Precise Astronomical Orientation Using Multiple Stars at Their Culmination and Analysis of Different Regression Models

Abstract

Precise determination of the astronomical azimuth using the local hour angle (LHA) of Polaris is only applicable in northern middle latitudes. Therefore, to achieve fast and precise astronomical orientation in any part of the world, this study proposes continuous observations from the same station of multiple north stars and south stars at their culminating positions, thereby reducing the impact of errors in observation station longitude and time measurement. This method, which uses the regression model, determines the astronomical azimuth from the observation station to the ground target. Model validity is affected by various factors including sample size, data distribution, and data quality; therefore, suitable model conditions and individual characteristics of parametric and nonparametric regression are analyzed. Then, a two-step regression method comprising data binning followed by linear regression is proposed. Experimental data are subjected to direct linear regression, the summation of north and south star data followed by linear regression, nonparametric regression of summed data, and two-step regression of summed data. The two-step regression method produces the most accurate results that agree with those of the LHA method within a range of ±1.2120 × 10−6 rad (0.25″). Compared to the LHA method, the proposed method extends the geographical application range and eliminates the need for precise astronomical positioning prior to determining the orientation.