Fast near-maximum likelihood phase estimation of X-ray pulsars

This letter addresses the problem of X-ray pulsar radiation phase estimation, encountered in research works concerning autonomous deep space navigation systems. Autonomous navigation systems represent an intriguing solution to be employed when Earth-assisted navigation is not viable for long range missions. In such applications, X-ray pulsars, as well as other celestial objects, may be employed as peculiar beacons to allow the spacecrafts to adjust their own route. State of the art techniques for estimation of X-ray pulsar radiation phase involve maximization of generally non-convex objective functions, thus resulting in computationally onerous procedures. Here, we show how the problem of pulsar phase estimation can be recast as a cyclic shift parameter estimation problem under multinomial distributed observations, whose maximum likelihood solution can be implemented by means of a fast, Discrete Fourier Transform based procedure. Numerical results show how the herein described fast, near maximum likelihood, estimator favorably compares with selected state of the art estimators, while presenting a significantly reduced computational complexity.