Applicable probability distribution model of refracted star number in field of view of indirectly sensing horizon star sensor

Aiming at the engineering problem that the refracted star number in the field of view (FOV) of a star sensor is not enough to carry out indirectly sensing horizon, it is necessary to study the probability distribution function (PDF) of refracted star number in the FOV. A brief introduction of the principle of stellar refraction is given. The proportion coefficient of the stratosphere strip area fallen in the FOV to the whole FOV area is deduced, and combined with the validated PDF of the total star number in FOV, the PDF of the refracted star number is obtained at last. The feasibility analysis on the analytic positioning method based on stellar refraction is finished by using the PDF model, presenting the quantification relationship between the FOV, apparent magnitude (M_v), apogee distance and probability distribution. The plotted refracted star number PDF curve is similar to that by Monte Carlo simulation results, with Poisson parameter bias of 1.48, an equivalent of relative error of 12.8%. The simulation results show the correctness of the PDF model, which will be helpful to the parameter design of the star sensor used for indirectly sensing horizon through starlight refraction.