Mathematical modeling of INS error dynamics for integration/debiasing

The goal of this work is two-fold: (1) arrive at an elegant scheme to study the effect of device bias on the position solution of a general Inertial Navigation System (INS) system; and (2) develop a simple integration method to robustly debias and efficiently estimate true position using potentially biased INS outputs and all other available external measurements. A characteristic set of possible bias trajectories is generated via a novel backward-forward solution approach. These trajectories are continuous functions and are forced to reliably reflect the effects of nominal platform trajectory. They are ultimately utilized to determine the maximum time beyond which approximation of such time-varying bias trajectories with simple piecewise polynomial curves is unrealistic. The times are then used to arrive at an estimation technique that best uses potentially biased INS outputs along with other non-inertial navigation measurements, such as SLAM-based and map-matching-based estimates, to yield minimum mean-squared error unbiased estimates of the time-varying location of the platform as well as simultaneously debias the INS solution. Theoretical arguments and real-data results are provided to reveal the potential of the approach. An Unmanned Undersea Vehicle (UUV) with on-board sonars and an INS suite is the platform for this work.