This paper is concerned with the Bayesian estimation with possibility theory of the number of targets in an area of interest when no prior information is available. The estimation relies solely on the number of detections that is reported every time the area is surveyed. It is assumed that detections can be true and false positives. Possibility theory is capable of quantifying the complete absence of prior information on the number of targets with the introduction of a prior possibility function that is equal to one everywhere on the set of natural numbers. This has no equivalent in probability theory. The prior possibility function is turned into a posterior possibility function from which a point estimate of the number of targets can be derived. Besides the point estimate, a meaningful notion of confidence interval can be derived from the posterior possibility and necessity associated with subsets of the natural numbers.

Efficient path-planning algorithms are a crucial issue for modern autonomous underwater vehicles. Classical path-planning algorithms in artificial intelligence are not designed to deal with wide continuous environments prone to currents. We present a novel Fast Marching (FM)-based approach to address the following issues. First, we develop an algorithm we call FM* to efficiently extract a 2-D continuous path from a discrete representation of the environment. Second, we take underwater currents into account thanks to an anisotropic extension of the original FM algorithm. Third, the vehicle turning radius is introduced as a constraint on the optimal path curvature for both isotropic and anisotropic media. Finally, a multiresolution method is introduced to speed up the overall path-planning process.