A near-real time nonlinear state estimation approach with application to initialization of navigation systems

The performance of any linearization based estimation algorithm like the Extended Kalman Filter (EKF) relies heavily on the accuracy of the nominal trajectory about which the system is linearized. When the linearization assumption does not hold, such an algorithm behaves in an unpredictable fashion and metrics of estimation error (i.e. state covariance) are invalid. This paper presents methods to identify in real-time those parts of the state vector whose uncertainties cause significant deviations from the linearized model and proposes a near-real time approach to address the issue. One important class of applications is initialization of navigation systems; therefore, as an example the paper applies the results of the theory to a simplified 7 state, two dimensional GPS aided INS. The near-real time approach is demonstrated in simulation.