Robust data fusion

Jean-François Grandin

THALES Airborne Systems
Z. I. du Pissaloup, 5 rue Jean d’Alembert,

78190 Trappes-Elancourt, France.

Miguel Marquès

Under training at THALES Airborne Systems
EPMI school

95092 Cergy-Pontoise, France.


Abstract - This paper compares different fusion processes in terms of error probability and robustness. To begin with, simple fusion operators are studied in the general framework of two binary sensors (Maximum Likelihood and logical fusion functions like ‘or’, ‘and’…). In the sequel, the comparison is extended to likelihood vectors adding other fusion operators (T-norms, T-conorms, means operators). Finally, different models of fusion processes informed with the source uncertainty are proposed and demonstrate to have good robustness properties.

Keywords: sensor data fusion process, error probability, robustness, imprecision, reliability, uncertainty.

1. Introduction

The combination of uncertain information is a fundamental need in the case of multi-sensor system observations [1]. Considering that we know the physical sensor model density of the conditional measure of the hypothesis, the fusion process capability is evaluated by the Bayes risk. Two frameworks are successively presented: the combination of detection or binary information and the combination of likelihood vectors.

In the binary framework, the behavior of typical logical fusion processes AND, OR are compared to the Maximum Likelihood application in terms of the Bayes risk. We highlight that the Maximum Likelihood is adaptive in function of the known capability of each sensor. It selects the logical operator with the minimum Bayes risk.

The Maximum Likelihood combination presents the drawback to be sensitive to the lack of knowledge of the sensor capabilities.

In the frame of likelihood vectors we compare the behavior of the typical operators MIN, MAX and MEAN with the Maximum Likelihood optimal operator in terms of capabilities and sensitivity. It is shown how the usage of sub-optimal operators allows to reach more robust results, but poorer performances.

Different models of uncertainty (reliability, entropy and precision) are presented. It is demonstrated that an operator informed by the sources uncertainties provides more robust results while preserving performances.


Due to numerous charts, we invite you to view or download here the full document in PDF format (182Ko)


Principes d’identification de signaux radars utilisant imprécisions, incertitudes, informations contextuelles et fiabilités

Jean-François GRANDIN, Didier.NEVEU

THALES Systèmes Aéroportés La Clef de Saint-Pierre 1, Boulevard Jean Moulin 78852 Elancourt Cedex

e-mail :

Résumé :

On décrit un mécanisme d’identification de modes radars destiné à être utilisé dans un système d’auto-protection ou de renseignement. Les informations prises en compte pour réaliser l’Identification sont : Les mesures, les signatures connues des objets á reconnaître (modes radars, plates-formes…), la situation tactique instantanée, les informations opérateurs. Afin de répondre aux principales exigences de l’identification (rapidité, robustesse aux erreurs, aux valeurs aberrantes, aux valeurs manquantes,..) des solutions originales sont mises en śuvre (indexage tolérant de la base de données, formalisation Bayesienne intégrant l’imprécision, l’incertain ainsi que la fiabilité des données).

Abstract :

This paper describes an identification mechanism devoted to be in a self-protection or an ELINT system. Information taken into account at the input of the Identification function is : measurements, labelled patterns of objects to be recognised (Radars modes, platforms..), instantaneous tactical situation, information given by operators. In order to fulfil the main requirements of the identification process (speed, robustness to errors, to outliers, to missing measurements,..) original solutions are implemented (database tolerant indexing, Bayesian formalism with integration of data accuracy, data uncertainty and data fiability).

Due to numerous charts, we invite you to view or download here the full document in PDF format (82Ko)

A cause de la présence de nombreuses figures, nous vous invitons à visualiser et télécharger ICI ou télécharger le document complet au format PDF (82Ko)