Вероятностный анализ требований к угломерной системе обнаружения смещения эллиптической орбиты

Abstract

The article addresses the requirements for a goniometric system intended to detect displacements of the space body orbit, which measures angles at discrete moments of time with a random error. Two statistical hypotheses about the zero and specified nonzero displacement values are considered. The likelihood ratio statistics is obtained, and the information distance for it is determined, which characterizes the discrimination confidence level, and which depends on the measurement device accuracy s and discreteness Dt, and also on the orbit parameters. By specifying the orbits and discrimination confidence level, the accuracy s and discreteness Dt are determined through information discrepancy. The information discrepancy is calculated on a family of orbits unfavorable for the observer, the plane of which touches the orbit of the moving observer, and the touching point is the intersection point of the corresponding trajectories. To refine the information distance, a simple flat approximate motion-measurement model is substantiated, in which the true motion of the observer (outside the space body orbit plane) is replaced, without changing its speed, by motion in the space body orbit plane over the earth's sphere circumference. The justification is corroborated by calculating the errors. The obtained simple model is used for estimating the potential possibility of detecting the specified displacement. Tables and graphs for practically determining the discreteness and accuracy of the system are given. The appendix contains all formulas necessary for carrying out similar calculations. Examples show that from angular measurements it is possible to obtain quite reliable detection for the range of orbit parameters that are of practical interest.