| A new algorithm is developed for relative navigation between two spacecraft using X-ray pulsar measurements. The signal processing aspects of photon time of arrivals are studied. Mathematical models are developed to characterize the X-ray pulsar signals, and the pulse delay estimation problem is addressed. The Cramer-Rao lower bound for estimation of the pulse delay is presented. Depending on the employment of photon counts or the direct use of the measured photon time of arrivals, two different estimation strategies are proposed and analyzed. An asymptotically efficient estimator is chosen, which is based on the maximum-likelihood criterion. It is assumed that the spacecraft velocity data, necessary to determine Doppler shifts, is available through a navigation system, which is integrated from the inertial measurement unit data. The pulse delay estimates are used as measurements, and based on models of spacecraft and IMU dynamics, a Kalman filter is employed to obtain the three-dimensional relative position estimate. Numerical simulations are performed to verify the theoretical results. |
