Long Baseline Aided Inertial Navigation System with Clock Offset Estimation

In underwater navigation the Global Positioning System is unavailable, hence other solutions must be pursued in the development of navigation systems. In this paper, filters for the position, linear velocity, and acceleration of underwater vehicles are derived by combining an inertial navigation system with a long baseline acoustic positioning system. A dynamic model is devised via state augmentation, including bias of the pseudo-ranges, which accounts for the effect of the unknown offset between the emitters' and receivers' clocks. The proposed solution, which includes the explicit dynamic estimation of the bias of the pseudo-ranges, is a linear Kalman filter. The observability of the system is assessed, which allows to establish globally exponentially stable error dynamics. The performance of the solution is evaluated with realistic simulation results, considering sensor noise and discrete-time measurements.