Qualitative model based multisensor data fusion and parameter estimation using norm Dempster Shafer evidential reasoning

This paper is concerned with model based parameter estimation for noisy processes when the process models are incomplete or imprecise The underlying representation of our models is qualitative in the sense of Interval Arithmetic and Qualitative Reasoning QR and Qualitative Physics from the Arti cial Intelligence literature We adopt a speci c qualitative representation namely that advocated by Kuipers in which a well de ned mathematical description of a qualitative model is given in terms of operations on intervals of the reals We investigate an weighted opinion pool formalism for multi sensor data fusion develop a de nition for unbiased estimation on quantity spaces and derive a consistent mass assignment function for mean estimators for two state systems This is extended to representations involving more than two states by utilising the relationships between coarse i e two state and ne i e N state representations explored by Shafer We then generalise the Dempster Shafer Theory of Evidence to a nite set of theories and show how an extreme theory can be used to develop mean minimum mean square error MMSE estimators applicable to situations with correlated noise We demonstrate our theory using real data from a mobile robot application which utilises sonar and laser time of ight and gyroscope information to disseminate surface curvature