SIMBAD references

We introduce a robust fitting method into pulsar timing analysis to cope with the non-Gaussian noise. The general maximum likelihood estimator (M-estimator) can resist the impact of non-Gaussian noise by employing convex and bounded loss functions. Three loss functions, including the Huber function, the Bisquare function and the Welsch function, are investigated. The Shapiro-Wilk test is employed to test whether the uncertainty in the observed times of arrival is drawn from a non-Gaussian distribution. Two simulations, where the non-Gaussian distribution is modelled as contaminated Gaussian distributions, are performed. It is found that M-estimators are unbiased and could achieve a root-mean-square error smaller than that obtained by the least square (LS) at the cost of a slightly higher computation complexity in a non-Gaussian environment. M-estimators are also applied to the real timing data of PSR J1713+0747. The results have shown that the fitting results of M-estimators are more accurate than those of LS and are closer to the result of very long baseline interferometry.