Eloi Bosse

A new distance between two bodies of evidence

Abstract We present a measure of performance (MOP) for identification algorithms based on the evidential theory of Dempster–Shafer. As an MOP, we introduce a principled distance between two basic probability assignments (BPAs) (or two bodies of evidence) based on a quantification of the similarity between sets. We give a geometrical interpretation of BPA and show that the proposed distance satisfies all the requirements for a metric. We also show the link with the quantification of Dempsters weight of conflict proposed by George and Pal. We compare this MOP to that described by Fixsen and Mahler and illustrate the behaviors of the two MOPs with numerical examples.

Measuring ambiguity in the evidence theory

In the framework of evidence theory, ambiguity is a general term proposed by Klir and Yuan in 1995 to gather the two types of uncertainty coexisting in this theory: discord and nonspecificity. Respecting the five requirements of total measures of uncertainty in the evidence theory, different ways have been proposed to quantify the total uncertainty, i.e., the ambiguity of a belief function. Among them is a measure of aggregate uncertainty, called AU, that captures in an aggregate fashion both types of uncertainty. But some shortcomings of AU have been identified, which are that: 1) it is complicated to compute; 2) it is highly insensitive to changes in evidence; and 3) it hides the distinction between the two types of uncertainty that coexist in every theory of imprecise probabilities. To overcome the shortcomings, Klir and Smith defined the TU1 measure that is a linear combination of the AU measure and the nonspecificity measure N. But the TU1 measure cannot solve the problem of computing complexity, and brings a new problem with the choice of the linear parameter delta. In this paper, an alternative measure to AU for quantifying ambiguity of belief functions is proposed. This measure, called Ambiguity Measure (AM), besides satisfying all the requirements for general measures also overcomes some of the shortcomings of the AU measure. Indeed, AM overcomes the limitations of AU by: 1) minimizing complexity for minimum number of focal points; 2) allowing for sensitivity changes in evidence; and 3) better distinguishing discord and nonspecificity. Moreover, AM is a special case of TU1 that does not need the parameter delta

Measures of effectiveness for high-level fusion

Current advances in technology, sensor collection, data storage, and data distribution have afforded more complex, distributed, and operational information fusion systems (IFSs). IFSs notionally consist of low-level (data collection, registration, and association in time and space) and high-level fusion (user coordination, situational awareness, and mission control). Low-level IFSs typically rely on standard metrics for evaluation such as timeliness, accuracy, and confidence. Given the broader use of IFSs, it is also important to look at high-level fusion processes and determine a set of metrics to test IFSs, such as workload, throughput, and cost. Three types of measures (measures of performance MOP, measures of effectiveness MOE, and measures of merit MOM) are summarized. In this paper, we seek to describe MOEs for High-Level Fusion (HLF) based on developments in Quality of Service (QOS) and Quality of Information (QOI) that support the user and the machine, respectively. We define a HLF MOE based on (1) information quality, (2) robustness, and (3) information gain. We demonstrate the HLF MOE based for a maritime domain situation awareness example.

Joint Data Association, Registration, and Fusion using EM-KF

In performing surveillance using a sensor network, data association and registration are two essential processes which associate data from different sensors and align them in a common coordinate system. While these two processes are usually addressed separately, they actually affect each other. That is, registration requires correctly associated data, and data with sensor biases will result in wrong association. We present a novel joint sensor association, registration, and fusion approach for multisensor surveillance. In order to perform registration and association together, the expectation-maximization (EM) algorithm is incorporated with the Kalman filter (KF) to give simultaneous state and parameter estimates. Computer simulations are carried out to evaluate the performances of the proposed joint association, registration, and fusion method based on EM-KF.

Classification of audio radar signals using radial basis function neural networks

Radial basis function (RBF) neural networks are used to classify real-life audio radar signals that are collected by a ground surveillance radar mounted on a tank. Currently, a human operator is required to operate the radar system to discern among signals bouncing off tanks, vehicles, planes, and so on. The objective of this project is to investigate the possibility of using a neural network to perform this target recognition task, with the aim of reducing the number of personnel required in a tank. Different signal classification methods in the neural net literature are considered. The first method employs a linear autoregressive (AR) model to extract linear features of the audio data, and then perform classification on these features, i.e, the AR coefficients. AR coefficient estimations based on least squares and higher order statistics are considered in this study. The second approach uses nonlinear predictors to model the audio data and then classifies the signals according to the prediction errors. The real-life audio radar data set used here was collected by an AN/PPS-15 ground surveillance radar and consists of 13 different target classes, which include men marching, a man walking, airplanes, a man crawling, and boats, etc. It is found that each classification method has some classes which are difficult to classify. Overall, the AR feature extraction approach is most effective and has a correct classification rate of 88% for the training data and 67% for data not used for training.

Uncertainty in a situation analysis perspective

This paperproposes a discussion on the role of iincerfainty in situation analysis. An overview of the princi- pal typologies of uncertainty foundin the recent literuture is presented. This wide array of uncet-tainty conceptions is a consequence of the intrinsic richness and ambiguity of nat- ural language, but also a consequence of the complexplivs- ical nature of information. Definitions of a liniited number of concepts are proposed in order to better understand the diflerent facets of uncertainty. The benefits sought are: (I) the avoidance of untimely uses of dejniriorls and models of uncertainty. (2) clarifications allowing links with the al- ready well developed logics of knowledge and belief; and (3) guidelines for the selection of the appropriate mathe- matical model to process uncertainty-based information.

A Maximum Likelihood Approach to Joint Image Registration and Fusion

Both image registration and fusion can be formulated as estimation problems. Instead of estimating the registration parameters and the true scene separately as in the conventional way, we propose a maximum likelihood approach for joint image registration and fusion in this paper. More precisely, the fusion performance is used as the criteria to evaluate the registration accuracy. Hence, the registration parameters can be automatically tuned so that both fusion and registration can be optimized simultaneously. The expectation maximization algorithm is employed to solve this joint optimization problem. The Cramer-Rao bound (CRB) is then derived. Our experiments use several types of sensory images for performance evaluation, such as visual images, IR thermal images, and hyperspectral images. It is shown that the mean square error of estimating the registration parameters using the proposed method is close to the CRBs. At the mean time, an improved fusion performance can be achieved in terms of the edge preservation measure QAB/F, compared to the Laplacian pyramid fusion approach.

A Pseudo-Measurement Approach to Simultaneous Registration and Track Fusion

In multi-sensor tracking, registration is expected to be performed at the track level instead of the measurement level especially for the distributed sensor networks. However, registration at the track level becomes more difficult due to the implicit sensor biases hidden behind the local tracks. We propose a pseudo-measurement approach to solve the simultaneous registration and fusion problem at the track level. A pseudo-measurement equation is derived from the local trackers, which explicitly reveals the relationship between the pseudo-measurements and the sensor biases in a closed-form expression. The resulting registration model then allows us to formulate the track registration and fusion as a maximum likelihood (ML) estimation problem. We propose using the expectation maximization (EM) approach to perform track registration and fusion simultaneously. Both batch and recursive EM algorithms are developed, accompanied by the performance analysis. Simulation results demonstrate that both EM algorithms are capable of providing accurate estimates. Moreover, we apply the proposed method to an air surveillance radar network which suffers from relatively serious registration problems. The proposed method is verified to effectively fuse and register the tracks generated by local radars and to provide a consistent air picture.

Ontology alignment in geographical hard-soft information fusion systems

Information fusion exists over many forms of hard data (e.g. from physical sensors) and soft data (e.g. from human reports) to interpret observations of real-world objects. As demonstrated from the Geographical Information Systems (GIS) community, there is a growing need for the linking and alignment of both (1) exploited physical imagery products and (2) derived ontological textual labels (semantic markup). Semantic markup can be done on both exploited data (e.g. automated image segmentation), as well as user reports (e.g. weather forecasts). Since the derived information is collected, stored, and displayed into distinct ontological structures by different agencies; ontological alignment is thus required whenever the semantic information is paired with distinct real-world imagery observations. In this paper, we explore issues of fusing hard and soft data as related to ontology alignment. A maritime domain situational awareness example with geographical imagery and textural ontologies is shown to demonstrate the need for ontology alignment to assist users for pragmatic surveillance.

Approximation techniques for the transformation of fuzzy sets into random sets

With the recent rising of numerous theories for dealing with uncertain pieces of information, the problem of connection between different frames has become an issue. In particular, questions such as how to combine fuzzy sets with belief functions or probability measures often emerge. The alternative is either to define transformations between theories, or to use a general or unified framework in which all these theories can be framed. Random set theory has been proposed as such a unified framework in which at least probability theory, evidence theory, possibility theory and fuzzy set theory can be represented. Whereas the transformations of belief functions or probability distributions into random sets are trivial, the transformations of fuzzy sets or possibility distributions into random sets lead to some issues. This paper is concerned with the transformation of fuzzy membership functions into random sets. In practice, this transformation involves the creation of a large number of focal elements (subsets with non-null probability) based on the @a-cuts of the fuzzy membership functions. In order to keep a computationally tractable fusion process, the large number of focal elements needs to be reduced by approximation techniques. In this paper, we propose three approximation techniques and compare them to classical approximations techniques used in evidence theory. The quality of the approximations is quantified using a distance between two random sets.