Belief functions induced by multimodal probability density functions, an application to the search and rescue problem

¹ E3I2-EA3876/ENSTA, 2 rue François Verny, 29806 Brest Cedex 09, France. Pierre-Emmanuel.Dore@ensta-bretagne.fr
² CERMID - Dpt. OSD, FSA - Université Laval, Québec, QC, G1K 7P4, Canada.
³ Defense R&D Canada-Valcartier, 2459 Pie-XI, Blvd North, QC, G3J 1X5, Canada.

Received: 28 February 2010
Accepted: 8 November 2010

Abstract

In this paper, we propose a new method to generate a continuous belief functions from a multimodal probability distribution function defined over a continuous domain. We generalize Smets' approach in the sense that focal elements of the resulting continuous belief function can be disjoint sets of the extended real space of dimension n. We then derive the continuous belief function from multimodal probability density functions using the least commitment principle. We illustrate the approach on two examples of probability density functions (unimodal and multimodal). On a case study of Search And Rescue (SAR), we extend the traditional probabilistic framework of search theory to continuous belief functions theory. We propose a new optimization criterion to allocate the search effort as well as a new rule to update the information about the lost object location in this latter framework. We finally compare the allocation of the search effort using this alternative uncertainty representation to the traditional probabilistic representation.