2.Evaluation of accuracy of lines of position and location of aircraft

Accuracy is the qualitative characteristic that determines the proximity of measurement results to the true value of the navigation parameter.

Navigation systems by accuracy are characterized by measurement error of navigation parameters (NP). In the RNS for evaluation of the accuracy of measurement is used the root mean square error (RME, ). These accuracy characteristics are expressed in the mean square error of measurement are given in the descriptions of the RNS. But for air navigation is more important the accuracy of the navigation solution of a specific problem (error estimation of control path in the direction and distance, determining AL, etc.).

The aircraft position(AP) is a point on the earth's surface over which is currently the AC, that is the point on the earth's surface, which at some point in time projected center of aircraft gravity. The spatial position (SP) - the position of the AC center of mass in space, i.e. taking into account the altitude over the point on the earth's surface over which at this time is AC.

As many navigational problems are solved using position lines – lines of the probable AC location which is characterized by the persistence of NP, it is necessary to know the accuracy of its determination.

Location of AC can be determined by radio methods of measurement of the two lines (PL) positions, the general point (point of intersection), which will give AP. In this case, the accuracy of the AP will depend on the accuracy of these operations, i.e. the accuracy of the LP defining. It must be borne in mind that the methods for determining the AP depend on the specific methods of determining the NP. They are different at use of specific types of RNS (rangefinder, goniometric, the distance difference, etc.).

Basic PL which are defined by radio methods are:

The line of equal distances (LED) - the locus of points equidistant from a fixed on the earth's surface, where the RNS is located, which in theory and practice of navigation is defined as radio navigational point (RNP). It is determined by using of information of distance measuring RNS.

Line of equal radiostation bearings (LRB) - the line, the great-circle bearing of which on the ground RNP is a constant. It is obtained while flying at RNP with maintaining of the steady-state value of radiostation bearing (RB).

The line of equal distance differences (LEDD) - a line for each point of which the difference of distances to two points on the earth's surface is constant. It goes to difference distant mesuring (hyperbolic) navigation systems.

AC position is defined as the intersection point of at least two different families of PL. Therefore the error of the PL determination leads to an error of AC coordinates determination.

2.1. The error of the position lines determination of rns

The error in determination of the surface (lines) of position are assessed by interval between the surface normal between the surfaces (lines) of position which satisfy the present and the measured value of the NP.

_{NP
equation in a Cartesian coordinate system can be written as: in the}space _,on the plane. These equations correspond to three-dimensional and two-dimensional scalar fields ofparameter. In the RNS working areas the functionis continuous and the differential, so changing of the PN scalar field can be described by its gradient, i.e. vector indicating the direction of fastest growth of parameter.