Data Fusion and Parameter Estimation Using Qualitative Models : The Qualitative Kalman Filter

Most sensor based systems employ a large variety of sensors to obtain information. How the information obtained from different sensing devices is combined to form a description of the system is the sensor fusion problem. Most statistical sensor fusion systems use differential equations to inter-relate the values of sensor observations and system parameters . In this paper, we investigate 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 Qualitative Reasoning (QR) and Qualitative Physics from the Artificial Intelligence literature . We adopt a specific qualitative representation, namely that advocated by Kuipers [13], in which a well defined mathematical description of a qualitative model is given in terms of operations on (possibly unbounded) intervals of the reals. This paper overviews a theory for fusion of noisy observations of a stochastic system when qualitative models of the system processes and sensor observations are employed . The interested reader is referred elsewhere [18] for a more detailed exposition . We demonstrate our theory using real data from a mobile robot application which utilises sonar and laser time-of-flight and gyroscope information to disseminate surface curvature.