The article proposes a digital model for determining permissible trajectories of objects moving within the air-port landside area. This model can be used for assessing the reliability of information provided by automatic dependent surveillance systems, as well as for filtering false targets. False targets can arise due to reflection of radio signals emitted by surveillance systems from large objects, as well as due to active interference or spoofing attacks. The developed model is of particular importance for assessing the reliability of information provided by automatic dependent surveillance-broadcast systems at aerodromes with an average level of traffic complexity, since it allows simpler solutions in terms of surveillance compared to multilateration systems or secondary surveillance radar systems operating in Mode S.

В статье предлагается цифровая модель движения на аэродроме, предназначенная для определения допустимых траекторий движения объектов в пределах аэродрома. Данную модель можно использовать для оценки достоверности информации наблюдения системы радиовещательного автоматического зависимого наблюдения и фильтрации ложных целей, возникающих в результате переотражения ра-диосигнала систем наблюдения от крупных объектов или в результате активных помех или спуфинга.

Особенно актуально использовать цифровую модель движения для оценки достоверности информации наблюдения от системы радиовещательного автоматического зависимого наблюдения на аэродромах со средним уровнем сложности движения, обеспечивая с помощью не менее затратное решение в плане наблюдения, чем при использовании многопозиционной системы наблюдения или вторичного обзорного радиолокатора, работающего в режиме S.

The Global Air Navigation Plan (GANP) for 2016-2030, section “Development Rate and Economic Stability of Modern Air Transport” states that the global scope of air transportation doubles every 15 years starting from 1977 and will grow at the same rate. Uncontrollable growth of the air traffic may increase flight safety risks under the circumstances when such growth exceeds the growth rates of the regulatory and infrastructure processes required to support them. Lack of automation of the air traffic control system (АТС) may put an enormous load on the dispatcher, making them increasingly prone to error. Control of surface traffic at the airports with high air traffic intensity is only possible with the state-of-the-art equipment and automated systems ensuring the required aerodrome handling capacity in conditions of limited visibility and traffic complexity, retaining the safety level due to automation of the functions of aerodrome traffic surveillance, supervision, routing, and control [

The main sources of surveillance information in the aerodrome area are the radars, multilateral surveillance system (MSS) and automatic dependent surveillance-broadcast (ADS-B) system. In 2003 at the Eleventh Air Navigation Conference (AN Conf/11) ICAO Council approved the concept of ADS-B application for surface traffic control and surveillance and included it in GANP (Module B0-SURF) [

Implementation of the ADS-B-based surveillance concept is supposed to improve the air traffic management and bring different advantages in this area. In the context of evaluation by a group of experts in separation and air space safety, two advantages should be highlighted: the surveillance coverage area will extend to low altitudes (lower than the existing radar coverage area) and to the areas where presently the radar service is not provided, which will ensure a more efficient use of air space; thanks to implementation of the ADS-B-based surveillance systems, cost saving will be attained compared with the expenses related to installation, maintenance, full life cycle, and expansion of the existing radar-based surveillance systems [

Document 9924 points out that:

Therefore, the ADS-B data validation will allow to use ADS-B as the main or additional information source. Currently, a method of comparison of the received object coordinate data with the data measured using a multilateral surveillance system or a secondary surveillance radar using Mode S is applied to validate the ADS-B information. But at small aerodromes with low traffic intensity installation of these information sources is not profitable due to their high price. Most of Russian airports have medium or low traffic intensity; herewith, despite the fact that a significant number of the aircraft are equipped with ADS-B, in most cases the latter is not used for air traffic control (ATC) and is installed as a standby information source.

Apart from surveillance information validation, there are other problems arising during the aerodrome surface traffic management. At the aerodromes using airfield surveillance radars to detect and evaluate object traffic parameters, the aerodrome structures (for example, a metal hangar) and large aircraft may cause false marks resulting from radio signal re-reflection from them. False marks may also be due to active jamming [

Large aerodromes with numerous taxiways on which several objects move simultaneously need a feature to calculate optimum traffic trajectories of such objects within the aerodrome perimeter. Optimization by the minimum taxiing time criterion will improve the aerodrome handling capacity. For prompt identification both of potential conflicts between objects and of violation of the surface traffic rules, it is required to evaluate and extrapolate object traffic parameters at the aerodrome. When the aerodrome workload is high, dispatcher’s work shall be facilitated by issuing recommendations as to the surface traffic control, thus reducing probability of conflicts between the objects. The urgency of this task is confirmed by the GANP requirement to increase the handling capacity and efficiency of the global civil aviation system, at the same time increasing or at least keeping the existing flight safety level [

The article offers a digital aerodrome traffic model which may be applied to solve the following tasks:

This work shows a potential application of this model only to validate the surveillance information. Its use for solving other tasks will be described in subsequent works.

The ADS-B information is validated in a dedicated module supplied with a multitude of admissible trajectories of object movements calculated using the proposed model, as well as current parameters of object movements and their history. The ADS-B information validation method in the aerodrome surface traffic surveillance and control system is described in [

The digital model of aerodrome surface traffic is a set of:

The aerodrome surface traffic sections are described by:

The aerodrome structure is described by the rules of movement along potential traffic trajectories using the weighted directed graph G: = (V, E), where V - the set of graph node numbers, E - the set of graph edges set in pairs,

the first element of which is the number of the edge source node and the second - the number of the edge destination node. Each edge (admissible traffic section θij) is matched with the weight wij, equal to its length. The graph nodes are the aerodrome points connecting different traffic sections, for example, runways, taxiways, etc. The nodes also designate parking aprons, locations of various maintenance procedures, for example, anti-icing, holding and lineup positions, etc. The principle of the aerodrome structure building as a graph is shown in Figure 1.

Fig. 1. Principle of aerodrome structure representation as a grap

The relevant graph is shown in Figure 2. Here the runway is represented by the edges passing between the nodes (1, 2), (2, 4), (4, 7), (7, 8), (8, 11), (11, 16), (16, 18); parking apronsare designated by node numbers 12, 17, 5 and 9; 18 and 1 – stopways; 2, 4, 7, 11 and 16 – lineup positions.

Fig. 2. Example of aerodrome graph

A traffic section set as a sequence of points located on the traffic axis is assigned to each edge of the graph. In Figure 3, large blue dots designate the point sets corresponding to admissible traffic trajectories.

Fig. 3. Sets of points corresponding to traffic trajectories

Therefore, graph G is defined by 18 nodes V = {vf }, where f = 1...18, and 25 edges E = {el}, where l = 1...25; en is described by the pair (n, m), where n and m - the numbers of nodes between which the edge passes. For example, for the graph shown in Figure 2, e1 = (1, 2), e2 = (2, 2), e3 = (2, 4), e4 = (3, 4), e5 = (3, 6), e6 = (4, 7), etc. To be definite, let us consider that the edges are numbered on the graph left to right and top to bottom.

To use the digital model of aerodrome traffic, first it is necessary to determine the numbers of the graph nodes corresponding to the object path start and end points. For arriving aircraft the path starts from a certain point on the runway, while for departing aircraft - from a parking area. If all the nodes are known, the admissible digital trajectory of the object traffic is completely known. If only the path start and end points are known, N shortest trajectories are laid between them, with the shortest one being the most probable one and the others - alternative ones. These trajectories create a set of admissible trajectories of the object traffic Φob, where it is allowed to move. When determining admissible trajectories of object traffic, the numbers of nodes corresponding to the intermediate points of their routes may be accounted for.

The set of admissible traffic trajectories of object traffic Φob is the combination N shortest trajectories φ;· from the start point to the end point Φ = Uiφi. Here, φ1 designates the shortest trajectory, φ2 - the second shortest, etc. φ1 is calculated using one of the known algorithms for solution of the shortest path problem on graph G. After which, we exclude the edge with the smallest length from among the edges to which the traffic sections mandatory for passing are not assigned, and using the same algorithm trajectory φ2 is calculated, etc. until φΝ is calculated. The most well- known algorithms for solution of the shortest path problem are the Dijkstra algorithm and Bellman - Ford algorithm [

The Dijkstra algorithm works as per the following principle: each node from V is matched with a mark equal to the minimum known distance from this node to the path start node designated as a. The algorithm works in steps — on each step it “visits” one node and attempts to reduce the marks. The algorithm work is completed when all the nodes have been visited. Before the algorithm start zero value is assigned to the mark of node a and infinite values are assigned to the other node marks. It indicates that the distances from a to other nodes are not known so far. All the graph nodes are marked as non-visited ones. At each step node u, with the minimum mark, is selected out of the nodes non visited yet. After visiting all the nodes the algorithm completes the work. Thus, all potential routes in which u is the last but one node of the route are considered. Let us designate the nodes to which edges from u lead, as neighbours of this node. For each neighbour of node u, except those marked as visited, let us consider a new path length equal to the sum of the values of the current mark u and length of the edge connecting u with this neighbour. If the length value obtained is smaller than the neighbour mark, let us substitute the mark value with the length value obtained. Having considered all the neighbours we will mark node u as visited and repeat the algorithm step.

Suppose it is necessary to determine the route at the aerodrome shown in Figure !, from the parking apron designated as node 17, to the lineup position designated as node 16, and pass an unchanged route along the runway from the lineup position to the takeoff. In this case the constant component of the trajectories includes the following edges {(16, 11), (11, 8), (8, 7), (7, 4), (4, 2)}. With N = 3, the shortest route will pass through edges φ1 = {(17, 14), (14, 15), (15, 16), (16, 11), (11, 8), (8, 7), (7, 4), (4, 2)}, and two alternative routes will pass through edges φ2 = {(17, 14), (14, 13), (13, 10), (10, 15), (15, 16), (16, 11), (11, 8), (8, 7), (7, 4), (4, 2)} and φ3 = {(17, 14), (14, 13), (13, 10), (10, 11), (11, 16), (16, 11), (11, 8), (8, 7), (7, 4), (4, 2)}. Respectively, the set of admissible traffic trajectories Φob = {((17, 14), (14, 15), (15, 16), (16, 11), (11, 8), (8, 7), (7, 4), (4, 2)), ((17, 14), (14, 13), (13, 10), (10, 15), (15, 16), (16, 11), (11, 8), (8, 7), (7, 4), (4, 2)), ((17, 14), (14, 13), (13, 10), (10, 11), (11, 16), (16, 11), (11, 8), (8, 7), (7, 4), (4, 2))}. Figure 4 shows the graph indicating admissible traffic routes. Solid lines show the edges and nodes of the shortest path and dotted lines - of alternative routes.

Рис. 4. Граф допустимых маршрутов движения

After determination of the graph of admissible traffic routes and the respective set of admissible trajectories Φob it is necessary to determine whether the object is located near traffic trajectories admissible for it. If the distance between the object and the nearest point of the trajectory φi from Φob does not exceed lmarch((xd, yd)ij), the object is considered moving along the trajectory admissible for it and the surveillance information of it - correct. The nearest point of the nearest trajectory is understood not as the nearest coordinate (xd, yd)ij of traffic trajectory φi, but as the nearest interpolated point between the two set coordinates (xd, yd)ij and (xd+1, yd+1)ij or (xd, yd)ij and (xd-1, yd-1)ij, where d designates the index of the initially set coordinate of trajectory φ, nearest to the object.

In case of several units of aircraft present at the aerodrome, admissible traffic trajectories for each individual aircraft are calculated in the same order as for one aircraft. This is admissible because when the model is used to validate the surveillance information, all potential trajectories of aircraft traffic are calculated and, with other objects present, the set of trajectories allowing aircraft traffic remains the same.

Prior to work commencement, the customer provides high-accuracy information (coordinates of the runway ends, taxiway-to-runway tie points, parking aprons, etc.), enabling computation of the digital traffic model. When such information is unavailable, digital traffic trajectories are calculated approximately using digital maps.

Points of the axes of admissible traffic trajectories are located at a distance from 1 to 3 meters (1 - with the high-accuracy information available).

Each point of the traffic axis is numbered and the following items are aligned with it:

For the vehicles, traffic trajectory start and end points are parking aprons.

Upon identifying a new moving object, the system creates a dedicated map (multitude) of potential traffic trajectories, which, as it moves, are reduced to the only actual trajectory.

As the vehicle moves, the system generates the trajectory of aircraft or vehicle actual traffic narrowing down the set of potential traffic trajectories.

Figure 5 shows a block diagram demonstrating monitoring of the surveillance information from ADS-B using the digital traffic model.

Fig. 5. Implementation of control over surveillance information using the digital model of aerodrome traffic

Therefore, the digital model of the aerodrome surface traffic is practically implemented as follows:

To check the efficiency of the algorithm proposed computer simulation of the aircraft landing and surface traffic was performed. The simulation was performed in Python. It was supposed that several units of aircraft, one by one, perform landing on the aerodrome with the structure as in Figure 1, so that 1-8 units of aircraft are on the taxiing surface at the same time. The landing speed was adopted equal to 75 m/s and changed with constant acceleration so that by the end of traffic on the runway the aircraft reduced its speed to 11 m/s. The taxiing speed was adopted equal to 11 m/s.

During aircraft traffic along the runway and taxiways, the value of its coordinate deviation from the taxiing axis was distributed as per the normal law of distribution with zero expectation function and root-mean square deviation σ, dependent on the width of the runway/taxiway on which the aircraft moves. The σ value was

Fig. 5. Implementation of control over surveillance information using the digital model of aerodrome traffic

selected so that the value of the aircraft coordinate deviation from the taxiing axis exceeded half the width of the taxiway (or runway) in maximum 5 % of cases. Whereas about 95 % of values lie at the distance of not more than two standard deviations 2σ, σ was adopted equal to a quarter of the runway/taxiway width (σRWY = 11.25; σTWY = 4.5–7 m, depending on the taxiway). Also, from 2 to 50 false marks with random coordinates distributed as per the uniform law were continuously simulated on the entire area of a 450 x 2200 m aerodrome.

An example of the aircraft trajectory on the background of false marks is provided in Figures 6 and 7. They show all the false marks which occurred during the simulation. Figure 6 shows the case with 2 false marks present simultaneously throughout the entire simulation time.

Fig. 6. Aircraft true trajectory and false marks which appeared over the aircraft traffic time (2 false marks for each survey period of 3 s)

Fig. 7. Aircraft true trajectory and false marks which appeared over the aircraft traffic time (50 false marks for each survey period of 3 s)

Figure 7 shows the case with 50 false marks present simultaneously throughout the entire simulation time.

Figure 8 shows true and false marks assessed as true during the simulation.

Fig. 8. True and false marks assessed as true during simulation

The simulation results showed that the algorithm proposed in such conditions and one aircraft on average filters 98-99 % of false marks regardless of their number. The simulation confirmed the hypotheses that efficiency of the filtration using the method proposed depends on the ratio of the area of admissible object location to the area of potential occurrence of marks of these objects.

Also, dependencies of the share of false marks taken for true ones on the width of the admissible location area were evaluated at the following time intervals of the 4D-area generation: 3, 6, 9 and 12 s. These dependencies are provided in Figure 9.

Fig. 9. Dependence of the number of false marks taken as true on the width of the aircraft admissible location area for different time intervals of 4D-area

Fig. 10. Dependence of the false mark filtration efficiency on the number of aircraft units at the aerodrome

Then, in subsequent experiments, the number of taxiing aircraft increased by one in steps, so that their number was from 1 to 8 at the same time. The experiments were conducted under the following conditions: the width of the prediction gate was equal to half the traffic section width, prediction time interval - 3 s, 50 false marks every 3 s were randomly distributed as per the uniform law along the entire aerodrome surface.

The experiments under similar simulation conditions but different random values were repeated 30 times and their results were averaged.

When the number of aircraft units at the aerodrome increases, the efficiency of false mark filtration linearly decreases from 0.997 to 0.965.

The filtration efficiency here is understood as the ratio of the number of filtered false marks to their total number.

To test the algorithm operation in extreme conditions, the situation was simulated of 1000 false marks with random coordinates generated as per the uniform distribution law after a routine reception of coordinate information. On average, 3-5 false marks within the predicted area of the aircraft location were erroneously taken for true ones. In this case a possible solution is the use of additional false mark filtration methods or delegation of surveillance information validation to a human after determination of the true marks using the algorithm proposed.

The article describes a digital model of aerodrome surface traffic defining a set of admissible trajectories of the controlled objects. The value of deviation of the object location obtained (for example, using ADS-B) from the admissible trajectory may be used to validate surveillance information. In the simplest case a threshold of the admissible maximum deviation is set, which, when exceeded, indicates low reliability of surveillance information. The threshold value depends on the location and type of the object in question and enables determination of the areas of admissible location of objects. The digital model of aerodrome traffic enables control of and supervision over the surface traffic using ADS-B as the surveillance information source at the aerodromes with the average level of traffic complexity in accordance with the ICAO Global Air Navigation Plan for 2016-2030 (module B0-SURF).

Also, in the presence of false marks of the objects resulting, for example, from re-reflection of the radio signal of large object observation systems, from active jamming or spoofing, most of the false marks may be filtered using the algorithm proposed in the article.

The authors declare that there are no conflicts of interest present.