Consistent estimation of pulse delay for X-ray pulsar based relative navigation

The relative navigation problem between two spacecraft in deep space is formulated based on employing X-ray pulsar signals. The proposed approach is to lock the detectors on the same pulsar and time-tag the detected X-ray photons. Then using the epoch folding procedure the observed pulsar rate functions on each spacecraft are retrieved and the time delay is estimated through a nonlinear least-squares (NLS) fitting of the empirical rate function to the known pulsar rate function. The relative distance between the space vehicles is proportional to the time delay. The pulsar signals are modeled mathematically and the epoch folding noise is characterized analytically. The mean and variance of the pulse delay estimator are calculated. The Cramer-Rao lower bound (CRLB) is also presented and the estimator´s performance is compared against it. The analytical results are verified numerically by computer simulations.