Use of Gaussian mixture distribution models to address non-Gaussian errors in radar target tracking

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Davis, Benjamin Peter
Verriest, Erik I.
Blair, William D.
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If radar measurements are performed in the polar coordinates of range and angle and the error orthogonal to the range dimension is much greater than the error in range, the true error region in Cartesian space is no longer well approximated by a Gaussian distribution. This effect is known as the "contact-lens" effect due to the shape of the error distribution in Cartesian space. In this dissertation, a method is presented for modeling Cartesian converted measurement distributions which suffer from the contact-lens effect using Maximum Likelihood (ML) Gaussian mixture (GM) parameters. In order to allow an efficient implementation of this process in a GM Kalman filter, a novel normalization of the ML parameters is introduced so that parameters can be efficiently stored in a lookup table for real-time use. Additionally, the measurement update process in the resulting GM filter is modified using a preconditioning process so that the GM measurement PDF is located in close proximity to the support of the state estimate PDF. This preconditioning allows fewer GM components to be used in the model, which significantly reduces the computational cost of the tracking. These techniques are then combined into the Measurement-Adaptive Gaussian Mixture Filter (MAGMF), and this filter is applied to tracking with measurements from a 2D monostatic radar, 2D bistatic radar, and 3D monostatic radar. For all three of these cases, the MAGMF is shown to have track accuracy and covariance consistency performance comparable to solutions that use a particle filter that requires significantly more computations.
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