Thisn paper introduces the concept of cross-entropy and relative entropy of two basic belief assignments. It is based on the new entropy measure presented recently. We prove that the cross-entropy satisfies a generalized Gibbs-alike inequality from which a generalized Kullback-Leibler divergence measure can be established in the framework of belief functions. We show on a simple illustrating example how these concepts can be used for decision-making under uncertainty.

In the context of single air picture fusion based on tracks produced by several heterogeneous C2 system, this paper presents our original algorithmic approach and results of the decentralized fusion process. In this applicative context, the decentralized fusion node receives potentially very numerous (thousands) tracks from all registered C2. Some registered C2 are inconstant in terms of performance and accuracy, resulting in heterogeneous data and possibly in ill associations or estimations; therefore tracks and covariances are not always reliable especially in regards to consistency and velocity. A fast, parallelizable and robust track association algorithm is presented, which cope with these C2 tracks information. Track association is made by partitioning a track graph. A tactical situation maintenance strategy inspired by the state of the art in MHT (multiple hypothesis tracking) implementation is proposed.

This paper presents a generic and versatile approach for implementing combining rules on preprocessed belief functions, issuing from a large population of information sources. In this paper, we address two issues, which are the intrinsic complexity of the rules processing, and the possible large amount of requested combinations. We present a fully distributed approach, based on a map-reduce (Spark) implementation.

This paper presents a methodology for the evaluation of a path planning algorithm based on a learning approach. Here this evaluation procedure is applied for the problem of optimizing the navigation of a mobile robot in a known environment. A metric map composed of landmarks representing natural elements is given to define the best trajectory which permits to guarantee a localization performance during its execution. The vehicle is equipped with a sensor which enables it to obtain range and bearing measurements from landmarks. These measurements are matched with the map to estimate its position. As the mobile state and the measurements are stochastic, the optimal planning scheme considered in this paper deals with posterior Cramer-Rao Bound as a performance measure. Because of the nature of the cost function, classical optimization algorithms like dynamic programming are irrelevant. Therefore, we propose to achieve the optimization step with the Cross Entropy algorithm for optimization to generate trajectories from a suitable parameterized probability density functions family. Nevertheless, although the convergence of this algorithm can be assessed with the analysis of the stationarity of its intrinsic parameters, we are not able to quantify the level of convergence around the optimal value. As a consequence, an external investigation can be applied from an alternative stochastic procedure followed by an analysis via extreme value theory.

Works have investigated the problem of the conflict redistribution in the fusion rules of evidence theories. As a consequence of these works, many new rules have been proposed. Now, there is not a clear theoretical criterion for a choice of a rule instead another. The present paper proposes a new theoretically grounded rule, based on a new concept of sensor independence. This new rule avoids the conflict redistribution, by an adaptive combination of the beliefs. Both the logical grounds and the algorithmic implementation are considered.

This paper defines and implements a non-Bayesian fusion rule for combining densities of probabilities estimated by local (non-linear) filters for tracking a moving target by passive sensors. This rule is the restriction to a strict probabilistic paradigm of the recent and efficient proportional conflict redistribution rule no 5 (PCR5) developed in the DSmT framework for fusing basic belief assignments. A sampling method for probabilistic PCR5 (p-PCR5) is defined. It is shown that p- PCR5 is more robust to an erroneous modeling and allows to keep the modes of local densities and preserve as much as possible the whole information inherent to each densities to combine. In particular, p-PCR5 is able of maintaining multiple hypotheses/modes after fusion, when the hypotheses are too distant in regards to their deviations. This new p-PCR5 rule has been tested on a simple example of distributed non-linear filtering application to show the interest of such approach for future developments. The non-linear distributed filter is implemented through a basic particles filtering technique. The results obtained in our simulations show the ability of this p-PCR5-based filter to track the target even when the models are not well consistent in regards to the initialization and real cinematic.

This paper introduces a common method, based on the cross-entropy method, in order to solve a variety of search problems when search resources are scarce compared to the size of the space of search. In particular, we solve: detection and information search problems, a detection search game, and a two-targets detection search problem. Our approach is built of two steps: first, decompose a problem in a hierarchical manner (two optimization levels) and then, solve the global level using the cross-entropy method. At local level, different solutions are conceivable, depending of the kind of the problem. Problems of interest are in the field of combinatorial optimization and are considered to be hard to solve: we find optimal solution in most cases with a reasonable computation time.

This paper addresses the problem of optimizing the navigation of an intelligent mobile in a real world environment, described by a map. The map is composed of features representing natural landmarks in the environment. The vehicle is equipped with a sensor which allows it to obtain range and bearing measurements from observed landmarks during the execution. These measurements are correlated with the map to estimate its position. The optimal trajectory must be designed in order to control a measure of the performance for the filtering algorithm used for the localization task. As the mobile state and the measurements are random, a well-suited measure can be a functional of the approximate posterior Cramer-Rao bound. A natural way for optimal path planning is to use this measure of performance within a (constrained) Markovian decision process framework. However, due to the functional characteristics, dynamic programming method is generally irrelevant. To face that, we investigate a learning approach based on the cross-entropy method

In this paper, we are interested in the optimal dynamical control of sensors based on partial and noisy observations. These problems are related to the POMDP family. In this case however, we are manipulating continuous-valued controls and continuous-valued decisions. While the dynamical programming method will rely on a discretization of the problem, we are dealing here directly with the continuous data. Moreover, our purpose is to address the full past observation range. Our approach is to modelize the POMDP strategies by means of dynamic Bayesian networks. A method, based on the cross-entropy is implemented for optimizing the parameters of such DBN, relatively to the POMDP problem. In this particular work, the dynamic Bayesian networks are built from semi-continuous probabilistic laws, so as to ensure the manipulation of continuous data

This paper is discussing about the collection of informations for military operations at the command level. A variety of sensors are available then, with different characteristics and ranges. The command is interested in helpful tools for the planning of these sensors. According to such objective, this work deal with the optimal covering of the requested information by the sensors. Inspired by the human operator methodology, it is based on a geometrical formalism of the sensors. A method based on the cross-entropy algorithm is proposed for optimizing the locations and geometrical parameters of the sensors in order to maximize the track covering