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Navigation accuracy characteristics of space complex “Nebosvod”, which is being designed now by the Russian Corporation “Cometa”, are presented. The complex is aimed to detect new near-Earth celestial bodies and estimate their orbit parameters to timely warn us about the Asteroid-Comet hazard. This complex includes two spacecraft (SC) on geo-synchronous orbits. Every SC will be equipped by a high-accuracy scanning telescope. Using these telescopes, identification of celestial bodies as well as determination of their angular coordinates, right ascension and declination, is supposed to be performed. By these measurements, the estimation of their orbital motion parameters must be made. Navigation algorithms are developed. The least squares method is used to determine the asteroid orbit. An algorithm for determination of initial orbit is also designed on the base of Gauss method. Algorithms for evaluation of the navigation accuracies are developed for cases of random and systematic errors in measurements. Here two methods are used, both analytical and “Monte-Carlo” method. On the base of two asteroid orbits that are close to the Apophis one, there is performed modeling the asteroid motion and its measurements, estimating its orbit parameters and evaluating the navigation accuracies. Three parts of the asteroid motion are analyzed. It is the far part with the distance to the asteroid from 100 million kilometers. The second part is the middle one with the distance to the asteroid from 50 million km. And the last part is close to the approach to the Earth, with distance from about 3.5 million km. The accuracy estimations for the asteroid’s position coordinates and velocity vector components at an evaluation position, for the asteroid’s orbit elements, for the asteroid aim vector near the Earth, for its perigee distance and perigee time are determined using several values of errors in the optical measurements and various measurements programs. Measurements by one or two SC are also analyzed. The analysis indicates that the analytical and statistical methods have close results. It is shown that the complex “Nebosvod” allows estimating the asteroid orbit well enough.