Diffusion-based trajectory observers have been recently proposed as a simple and efficient framework to solve diverse smoothing problems in underwater navigation. For instance, to obtain estimates of the trajectories of an underwater vehicle given position fixes from an acoustic positioning system and velocity measurements from a DVL. The observers are conceptually simple and can easily deal with the problems brought about by the occurrence of asynchronous measurements and dropouts. In its original formulation, the trajectory observers depend on a user-defined constant gain that controls the level of smoothing and is determined by resorting to trial and error. This paper presents a methodology to choose the observer gain by taking into account a priori information on the variance of the position measurement errors. Experimental results with data from an acoustic positioning system are presented to illustrate the performance of the derived observers.
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