Space vehicles, deep space explorers, long-endurance aircraft, and other equipment have increasingly high requirements on navigation accuracy. In this aspect, a major issue to solve is how to improve the space navigation accuracy of aircraft, achieve fully autonomous interference-free navigation, and reduce the cost of expensive equipment. Starlight atmospheric refraction navigation technology neither involves the transmission and exchange of information with the outside world nor depends on the navigation and positioning by ground equipment. It is thus characterized by remarkable concealment and strong resistance to the external environment. However, due to the complex atmospheric environment in the near-Earth space, the bending of starlight toward the center of the Earth after entering the atmosphere will affect the accuracy of starlight atmospheric refraction navigation. For this reason, building an accurate starlight atmospheric refraction model is crucial for improving navigation accuracy. In related studies of starlight atmospheric refraction models, analysis is mostly based on the data from the United States Standard Atmosphere (USSA) parameter model, the COSPAR International Reference Atmosphere (CIRA) model, and the Neutral Atmosphere Empirical Model-2000 (NRLMSISE-00). However, the data from these universal models have a low resolution. Therefore, a corrected starlight atmospheric refraction model is constructed using the data from the National Centers for Environmental Prediction (NCEP) in this paper. NCEP data are recorded four times a day to give due consideration to the effect of the day and night temperature difference, and the resolution is 1°×1° in latitude and longitude. The model built on this basis will be more accurate than the traditional models with CIRA as the typical representative.

The accuracy of the commonly used USSA and CIRA atmospheric reference models is low. To solve this problem, this study builds a spatiotemporally varying atmospheric parameter model using the high-resolution NCEP atmospheric parameter data and employing the Fourier interpolation algorithm. The atmospheric refractive indices at different altitudes, latitudes, and longitudes are used to calculate the propagation path of starlight in the atmosphere, and a corrected starlight atmospheric refraction model is constructed.

The comparison among the corrected starlight atmospheric refraction model and the existing models shows that the spatiotemporally varying atmospheric temperature model developed in this study has a relative error smaller than 2% and an average absolute error of 1.86 K when fitting measured data (Fig. 1) and a relative error below 4.39% when fitting the atmospheric density (Fig. 4). Moreover, the relative error between the refractive spatiotemporal model and the traditional single-point model at low, middle, and high latitudes in January is 37.64%, 9.79%, and 28.78%, respectively [Fig. 9(a)]. The relative error between the two models at low, middle, and high latitudes in July are 27.95%, 26.89%, and 39.10%, respectively [Fig. 9(b)]. Therefore, the proposed starlight atmospheric refraction model considering spatiotemporal variations has higher theoretical accuracy.

In this study, high-resolution data from the NCEP are selected for the reanalysis of the atmospheric parameter data. The reanalysis data are further used to build a spatiotemporally varying atmospheric parameter model. Model simulation results are presented, with due consideration given to the effects of temporal, horizontal, and vertical atmospheric parameters on starlight atmospheric refraction. The propagation path of starlight in the atmosphere is calculated, and the corrected starlight atmospheric refraction model is constructed on the basis of the spatiotemporally varying atmospheric parameter model. The changes in the refraction angle with height at different time, longitudes, and latitudes are calculated, and the deviations of the refraction angle with height at different time, longitudes, and latitudes are obtained through analysis. The results show that the relative errors between the refractive spatiotemporal model and the traditional single-point model at low, middle, and high latitudes in January are 37.64%, 9.79%, and 28.78%, respectively. The relative errors between the two models at low, middle, and high latitudes in July are 27.95%, 26.89%, and 39.10%, respectively. Finally, the apparent height is obtained by inverting the refraction angle, and its relative deviations from the traditional apparent height at low, middle, and high latitudes are 6.27%, 5.10%, and 5.42%, respectively. Because the corrected model takes into account the spatial and temporal variations in the atmosphere, the simulation results are closer to the changes in the real atmosphere.