Adaptive Grid Search Based Pulse Phase and Doppler Frequency Estimation for XNAV

Estimating the pulse phase from the recorded photons from pulsars is one of the key problems in X-ray pulsar-based navigation (XNAV). The current flight experiments on XNAV commonly estimate the pulse phase and the Doppler frequency by the maximum likelihood estimator (MLE). Because the likelihood function is nonconvex, the MLE is usually solved by a computationally expensive grid search. The computational complexity of the grid search is proportional to the upper and lower bounds of the pulse phase and the Doppler frequency, which are always set empirically. This article proposes an adaptive grid search (AGS) method for estimating the pulse phase and the Doppler frequency. In this method, the grid is adjusted adaptively by the priors of the pulse phase and the Doppler frequency, which are derived from the orbit uncertainty of the space vehicle. It is proved that the proposed AGS can also be viewed as a maximum a posteriori estimator for pulse phase and Doppler frequency estimation. Besides, because the AGS can adaptively adjust the grid, it provides a framework for pulse phase and Doppler frequency estimation and can be combined with intelligent optimization algorithms such as the particle swarm optimization. The performance of the proposed method is verified by the real data of Crab pulsar from the Neutron star Interior Composition Explorer.