Spacecraft tracking using sampled-data Kalman filters

The goal of this article is to illustrate and compare two algorithms for nonlinear sampled-data state estimation. Under idealized assumptions on the astrodynamics of bodies orbiting the Earth, we apply SDEKF and SDUKF for range-only as well as range and angle observations provided by a constellation of six LEO satellites in circular, equatorial orbits. We study the ability of the filters to acquire and track a target satellite in geosynchronous orbit as a function of the sample interval, initial uncertainty, and type of available measurements. For target acquisition, SDUKF yields more accurate position and velocity estimates than SDEKF. Moreover, the convergence of SDEKF is sensitive to the initialization of the error covariance; in fact, a nondiagonal initial covariance is found to be more effective than a diagonal initial covariance. Like SDUKF, by properly setting a nondiagonal initial error covariance, SDEKF also exhibits global convergence, that is, convergence is attained for all initial true-anomaly errors.