Estimation of the error of navigation parameters in single-mirror sextant observations

The paper presents a new type of sextants, namely two-parameter sextants, which are currently at various stages of development and remain little known to navigators. One of the most promising technical implementations of a two-parameter sextant is a single-mirror sextant, the design of which is based on the use of a single semi- transparent mirror with two rotational degrees of freedom. Initial studies have shown that a single-mirror sextant makes it possible to obtain several navigation parameters within a single observation, including the sum of the altitudes of celestial bodies, the difference in their altitudes, the elevation of the upper observed celestial body relative to the lower one, and, under conditions of horizon visibility, the altitude of a celestial body relative to the horizon as well as the azimuth difference between the observed celestial bodies. The main advantage of two-parameter sextants lies in their applicability throughout the entire period of darkness and their independence from horizon visibility. However, the determination of navigation parameters using a single-mirror sextant requires prior knowledge of the altitude of the lower observed celestial body. In the absence of a visible horizon, this altitude can only be obtained by calculation and is therefore known with a certain error. This paper addresses the influence of errors in the calculated altitude of the lower observed celestial body on the resulting navigation parameters; for the analysis, an altitude error of 0.1° is assumed. Analytical expressions for the errors of navigation parameters, namely the altitude and the azimuth difference between the sextant mirror normal and the second observed celestial body, are derived. A numerical analysis of the obtained errors shows that favorable observation conditions correspond to a specific range of angular separation between the observed celestial bodies.