| dc.description.abstract | Linear estimators, like the extended Kalman filter (EKF), find continual use (especially in the
field of navigation) mostly for their familiarity and computational efficiency. Often, these estimations must be safeguarded from the realistic elements of physical systems, such as nonlinearities, non-Gaussian noises, and unmodeled effects. To this end, existing linear estimators are frequently outfitted with procedure-first robustness techniques—ad hoc mechanisms designed specifically to prevent filter failure—such as measurement editing, gain underweighting, filter resets, and more. As an alternative, this dissertation elects a model-first ethos, proposing nonlinear Gaussian mixture (GM) filters that are derived from first principles to be robust. These inherently robust algorithms are split into two approaches—1) non-Bayesian filters and 2) fault-cognizant filters—the end result being a collection of filters that challenge the status quo of current practical estimation; instead of reusing preexisting filter frameworks for the sake of ease, customized filters can be designed specifically for the system at hand.
1) Bayes’ rule, while the archetypal basis for measurement fusion, relies on a fundamental
assumption; all specified models, such as prior distributions and measurement likelihoods, are presumed to exactly reflect reality. In practice, this is rarely the case, warranting an investigation into non-Bayesian alternatives to traditional measurement updates. Fortunately, generalized variational inference (GVI) provides an established foundation for such updates and is used in this work to prototype several robust non-Bayesian filters. As closed-form filters are usually preferred, an iterative confidence-based update is derived, which, through Monte Carlo analyses, is shown to be selectively conservative, such that a desired level of robustness can be user-appointed.
2) Whereas traditional filtering screens out undesirable, or faulty, measurements, fault-cognizant filtering attempts to directly model these erroneous measurements, yielding estimators inherently capable of processing returns that conflict with the conventional model of a sensor. As the nature of both valid and faulty measurements can differ significantly between systems, several different fault-cognizant updates (FCUs) are derived, each purposed for a specific application. Subsequent analyses illustrate the robustness of the FCU to faulty measurements, both known and unknown. | |
