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

Abstract

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 and Qualitative Physics from the Artificial Intelligence literature. We adopt a specific qualitative representation, namely that advocated by Kuipers, in which a well defined 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 definition 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 utilizing the relationships between coarse (i.e. two state) and fine (i.e. N state) representations explored by Shafer. We then generalized the Dempster-Shafer Theory of Evidence to a finite set of theories and show how an extreme theory can be used to develop mean minimum-mean-square-error estimators applicable to situations with correlated noise. We demonstrate our theory using real data from a mobile robot application which utilizes sonar and laser time-of-flight and gyroscope information to disseminate surface curvature.