In this paper, a nonlinear least squares estimator based on the extending cost function is derived, and its performance is analyzed in a Monte-Carlo simulation. Numerical results show that estimation error of the pulse time of arrival satisfies the normal distribution, the relation between the variance and the number of X-ray photon obtained by our simulation is compared with the analytical model. In addition, the effect of time bin size on the statically behavior of estimation error is also studied. This work holds great promise for designing the parameters of X-ray camera adopted in the pulsar navigation system.
Characterization of X-Ray Pulsar Navigation for Tracking Closed Earth Orbits