Compressed estimation in coupled high-dimensional processes

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Copyright: Narula, Karan
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Abstract
The state estimation of high-dimensional problems is a topic of great interest in diverse research and application areas. In such problems, the conventional methods, although highly capable and powerful, suffer from the high-computational requirement. Compressed Estimation approaches, such as the Generalised Compressed Kalman Filter (GCKF), are capable of reducing the computational cost and complexity of high-dimensional and high-frequency data assimilation problems; usually without sacrificing optimality. However, the application of a compressed estimation process is limited to a class of problems which inherently allow the estimation process to be divided, at certain intervals of times, into a set of lower-dimensional problems. This limitation prohibits applying the compressing techniques for estimating coupled high-dimensional processes. To this end, the concepts of subsystem switching and information exchange architectures have been derived and explored in this thesis, for allowing the compressed estimators to mimic optimal full Gaussian estimators in coupled processes. Furthermore, concepts such as Marginalised Likelihood and Perfect Global update have been derived to allow the application of compressed estimation in overlapping architecture with certain assumptions. The performances of these methods have been verified through its application in solving usual types of stochastic partial differential equations (SPDEs), where the compressed estimator is compared against the full Gaussian estimator. The proposed solution is general and can be adapted for non-linear estimation with the assumption of Gaussian Probability Density Function (PDF). The general framework is shown along with the example of replacing the Kalman Filter (KF) core with the better-suited point-based Gaussian filter core, such as Unscented Kalman Filter (UKF) or Cubature Kalman Filter (CuKF), for solving non-linear SPDEs. The compressed Gaussian filter is later applied to solve the usual estimation problems in the literature such as dual estimation and 2D Simultaneous Localization and Mapping (SLAM). In all these cases, substantial computational savings can be achieved when dealing with high-dimensional and high-frequency data assimilation. Following on from this research, the developed framework can be adapted and applied in a wide range of engineering and scientific fields.
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Author(s)
Narula, Karan
Supervisor(s)
Guivant, Jose
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Publication Year
2019
Resource Type
Thesis
Degree Type
PhD Doctorate
UNSW Faculty
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