Asymptotically Efficient Estimation of Pulse Time Delay for X-Ray Pulsar Based Relative Navigation

The problem of relative position estimation between two spacecraft based on X-ray pulsar measurements is addressed. A mathematical model is developed for the pulsar’s intensity as observed at each spacecraft. The time of arrival (TOA) of photons is modeled as a Poisson point process, and the relevant probability density functions are provided. A solution to the relative navigation problem is suggested based on estimation of the pulse delay between the detected signals. The problem of pulse time delay estimation is formulated and the Cramér-Rao lower bound (CRLB) is presented. Based on probability distribution of photon time of arrivals, a maximum likelihood estimation (MLE) problem is formulated and the pulse delay estimator is proposed. It is proven that the proposed estimator is asymptotically efficient. The analytical results are verified numerically employing computer simulations.