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Abstract
This thesis presents a means for representing and computing beliefs in the form of arbitrary probability density functions with a guarantee for the ongoing validity of such beliefs over indefinte time frames. The foremost aspect of this proposal is the introduction of a general, theoretical, solution to the guaranteed state estimation problem from within the recursive Bayesian estimation framework. The solution presented here determines the minimum space required, at each stage of the estimation process, to represent the belief with limited, or no, loss of information.
Beyond this purely theoretical aspect, a number of numerical techniques, capable
of determining the required space and performing the appropriate spatial reconfiguration, whilst also computing and representing the belief functions, are developed. This includes a new, hybrid particle-element approach to recursive Bayesian estimation.
The advantage of spatial reconfiguration as presented here is that it ensures that the belief functions consider all plausible states of the target system, without altering the recursive Bayesian estimation equations used to form those beliefs. Furthermore, spatial reconfiguration as proposed in this dissertation enhances the estimation process since it allows computational resources to be concentrated on only those states considered plausible.
Autonomous maritime search and rescue is used as a focus application throughout this dissertation since the searching-and-tracking requirements of the problem involve uncertainty, the use of arbitrary belief functions and dynamic target systems. Nevertheless, the theoretical development in this dissertation has been kept general
and independent of an application, and as such the theory and techniques presented
here may be applied to any problem involving dynamic Bayesian beliefs.
A number of numerical experiments and simulations show the efficacy of the proposed spatially reconfigurable representations, not only in ensuring the validity of the belief functions over indefinite time frames, but also in reducing computation time and improving the accuracy of function approximation. Improvements of an order of magnitude were achieved when compared with traditional, spatially static representations.