Estimator for Deep-Space Position and Attitude Using X-ray Pulsars

In this article, we develop an algorithm for the estimation of a full six degree of freedom position, navigation, and timing solution in deep space by measuring the time and angle of arrival of x-rays photons from pulsars and other bright stars. We show that for pulsar navigation, the position and attitude determination problems are coupled. This is due in part to the small signal-to-noise ratio of pulsar signals and the fact that x-ray photons emanating from various pulsars and bright stars have no unique identifier that can be used to associate them with their source. To address this challenge, a joint probabilistic data association filter is developed. The filter fuses angular rate measurements from a three-axis rate gyro with time-of-arrival and angle-of-arrival measurements from an x-ray detector. The performance of the filter is validated in simulation, and the tradeoffs associated with detector size and initial conditions are evaluated. Additional validation of the algorithm is performed by playback of data from x-ray detectors on the Chandra spacecraft. The results show that positioning accuracy on the order of 1000 km and attitude accuracies on the order of 5 arcseconds can be achieved.