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doi 10.24411/2409-5419-2018-10023
THE TRACKING STROBE FORMATION ALGORITHM ON THE MANEUVERING AIRCRAFTS ON THE BASIS OF AN FUZZY LOGICAL CONCLUSION
PROROK
Valery Yaroslavovich1
KHALIKOV Eldar Mavlyutovich2
OKHOTNIKOV Yury Yurievich3
SHAYMUKHAMETOV Shamil Ildusovich4
Information about authors:
1PhD, Full Professor, Professor of the Military Space Academy, St.Petersburg, Russia, val_prorok@mail.ru; 2PhD, Head of the Department of the Military Institute (Research) of the Military Space Academy, St.Petersburg, Russia, hell_2@mail.ru;
3Lecturer of the Military Space Academy, St.Petersburg, Russia, Georgy_03@mail.ru;
"Postgraduate student of the Military Space Academy, St.Petersburg, Russia, 28 172@mail.ru.
ABSTRACT
The process of maneuvering aircraft tracking with radar equipment is a difficult task, because it is carried out under conditions of uncertainty about the nature of a possible maneuver, which leads to considerable errors in calculating the size of the strobe. One of the most perspective ways to overcome this uncertainty task is the use of fuzzy logical conclusion. The aim of the work is the lowering of the possibilities of skipping marks and the formation of false trajectories by using correction expansion factor of the strobe when it is accompanied with maneuvering aircraft.
Recently, active introduction of new methods and models into industry and military affairs began, which were developed on the basis of fuzzy logic. The use of "fuzzy systems" allows to reduce resource and energy costs and provides a higher resistance to the influence of interfering factors than traditional automatic control systems can provide.
Fuzzy control is especially relevant when the processes under investigation are too complicated to be analyzed by conventional methods or when available sources of information are interpreted poorly, inaccurately or indefinitely. Fuzzy logic is closer to human thinking and natural languages than traditional logical system and it could provide effective means of displaying uncertainty and inaccuracies of the real world.
The machine of fuzzy sets and fuzzy logic is successfully used to solve the problems in which the initial data are unreliable and weakly formalized.
This work presents an algorithm of forming of the tracking strobe, in which the calculation of the required strobe size is carried out by using of linguistic variables for the variance of measurement and extrapolation errors, changes in speed and in estimated time before the start of maneuver and which increases the probability of sustained support for maneuvering aircraft.
KEYWORDS: maneuvering aircraft's; strobing; fuzzy logical conclusion; linguistic variable.
For citation: Prorok V. Y., Khalikov E. M., Okhotnikov Y. Y., Shaymukhametov S. I. The tracking strobe formation algorithm on the maneuvering aircrafts on the basis of an fuzzy logical conclusion. H&ES Research. 2017. Vol. 10. No. 1. Pp. 100-107. doi 10.24411/2409-5419-2018-10023
Vol. 10. No. 1-2018, H&ES RESEARCH
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INTRODUCTION
It is quite difficult to solve the task of the sustainable support of maneuvering aircrafts (MA) by radar stations (RS) at the moment [1]. This is due to the uncertainty of conduct of this type of target in the area of the RS, which leads to an increase of the number of measurement and extrapolation errors in the processing of treatment of radar information. The visual target does not fall into the next strobe and is dropped from the accompanying as a result [2].
Strobe is a preselected area of the RS field of view, which coordinates of the center is the same with the coordinates of the extrapolated mark. The type and size of the strobe are determined on the basis of statistical data about the accuracy characteristics of information sources, errors in information processing and maneuverable capabilities of targets [3]. At the same time, the required values of the quality of the support should be provided (for example, the reliability of the tracking, the resolution of the tracking system, the probability of correct selection) [4].
We will consider structure of the operations which are carried out at stages of processing of radar information (RI):
1) stage of the tying the trajectory: strobing, rough estimation of parameters;
2) stage of the tracking: extrapolation, strobing, selection of the marks, parameter's estimation [5].
The process of detecting and tying a trajectory is presented on the fig. 1.
In the first period of overview received a mark from the target Zj with the coordinates r = 576,2 km, p = 43°, 8 = 3,53°. The strobe of capture is exposed around her. The strobe of capture is based on the known maximum speed capabilities of the target. In the next period of overview, the mark Z2 (r = 575 km, p = 42°, 8 = 3,52°) was caught in the strobe. A rough estimate of the speed is made by using two marks, and the coordinates of the second (last) mark are taken as the estimated coordinate values, after that the transition to the accompaniment phase is carried out [6].
The extrapolated parameters of the first strobe are calculated by formulas:
re = ri + T0 ' pe = + To2', e e =£i + To £,
where r, pe,8e — extrapolated range values, bearing angle and angle of elevation;
T0 — RS overview period;
r, f3, s — measured values radial, azimuthal and angular speeds [7].
The strobe is exposed around the extrapolated value, which was calculated with allowance of the measurement and extrapolation errors. In this case, the strobe sizes are calculated by formulas:
Ar = 2 • n
Aa = 2 • n •JDZm' Aa *=2 •n •yDa,
where Ar, Aa . , Aa , — the size of the strobe in azimuth,
' azim pla '
elevation angle and range;
D , D , D — dispersion of extrapolated azimuth, el-
r aazim a pla
evation angle and range;
n - expansion coefficient of strobe [8]. The accuracy of the coordinates and speed is determined when the next mark from the target hits this strobe. Let us consider the reasons for the appearance of false trajectories in the secondary radar processing system. Let's say that two marks hit the strobe of capture. In accordance with the criteria of the string, trajectories will be formed for both of them and sent for confirmation [9]. At the confirmation stage, extrapolated coordinates are calculated around which confirmation strobe are exposed. In the strobe of the true trajectory a mark has fallen in the current review period, but the false one has not. That's why the coordinates are smoothed out and transmitted to the tracking along the true trajectory, and a decision about the dump from processing is taken on the false trajectory (fig. 2)
If mark Z is not get into the strobe of the true trajectory (maneuver, malfunction, gross measurement error, etc.), then the extrapolated values on this trajectory are taken as estimat-
Fig. 1. The process of detecting and tying a trajectory along a target
Fig.2. The formation of the false trajectories
ed values of the coordinates and extrapolation is carried out for the next (fourth) review period.
The strobe of capture is exposed around the mark Z and the size of the strobe of capture much bigger than the size of the strobe of tracking. And that's the reason why the true mark can get into the strobe of capture and the strobe of tracking at the same time with a high possibility (fig. 2). The false trajectory is forming as a result.
The errors in the extrapolation of coordinates sharply increase while tracking the maneuvering target and to achieve a high possibility of hit the target in the strobe it is necessary to increase its size, which depends on the intensity of the maneuver and the smoothing ability of the extrapolation algorithm in that case. If in the tracking algorithm only two hypotheses are taken into account - whether there is a maneuver or not, then for maneuvering targets the strobe should be calculated on the basis of the intensity of the maneuver [10].
THE FORMING OF THE TRACKING STROBE ON THE BASIS OF FUZZY LOGIC
This work presents a strobing algorithm based on fuzzy logic, which is used to increase the sustained track for maneuvering aircraft and allows to reduce the possibility of skipping marks and the formation of false trajectories by improving the coefficient of expansion of the strobe n. The scheme of the algorithm is given on fig.3.
The description of the solution of a problem of determination of the sizes of tracking strobe is submitted further. The size of dispersion of errors of measurement and extrapolation is defined and it is given to an fuzzy look, then the functions of
belonging are forming to determine the degree of truth of the next preconditions of each rule [11-12].
The value of the dispersion of measurement errors and extrapolations D is proposed to be estimated by a linguistic variable with terms: LOW (LOW), MEDIUM (MED), HIGH (HIGH). The functions of affiliation to a linguistic variable are determined by using the fuzzy classification algorithm. The training sample for constructing the affiliation functions of characteristic D is exposed in tab.1.
The results of calculating the class centers of the classification scale for characteristic D are given in table 2. The type of the proposed characteristics of affiliation functions is given on fig.4.
Table 1
A training sample for constructing affiliation functions of the characteristic D
Characteristic values D, km2 Function of affiliation
Low Medium High
0.09 1.00 0.00 0.00
0.10 0.98 0.02 0.00
0.13 0.66 0.34 0.00
0.17 0.23 0.77 0.00
0.20 0.01 0.98 0.01
0.23 0.00 0.73 0.27
0.27 0.00 0.31 0.69
0.30 0.00 0.01 0.99
0.31 0.00 0.00 1.00
Fig.3. The scheme of an algorithm of formation of a tracking strobe on the basis of an fuzzy logical conclusion
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Table 2
The results of calculation of class centers
Characteristic D, km2
Low Medium High
0.093 0.201 0.308
The procedure of a fuzzification is carried out according to expression:
Df = max(^(D)A^2(D)A.. .^(D)), VDe®,
where Df — fuzzy value of the dispersion, l — total number of affiliation functions (l = 3 for fig.4), © — domain of definition D (S> = [0.09, 0.31]).
Next, the value of the change in speed dv is calculated for each of the coordinates between the previous and the current step and is reduced to an fuzzy form, then the affiliation functions are formed.
The value of dv is suggested to be estimated by a linguistic variable with terms: LOW (LOW), MEDIUM (MED), HIGH (HIGH). The functions of affiliation to a linguistic variable are determined by using the fuzzy classification algorithm [13]. A training sample for constructing the affiliation functions of the characteristic dv is presented in table 3.
Table 3
A training sample for constructing affiliation functions of the characteristic dv
Characteristic values dv, km/s Function of affiliation m(dv)
Low Medium High
0.00 0.95 0.05 0.00
0.05 0.30 0.40 0.00
0.10 0.04 0.90 0.06
0.15 0.00 0.40 0.50
0.20 0.00 0.05 0.95
The results of calculating the class centers of the classification scale for the dv characteristic are presented in table 4. The type of proposed affiliation functions is presented on fig.5.
Table 4
The results of calculation of class centers
Characteristic dv, km/s
Low Medium High
0.002 0.101 0.198
The procedure of a fuzzification is carried out according to the expression:
Fig. 4. The functions of affiliation of a linguistic variable D
-1-1- LOW —I-1-1-1-1— MED -1-1- HIGH
\
I I I i i I I I I
<A',kra/s
Fig. 5. The affiliation functions of the linguistic variable dv
dvf = max(^1(dv)A^2(dv)A_^ra(dv)), VdveQ,
where dvf - fuzzy value of speed change,
m - total number of affiliation functions (m = 3 for fig.5), Q - domain of definition dv ( Q = [0,0.2]). Further, the estimated time tman is determined before the start of the target maneuver in the radar field of view (when the execution is found to be the target of a maneuver, the algorithm generates the sign of Pman, the value tman is not taken into account in this case (table 7)), fuzzificating and the affiliation function is forming.
The value of tman is suggested to be estimated by a linguistic variable with terms: LOW (LOW), MEDIUM (MED), HIGH (HIGH). The functions of affiliation to a linguistic variable are determined by using the fuzzy classification algorithm. The training sample for constructing the affiliation functions of the characteristic tman is presented in table 5.
Table 5
Training sampling for constructing the affiliation functions of the characteristic tman
Characteristic values t , sec man' Function of affiliation m(t ) v man'
Low Medium High
0 0.95 0.05 0.00
3 0.70 0.30 0.00
5 0.30 0.70 0.00
7 0.05 0.90 0.05
10 0.00 0.85 0.15
12 0.00 0.50 0.35
15 0.00 0.05 0.95
In table 6 the results of the calculation of the class centers classification scale for the characteristic of tman are given. The membership functions presented in fig.6.
The procedure of fuzzification in accordance with the expression is carried out:
t, = max(u,(t )au,(? )a...u,(? )), Vt e
f vr 1v man' rzv man' r kv man"' man '
where tf — the fuzzy value of the time amount before the maneuver,
k — the total number of membership functions (k = 3 for fig.6),
5E — a domain of definition tman (S = [0,15]).
Table 6
The results of the calculation of the class centers
Characteristic of t , seconds man
Low Medium High
0.000 7.521 14.993
By obtaining the linguistic values of the strobe expansion coefficient n which is the key in determining the size of the strobe to implement the fuzzy inference rules were developed [14]. According to the following template based on the table 7 rules are formulated:
IF the dispersion value D is LOW AND the value of dv is HIGH AND the value of t is MED, THEN the value of
man
n is MED.
In fig 7 the dependence of coefficient n from the input value of dispersion, value of velocity changes and value of the time before the start of maneuver is shown. The intensity of the black color reflects the value of n (the darker the color, the smaller the n value).
To perform defuzzification (conversion to definition) of value n the method of center of gravity is used. The ratio for modification to a definite view looks like:
n = | ny ( n ) dn /1 y ( n ) dn,
n In
where n — is a estimation of definite value of n obtained by selecting method of the center of gravity [15].
Fig. 6. The membership function of the linguistic variable tman
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Table 7
The rule base to obtain the value of n
The value of t , sec man' The value of D, km2
LOW MED HIGH
The value of dv, km/s
LOW MED HIIGH LOW MED HIIGH LOW MED HIIGH
LOW LOW LOW LOW LOW MED MED MED MED HIIGH
MED LOW LOW MED LOW MED MED MED MED HIIGH
HIIGH LOW MED MED MED MED HIIGH MED HIIGH HIIGH
P man MED MED MED MED HIIGH HIIGH HIIGH HIIGH HIIGH
c)
Fig. 7. a) the dependence of n on input values of time before the start of the maneuver and the value of the velocity changes; b) the dependence of n on input values of dispersion and the value of the velocity changes; c) the dependence of n on input values of time before the start of the maneuver and dispersion
ANALYSIS OF THE ALGORITHM STROBING PERFORMANCE RESULTS
For illustration of the proposed algorithm based on fuzzy logic, consider the results of the operation of the strobing on target. In fig.8 are graphs of the dependency of the probability of missing the mark Pmiss (fig.8 a) and the probability of ties of false trajectories Pfl (fig.8 b) by the intensity of the maneuvering target 1=dv/g, where dv is the acceleration of the target in the coordinate, g = 9,8 m/s2. In the figures red curves — correspond to an existing algorithm, blue curves — using an algorithm based on fuzzy logic is obtained.
Analysis of the graphs shows that using the proposed algorithm based on fuzzy logic, when accompanied maneuvering target allows to reduce the probability of missing the mark Pmiss and tie false trajectory Pft of 5-10% compared to existing algorithm.
CONCLUSION
Thus, we can conclude that the solution of the problem of MA tracking in conditions of uncertainty of its behavior in the coverage of the radar with existing methods and algorithms is carried out with significant errors, which leads to entanglement of the trajectories or the tie of a new, and in the worst case, reset the targets with tracking. The algorithm of strobe formation on the basis of fuzzy logical conclusion allows to increase the stability of tracking of the MA and reduce the probability of mark missing and the false trajectories tie.
REFERENCES
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13. Zadeh L.A. Calculus of fuzzy restrictions. Fuzzy sets and its application to cognitive and decision processes. In eds. L.A. Zadeh, K.S. Fu, K. Tanaka, M. Shimura. New York, 1975. Pp. 1-39.
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алгоритм формирования строба сопровождения по маневрирующим летательным аппаратам на основе нечеткого логического вывода
ПРОРОК Валерий Ярославович,
г. Санкт-Петербург, Россия, val_prorok@mail.ru
ХАЛИКОВ Эльдар Мавлютович,
г. Санкт-Петербург, Россия, hell_2@mail.ru
ОХОТНИКОВ Юрий Юрьевич,
г. Санкт-Петербург, Россия, Georgy_03@mail.ru
АННОТАЦИЯ
Процесс сопровождения маневрирующих летательных аппаратов радиолокационными средствами является сложной задачей, так как осуществляется в условиях неопределенности о характере возможного маневра, что приводит к значительным погрешностям при расчете размера стробов сопровождения. Одним из перспективных направлений преодоления такой неопределенности является использование нечеткого логического вывода. Целью работы является понижение вероятностей пропуска отметок и завязки ложных траекторий при сопровождении маневрирующих летательных аппаратов с помощью коррекции коэффициента расширения строба.
В последнее время началось активное внедрение новых методов и моделей разработанных на основе нечеткой логики в промышленность и в военное дело. Использование «нечетких систем» позволяет уменьшить ресурсо- и энергозатраты и обеспечивает более высокую устойчивость к воздействию мешающих факторов по сравнению с традиционными системами автоматического управления. Нечеткое управление оказывается особенно актуальным, когда исследуемые процессы являются слишком сложными для анализа с помощью общепринятых методов или когда доступные источники информации интерпретируются некачественно, неточно или неопределенно. Нечеткая логика, предоставляющая эффективные средства отображения неопределенностей и неточно-
ШАЙМУХАМЕТОВ Шамиль Ильдусович,
г. Санкт-Петербург, Россия, 28_172@mail.ru
КЛЮЧЕВЫЕ СЛОВА: маневрирующие летательные аппараты; стробирование; нечеткий логический вывод; лингвистическая переменная.
стей реального мира, и на которой основано нечеткое явление, ближе к человеческому мышлению и естественным языкам, чем традиционные логические системы.
Аппарат нечетких множеств и нечеткой логики уже давно с успехом применяется для решения задач, в которых исходные данные являются ненадежными и слабо формализованными. В работе представлен алгоритм формирования строба сопровождения, в котором с использованием лингвистических переменных величин дисперсии ошибок измерения и экстраполяции, изменения скорости движения и предполагаемого времени до начала маневра осуществляется расчет необходимого размера строба повышая вероятность устойчивого сопровождения маневрирующих летательных аппаратов.
СВЕДЕНИЯ ОБ АВТОРАХ:
Пророк В. Я., д.т.н., профессор, профессор Военно-космической академии имени А.Ф. Можайского;
Халиков Э. М., к.т.н., начальник отдела Военного института (научно-исследовательского) Военно-космической академии имени А.Ф. Можайского;
Охотников Ю. Ю., преподаватель Военно-космической академии имени А.Ф. Можайского;
Шаймухаметов Ш. И., адъюнкт Военно-космической академии имени А.Ф. Можайского.
Для цитирования: Пророк В. Я., Халиков Э. М., Охотников Ю. Ю., Шаймухаметов Ш. И. Алгоритм формирования строба сопровождения по маневрирующим летательным аппаратам на основе нечеткого логического вывода // Наукоемкие технологии в космических исследованиях Земли. 2018. Т. 10. № 1 С. 100-107. с^ 10.24411/2409-5419-2018-10023
