State space reparametrization for approximating nonlinear models in Bayesian state estimation
Franco Monsalve, Jose Luis
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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.