X-Ray Pulsar-Based Relative Navigation using Epoch Folding

How the relative position between two spacecraft can be estimated utilizing signals emitted from X-ray pulsars is explained. The mathematical models of X-ray pulsar signals are developed, and the pulse delay estimation problem is formulated. The Cramér-Rao lower bound (CRLB) for any unbiased estimator of the pulse delay is presented. To retrieve the pulsar photon intensity function, the epoch folding procedure is characterized. Based on epoch folding, two different pulse delay estimators are introduced, and their performance against the CRLB is studied. One is obtained by solving a least squares problem, and the other uses the cross correlation function between the empirical rate function and the true one. The effect of absolute velocity errors on position estimation is also studied. Numerical simulations are performed to verify the theoretical results.