Fast non-linearly constrained least square joint estimation of position and velocity for X-ray pulsar-based navigation

Considering the limited computational capacity of on-board computer, a fast non-linearly constrained least square joint estimation of position and velocity is proposed for X-ray pulsar-based navigation (XNAV). The authors found that besides the distortion of the pulse profile, the Doppler caused by the spacecraft velocity alters the pulse time-of-arrival (TOA). The relationship model between the pulse TOA and the spacecraft velocity is built. Based on this, they can estimate the spacecraft velocity according to the variation of TOAs instead of the pulse profile distortion. In the proposed estimation method, the total observation interval is divided into several equal observation sub-intervals. Then a set of TOAs for sub-intervals can be obtained by the Fourier transform-based TOA estimation method. Finally, the non-linearly constrained least square estimation method is developed to estimate the spacecraft position and velocity. The simulation results have demonstrated that the proposed method is far faster than the maximum-likelihood estimation method, in which the spacecraft velocity is estimated via detecting the distortion of the folded pulse profile. The accuracy of the proposed method is robust to the initial errors and the elements of orbit.