A technique for accuracy evaluation for airborne target movement parameters determining under condition of its covert observation based on iteration method application


DOI: 10.34759/trd-2021-117-18

Аuthors

Efanov V. V.*, Zakota A. A.**, Gunkina A. S.***

MESC Air Force “Air Force Academy named after professor N.E. Zhukovskii and Yu.A. Gagarin”, 54a, Starykh bol'shevikov, Voronezh, 394064, Russia

*e-mail: efanov55@mail.ru
**e-mail: 500vvs@rambler.ru
***e-mail: volan100@mail.ru

Abstract

The article presents the analysis of the two approaches, namely positional and positional-rapid ones, for target movement parameters determining based on its track angles. It was revealed herewith that methods based the above said approaches are not employed at present.

With the positional approach application, only absolute or relative coordinates characterizing the target space position are being employed, while the positional-velocity method allows determining both velocity and acceleration of the moving target, enabling dynamics evaluation of its spatial movement. Within the framework of the latter approach phase coordinates of the target, mother aircraft and measurement are being represented as vectors in multi-dimensional space of states. The coordinates’ estimates herewith may be formed either in both Cartesian and polar coordinates based on either real or artificially generated measurements.

The positional approach to the coordinates’ evaluation is being realized based on the azimuthal-elevation, triangulation and kinematic methods. The azimuthal-elevation method employs the results of azimuth and elevation angle simultaneous measurements of the stationary ground target. The slant distance to the target is being determined based on the values of altitude and elevation angle. The scope of its application is restricted.

With the action against stationary ground targets, both triangulation and kinematic methods are used. The triangulation method for the target position determining employs analytical dependencies between the sides and angles of a triangle, which vertexes are associated with the target and radar station. This method implies solving algebraic equations. However, its application is restricted due to problems associated with the targets identification, staying at the same angular position. The simplest kinematic method rests upon the notion of the equations describing the process of reciprocal motion of the aircraft and the target including a motioning target. The state-of-the-art kinematic method, which might be named dynamic-kinematic, is based on mathematical description of reciprocal movement of a target and radar carrying aircraft in the state space.

The positional-velocity approach to estimating the target coordinates is being realized base on the pseudo triangulation and kinematic methods. The kinematic method is inapplicable due to the impossibility of nonlinear filtering of Markov processes implementation.

The authors propose a mathematical model for indirect parameters determining of the airborne target based on description of the objects rendezvous procedure in the form of linear equations corresponding to various options of the situational scenery while rendezvous. The article demonstrates the process of the system of linear equations preparation to the iteration process. Estimation of degree of convergence of system of linear equations, describing the rendezvous process of the objects at various values of the input parameters, was performed. It was revealed herewith that:

The degree of convergence for the system of equations which describe the process for objects approaching each other with different values of input parameters has been estimated. The results obtained show that:

– In case of the exact input parameters the degree of convergence is high, and the number of iterations achieves k = 55 for the mean-square values of range and velocity of correspondingly from δD1 = 1.5% to δD1 = 4.2% and δLt = 11.8%;

– In case of inaccurate input parameters (the error Δβ = ±0.1°, Δβ = ±1´,
Δβ = ±3.6” = 0.001°) the number of iterations equals correspondingly k = 7490; k = 598;
k = 355, the degree of convergence is poor, which does not ensure satisfactory closeness to the solution. Zeidel method application in this case herewith is stipulated by its constant convergence for the normal systems of linear algebraic equations.

Accuracy evaluation of the range to the airborne target and its velocity can be increased with multiple measuring of angular coordinates (using a «bunch» of measurements). Practical computations revealed that with n = 20–25 the error in the range determining was from 15% to 20%, and in velocity determining was 20%—25%.

Keywords:

indirect determination of airborne target parameters, accuracy characteristics, target movement parameters determining algorithms

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