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Title: State space reparametrization for approximating nonlinear models in Bayesian state estimation
Author: Franco Monsalve, Jose Luis
ISNI:       0000 0004 8503 6300
Awarding Body: Heriot-Watt University
Current Institution: Heriot-Watt University
Date of Award: 2017
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Recursive Bayesian state estimation is a powerful methodology which is useful for the integration of data about a process of interest while considering all the sources of uncertainty which are present in the observations and in modeling inaccuracies. However, in its general form it is intractable and approximations need to be made in order to use it in real life applications. The most widely used algorithm to perform recursive state estimation is the Kalman filter, which assumes that the probability distributions that it propagates are Gaussian and that the measurement and dynamical processes are linear. If these assumptions are satisfied, the Kalman filter is optimal. In most applications, however, this proves to be an oversimplification, due to which several techniques have arisen to handle model non-linearity and different types of distributions. In this thesis, a novel method for the estimation of distributions with nonlinear dynamical and measurement models is presented, which uses a reparametrization of the state space of the distributions in order to exploit the linear properties of the Kalman filter. This involves the mapping of the distribution into a different space, and a subsequent approximation as a Gaussian distribution. An analysis of the adequacy of this transformation is presented, which shows that it is a valid approach in a number of practically interesting filtering problems. The proposed approach is applied to the estimation of the state of Earth-orbiting objects, as it is a challenging estimation scenario which can benefit from the use of filter. Space situational awareness is increasingly important as near-Earth space becomes cluttered with satellites and debris. In this work, the sensors that are most commonly used to track objects in orbit, radars and telescopes, are modeled and a filter based on the previously discussed ideas is proposed. Finally, a multi-object estimation filter based on a recent estimation framework is presented which propagates high amounts of information while maintaining low computational complexity. This is important as there are many challenges to tracking large amounts of orbiting objects in a principled way using ground-based sensors, and naturally extends the single object filter described above to the multi-sensor, multi-object case.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available