Regression with Gaussian Mixture ModelsApplied to Track Fitting

This note describes the application of Gaussian mixture regression to track fitting with a Gaussian mixture model of the position errors. The mixture model is assumed to have two components with identical component means. Under the premise that the association of each measurement to a specific mixture component is known, the Gaussian mixture regression is shown to have consistently better resolution than weighted linear regression with equivalent homoskedastic errors. The improvement that can be achieved is systematically investigated over a wide range of mixture distributions. The results confirm that with constant homoskedastic variance the gain is larger for larger mixture weight of the narrow component and for smaller ratio of the width of the narrow component and the width of the wide component.