kalman filter, without loss of global convergence.