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8
Civil Aviation High Technologies
Vol. 26, No. 04, 2023
УДК 621.396.933.25; 629.7.058.53 DOI: 10.26467/2079-0619-2023-26-4-50-63
ADS-B data gating technique and its probabilistic models
E.A. Rubtsov1, S.A. Kudryakov1, I.M. Dalinger1, A.S. Kalintsev2
1 Russian University of Transport (MIIT), Moscow, Russia 2 FSUE "State Air Traffic Management Corporation of the Russian Federation", Arkhangelsk Air Traffic Management Center, Mezen, Russia
Abstract: The article developed a gating technique that allows us to validate ADS-B data without the necessity to verify using the secondary surveillance radar or multilateration. Probabilistic models of the ADS-B data gating technique, as well as the algorithm for applying these models were proposed. Benchmark cases that occur when aircraft (A/C) positioning by ADS-B systems, determined by threshold values of navigation and pilot's errors, were analyzed. The first benchmark case assumes not exceeding of navigation and pilot's errors the bounds of the tolerance limits, which allows us to draw up a conclusion concerning the ADS-B data validation. The second one assumes exceeding of a pilot's error the bounds of the tolerance limits under an allowable navigational error. Herewith, the air traffic controller (ATC) obtains a message about the proper ADS-B operation and the necessity to issue instructions to the pilot to correct a flight. The third benchmark case assumes exceeding of a navigation error the bounds of the tolerance limits under an allowable or not allowable pilot's error. In this case, the ATC obtains a message about not valid ADS-B data and the incapability to use these systems. The simulation of the given benchmark cases was performed. In addition, the Rayleigh and Rice distributions were applied to implement the ADS-B data gating technique. The simulation results allow us to assess the required amount of accumulated ADS-B data for the evaluation. Thus, it was found that during the estimate based on the Rayleigh distribution, it is sufficient to accumulate 15-20 measurements, which, when transmitting 2 messages per second and under the condition of the normal ADS-B equipment operation, will take 8-10 s. During the estimate, using the Rice distribution, an accumulation of 25-30 measurements is sufficient, which will take 13-20 s. The developed method will allow the use of ADS-B systems at regional aerodromes with the low intensity of air traffic as the primary or sole surveillance means.
Key words: flight safety, ADS-B, gate, Rayleigh distribution, Rice distribution, distribution parameter estimate, error of navigational measurements, pilot's errors.
For citation: Rubtsov, E.A., Kudryakov, S.A., Dalinger, I.M., Kalintsev, A.S. (2023). ADS-B data gating technique and its probabilistic models. Civil Aviation High Technologies, vol. 26, no. 4, pp. 50-63. DOI: 10.26467/2079-0619-2023-26-4-50-63
Метод стробирования данных АЗН-В и его вероятностные модели
1112 Е.А. Рубцов , С.А. Кудряков , Я.М. Далингер , А.С. Калинцев
1 Российский университет транспорта (МИИТ), г. Москва, Россия 2ФГУП «Госкорпорация по организации воздушного движения», Архангельский центр ОВД, г. Мезень, Россия
Аннотация: В статье разработан метод стробирования, который позволяет оценить достоверность данных АЗН-В без необходимости проверки с помощью вторичного радиолокатора или многопозиционной системы наблюдения. Предложены вероятностные модели метода стробирования данных АЗН-В, а также алгоритм применения данных моделей. Проанализированы типовые ситуации, возникающие при определении местоположения воздушного судна с помощью систем АЗН-В, определяемые пороговыми значениями погрешностей навигации и пилотирования. Первая типовая ситуация предполагает невыход погрешностей пилотирования и навигации за пределы допуска, что позволяет сделать вывод о подтверждении достоверности данных АЗН-В. Вторая типовая ситуация предполагает выход погрешности пилотирования за пределы допуска при допустимой погрешности навигации, при этом диспетчер получает сообщение о корректной работе АЗН-В и о необходимости выдачи команды пилоту на корректировку полета. Третья типовая ситуация предполагает выход погрешности навигации за пределы допуска при допустимой или недопустимой
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Civil Aviation High Technologies
погрешности пилотирования; в этом случае диспетчер получает сообщение о том, что достоверность данных АЗН-В не подтверждается и применять эти системы нельзя. Выполнено моделирование этих типовых ситуаций, при этом для реализации метода стробирования данных АЗН-В применялись распределения Рэлея и Райса. Результаты моделирования позволяют оценить требуемое количество накопленных данных АЗН-В для проведения достоверной оценки. Так, было установлено, что при выполнении оценки с применением распределения Рэлея достаточно накопления 15-20 измерений, что при передаче двух сообщений в секунду и при условии штатной работы оборудования АЗН-В потребует 8-10 с. При выполнении оценки с применением распределения Райса достаточно накопления 25-30 измерений, что потребует 13-20 с. Разработанный метод позволит применять системы АЗН-В на региональных аэродромах с низкой интенсивностью полетов как основное или единственное средство наблюдения.
Ключевые слова: безопасность полетов, АЗН-В, строб, распределение Рэлея, распределение Райса, оценка параметров распределения, погрешность навигационных измерений, погрешности пилотирования.
Для цитирования: Рубцов Е.А. Метод стробирования данных АЗН-В и его вероятностные модели / Е.А. Рубцов, С.А. Кудряков, Я.М. Далингер, А.С. Калинцев // Научный Вестник МГТУ ГА. 2023. Т. 26, № 4. С. 50-63. DOI: 10.26467/2079-0619-2023-26-4-50-63
Introduction
An automatic dependent broadcasting-type surveillance (ADS-B) is referred by the International Civil Aviation Organization to the cutting-edge surveillance technologies which is reflected in the provisions of the Global air navigation plan1.
The reduced cost to implement ground stations, compared to costs to deploy secondary surveillance radars (SSR) and multilaterations (ML), is attributed to the ADS-B benefits. The operation cost is also considerably below. If high-precision navigation sensors are installed on board aircraft (as a rule, receivers of the Global Navigation Satellite Systems -GLONASS), ADS-B provides surveillance accuracy not worse than radar aids [1-3].
However, the Aeronautical Surveillance Manual2 points to the relevance for the data validation derived from ADS-B with the aid of SSR and ML. It is associated with the possibility of an increase in the navigation error (when using self-contained inertial systems and range/azimuth positioning systems of navigation). Thus, the relevance for the data validation levels out the economic ADS-B technology attractiveness.
1 The Global Air Navigation Plan. ICAO GANP Portal. Available at: https://www4.icao.int/ganpportal (accessed: 17.03.2023).
2 Doc. 9924 AN/474: Aeronautical Surveillance Manual. 3rd ed. ICAO 2020, 432 p.
The task of the ADS-B data validation without applying additional surveillance facilities can be accomplished by the techniques of the algorithmic data validation. The paper [4] dealt with the techniques of the algorithmic ADS-B data validation to ensure ground maneuvers at an aerodrome. The techniques, presented in the article [4], are based on the accumulation of aircraft coordinates measurements with the subsequent statistical analysis of derived data. The given paper proposes to modify the methods, described in [4], and employ the gating technique, which has already found practical use in radar surveillance [5, 6], when processing ADS-B data.
When processing ADS-B data, the gating technique will make it possible to evaluate the data validity about the aircraft position and use reasonably priced ADS-B ground stations as the sole or primary surveillance means, which is pertinent for regional airports with the low intensity of air traffic.
In conformity with the analysis of ADS-B data [7], most of aircraft operate normally in the direction of a rectilinear trajectory without tending toward violating boundaries of airways. Notably, the proportion of such aircraft amounts to 76% in general traffic.
A maneuver in horizontal or vertical planes is inherent in 9% of aircraft. It is worth noting that a maneuver can be carried out with the deviation from the route (Flight Planed Route - FPR) due to flight crew errors concerned with the incorrect interpretation of reliable navigation data. The probability of such an event can reach 10-3 [8].
For approximately 6% of aircraft, the tendency toward violating boundaries of airways or separation regulations is displayed, or the violation of airway boundaries is revealed. It can result from significant errors of navigation systems. The situation can be affected by pilot's errors which will cause a greater deviation from a nominal aircraft path [7].
Subsequently, while determining the position of an aircraft using ADS-B, the described possible situations during the aircraft flight operation can be displayed in the form of the following benchmark cases:
1. A flight operation according to the FPR, in this event, pilot's and navigation errors are within the tolerance limits.
2. A flight deviates from the FPR (due to significant pilot's errors) under allowable navigation errors.
3. Not tolerated significant pilot's and navigation errors.
The first scenario can be considered routine, at the same time, navigation error values of the board navigation complex are minor, and a flight crew operates a flight in full compliance with the FPR with insignificant pilot's errors. The patterns of conducting maneuvers as well as the air traffic management (ATM) requirements in the vicinity of the airport are regulated and contained in the Aeronautical Information Publications (AIP).
Scenarios 2 and 3 can be considered nonroutine, while in scenario 2, ADS-B data meets the requirements in terms of accuracy, and it is valid. In scenario 3, allowable values are exceeded, and data is not valid. In practice, it is necessary to identify all the listed variants and provide an ATC with information concerning the ADS-B data validity.
When solving the ADS-B data validation problem, the paper [9] illustrates the features of employing the gating technique to process ADS-B data. In radar surveillance, this technique is employed to reveal false coordinates, when developing a motion trajectory [5]. Applicably to the assigned problem, let us take a gate as an area of space around the extrapolation point of the aircraft path with the center at the point of extrapolated aircraft coordinates within which the
estimate of aircraft coordinates will be considered reliable.
For aircraft with the maximum take-off mass exceeding 5700 kg, or with a maximum cruising true airspeed capability greater than 250 knots, the European Commission Implementing Regulation (EU) No 1207/20113 and its first amendment 1028/20144 lays down the mandatory carriage and operation of the ADS-B mode S (EHS) and mode 1090 ES Enhanced Surveillance installations. Mode S (EHS) enhanced surveillance represents a set of advanced features of mode S and comprises reports about a chosen intention in the vertical plane (BDS 4.0), a report about a track and a turn (BDS 4.0), as well as a report about a track and a turn (BDS 5.0). The listed types of reports contain information about values of velocity, track variations, heading, indicated airspeed (IAS) and a chosen intention in the vertical plane.
In the Russian Federation, mode S (EHS) and ADS-B mode 1090 ES enhanced surveillance applications are installed in different aircraft (DA-42, L-410, An-148, etc.) and helicopter (Mi-8, etc.) models.
The use of mode S transponder allows for current and planned aircraft coordinates (intentions) to be derived from the ADS-B ground station. However, a nautical data error remains unknown. In order to solve this problem, the use of the gating technique [9] is proposed, for which, it is necessary to accumulate the sufficient number of measured values of aircraft coordinates to determine a center of gate by the extrapolation method. Afterwards, in conformity with the obtained sampling of accumulated measurements, the interval parameter estimate for the distribution of aircraft positioning error is made, and the probability of entering aircraft an area of gate is computed. A key point is to ensure the conformity of the distribution parameter estimate for the sampling of accumulated values with the entire
3 Regulation 1207/2011. Requirements for the performance and the interoperability of surveillance for the SES. Official Journal of the European Union, pp. 35-52
4 Regulation 1028/2014. Requirements for the performance and the interoperability of surveillance for the SES. Official Journal of the European Union,
pp. 7-8.
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assembly parameters. The interval estimate is made with the assigned level of reliability. Sizes of gate are assigned based upon the requirements for allowable errors of surveillance systems. The probability of aircraft entering an area of gate can be found based on the Rayleigh and Rice distributions.
Methods of research
According to the Aviation Regulations of the Interstate Aviation Committee "Certification Requirements for Aerodrome and Airway Facilities" (AR-170, volume 2), allowable values of the mean square error (MSE) of an airport surveillance radar amount to 150 m at a maximum range of 100 km.
The requirements for MSE accuracy of the aerodrome radar facility, stated in the Certification requirements (Basis), amount to 120 m for the primary channel and 70 m for the secondary one (under the probability of coordinate and supplemental information integration not less than 0.95).
The specifications of surveillance systems "Eurocontrol"5 provide the recommended MSE value to determine aircraft coordinates horizontally equal to 300 m with the minimum separation of 3 nautical miles.
As far as we can see, the requirements of national and international standards for tracking an aircraft in the aerodrome zone slightly differ and vary from 70 to 300 m. In order to assign sizes of a gate area and solve a problem of the ADS-B data validation, it is feasible to choose some averaged value. It is supposed to assume a radius of a gate area equal to the allowable MSE value of 150 m (which complies with the Interstate Aviation Committee Requirements published in AR-170, volume 2).
The condition of the ADS-B data validity is met if the parameter estimate in conjunction with the confidence intervals, with the assigned reliability, does not exceed assigned gate sizes. Thus, when confidence interval values of the random
variable estimate do not exceed the value for a radius of a gate area, assumed data is considered valid. If the interval estimate exceeds a radius of a gate area, the condition of data validity is not met.
Since the time for the ADS-B data validation is an important factor, it is feasible to identify such a level of reliability which will ensure the data validation within the acceptable time. In conformity with [9], for the level of reliability 0.95, data about aircraft entering or not entering an area of gate will be valid.
Errors of aircraft deviation from the assigned trajectory (FPR) can be described in the normal distribution law [3]. For the Cartesian coordinates, the distribution density of the bivariate normal law with parameters mx, my, ox, oy is defined as [10, 11]:
f(x, y) =
1 (x-mx9
2(1->2) eg
-2>
(x-mk)(y-my) (У-ту)
exPy
eg
2^axCTyA/l->2
(1)
Euro control Specification for ATM Surveillance System Performance (Volume 1). (2021). 92 p.
where mx, my - the mathematical expectation of a random variable along the Ox - and Oy -axis accordingly,
ox, oy - MSE of a random variable along the Ox - and Oy -axis accordingly, p - coefficient of correlation. A solution to define the probability of aircraft position in the gate can be formulated as a computation problem of the probability of a random variable entering a circle of radius R (defined with the requirements for errors of surveillance systems) with the center at the point of extrapolation, which coordinates belong to a maneuver pattern.
Depending on values of random variable parameters inherent in various benchmark cases, errors of aircraft positioning can be characterized by different distribution laws.
Let us consider a problem solution for benchmark cases to determine the aircraft position using ADS-B. In the simplest case, let us assume that errors of determining the aircraft position along the Ox - and Oy -axis of the Cartesian coordinates are equal.
l
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The first benchmark case is indicative of an insignificant pilot's error, for the problem formalization, let us assume it as zero. Thus, the mathematical expectation (ME) of aircraft positioning error equals zero, MSE along the Ox -and Oy -axis equal each other: m = 0, ax = ay = a. In this case, an ADS-B error depends merely on a board navigation complex error. Such a situation is inherent in the aircraft rectilinear motion case.
When meeting the condition ax = ay = a, the random variable distribution is referred to as the circular normal distribution [10-12].
Thereafter, a random variable r = V X2 +Y2, where X, Y - independent Gaussian distributed random variables, under the condition of the circular normal distribution of a random variable and the lack of a fixed error, follows the Ray-leigh law. Thereupon, the probability of aircraft exiting an area of gate for R radius can be found as the miss probability [13-15]:
m ± 0, ax = ay. Thereafter, a random variable
r = 4X +Y , where X, Y - independent Gaussian distributed random variables, has the Rice distribution with the density of distribution [13, 16]:
x
f (x 1 s, a) = —rexp
a
x2 + s2) > 2a2
I0
Va2 у
(4)
where I0 - the modified zero-order Bessel function of the first kind;
^ - bias equal to s = -J// + // , where l2,
/ - Ox and Oy ME;
a - the scale parameter.
The distribution function is presented as:
u,
F (a) = i"TexP J a2
-(x 2 + s 2)Л 2a2
I0
Va2 у
(5)
F (r ) = P (R < r ) =
i - e
2 bz
r > 0
' (2)
r < 0
f (r )=e
r " 2b2, r > 0,
(3)
where b - a scale parameter.
The second benchmark case is indicative of a flight technical error and a navigation error. A similar scenario can occur when an aircraft deviates from the trajectory of motion. In this context, the ADS-B system can operate properly under the condition of non-exceedance of a navigation error the bounds of the tolerance limits. If errors of the board navigation complex exceed the bounds of the tolerance limits, we have the third benchmark case under which it is impossible to apply ASD-B.
In this case, a problem of the fixed and navigation errors evaluation arises. A fixed error, that is ME is not equal to zero, is the distinctive feature of the situation under consideration from the previous one. For the simplest case under consideration, MSE are equal to each other:
The probability of entering aircraft an area of gate (Pi„) can be found as the probability of non-exceedance of a random variable r of the assigned radius of gate and can be computed using (5). In this case, the probability of deviation from the trajectory can be found as
P = 1 - P
1 out 11 "
in '
(6)
where Pout - the probability of aircraft deviation from the assigned trajectory, P„ - the aircraft position probability in an area of gate.
A two-phase algorithm of applying probabilistic models of the ADS-B data gating technique is proposed for the practical implementation. The estimate of the Rayleigh distribution parameters is calculated in the first phase of the analysis. If the upper confidence interval of the b parameter estimate does not exceed an allowable value, a conclusion about the ADS-B data validation is drawn up (the first benchmark case). In case of exceedance of the b parameter estimate, the estimate of the Rice distribution parameters is calculated. If during the analysis, a significant
2
r
2
r
pilot's error is revealed with the allowable navigation error, the ATC obtains a message about the proper ASD-B operation and the necessity to issue instructions to the aircraft flight crew (the second benchmark case). If during the analysis, significant pilot's and navigation errors, exceeding allowable values, are revealed, the ATC obtains a message that ADS-B data validation is not ensured, and other ATC methods are required (the third benchmark case). The Rayleigh distribution b parameter as well as the Rice distribution ^ and a parameters are estimable parameters in these simplest cases.
It is essential to note that the A/C airspeed and the frequency of position reporting impose limitations for the surveillance number. Taking into consideration the limited surveillance number, the parameter estimate is calculated based on the sampling of the entire assembly. The interval parameter estimate is calculated with the assigned level of reliability.
The benchmark cases were considered while assuming the equality of errors of determining the position along the Ox- and Oy -axis of the Cartesian coordinates. The stated simplification allowed for the Rice and Rayleigh distributions to be used as an example.
In practice, error values along the Ox - and Oy -axis will be distinguished from each other. Therefore, for the data validation, we should use more complicated distributions: the Hoyt distribution [17, 18] and the Beckmann distribution [19-22].
Research results
For simulating benchmark cases, MATLAB and Wolfram software packages were applied. The simulation modelling of the aircraft positioning error was conducted. The error of aircraft positioning was assigned as a random variable distributed in accordance with the Rayleigh and Rice laws. Based on the sampling from the entire assembly, the Interval estimate of distribution parameters with the level of accuracy 0.95 was obtained. The parameter estimate was calculated by means of the maximum likelihood method.
As a result of the simulation, the dependencies of distribution parameter estimate on the number of measurements N, i.e., data derived from the ADS-B ground station, were obtained. Figure 1 illustrates the results of the b parameter estimate of the Rayleigh distribution (corresponds to the error of aircraft positioning). Figure 1 and the subsequent ones, using a dotted line, illustrate simulated parameter values of distribution (input data). The red line illustrates the input data parameter estimate, the light blue and blue lines illustrate the upper and lower 95% confidence intervals as applicable.
In Figure 1, b parameter values of the Ray-leigh distribution amount to 50 and 100, which conforms with MSE values 50 and 100 m. In Figure 2, input b value parameters of the Ray-leigh distribution amount to 50 and 100, which conforms with MSE values 50 and 100 m. In the Figures, the following designations are assumed: PCI b Up and PCI b Low - the upper and lower 95% confidence interval of the b parameter estimate of the Rayleigh distribution; Param b -the assigned source of the b parameter value; Est param b - the b parameter estimate; Rline - the gate area boundary (the condition of the ADS-B data validity).
Figure 3 illustrates the results of the Rayleigh distribution parameter estimate when the input distribution parameters: s = 100, a = 50, which conforms with ME 100 m, MSE 50 m. Figure 4 illustrates the results of the Rice distribution parameter estimate based on the sampling from the entire assembly for a random value distributed in accordance with the Rice law when input distribution parameters: s = 200, a = 100, which conforms with ME 200 m, MSE 100 m. Figure 5 illustrates the results of the Rice distribution parameter estimate when input distribution parameters: s = 300, a = 150, which conforms with ME 300 m, MSE 150 m. The input data parameter estimate by accumulated values commences after 5 measurements. The Figures have the following designations: PCI Sigma Up and PCI Sigma Low - upper and lower 95% confidence interval of the parameter estimate a; PCI S Up and PCI S Low - upper and lower 95% confi-
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Vol. 26, No. 04, 2023
Fig. 1. Graphs for the estimate of the Rayleigh distribution parameters for the input values: b = 50 and b = 100
Fig. 2. Graphs for the estimate of the Rayleigh distribution parameters for the input values: b = 120 and b = 150
dence interval of the parameter estimate s; Est param Sigma and Est param S - the parameter estimate a and s; SigmaLine and Sline - assigned values of parameters a and s; Rline - the gate area boundary (condition of ADS-B data validity).
The results of simulation established that for meeting validity conditions, the estimate of random variable parameters distributed in conformity with the Rayleigh law can be obtained during 15-20 measurements, which, provided that two messages per second are transmitted by ADS-B installations, takes 8-10 s. In order to meet the validity conditions, the estimate of random vari-
able parameters distributed in accordance with the Rice distribution law - 25-30 measurements, which, provided that two messages per second are transmitted by ADS-B installations, takes 13-15 s.
The obtained results allow us to draw up a conclusion about the capability to utilize ADS-B ground stations at regional airports with the low intensity of air traffic as the primary surveillance means. For example, at aerodromes Ust-Kuiga, Chokurdakh, Cherskiy and other G and D-class aerodromes, it is feasible to replace exhausted life-span radars (generally DRL-7 SM) for ADS-B stations, upgrading software (ADS-B data
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Fig. 3. Graphs for the estimate of the Rice distribution parameters for the input values s = 100, a = 50
Fig. 4. Graphs for the estimate of the Rice distribution parameters for the input values s = 200, a = 100
processor), to ensure ADS-B data validation. Compared to implementing up-to-date surveillance radars (for example, AORL-1 AS), it will yield savings of approximately 120-150 million rubles for each aerodrome.
Discussion of the obtained results
The position determination error is computed relatively a point of extrapolation of aircraft coordinates, i.e., relatively the center of the gate area. For the given benchmark cases, under the
assumption concerning the equality of errors along the axes of the Cartesian coordinates, it is feasible to apply the Rayleigh and Rice distributions. However, in practice, there are more plausible situations going beyond the scope of the considered. Errors along the Ox- and Oy -axis can be distinguished, notably substantially. Thus, in case of an insignificant pilot's error, a substantial navigational error can occur, i.e., ME equals zero, navigation MSE do not equal each other: m = 0, ax ^ ay. In that event, the error of aircraft positioning has the Hoyt distribution (Nakagami-Q) [17, 23, 24]:
Научный Вестник МГТУ ГА_Том 26, № 04, 2023
Civil Aviation High Technologies Vol. 26, No. 04, 2023
Fig. 5. Graphs for the estimate of the Rice distribution parameters for the input values s = 300, a = 150
w{r} = ■
a a
X У
-exp
1 1
y У
1 1
y У
(7)
Another scenario is possible in-flight when there is a significant deviation from the FPR (ME does not equal zero) and the navigation MSE inequality ax ^ ay. In this case, an error of aircraft positioning has the Beckmann distribution [20].
The distribution laws of Rayleigh, Rice and Hoyt are the specific cases of the Beckmann distribution. Thus, the probability of the aircraft position in an area of gate can be computed using the Beckmann distribution as the given distribution comprises all the plausible benchmark cases for the distribution of aircraft positioning error. The development of models for the parameter estimate of the Hoyt and Beckmann distributions for the ADS-B data validation by the gating technique is the subject for further research.
Conclusion
The paper considers the algorithmic technique of the ADS-B data validation based on gating. Errors of determining coordinates were found relatively the point of extrapolation which
is the center of gate. Three simplest benchmark cases, which might occur when determining the aircraft position by ADS-B, were considered. The algorithm of the derived data validation was proposed. The estimate based on the Rayleigh distribution is obtained in the first phase. If the parameter b does not exceed the bounds of the tolerance limits, a conclusion concerning ADS-B data validity (the first benchmark case) is drawn up. If an error exceeds the bounds of the tolerance limits, the estimate is obtained via the use of the Rice distribution. If not tolerated significant pilot's errors with allowable navigation errors (the second benchmark case) are detected, a conclusion concerning ADS-B data validity is drawn up, the ATC obtains a message about the aircraft deviation from the FPR. If not tolerated significant pilot's and navigation errors are detected, the ATC obtains the ADS-B data-not-valid message and the necessity to use other ATC procedures. The results of simulation established that during the estimate based on the Rayleigh distribution, it is sufficient to accumulate 15-20 measurements, which, under the transmission of 2 messages per second and provided that ADS-B equipment operates normally,
will take 8-10 s. During the estimate based on the Rice distribution, the accumulation of 25-30 measurements is sufficient, which will take 13-20 s.
The practical research importance is that it is possible to employ the gating technique for ADS-B data validation without the necessity to validate with the aid of SSR or ML. It will enable regional airports with the low intensity of air traffic to replace exhausted life-span radars for ADS-B ground stations (with upgraded software), which will yield considerable savings.
References
1. Kozovic, D.V., Durdevic, D.Z., Dinu-lovic, M.R., Milic, S., Rasuo, B.P. (2023). Air traffic modernization and control: ADS-B system implementation update 2022: a review. FME Transactions, vol. 51, no. 1, pp. 117-130. DOI: 10.5937/fme2301117K
2. Rozel, M., Gonçalves, N., Reygrobel-let, A., Bruneel, P. (2022). Construction of a radar cross-section database using ADS-B data from the OpenSky network. In: Engineering Proceedings, vol. 28 (1), no. 4, pp. 1-10. DOI: 10.3390/engproc2022028004
3. Mba Andeme, J.M.N., Liu, Q., Hadi, A. (2021). FAA Transition Away from Radar and Towards ADS-B Aircraft Communication-Based on Accuracy. Data Mining and Big Data. DMBD 2021. Communications in Computer and Information Science, vol. 1454, pp. 358-374. DOI: 10.1007/978-981-16-7502-7_35
4. Kalintsev, A., Rubtsov, E., Povaren-kin, N. (2023). Application of ADS-B for providing surveillance at civil aviation regional aerodromes. In: Proceedings of 10th International Conference on Recent Advances in Civil Aviation. Lecture Notes in Mechanical Engineering, in Gorbachev, O.A., Gao, X., Li, B. (eds). Springer, Singapore, pp. 371-382. DOI: 10.1007/978-981-19-3788-0_33
5. Levin, D.V., Parshutkin, A.V., Timo-shenko, A.V. (2022). Reliability of target selection in the network of geographically separated radar stations in joint processing of radar infor-
mation in the conditions of relayed interference. Information and Control Systems, no. 3 (118), pp. 55-66. DOI: 10.31799/1684-8853-2022-355-66 (in Russian)
6. Zhou, H., Dong, C., Wu, R., Xu, X., Guo, Z. (2021). Feature fusion based on Bayesian decision theory for radar deception jamming recognition. IEEE Access, no. 9, pp. 16296-16304. DOI: 10.1109/ACCESS.2021.3052506 (accessed: 08.12.2022).
7. Akhmedov, R.M., Bibutov, A.A., Vasi-liev, A.V. et al. (2004). Automated air traffic control systems: New information technologies in aviation: Tutorial. St. Petersburg: Politekhni-ka, 446 p. (in Russian)
8. Bogatyuk, A.S., Vitushkin, V.V., Zatuchnyy, D.A. (2018). Algorithms for identifying various navigation errors during an aircraft flight based on the integrated use of information. Transactions of the International Symposium on Reliability and Quality, vol. 1, pp. 287-290. (in Russian)
9. Kalintsev, A.S., Rubtsov, Е.А., Plya-sovskih, А.Р. (2021). Confirmation of ADS-B data in the aerodrome traffic zone by gating method. T-Comm, vol. 15, no.7, pp. 39-49. DOI: 10.36724/2072-8735-2021-15-7-39-49 (in Russian)
10. Ventzel, E.S., Ovcharov, L.A. (2000). Probability theory and its engineering applications. 2nd ed. ster. Moscow: Vyshaya shkola, 480 p. (in Russian)
11. Sherstneva, A.A. (2020). Parameters estimation of one-dimension and two-dimension distribution of random variables. Vestnik NOVSU, no. 5 (121), pp. 63-67. DOI: 10.34680/2076-8052.2020.5(121).63-67 (in Russian)
12. Oblakova, T.V., Zubarev, K.M., Sal-nikova, A.A., Shinakov, D.S. (2022). Mathematical and engineering examples of random variable distribution law in DLS Nomotex. Dnevnik Nauki, no. 12 (72), ID: 58. DOI: 10.51691/2541-8327_2022_12_29 (in Russian)
13. Perov, A.I. (2003). Statistical theory of radio engineering systems: Tutorial for Universi-
ties. Moscow: Radiotechnika, 400 p. (in Russian)
14. Pitsyk, V.V., Sukhoverkhova, L.V., Dmitriev, S.A. (2020). Model for assessing the accuracy of controlling the robotic complex using Rayleigh's right truncated distribution. Fire and Emergencies: Prevention, Elimination, no. 1, pp. 54-59. DOI: 10.25257/FE.2020.1.54-59 (in Russian)
15. Pakhotin, V.A., Vlasova, K.V., Bogach, M.V., Bessonov, V.A. (2022). Separate detection of signals in radiolocation. Digital signal processing and its applications (DASPA-2022). Moscow: RNTORES imeni A.S. Popova, vol. XXIV, pp. 192-196. (in Russian)
16. Yakovleva, T.V. (2020). Stable character of the rice statistical distribution: the theory and application in the tasks of the signals' phase shift measuring. Computer research and modeling,, vol. 12, no. 3, pp. 475-485. DOI: 10.20537/ 2076-7633-2020-12-3-475-485 (in Russian)
17. Das, D., Subadar, R. (2019). Performance analysis of QAM for L-MRC receiver with estimation error over independent Hoyt fading channels. AEU-International Journal of Electronics and Communications, vol. 107, pp. 15-20. DOI: 10.1016/j.aeue.2019.05.005
18. Jia, H., Zhong, J., Janardhanan, M.N., Chen, G. (2020). Ergodic capacity analysis for FSO communications with UAV-equipped IRS in the presence of pointing error. In: 2020 IEEE 20th International Conference on Communication Technology (ICCT), pp. 949-954. DOI: 10.1109/ICCT50939.2020.9295740
19. Simon, M.K., Alouini, M.-S. (2000). Digital communication over fading channels. A unified approach to performance analysis. John Wiley & Sons, 546 p.
20. Beckmann, P. (1972). Statistical distribution of the amplitude and phase of multiply scattered field. Journal of Research of the National Bureau of Standards, vol. 66D, no. 3, pp. 231-240.
21. Al-Hmood, H., Al-Raweshidy, H. (2019). Performance analysis of physical-layer security over fluctuating Beckmann fading chan-
nels. IEEE Access, vol. 7, pp. 119541-119556. DOI: 10.1109/ACCESS.2019.2937631 (accessed: 08.12.2022).
22. Sawicki, D. (2021). Microfacet distribution function: To change or not to change, that is the question. In: Proceedings of the 16th International Conference on Computer Graphics Theory and Applications (VISIGRAPP 2021), vol. 1, pp. 209-220. DOI: 10.5220/001025 2702090220
23. Shawkat, S.B., Md. Mazid-Ul-Haque, Md. Sohidul, Sarker, B. (2020). Fundamental capacity analysis for identically independently distributed Nakagami-Q Fading. International Journal of Advanced Computer Science and Applications, vol. 11, no. 9, pp. 659-663. DOI: 10.14569/ijacsa.2020.0110978
24. Md. Mazid-Ul-Haque, Md. Islam, S. (2020). Data rate limit in low and high SNR regime for Nakagami-Q Fading Wireless Channel. International Journal of Advanced Computer Science and Applications, vol. 11, no. 7, pp. 636-641. DOI: 10.14569/IJACSA.2020.0110776
Список литературы
1. Kozovic D.V. Air traffic modernization and control: ADS-B system implementation update 2022: a review / D.V. Kozovic, D.Z. Bur-devic, MR. Dinulovic, S. Milic, B.P. Rasuo // FME Transactions. 2023. Vol. 51, no. 1. Pp. 117-130. DOI: 10.5937/fme2301117K
2. Rozel M. Construction of a radar cross-section database using ADS-B data from the OpenSky network / M. Rozel, N. Gon9alves, A. Reygrobellet, P. Bruneel // Engineering Proceedings. The Netherlands, Delft, 10-11 November 2022. Vol. 28 (1), no. 4. Pp. 1-10. DOI: 10.3390/engproc2022028004
3. Mba Andeme J.M.N., Liu Q., Hadi A. FAA Transition away from radar and towards ADS-B aircraft communication-based on accuracy // Data Mining and Big Data. DMBD 2021. Communications in Computer and Information Science. 2021. Vol. 1454. Pp. 358-374. DOI: 10.1007/978-981-16-7502-7 35
4. Kalintsev A., Rubtsov E., Povaren-
kin N. Application of ADS-B for providing surveillance at civil aviation regional aerodromes // Proceedings of 10th International Conference on Recent Advances in Civil Aviation. Lecture Notes in Mechanical Engineering, in O.A. Gorbachev, X. Gao, B. Li (eds). Springer, Singapore, 2023. Pp. 371-382. DOI: 10.1007/978-981-19-3788-0_33
5. Левин Д.В., Паршуткин А.В., Тимошенко А.В. Достоверность селекции целей в сети разнесенных радиолокационных станций при совместной обработке радиолокационной информации в условиях ретранслированных помех // Информационно-управляющие системы. 2022. № 3 (118). С. 55-66. DOI: 10.31799/1684-8853-2022-3-55-66
6. Zhou H. Feature fusion based on Bayes-ian decision theory for radar deception jamming recognition / H. Zhou, C. Dong, R. Wu, X. Xu, Z. Guo [Электронный ресурс] // IEEE Access. 2021. No. 9. Pp. 16296-16304. DOI: 10.1109/ ACCESS.2021.3052506 (дата обращения: 08.12.2022).
7. Ахмедов Р.М., Бибутов А.А., Васильев А.В. и др. Автоматизированные системы управления воздушным движением: новые информационные технологии в авиации: учеб. пособие. СПб.: Политехника, 2004. 446 с.
8. Богатюк А.С., Витушкин В.В., За-тучный Д.А. Алгоритмы выявления различных навигационных погрешностей во время полета воздушного судна на основе комплексного использования информации // Труды Международного симпозиума «Надежность и качество». 2018. Т. 1. С. 287-290.
9. Калинцев А.С., Рубцов Е.А., Пля-совских А.П. Подтверждение данных АЗН-В в аэродромной зоне методом стробирова-ния // T-Comm: Телекоммуникации и транспорт. 2021. Т. 15, № 7. С. 39-49. DOI: 10.36724/2072-8735-2021-15-7-39-49
10. Вентцель Е.С., Овчаров Л.А. Теория вероятностей и ее инженерные приложения. 2-е изд., стер. М.: Высшая школа, 2000. 480 с.
11. Шерстнева А.А. Оценка параметров одномерного и двумерного распределения случайных величин // Вестник Новгородского государственного университета им. Ярослава Мудрого. 2020. № 5 (121). С. 63-67. DOI: 10.34680/2076-8052.2020.5(121).63-67
12. Облакова Т.В. Математические и инженерные примеры законов распределений случайных величин в ЦОС Nomotex / Т.В. Облакова, К.М. Зубарев, А.А. Сальникова, Д.С. Шинаков [Электронный ресурс] // Дневник науки. 2022. № 12 (72). ID: 58. DOI: 10.51691/2541-8327_2022_12_29 (дата обращения: 08.12.2022).
13. Перов А.И. Статистическая теория радиотехнических систем: учеб. пособие для вузов. М.: Радиотехника, 2003. 400 с.
14. Пицык В.В., Суховерхова Л.В., Дмитриев С.А. Модель оценки точности управления робототехническим комплексом с использованием усеченного справа распределения Рэлея // Пожары и чрезвычайные ситуации: предотвращение, ликвидация. 2020. № 1. С. 54-59. DOI: 10.25257/FE.2020.1.54-59
15. Пахотин В.А. Раздельное обнаружение сигналов в радиолокации / В.А. Пахотин, К.В. Власова, М.В. Богач, В. Бессонов // Цифровая обработка сигналов и ее применение (DSPA-2022): сборник трудов 24-й Международной конференции. Москва, 30 марта -01 апреля 2022 г. М.: РНТОРЭС им. А С. Попова, 2022. Т. XXIV. С. 192-196.
16. Яковлева Т.В. Свойство устойчивости статистического распределения Райса: теория и применение в задачах измерения фазового сдвига сигналов // Компьютерные исследования и моделирование. 2020. Т. 12, № 3. С. 475-485. DOI: 10.20537/2076-76332020-12-3-475-485
17. Das D., Subadar R. Performance analysis of QAM for L-MRC receiver with estimation error over independent Hoyt fading channels // AEU-International Journal of Electronics and Communications. 2019. Vol. 107. Pp. 15-20. DOI: 10.1016/j.aeue.2019.05.005
18. Jia H. Ergodic capacity analysis for FSO communications with UAV-equipped IRS in the presence of pointing error / H. Jia, J. Zhong, M.N. Janardhanan, G. Chen // 2020 IEEE 20th International Conference on Communication Technology (ICCT), 2020. Pp. 949-954. DOI: 10.1109/ICCT50939.2020.9295740
19. Simon M.K., Alouini M.-S. Digital communication over fading channels. A unified approach to performance analysis. John Wiley & Sons, 2000. 546 p.
20. Beckmann P. Statistical distribution of the amplitude and phase of multiply scattered field // Journal of Research of the National Bureau of Standards. 1972. Vol. 66D, no. 3. Pp. 231-240.
21. Al-Hmood H., Al-Raweshidy H. Performance analysis of physical-layer security over fluctuating Beckmann fading channels [Электронный ресурс] // IEEE Access. 2019. Vol. 7. Pp. 119541-119556. DOI: 10.1109/ACCESS. 2019.2937631 (дата обращения: 08.12.2022).
22. Sawicki D. Microfacet distribution function: To change or not to change, that is the question // Proceedings of the16th International Conference on Computer Graphics Theory and Applications (VISIGRAPP 2021), 2021. Vol. 1. Pp. 209-220. DOI: 10.5220/0010252 702090220
23. Shawkat S.B. Fundamental capacity analysis for identically independently distributed Nakagami-Q Fading / S.B. Shawkat, Md. Mazid-Ul-Haque, Md. Sohidul, B. Sarker // International Journal of Advanced Computer Science and Applications. 2020. Vol. 11, no. 9. Pp. 659-663. DOI: 10.14569/ijacsa.2020.0110978
24. Md. Mazid-Ul-Haque, Md. Islam S. Data rate limit in low and high SNR regime for Nakagami-Q Fading Wireless Channel // International Journal of Advanced Computer Science and Applications. 2020. Vol. 11, no. 7. Pp.636-641. DOI: 10.14569/IJACSA.2020.0110776
Information about the authors
Evgeny A. Rubtsov, Candidate of Technical Sciences, Specialist of the Scientific and Educational Center of Air Transport, Russian University of Transport (MIIT), [email protected].
Sergey A. Kudryakov, Doctor of Technical Sciences, Senior Researcher, Director of the Scientific and Educational Center of Air Transport, Russian University of Transport (MIIT), [email protected].
Iakov M. Dalinger, Candidate of Technical Sciences, Associate Professor, Vice-Rector of the Russian University of Transport (MIIT), [email protected].
Andrey S. Kalintsev, Radio Navigation, Radio Location and Communication Engineer, Arkhangelsk Air Traffic Management Center, North-West Air Navigation Branch, FSUE "State Air Traffic Management Corporation of the Russian Federation", [email protected].
Сведения об авторах
Рубцов Евгений Андреевич, кандидат технических наук, специалист научно-образовательного центра воздушного транспорта Российского университета транспорта (МИИТ), [email protected].
Кудряков Сергей Алексеевич, доктор технических наук, старший научный сотрудник, директор научно-образовательного центра воздушного транспорта Российского университета транспорта (МИИТ), [email protected].
Далингер Яков Михайлович, кандидат технических наук, доцент, проректор Российского университета транспорта (МИИТ), [email protected].
Том 26, № 04, 2023_Научный Вестник МГТУ ГА
Vol. 26, No. 04, 2023 Civil Aviation High Technologies
Калинцев Андрей Сергеевич, инженер по радионавигации, радиолокации и связи, Архангельский центр ОВД филиала «Аэронавигация Северо-Запада» ФГУП «Государственная корпорация по организации воздушного движения в Российской Федерации», [email protected].
Поступила в редакцию 22.03.2023 Received 22.03.2023
Одобрена после рецензирования 20.04.2023 Approved after reviewing 20.04.2023
Принята в печать 20.07.2023 Accepted for publication 20.07.2023
