Real time and batch navigation solutions: alternative approaches

Inertial geodesy for kinematic surveying and navigation historically maintain different approaches for the optimal estimation of the parameters of interest: navigational solutions are real time always, while geodetic solutions are in general obtained in post processing by means of a batch optimisation algorithm. If Kalman filtering is the typical method of real time data processing, Kalman filtering plus Kalman smoothing is the method generally used for geodetic navigation. In this work we demonstrate that, alternatively to a Kalman filtering plus Kalman smoothing solution, a new method that we call geodetic solution can be used. This method, by exploiting some simple expedients, allows obtaining least squares solutions equivalent to Kalman solutions with a comparable computational load. The equivalence of the two procedures has been verified by some simulated numerical examples.