Gaussian-Mixture Kalman Filter for Orbit Determination Using Angles-Only Data

A study applies the new Gaussian-mixture Kalman filter (GMKF) to the problem of orbit determination. This filter uses the new Gaussian-mixture resampling algorithm. Resampling is applied between the dynamic propagation and the measurement update to enforce covariance upper bounds on the mixands that ensure accurate posterior probability density approximation via EKF calculations. The use of this new resampling algorithm distinguishes this filter from those used in other methods. It is multidimensional, whereas the other methods use one-dimensional resampling algorithms and apply them in product form over the eigendirections of each mixand’s covariance matrix. Another feature of the new resampling algorithm is its guarantee to converge to the original mixture in the limit of very many mixands.