Abstract: The subject of this research is the complexes and means of navigational positioning, as well as multi-parameter phasometric systems of trajectory changes, which contain channels capable of safely measuring the angular coordinates and the rate of changes of the angular coordinates of moving objects. The downside to such systems is the fact that the lines of positioning on which the object is located are considered to be linear. Thus, the acceptable precision of the measurements of angular coordinates is preserved only when the distance to object is several times greater than the base of measurement. This article explores an important case, when the length of the measurement base is equal or even greater than the distance to the object. The research was conducted on the possibility of transitioning towards the hyperbolic system of trajectory changes (or a system of changes when the lines of positioning on which the moving object is located are hyperbolas). The achieved analytical dependencies of precision of determining the angular coordinates in arbitrary distances to the moving objects in the presupposition that the line of positioning is a line of intersection of two hyperboloids of rotation formed by two mutually perpendicular bases. These analytical dependencies allow us to not only a priori assess the precision, validity, and reliability of receiving navigational parameters of the moving objects, but also calculate the scientifically grounded limitations of the work of the complexes and measuring means.