Albena Tchamova

On the Validity of Dempster's Fusion Rule and its Interpretation as a Generalization of Bayesian Fusion Rule

The purpose of this paper is to focus on and discuss both: (i) the validity of the Dempsters rule of combination and foundations of Dempster–Shafer theory and (ii) the real compatibility (or not) of the Dempsters rule with the Bayes fusion rule. We analyze and explain, on the basis of a generic example, the inconsistent behavior of the Dempsters rule of combination, introduced by Shafer in his mathematical theory of evidence, as a valid method to combine sources of information. We identify the cause and the effect of the dictatorial power behavior of this rule and of its impossibility to manage the conflicts between the sources no matter of their level. For comparison purpose, we present the respective solutions obtained by the more efficient proportional conflict redistribution rule number 5 proposed originally in Dezert–Smarandache theory framework. The inherent contradiction of Dempster–Shafer theory foundations is identified and proved. Then, a deep analysis of the compatibility of the Dempsters fusion rule with the Bayes fusion rule (from a fusion standpoint) is made on the basis of proposed new interesting formulation of the Bayes rule. We prove that the Dempsters rule does not behave as the Bayes fusion rule in general, because both methods deal very differently with the prior information when it is really informative (not uniform). Only in the very particular case where the basic belief assignments to combine are Bayesian and when the prior information is uniform (or vacuous), the Dempsters rule remains consistent with the Bayes fusion rule. It is proved, that in more general cases, the Dempsters rule is incompatible with the Bayes rule and it is not a generalization of the Bayes fusion rule.

Target Type Tracking with PCR5 and Dempster's rules: A Comparative Analysis

In this paper we consider and analyze the behavior of two combinational rules for temporal/sequential attribute data fusion for target type estimation. Our comparative analysis is based on Dempsters fusion rule proposed in Dempster-Shafer theory (DST) and on the proportional conflict redistribution rule no. 5 (PCR5) recently proposed in Dezert-Smarandache theory (DSmT). We show through very simple scenario and Monte-Carlo simulation, how PCR5 allows a very efficient target type Tracking and reduces drastically the latency delay for correct target type decision with respect to Dempsters rule. For cases presenting some short target type switches, Demspters rule is proved to be unable to detect the switches and thus to track correctly the target type changes. The approach proposed here is totally new, efficient and promising to be incorporated in real-time generalized data association-multi target tracking systems (GDA-MTT) and provides an important result on the behavior of PCR5 with respect to Dempsters rule. The MatLab source code is also provided in the paper

On the behavior of Dempster's rule of combination and the foundations of Dempster-Shafer Theory

On the base of simple emblematic example we analyze and explain the inconsistent and inadequate behavior of Dempster-Shafers rule of combination as a valid method to combine sources of evidences. We identify the cause and the effect of the dictatorial power behavior of this rule and of its impossibility to manage the conflicts between the sources. For a comparison purpose, we present the respective solution obtained by the more efficient PCR5 fusion rule proposed originally in Dezert-Smarandache Theory framework. Finally, we identify and prove the inherent contradiction of Dempster-Shafer Theory foundations.

On the blackman's association problem

Modern multitarget-multisensor tracking systems involve the development of reliable methods for the data association and the fusion of multiple sen- SOT infonnation, and more specifically the partioning of observations into tracks. This paper discusses and compares the application of Dempster-Shafer Theory (DST) and the Dezert-Smarandache Theory (DSmT) methods to the fusion of multiple sensor attributes for target identification purpose. We focus our attention on the paradozical Blackmans association problem and propose several approaches to outperfom Blackmans solution. We clarih some preconceived ideas about the use of degree of conflict between sources as potential criterion for partitioning evidences.

Estimation of target behavior tendencies using dezert-smarandache theory

This paper presents an approach for tar- get behavior tendency estimation (Receding, Approach- ing). It is developed on the principles of Dezert- Smarandache theory (DSmT) of plausible and para- doxical reasoning applied to conventional sonar ampli- tude measurements, which serve as an evidence for COT- responding decision-making procedures. In some real world situations it is dificult to finalize these proce- dures, because of discrepancies in measurements inter- pretation. In these cases the decision-making process leads to conflicts, which cannot be resolved using the well-know methods. The aim of the perjomed study is to present and to approve the ability of DSmT to fi- nalize successfully the decision-making process and to assure awareness about the tendencies of target behav- ior in case of discrepancies in measurements interpre- tation. An example is provided to illustrate the bene- fit of the proposed approach application in comparison of fuzzy logic approach, and its ability to improve the overall tracking perfonnance.

Target Identification Based on DSmT

An approach providing a rapid reduction of total ignorance in the target identification process is proposed. It is based on a combination of the new Dezert-Smarandache theory (DSmT) for plausible and paradoxical reasoning, and fuzzy set theory. This approach utilizes information from the adjoint sensor and additional information obtained from a priori defined objective and subjective considerations. As a result, the pignistic probabilities for a target’s nature are obtained and analyzed.

A new class fusion rule for solving Blackman’s Association Problem

This paper presents a new approach for solving the paradoxical Blackmanpsilas association problem. It utilizes the recently defined new class fusion rule based on fuzzy T-conorm/T-norm operators together with Dezert-Smarandache theory based, relative variations of generalized pignistic probabilities measure of correct associations, defined from a partial ordering function of hyper-power set. The ability of this approach to solve the problem against the classical Dempster-Shaferpsilas method, proposed in the literature is proven. It is shown that the approach improves the separation power of the decision process for this association problem.

A comparative analysis of QADA-KF with JPDAF for multitarget tracking in clutter

This paper presents a comparative analysis of performances of two types of multi-target tracking algorithms: 1) the Joint Probabilistic Data Association Filter (JPDAF), and 2) classical Kalman Filter based algorithms for multi-target tracking improved with Quality Assessment of Data Association (QADA) method using optimal data association. The evaluation is based on Monte Carlo simulations for difficult maneuvering multiple-target tracking (MTT) problems in clutter.

Performance evaluation of fuzzy-based fusion rules for tracking applications

The objective of this paper is to present and to evaluate the performance of particular fusion rules based on fuzzy T-Conorm/T-Norm operators for two tracking applications: 1) tracking object’s type changes, supporting the process of objects’ identification (e.g., fighter against cargo, friendly aircraft against hostile ones), which, consequently is essential for improving the quality of generalised data association for targets’ tracking; 2) alarms’ identification and prioritisation in terms of degree of danger relating to a set of a priori defined, out of the ordinary dangerous directions. The aim is to present and demonstrate the ability of these rules to assure coherent and stable way for identification and to improve decision-making process in a temporal way. A comparison with performance of Dezert-Smarandache Theory-based Proportional Conflict Redistribution rule no. 5 and Dempster’s rule is also provided.

Tracking applications with fuzzy-based fusion rules

The objective of this paper is to present and evaluate the performance of a particular fusion rule based on fuzzy T-Conorm/T-Norm operators for two tracking applications: (1) Tracking Objects Type Changes, supporting the process of identification, (e.g. friendly aircraft against hostile ones, fighter against cargo) and consequently for improving the quality of generalized data association; (2) Alarms identification and prioritization in terms of degree of danger relating to a set of a priori defined, out of the ordinary dangerous directions. The aim is to present and demonstrate the ability of TCN rule to assure coherent and stable way for identification and to improve decision-making process in temporal way. A comparison with performance of DSmT based PCR5 fusion rule and Dempsters rule is also provided.