Approximate methods for state estimation with nonlinear measurements and unknown noise covariances

Date

2023-7-04

Author

Laz, Eray

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Bayesian state estimation problems with nonlinear measurements and unknown noise covariances are investigated in this thesis. First, a Gaussian mixture/sum filter in the framework of assumed density filtering is proposed for systems with nonlinear measurement equations. The filter minimizes the Kullback-Leibler divergence from the assumed Gaussian mixture posterior to the true posterior. Since the analytical minimization is not possible, an iterative procedure is developed to obtain the optimal weights, means and covariances of the approximate Gaussian mixture posterior. The resulting Gaussian mixture filter turns out to be a generalization of the (damped) posterior linearization filter to Gaussian mixture posteriors. The performance of the proposed filter is illustrated and compared to alternatives on target tracking examples. The results show that the proposed filter can outperform Gaussian filters as well as the Gaussian sum filter obtaining results very close to a bootstrap particle filter when the number of components in the assumed posterior is sufficiently large. Second, Bayesian state estimation algorithms are proposed for linear Gaussian systems with the unknown process and measurement noise covariances. The unknown time-varying noise covariances are assumed to be inverse Wishart distributed with Beta-Bartlett transitions. The intractable joint filtered and smoothed posteriors for the state and the noise covariances are calculated by using a scale Gaussian mixture approximation of the Student's t-distribution and moment matching. The resulting filters and smoothers are non-iterative unlike the existing solutions in the literature, which brings computational advantages. Furthermore, the proposed filters and smoothers calculate explicit estimates of the noise covariances which might be useful in downstream applications like clutter map formation and/or target classification in radar target tracking. The simulation results show that the proposed algorithms have similar performance as the state of the art solutions while requiring less computational resources.

Subject Keywords

Nonlinear filtering, Target tracking, Gaussian mixture, Gaussian sum, Kullback-Leibler divergence, Newton's method, Linear systems, Bayesian filtering, Bayesian smoothing, Unknown process and measurement noise covariances, Inverse Wishart distribution

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https://hdl.handle.net/11511/104481

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Graduate School of Natural and Applied Sciences, Thesis