Mid-air collision in air transportation is one of the most dangerous safety categories. The risk of mid-air collision assessment is an important component of aviation safety estimation. Due to the low number of accidents happened, risk of mid-air collision within limited airspace may be estimated by evaluation of its main components. Paper is more focused on assessing the risk of air traffic separation lost in lateral plane based on air traffic deep learning within predefined airspace. Statistical analysis of current air traffic data and geometrical configuration of routes network are used for probability distribution function fitting. Position of airspace users is obtained from location reports coded by Automatic Dependent Surveillance-Broadcast data format, which is received by ground-based software defined radio. Risk of separation lost in the lateral plane is estimated based on density probability distribution function of airplane unintentional deviations. Finally, the risk of a mid-air collision in the lateral plane is estimated by Reich formula for Ukrainian airspace.
Airplane navigation is a key element of successful transport system operation that
Mid-air collision is an important problem of air transportation that is connected with
limited airspace volume and continuously increasing number of airspace users. The
problem of mid-air collision was extremely important in the early 90th due to speed
aviation development and lack of collision avoidance technology [
Probabilistic methods of risk estimation usually based on estimating the probability
of at least two airplanes locates closer at distance less than its geometrical
dimensions. Risk value may be obtained from computer-based simulation of air traffic based
on Monte Carlo method [
A Bayesian network and Information theory can be used to estimate the occurrence
of mid-air collisions based on accident precursors. In this case influence of each
factor is considered as fault tree which can lead to mid-air occurrence [
Other research is focused on simulation of collision risk based on free-flight
concept [
Some studies are based on the fact that two aircraft that are on the same level and fly in the same direction, have overlapping, or tendency to overlap, their longitudinal measurements from tiny to tend moment beginning and end of overlay. As there was an overlap of lateral measurements, it means that there is a possibility of collision of planes during the time of application. But, this study did not take into account the safety barriers that should prevent such situations. Such barriers include ACAS and air traffic controllers (ATC).
The chance of ACAS failure is quite small, but it exists and can be caused by the following factors: ─ break transmitter prevents the transmission of any signals, including ACAS signal; ─ breach or duplication of “mode S”, can result in unpredictable behavior of the system; ─ breakdown or failure in mode C will lead to inaccurate (incomplete) ACAS operation.
ATC receives data from surveillance systems and based on them draws
conclusions about the air situation and makes decisions on conflict resolution. However, in
the human-technical relationship, the weak point is the person himself, because he has
mistakes [
The main objective of the research presented in this paper is to develop a model to estimate a risk of mid-air collision based on statistical analysis of prerecorded air traffic data within a defined volume of airspace. We propose an integrated approach for airspace performance estimation based on risk category of a mid-air collision. Obtained risk of a mid-air collision in the lateral plane is an important part of total airspace safety estimation. 2
The conventional air traffic system is based on the number of flight routes. Air traffic
can be only within defined routes developed and supported by the National
airnavigation service provider [
At the flight planning stage, each airspace users have to prepare a flight plan and coordinate it with the flight data center. Flight plan considers airspace usage only within the network of routes. Once the flight plan is agreed, the aircraft must carry it exactly, because it is coordinated with the flight plans of other aircraft. Exact maintaining the cleared flight level and route is the key of aviation safety.
An air traffic flow is organized in compliance with the standards and recommended
practices prescribed by aviation law [
Vertical separation is the creation of a vertical interval between aircraft, based on
data obtained from radars and surveillance devices and their reduction into a single
system of measurements. Therefore, all aircraft use the same parameters of the
standard atmosphere to calculate altitude. Flight level (FL) is a predetermined altitude,
which is calculated from the average sea level. The minimum vertical separation
between aircraft is 300 m below 290 FL and 600 m for altitude of 290 FL and above
[
Lateral separation is achieved by flying aircraft on different routes or being in
different geographical locations. The minimum of lateral separation is based on means
and methods of navigation. The width of the route is clearly prescribed by the air
traffic authority. All data on the network of air routes and the structure of the airspace
are registered in the collection of aeronautical information publication issued by the
air traffic authority [
Minimums of Lateral separation utilize requirements of performance-based
navigation (PBN) to on-board positioning system [
• RNP 4, 10 – 50 NM;
• RNP 2,4 – 30 NM [
─ routes planned on an ongoing basis, they are part of strategic planning; ─ routes in the unspecified scenario for specific tasks; ─ routes of operational use only at the instruction of the ATC.
Longitudinal separation setups minimal interval between airplanes to ensure the required level of flight safety.
In addition to conventional Free Routes air traffic concept was integrated into many regions around the globe. Within a free routes area airspace, users can fill free to use any trajectory to fly. Safety levels support by high accuracy of navigation and surveillance systems. 3
Each air space user can be represented as a thee- dimensional object in forms of
sphere, ellipse, or box [
Also, airspace user may be represented as a box with double size and all other airplanes as a single point for tasks of risk assessment. Thus, risk of separation lost is a probability of any airspace user occurrence in the double size box.
In case of box model a risk of mid-air collision can be estimated by Reich formula
[
R = Pxy Pz 1 + λ xvy + λ xvz , λ v y x λ zvx (1) where Pxy is a probability of lateral overlap; Pz is a probability of vertical overlap; vx, vy, vz are relative velocities by axes between airplanes.
Relative velocities depend on particular simulation case. For example, in the case
of collision simulation at the en-route phase vz=0. Values of vx and vy depend on
particular conflict geometry in the lateral plane, and their calculation is based on mean
relative velocity in a particular airspace.
Probabilities of lateral and vertical overlaps are estimated based on the assumption of
known probability density functions (PDF) of airplane deviation from cleared flight
route centerline. Double Exponential Density Function [
Parameters of PDFs are estimating based on statistical data processing of airplanes trajectories within a limited volume of airspace.
Airplane vertical deviations from cleared flight level are estimating with the help
of precise radar. Results of altitude measurements along particular length of flight
route are used for statistical data processing and PDF fitting to histogram of airplane
deviations. Result of fitting gives parameters of PDF. For example, in the task of
reduced separation minima selection, a mixture of two double exponential PDF was
used [
Probability of lateral overlap may be estimated based on PDF of the relative lateral position of airspace users. In this case, probability is an area under PDF within the separation minimum (see Fig. 2).
Thus, probability can be estimated as follows:
λy Pxy = 1 − ∫ ρ(y)dy , −λy (2) (3) where ρ(y) is a PDF.
We use Triple Univariate Generalized Error Distribution (TUGED) function as
PDF in the next form [
ρ(y) = αρNSE (y) + βρ FTE (y) + (1 − α − β)ρT (y) , where ρNSE(х) is the PDF utilizing the errors of navigation system; ρFTE(х) is the PDF characterizing the FTE; ρT(х) is the PDF characterizing the appearance of rare events; α and β are weight coefficients. Triple component of PDF provides the best fit of input statistical data due to taking into account two different levels of deviations connected with Navigation System Error (NSE) (or error of positioning system), Flight Technical Error (FTE) (or error of airplane maintaining at predefined route), and influence of rare events. In the case of manual control, FTE utilize influence of human factor.
In general form TUGED model can be represented by the following form [
α 2a1b1Γ(b1 ) exp − y a−1b1 b1−1 + 2a2bβ2Γ(b2 ) exp − (4) where a1,a2,a3 are of scale factors; b1,b2,b3 are shape coefficients; μ1, μ2, μ3 are mean values.
Sum of weight coefficients is limited by the following:
0 ≤ α + β ≤ 1.
1 ≤ a ≤ ∞; 0.5 ≤ b ≤ 1. μ =μ1= μ2= μ3; -∞≤ μ ≤∞.
Let’s consider the case of equal probabilities of deviations in the left and right sides in
order to improve computation performance:
Weight, scale, and shape coefficients are estimated by statistics of airplane unplanned
deviations from cleared trajectories by Maximum Likelihood Method [
According to basic airspace rules, each user of controlled airspace has to be equipped with automatic dependent surveillance-broadcast (ADS-B) equipment. According to ADS-B regulation, each user has to share his own location with other airspace users.
Basic regulation required to use modified on-board air traffic control radar beacon system transponder with Mode “1090ES”. Transmitted data at 1090 MHz includes position reports from all airspace users around. These reports can be received by Software Defined Radio (SDR) and decoded by specific software (see Fig. 3). User location transmitted in Latitude, Longitude, and Altitude data format (WGS-84). Obtained via ADS-B “out” air traffic data is a result of on-board positioning which performs by Global Navigation Satellite System. Also, each transponder transmits a position report in the non-synchronized mode with different repeating frequency, which depends on transponder installation settings. One SDR gives an opportunity to receive position reports from numerous airspace users with the radius of maximal length of communication line which is approximately equal to 300NM for a Very High-Frequency spectrum. Thus, one SDR covers air traffic data within a circle of 300NM radius. A network of SDR can be used in order to get a data sample across the long territory. We use air traffic data recorded by SDR for 30 minutes on April 23, 2019. Statistical data processing of airplanes deviations from the Ukrainian routes network is provided based on digital database of flight routes and accumulated air traffic data from SDR. Obtained learning sample includes deviations of all air traffic, independently from the flight phase within investigated airspace volume (see Fig. 4).
Digital database of flight routes includes 331 waypoints within Ukrainian airspace. These waypoints are a connection points of direct flight routes. Our database includes 497 direct routes between two waypoints. Total length of investigated flight routes is 20840 NM for altitudes above 30000 ft. Detection of airspace users deviation from flight routes network is based on finding a minimal distance between airplane and each line of network.
A histogram of calculated deviations in the lateral plane accumulated for 30 minutes of input air traffic data is represented in Fig. 4. Amount of learning sample is 2723 measurements. We use bin width equal to 1 NM. The mean value is equal to 786 m and the standard deviation is 7924 m.
After fitting TUGED to input learning sample, parameters of ρ(y) are estimated: α=0.59; β=0.03; μ=0; a1=10.19; a2=8.35 a3=1; b1=0.75; b2=0.99; b3=0.99.
Probability of lateral overlap estimated by (2) depends on model width λy related to air navigation specification and separation minimum. Distribution of Pxy is represented in Fig. 5.
15 y , [NM] 5 10 20 25 30 An input air traffic data sample gives us Pxy=0.13 for RNAV1 specification.
Then the risk of a mid-air collision in the lateral plane can be estimated by (1). The airplane model is used to satisfy RNAV 1 requirements valid below FL 290 (λx=12964m, λy=55560m, λz=300m). Due to study overall risk at an en-route phase of flight vz=0 and considering the case of a collision with condition vx=vy than (1) can be represented in the following simplified form: y x P 0.5 0.4 0.3 0.2 0.1 0
RNAV 1
RNP 2
RNP 4
TUGED
ND Finally, risk of a mid-air collision in the lateral plane for air traffic data valid for Ukrainian airspace risk obtained by (5) is equal to 0.84 ×10-7. 6
In our study, we estimated the probability of mid-air collisions in lateral plane based on Reich equation and recorder by SDR air traffic data for Ukrainian airspace. Air space users' deviations in the lateral plane are estimated based on received user locations and national routes network.
Usage of TUGED at statistical analysis stage gives better performance than Double exponential or Normal PDFs due to taking into account flight technical error which is mostly utilized human factor influence based on input data.
Obtained value for risk of a mid-air collision in the lateral plane is higher in
comparison with a risk value obtained for the Asian region [
The results of this study can be used by controllers, pilots, and other air traffic participants for better flight planning and improving the structure of airspace in order to increase flight safety. The obtained results can be used to predict dangerous situations when flying on parallel routes and when creating lateral separation on routes.