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# Abstracts

## On the estimation of some parameters of orbits by angular measurements

Goritskiy Yu.A.

Moscow Power Engineering Institute 111250, Moscow, Krasnokazarmennaya str., 14

1 pp. (accepted)

The problem of the potential accuracy of parameter estimation when measuring only the angular coordinates of an object in free motion is considered. The least favorable mode of movement for the observer is the absence of a change in azimuth, only the angle of the seat changes. The analysis is carried out in a parabolic approximation of motion, taking into account the sphericity of the Earth and the motion of the meter. In this motion-measurement model, difficulties remain in determining estimates of important parameters. Among the developers of trajectory measurement processing systems, there is an idea that, according to angular measurements, parameters such as coordinates and the moment of landing cannot be obtained with almost interesting accuracy. However, some estimates suggest that there are conditions under which it is possible to obtain the desired accuracy, namely, if the trajectory is such that the point of incidence is in some neighborhood of the observer. The purpose of the work is to quantitatively analyze the conditions (namely, the parameters of the orbits, the accuracy and frequency of measurements, the distance to the landing point) under which practically interesting accuracy is achievable. We are interested in the potential accuracy of the following parameters: the moment of landing, the displacement ∆ relative to the observer and, secondly, Vx-horizontal velocity. It is assumed that the main source of errors in parameters are random errors of angle measurements, so the problem is statistical. To solve it, the motion-measurement model was written in terms of parameters other than the traditional ones, the moment of landing, displacement relative to the meter and horizontal velocity are used. The same parameters determine the distribution law of the entire set of measurements. Next, we use information estimates based on the calculation of the Fisher matrix. The calculation results are presented in the form of tables of values of the lower bounds for standard errors and in the form of graphs. In conclusion, we note that the results of the work can be used by engineers when creating angle-measuring systems for processing trajectory observations.

References.

1. Goritsky Yu.A., Tigetov D.G., Anufriev A.M.A two-dimensional model for evaluating the effectiveness of angular measurements on elliptical orbits // "Izvestiya RAS. Theory and Control systems", 2020, No. 6, 12c

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