A Gaussian sum filter framework for space surveillance

Abstract

While standard Kalman-based filters, Gaussian assumptions, and covariance-weighted metrics work remarkably well in data-rich tracking environments such as air and ground, their use in the data-sparse environment of space surveillance is more limited. In order to properly characterize non-Gaussian density functions arising in the problem of long term propagation of state uncertainties in the two-body problem, a framework for a Gaussian sum filter is described which achieves uncertainty (covariance) consistency and an accurate approximation to the Fokker-Planck equation up to a prescribed accuracy. The filter is made efficient and practical by (i) using coordinate systems adapted to the physics (i.e., orbital elements), (ii) only requiring a Gaussian sum to be defined along one of the six state space dimensions, and (iii) the ability to initially select the component means, covariances, and weights by way of a lookup table generated by solving an offline nonlinear optimization problem. The efficacy of the Gaussian sum filter and the improvements over the traditional unscented Kalman filter are demonstrated within the problems of data association and maneuver detection.