Errors in prognostic relief characteristics in statistic approach to low-altitude aircraft flight control synthesis according to a digital height map

Аuthors

Yampol'skii S. M.^1*, Naumov A. I.^2**, Kichigin E. K.^3***, Rubinov V. I.^3****, Mokh M. A.^3****

1. Higher School of Economics, 20, Myasnitskaya str., Moscow, 101000, Russia
2. Сompany "Gefest and T", 1, Narkomvod str., Zhukovsky, Moscow region, 140180, Russia
3. Air force academy named after professor N.E. Zhukovskii and Y.A. Gagarin, Voronezh, Russia

*e-mail: yampolsm@mail.ru
**e-mail: al_naumov@rambler.ru
***e-mail: kichigin92@.yandex.ru
****e-mail: rubinov777@.mail.ru

Abstract

The subject of the research are developed tabular-analytical and tabular-approximating methods of altitude evaluation statistic performance calculations according to a relief height digital map.
The subject matter is the comparative evaluation of the developed relief height statistics calculations methods. Analysis of mathematical expectation and height dispersion method errors by means of tabular-approximating method is provided.
The aim goal of this is to increase the accuracy of flight altitude evaluation according to a digital height map while counting prognostic flight path by means of on-board inertial navigation systemfor flight security.
The research methodology includes the application of statistics approach for relief height calculations in lying ahead points along the aircraft flight trajectory, that should be regarded as random variables. The knowledge of the random variables distribution laws allows forming at any time t such profile of «cartographic heights», which rounding according to the aircraft control law will ensure the specified probability rates of low-flight security over the real relief.
As a result of a numerical experiment using the tabular-approximating method the following boundary values of errors are defined: the maximum error of mathematical expectation does not exceed 0,3 meters for a mathematical expectation evaluation and 0,25 meters for root-mean-square deviation of relief height evaluation.
The range of research application is the formation of the low-altitude flight informational support according to a relief height digital map by means of development of relief height array of given dimension on forward points along the aircraft flight trajectory for any time t of control signal calculation.
The research results allow recommending the tabular-approximating method for practical use during low-altitude aircraft flight echelon formation. Also it is necessary to point out the fact that the needed computing resources do not depend on planned coordinates errors during a fixed flight time.

Keywords:

tabular-approximating method, relief height evaluation statistics, low-altitude flight, digital height map, on-board navigation system, method errors

References

1. Venttsel’ E.S., Ovcharov L.A. Teoriya veroyatnostei i ee inzhenernye prilozheniya (Probability theory and its engineering applications), Moscow, ACADEMIA, 2003, 464 p.
2. Merculov V.A., Naumov A.I., Chigin G.P. Teoriya i sistemy upravleniya, 1999, no. 6.
3. Naumov A.I., Kichigin E. K., Mokh Akhmed Medani Akhmed Alamin Akademicheskie zhukovskie chteniya. Sbornik statei, Voronezh, 2013.

Download