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The X-ray timing data for the Crab pulsar obtained by the Chinese X-ray pulsar navigation test satellite are processed and analyzed. The method to build the integrated and standard X-ray pulse profiles of the Crab pulsar by using the X-ray pulsar observation data and the satellite orbit data is described. The principle and algorithm for determining the pulsar's pulse time of arrival (toa) in the frequency domain are briefly introduced. The pulsar's pulse time of arrival is calculated by using the timing data of 50 min integration for each set of observational data. By the comparison between the observed Crab pulsar's pulse time of arrival at the solar system barycenter and that predicted with the Crab pulsar ephemeris, it is found that the timing accuracy is about 14 μs after the systematic error is removed by a quadratic polynomial fitting.

Pulsar rotational and astrometric parameters can be measured with a very high precision by pulsar timing observations. The pulsar timing model, the methods to measure the pulsar parameters by least squares fitting and to estimate their covariances are briefly described. The mathematical relations between the timing residuals of a pulsar and the errors of its different parameters are derived in the ecliptic coordinate system. The relationships of the measuring precisions of pulsar's ecliptic longitude, latitude, and annual parallax with the absolute value of pulsar's ecliptic latitude are shown by curves. And the relations of the measuring precisions of pulsar's astrometric parameters with the pulsar's latitudinal parameter itself are discussed as well.

The timing residual characteristics of of 14 millisecond pulsars monitoredwith North American Nanohertz Observatory for Gravitational Waves (NANOGrav) in the time-domain was analyzed. It was found that the root mean square of timing residuals has nothing to do with Hurst parameters. The long data span will help to estimate the biased random characteristics of timing residual according to Hurst parameters. By data comparison, it was showed by several timing noise estimations that Hurst parameters were valid in estimating if a low frequency red noise exists, which can serve as a complementary to mainstream method for analysis of red noise analysis. These results will further expand the analysis of pulsar timing noise in time-domain.

The precise measurements of the model parameters in pulsar timing are the basisof the applications of pulsar timing. Pulsar timing model contains geometrical, physical, orbital effects, and so on. In this paper, we regarded the Earths revolution as the elliptical orbit and obtained general conclusions in the ecliptic system of coordinates. Based on that, we gave the analytic expressions of estimating the measurement precision of these model parameters, and obtained the measurement precision of some model parameters depending on ecliptic latitude. In particular, for the estimation of the measurement precision of the parallax, a quite different result from the previous work was obtained.This is meaningful for the choices of pulsars in the practical observations.

The establishment of a time scale is one of the main aims of time measurement. The time scale prediction is necessary for real atomic time. The wavelet theory is a new subject which will be developed in the near future. It can be used to analyze signals with different resolution. Besides, it may be applied whenever the Fourier analysis is available. A subsectional recurrence model for time scale based on wavelet theory is put forward in this paper. It is different from the ARMA(p,q) model requires that the process should satisfy the stationary condition, while the Kalman filter is not so. The forecast step of our model is finite and the signals are orthogonally analyzed at different frequency scales. The wavelet coefficients are given for each frequency scales. Finally, our model is checked with data of CSAO. The forecast error of ARMA(p,q) is about 10 ns in one step. That of the subsectional recurrence model is less than 4.5 ns in 5 step. Our model is simple and practicable. The results show that this method is better than the other in the accuracy of measurement.

Pulsars rotate extremely stably, they can be used as time standard. However, pulsar time defined by single pulsar is influenced by several noise resources. To weaken these influences to get a more stable time scale, one can take ensemble analysis to obtain the ensemble pulsar time. Since different pulsars have different rotation frequency, and the noise source have different influence on different frequency of each pulsar，we can apply wavelet analysis to integrate the pulsar time, and this algorithm can take consideration of the long-term and short-term stability of pulsar time. On the other hand, the pulsar timing residuals are caused by reference atomic clock and pulsar itself, so we can apply Wiener filtration analysis to distinguish the two parts, and then calculate the ensemble pulsar time with the residuals after removing the error of reference atomic clock. Based on both of the two algorithms, a new algorithm of Wiener filtration in wavelet domain has been presented, which combines the merits of wavelet analysis and Wiener filtration and can remove the noise influence to pulsar time more effectively. Experimental results prove that Wiener filtration in wavelet domain can reduce noise influence of pulsar timing residuals effectively.

In this paper,the theory and numerical method for the propagation of a pulse wave through a strong turbulence medium are presented.According to the variousy wave structure function,we have computed the two-frequency cross correlation function,shown the numerical value of the pulse broadening and the scintillation index in the screen and extended medium respectively,and made some comparison with the observation data.

The Third Catalogue of Nearby Stars (CNS3) was analyzed. A study of the stellar luminosity function in the solar neighborhood with CNS3 was described. The luminosity function for main sequence stars derived from CNS3 was compared with that from CNS2 and that based on the method of photometric parallaxes. The results from CNS3 for stars with Mv <15.5 were well defined. Luminosity functions for the giants and A, F, G, K and M type main sequence stars are also given, based on CNS3.

We give the revisions to the FK4 Catalogue based on the observations made with a Type-1 photoelectric astrilabe in the period 1973 October to 1976 October, together with a description of the procedures and the accuracies obtained, and a study of the systematic errors of Δα δ and Δδ δ types in the catalogue. The results obtained show that the Type-1 photoelectric astrolabe is better than the Danjon astrolabe for the purpose of improving star positions.