Collision risk assessment of reduced aircraft separation minima in procedural airspace using advanced communication and navigation

Qing CAI, Hao Jie ANG, Sameer ALAM

Air Traffic Management Research Institute, School of Mechanical & Aerospace Engineering, Nanyang Technological University, 639798, Singapore

KEYWORDSAir transportation;Collision risk;Procedural airspace;Separation minima;Space-based Automatic Dependent Surveillance-Bro adcast/Contract (ADS-B/C)

AbstractWith the advancement of Communication,Navigation and Surveillance(CNS)technologies such as space-based Automatic Dependent Surveillance-Broadcast/Contract (ADS-B/C), large separation minima may be reduced in procedural airspaces.It is of great significance to know the upper limit of the Reduced Separation Minima (RSM) for a procedural airspace and the corresponding consequences on collision risk with specifics of the advanced ADS-B and control intervention model.In this work,an interactive software is first developed for collision risk estimation.This software integrates the International Civil Aviation Organization (ICAO) collision risk models for lateral and longitudinal collision risk calculation for the Singapore procedural airspace.Results demonstrate that the lateral and longitudinal collision risk of Singapore procedural airspace with respect to current control procedures meets the ICAO Target Level of Safety (TLS) standard.Moreover,the feasibility of reducing the horizontal separations implemented in the Singapore procedural airspace with respect to advanced CNS techniques is investigated.It is found that if advanced CNS technologies are applied, then the current 50-NM lateral and longitudinal separation standards can be reduced to 22 NM (1 NM = 1.825 km) and 20 NM, respectively, to meet the TLS standards based on current demand.A method is then devised to expand the traffic demand by p for p ?[10%, 200%].It is found that the minimum lateral and longitudinal separations can be reduced from 50 NM to be within the range of[23,31]NM,and 20 NM,respectively,for p ?[10%, 200%], while the collision risk still meets the TLS standards.

1.Introduction

Given the continued growth in air transportation,one of the key challenges faced by Air Navigation Service Providers(ANSPs)and airlines is: how to increase airspace capacity without compromising on safety.New air traffic management (ATM)paradigms, e.g.European SESAR1–3and US NextGen,4,5aim for doubling the airspace capacity while increasing the safety by a factor of 10 by 2030.To achieve such ambitious targets,the development of new operational concepts, safety measures and safety performance indicators in the air traffic system are not only expected but also necessary6–9.

In order to increase airspace capacity so as to accommodate the ever-increasing traffic demand, one of the most effective methods is to reduce the separation standards between aircraft.10The en-route airspace,also known as the Reduced Vertical Separation Minimum(RVSM)airspace ranging vertically from 29000 ft(FL290)to 41000 ft(FL410)(1 ft=0.305 m),is one of the most heavily congested components of a national airspace system.11–14In an RVSM airspace,the vertical separation had been reduced from 2000 ft to 1000 ft, adding 6 extra flight levels15.An RVSM airspace is preferred by commercial jetliners as it maximizes fuel efficiency,while observing special safety measures,based upon stringent,continuous altitude and track monitoring14.

With more and more flights flying in RVSM airspaces, the en-route airspaces become more and more congested, leading to a potentially higher risk of mid-air aircraft collision.16–18Airspace collision risk estimation is a vital indicator for estimating safety in en-route airspaces.19–22The collision risk is computed using complex mathematical models involving complex data-set ranging from aircraft track data,kinematic data,flying time, CNS parameters etc.20,23–25The model computations are dynamic in nature and include convolution of the statistical distribution of deviations of two aircraft on intersecting and non-intersecting tracks26–29.

When two aircraft are flying at two intersecting tracks at the same flight level,then controllers will apply horizontal separation minima to segregate the aircraft to avoid loss of separation.30It should be pointed out that the horizontal separation minima may vary from sector to sector depending on the corresponding CNS capabilities.31For a certain Flight Information Region (FIR), its configuration may involve procedural airspaces.A procedural airspace is an airspace volume in which the air traffic control services are provided without the use of radar.Procedural airspaces are normally planned for sparsely populated land areas and oceans,where radar coverage is either prohibitively expensive or is simply not feasible.Due to the limited CNS services in procedural airspaces,larger horizontal separation minima (eg., 30 NM or 50 NM longitudinal and 30 NM or 50 NM lateral separation minima in the Santa Maria Oceanic control area over the Atlantic Ocean)had been implemented in procedural airspaces as compared to that of non-procedural airspaces.

With the advancement of CNS technologies especially space-based ADS-B and Global Navigation Satellite System(GNSS),32–34flights flying in procedural airspace are better monitored and have improved navigation performance.As a consequence, such large horizontal separation minima in procedural airspace may be further reduced to increase the airspace capacity and save fuel burning18,35non compromising safety.For example, a 50 NM instead of 100 NM lateral separation had been adopted in the South Atlantic FIRs.36Many ANSPs are considering reducing the separations in procedural airspaces.See the VOICE project funded by SESAR JU for more information.Note that the reduction in separation minima is likely to increase the collision risk for the traffic within a given procedural airspace.Collision risk estimation is pertaining to both airspace structure management and air traffic flow management.19,22,37–39According to the ICAO circular 319‘‘the purpose of collision risk models in the context of the determination of separation minima is to model the chain of events leading a pair of initially separated aircraft to a collision”40.

Scientists have proposed several mathematical models for collision risk estimation.21,28,41–43However,those collision risk models are mathematically complicated and they were developed based upon old CNS technologies.If new RSM are implemented in a given procedural airspace, it is not known how the RSM will affect the traffic safety as well as the efficiency of the given airspace.As a consequence, before new RSM are to be implemented in a procedural airspace, the following four key research questions need to be answered.

(1) First,what is the baseline collision risk for the air traffic within a given procedural airspace under current CNS services?

(2) Second,how to model advanced CNS services and RSM in the existing collision risk models for procedural airspace?

(3) Third, what are the collision risk parameters and the upper limits of the RSM that can be achieved while maintaining the TLS of the airspace with respect to current traffic demand?

(4) Fourth, what are the collision risk parameters and the upper limits of the RSM that can be achieved while maintaining the TLS of the airspace with respect to increased future traffic demand?

This paper attempts to answer the above four questions.The answers can help ANSPs to build a holistic view of the safety assessment of their FIRs.Meanwhile,the corresponding research findings can be used as a reference by ANSPs to manage/improve the configurations of procedural airspaces in terms of separation standards,ATS route structures,air traffic flow management protocols, CNS technologies, etc.The main contributions of this paper are highlighted as follows:

(1) A collision risk modelling and simulation software is developed with interactive and visualization capabilities.This software is named CREAM.The CREAM software integrates the ICAO models for collision risk computation and analysis.The CREAM software is able to provide visual clues regarding the collision risk at given waypoints and airway segments for decision makers.

(2) The horizontal collision risk of the procedural airspace of Singapore FIR is analyzed using the CREAM software with respect to current control procedures and traffic demand.Experimental results show that the lateral and longitudinal collision risk of Singapore procedural airspace meets the ICAO TLS standard.

(3) The feasibility of reducing the horizontal separations,that are currently implemented in the Singapore procedural airspace,with respect to advanced CNS techniques is investigated.Experimental results show that the 50-NM lateral and longitudinal separation standards applied to the Singapore procedural airspace can be respectively reduced to 22 NM and 20 NM with respect to current demand,while the collision risk still meets the TLS standards.

(4) A method is proposed to expand the traffic demand by p based on existing traffic data.The collision risk is then analyzed based on the expanded demands by varying p from 10 to 200 to explore the corresponding minimum horizontal separations.It is found that the minimum lateral separation can be reduced from 50 NM to be within the range of [23, 31] NM for p ?[1 0%; 200%], and the minimum longitudinal separation can be reduced from 50 NM to 20 NM for p ?[10%; 200%], while the horizontal risk still meets the TLS standards.

The remainder of this paper is organized as follows.Section 2 provides the preliminaries for a better understanding of this research.Section 3 describes amply the research methodology.Section 4 displays the experimental settings.Section 5 demonstrates the case study on Singapore airspace,including the baseline collision risk analysis using the CREAM software,the feasibility of separation reduction and its impact on collision risk with respect to current and future traffic demand.Section 6 concludes the paper.

2.Preliminaries

For a smooth reading of this paper,this section provides some basic knowledge.These knowledge include aircraft separation standards, collision risk definition, and ICAO mathematical models for collision risk estimation.

2.1.Aircraft separation standard

Due to the growing demands of the air traffic in upper airspace and the need for more fuel-efficient flight levels, ICAO, in 1982, introduced the concept of RVSM which decreases the vertical separation minimum from 2000 ft (Conventional Vertical Separation Minimum – CVSM) to 1000 ft (RVSM) for aircraft operating at FL290 to FL410.

Apart from vertical separation standard, aircraft are also separated by horizontal separation standards, namely lateral separation and longitudinal separation.A typical 50-NM lateral separation and a 50-NM longitudinal separation are applied to the Singapore procedural airspace.Note that the exact separation standards are dependent on the specific CNS technologies.More details about the separation standards under various scenarios can be found in the ICAO documents in Ref.30,31,44.

2.2.Collision risk

In all regions where RVSM has been implemented, Regional Monitoring Agencies (RMAs) have been established by the appropriate Planning and Implementation Regional Groups(PIRGs) to satisfy the goals of the RVSM monitoring program.It is an RMA’s duty and responsibility to provide annual reports to the PIRG to report the assessment of the collision risk in the system against the overall safety objectives to support the continued safe use of the RVSM.

According to ICAO, collision risk is defined as ‘‘the expected number of mid-air aircraft accidents in a prescribed volume of airspace for a specific number of flight hours due to loss of planned separation”.Collision risk provides a holistic view of the safety level of the traffic within a given airspace for a given period of time.

Based on ICAO regulation, there are two specific safety objectives for collision risk assessment, namely an assessment of the technical vertical risk against a TLS of 2.5×10-9fatal accidents per flight hour(fapfh),and an assessment of the total vertical risk against a TLS of 5×10-9fapfh.45The horizontal risk that consists of lateral risk and longitudinal risk is also assessed against a TLS of 5×10-9fapfh.According to Federal Aviation Administration (FAA), the 2015 annual flight hours for the USA was 9.8 million flight hours.Therefore, a vertical TLS of 5×10-9fapfh equates to an acceptable value of risk of roughly 1 fatal accident every 20 years resulting from a loss of vertical separation.

2.3.Horizontal collision risk models

This section presents the concise forms of the mathematical models developed by ICAO for horizontal collision risk estimation.More mathematical details pertaining to the horizontal collision risk models can be found in the Appendix.Interested readers are also encouraged to refer to materials in Ref.31,40,46–48.

2.3.1.Key parameters and definitions

Before presenting the horizontal collision risk models, all the related parameters are first summarized.Table 1 lists out the definitions of the key parameters pertaining to the horizontal collision risk models.

Keeping in mind all the key parameters as listed out in Table 1, we briefly elucidate in what follows the probabilistic models for estimating lateral and longitudinal risk.

2.3.2.Lateral collision risk model

The probabilistic model that is used for calculating the lateral collision risk for parallel tracks can be written as

2.3.3.Longitudinal collision risk model

The longitudinal risk within the time interval [0;Ti] with respect to a certain longitudinal separation Sjis calculated as

Table 1 Definitions of parameters involved in the collision risk models.See Refs.28,40,49for more details.

There are two types of collision risk, i.e., vertical and horizontal risk.However,this research will only focus on the horizontal risk, i.e., lateral and longitudinal risk.The reason is that the purpose of this paper is to investigate the feasibility of RSM and its impact on airspace safety in terms of collision risk.

Regarding the RSM, only reduced horizontal separation will be analyzed while RVSM is not considered.This is because an aircraft is subject to the Total Vertical Error(TVE)–difference between the actual altitude flown and the assigned pressure altitude – which is mainly captured by the Altimetry System Error (ASE) – difference between the instrument displayed pressure altitude and the actual altitude flown – and the Assigned Altitude Deviation (AAD) – difference between assigned altitude and the altitude flown transponded or provided from the aircraft equipment.The tolerances for ASE and AAD are 245 ft and 300 ft,respectively,leading to the tolerance for TVE being 300 ft.Consequently,it is very challenging to further reduce the RVSM of 1000 ft.Meanwhile, the 1000 ft vertical separation standard has been verified to be fuel friendly and operationally safe14.

3.Research methodology

This section is divided into seven subsections.The 1st subsection presents an overview of the research methodology.The second subsection gives a brief introduction to the CREAM software.The 3rd and 4th subsections show how the collision risk models which are currently used by ANSPs can be adopted to estimate collision risk with RSM and advanced CNS techniques.The 5th subsection illustrates how we derive the initial longitudinal separation distributions for subsequent longitudinal collision risk calculation.The 6th subsection explicitly summarizes the research assumptions that we have made in this research.The last subsection describes the proposed method for simulating future traffic demand based on current one.

3.1.Methodology overview

As mentioned in the introduction section,this research aims to answer four research questions.Fig.1 presents a concept diagram of the proposed methodology for seeking answers to the four research questions.

As can be seen from Fig.1, collision risk calculation for a given procedural airspace is non-trivial as it is involved not only with data pre-processing and analytics for several types of input data such as traffic sample data,aircraft performance data,airway information,etc.,but also with the understanding and adoptions of mathematical collision risk models.Meanwhile, it is difficult to measure the resultant impact of RSM in a procedural airspace with respect to advanced CNS on the corresponding collision risk.

In this work, we aim to overcome the above challenges through three key steps:(A)development of a software for collision risk calculation; (B) adoption of ICAO collision risk models to account for advanced CNS;(C)simulation of future traffic demand by expanding current traffic scenario.Those three steps will be elucidated amply in what follows.

3.2.CREAM software

CREAM is a software developed by the authors using Python programming language.In what follows we present a brief introduction to the CREAM software in terms of software framework, software interface demonstration and collision risk estimation validation on Singapore FIR.

3.2.1.Framework of CREAM

Fig.1 Concept diagram of proposed methodology for seeking answers to research questions.

Fig.2 Framework of CREAM software for air traffic collision risk estimation and management.

Fig.2 presents the framework of the CREAM software.As can be seen from the central part of Fig.2, the CREAM software has two core modules, i.e., the collision risk estimation module and the collision risk management module.The estimation module adopts the ICAO models for collision risk estimation, while the management module integrates data-driven approaches developed by the authors for collision risk mitigation.

CREAM can be used to estimate the collision risk of the enroute traffic within any given FIR (default) or an airspace region,as long as the airspace configuration data,aircraft performance data and the corresponding traffic data can be provided to the software.It is able to estimate air traffic collision risk in three different planes,i.e.,vertical,lateral,and longitudinal planes (Nax, Nay, Nazas shown on the right-hand side of Fig.2).Regarding the risk estimation, the software can provide a basic report for the traffic data.Meanwhile, as can be seen from Fig.2, CREAM is also equipped with the component ‘‘Air Traffic Simulator”.This simulator contains two functionalities,i.e.,visualization and validation.The visualization functionality is oriented to air traffic movement visualization and collision risk visualization (at given waypoints and airway segments),thereby providing visual clues to assist decision makers with a better understanding of the estimated collision risk.The validation functionality mainly helps with a fast simulation of traffic control protocols aiming at improving the traffic safety.For example, when the visual clues indicate that the collision risk at a certain area is relatively higher than other areas,then traffic planners can modify the traffic data to simulate the traffic management interventions made by means such as flight level change,vectoring,speed control,and so on.Once new traffic data is obtained,then users can easily upload the data to the CREAM software to recalculate the resultant collision risk to validate if the traffic management interventions can reduce the collision risk or not.Meanwhile,the software is also integrated with the functionality of collision risk hotspot analysis.This functionality deals with collision risk hotspot detection and prediction.Collision risk hotspot detection helps decision makers to locate airspace regions that witness high collision risk,while hotspot prediction helps decision makers to get to know the possible airspace regions that will suffer from high collision risk in the near future such that decision makers can take precaution measures.

Regarding the collision risk management, CREAM is integrated with a couple of risk mitigation solutions which can be categorized into two groups, i.e.,traffic flow management and airway network structure management.The traffic flow management solutions aim to manage the traffic in terms of flight plans, aircraft speeds, and flights’assigned levels, in such an optimal way that the overall risk can be further reduced.The airway network structure management solutions aim to optimize the structure of a given airway network such that the vertical and/or horizontal overlap between the en-route aircraft can be reduced which then will lead to the reduction of collision risk.When designing data-driven approaches for collision risk management, a promising direction is to do partial flow and/or airway structure management by referring to the collision risk hotspot analysis results.For a given airspace, there could be only several sub-regions suffering from high risk.Therefore, management of traffic flows and the airway structures within those sub-regions could be computationally and operationally friendly.Last but not least, facilitated by the CREAM software, a solution aiming for risk mitigation can be tested through the software.

3.2.2.Demonstration of CREAM

The CREAM software in its current version exempts aviation decision makers from playing with obscure mathematical equations and tedious data pre-processing efforts.The CREAM software can automatically do the data preprocessing and calculate the three types of collision risk.Fig.3 shows a snapshot of the main interface of the CREAM software.

In the top-left corner of Fig.3,the TSD is short for Traffic Sample Data and it is the most important data required for the collision risk estimation process.The supplementary data(‘‘Suppl”as shown in the interface) includes the waypoints,aircraft dimensions, ASE parameters, AAD samples and LHD occurrences and these data are used to estimate the parameters involved in the collision risk models.In the bottom-left corner of the interface, the software visualizes the values of the key parameters involved in the collision risk models.Users can make a coarse comparison between the estimated values against those for other airspaces.Meanwhile,the software also allows users to tune the parameters and recalculate the risk.On the left-hand side of the interface, users can click the shaded boxes showing the values of the key parameters involved in the collision risk models to change their values.Then users can hit the‘Recompute’button to get the new collision risk value.By doing so, users can get to know which parameters impact the most the collision risk.This helps users to draw inspiration for their subsequent measures for traffic management and risk mitigation.

In the upper-middle part of the interface, there are three icons,i.e.,‘‘Vertical Risk”,‘‘Lateral Risk”,and‘‘Longitudinal Risk”,which enable users to switch between them to see all the related information regarding the corresponding risk calculation.Those information includes all the intermediate results and the final estimated risk,and is shown in the window below those icons.Note that users can fold up and unfold the window for better visualization of the results.Apart from the window, the software also generates external files storing all the related results.

At the bottom of the right-hand side of the interface,it presents visual clues pertaining to the collision risk.Those include the 2D and 3D visualizations of the traffic movement, the crossing points pertaining to the vertical risk, collision risk at given waypoints and airway segments.Those clues help aviation decision makers to draw inspiration to do air traffic flow management or even airspace configurations with the aim being improving traffic safety and airspace utilization.Note that the visualizations can be controlled using the options provided in the middle of the right-hand side of the interface.The option button‘‘Interactive Plot”will open an external window to better visualize the structure of a given airspace and the corresponding collision risk.

Fig.3 Demonstration of main interface of CREAM software.

3.2.3.Validation of CREAM

In what follows we present a validation of the software for collision risk estimation.Without loss of generality,here we show the technical vertical collision risk estimation for Singapore airspace.Technical vertical risk is the risk of collision between aircraft that are on adjacent flight levels due to normal or typical height deviations of RVSM approved aircraft.We compare the values of the key parameters obtained using CREAM against those reported by other ANSPs in ICAO documents.

The vertical collision risk consists of two basic factors which include the likelihood of the loss of vertical separation(reflected by parameter Pz（Sz）) and the exposure to the loss of vertical separation (reflected by parameter nz（equiv）).Table 2 presents the comparison results.Note that the values of the parameters obtained by CREAM are based on the TSD for December 2018.In Table 2, most of the parameters can be referred to Table 1.We use NTazto denote the technical vertical collision risk, parameter α denotes the portion of aircraft using GNSS navigation.More information regarding the technical vertical risk can be found in Ref.20,52.

As can be seen from Table 2, the values of the kinematic parameters (aircraft dimensions, aircraft speeds) as obtained by CREAM are quite close to those reported by other ANSPs.The values of Py（0 ）are also close to each other.However,the values of Pz（Sz）and nz（equiv）differ a lot which then leads to the difference of the eventual risk NTaz.The differences are due to the specific airspace configurations and traffic flow management.For the four airspaces reported in Table 2, their technical vertical risk are all below the ICAO TLS of 2.5×10-9fapfh.

3.3.Adoption of lateral risk model

When RSM with respect to advanced CNS technologies are employed in a procedural airspace, the collision risk models shown in the above section need to be adopted to comply with advanced CNS technologies.This section shows how the models are adopted for collision risk estimation with respect to RSM for procedural airspace.

When a reduced lateral separation standard is implemented in a procedural airspace, the following adoptions need to be considered regarding the lateral collision risk model:

3.4.Adoption of longitudinal risk model

When a reduced longitudinal separation standard is implemented in a procedural airspace,the following adoptions need to be considered:

(1) RNP: The RNP specification needs to be updated to enable reduced longitudinal separation minimum.In this study,RNP 4 is considered as this RNP specification has been adopted by many procedural airspaces.

(2) Sx: The parameter Sxneeds to be updated to calculate the horizontal overlap probability.

(3) The Intervention Model: Note that the calculation of the longitudinal risk heavily depends on the model used to describe controller intervention to resolve a conflict.The intervention model accounts for surveillance latency,controller and pilot responses,and aircraft trajectory change.With advanced CNS techniques, the intervention model needs to be adopted.

3.4.1.Longitudinal risk based on existing intervention model

Currently,the widely used intervention model for longitudinal risk estimation with respect to existing CNS techniques considers the following three scenarios.See ICAO manual 10120 for more information.

Table 2 Validation of CREAM software for technical vertical collision risk estimation for Singapore airspace.

Scenario 1.The ADS-C report is delivered to the ATC,which happens with a probability PYS, and the ATC successfully communicates with the pilot via Controller Pilot Data Link Communication (CPDLC) within a maximum transaction time of τA, which happens with a probability PYC.

Scenario 2.The ADS-C report is delivered to the ATC which happens with a probability PYS, and the ATC failed to communicate with the pilot via CPDLC which happens with a probability PNC, but successfully gets in touch with the pilot using high frequency radio within a maximum transaction time of τB.

Scenario 3.The ADS-C report is not delivered to the ATC which happens with a probability PNS,and the ATC communicates with the pilot via high frequency radio within a maximum transaction time of τC.

in which TA=T+τA; TB=T+τBand TC=T+τCwith T being the periodic reporting interval.

Note that the existing intervention model is based on the Required Communication Performance(RCP) Communication and Surveillance Timing Model (RCSTM) developed for ATS surveillance separation using RCP 240 communications and ADS-B, and modified to account for differences between ADS-B and ADS-C.Fig.4 graphically exhibits the detailed intervention model that is being used by many ANSPs.In the intervention model, three scenarios are considered.Each scenario happens with a certain probability and a specific buffer time as shown in the figure.

3.4.2.Longitudinal risk based on new intervention model

The intervention model shown above only considers three scenarios.With advanced CNS techniques, a new intervention model that is able to capture all possible scenarios related to Performance Based Communication and Surveillance (PBCS)is needed.

Fig.5 demonstrates the new intervention model with details for the 48 scenarios.As can be seen from Fig.5,the 48 scenarios can be categorized into three main branches, viz., ADS-C nominal, ADS-C failure followed by successful resend and ADS-C failure twice, each of which has branches for communication via CPDLC or High Frequency (HF) radio.In the new intervention model,48 scenarios are considered.Each scenario happens with a certain probability and a specific buffer time as shown in the figure.

3.5.Longitudinal separation distribution derivation

For the estimation of longitudinal risk, we need to know the initial longitudinal spacing distribution of the aircraft.Different distributions will lead to different longitudinal risk estimations.In this study, we consider three cases pertaining to the initial longitudinal spacing distribution of the aircraft and those cases are elucidated below.

Fig.4 Illustration of currently used intervention model for longitudinal risk calculation.

Fig.5 Illustration of the new intervention model for longitudinal risk estimation.

3.5.1.Case 1 – uniform distribution

In Case 1,we take it that the initial longitudinal separation follows a uniform distribution with the separation ranging from the minimum separation of Sxto the maximum separation of Sx+250.Studies carried out by the ICAO Separation and Airspace Safety Panel(SASP)showed that a uniform distribution of the initial longitudinal separation yields a far higher risk than any reasonable gamma distribution.48This is due to the rapid, approximately exponential decay in risk with distance.Thus, Case 1 will lead to a conservative estimation of the longitudinal risk.This suggests that it might be possible to reduce the longitudinal separation standard further with close monitoring of aircraft spacings and the use of a more realistic spacing distribution.

3.5.2.Case 2 – at the entry fix

In Case 2,we derive the separation distribution from the TSD.Specifically, we derive the distribution based on the FIR entry fix and entry time.The key idea of Case 2 involves three steps:First, for a cleaned TSD, all the flights are sorted based on their entry flight levels in an ascending order from FL290 to FL410;Second,their entry times are sorted in ascending order(earliest to latest) with respect to each flight level; Third, the longitudinal separations of aircraft pairs are determined.More specifically, for a given sequence of aircraft at a certain flight level, the time duration between the aircraft first entering the FIR and the subsequent aircraft is determined.Then the separation between those two aircraft is obtained by multiplying the speed of the subsequent aircraft with the obtained time duration.

Fig.6 gives a graphical example of Case 2 for deriving the longitudinal separations.As shown in Fig.6, aircraft at each FL are sorted based upon their entry times.Then the longitudinal separation between two adjacent aircraft (one at the entry fix and the other is about to reach the entry fix)at a certain FL can be obtained, such as the 50 NM and 65 NM separations as shown in Fig.6.The above process applies to the entire TSD and a sequence of longitudinal separations is therefore obtained.

Fig.6 An example of Case 2 for deriving longitudinal separations between aircraft from TSD.

Fig.7 Illustration of the key idea of Case 3 for deriving the longitudinal separations with an observation time window of 5 min for aircraft flying at FL350.

3.5.3.Case 3 – after entry fix

Case 3 can be viewed as the extension of Case 2.Based on Case 2,in Case 3 we determine the separations for aircraft within an FIR.After sorting the flights as what has been done in Case 2,a time window of δ is adopted to watch the traffic movements.Then the temporal separations are determined.Fig.7 illustrates the key idea of Case 3 with δ = 5 min for flights flying at FL350.As shown in Fig.7, the yellow aircraft reaches the entry fix at 8:00 AM.For a given time period of 15 min with δ = 5 min, two separations, i.e., 56 NM and 60 NM, are observed.

In Case 3, the longitudinal separations are observed within the FIR.The time window δ is a critical parameter for determining the separation distribution.Therefore, multiple time windows are needed to analyze their impact on the collision risk.In this study, 6 time windows, i.e., 1, 3, 5, 10, 15,20 min, have been adopted.Note that the shortest length of the four studied routes is 204 NM.Therefore, δ cannot be too large.Because if so,then many flights will fly over the procedural airspace (the averaged speed is around 480 knots) and traffic observation samples would be reduced,eliciting inaccurate estimation of the longitudinal separation distribution.

As mentioned earlier, Case 1 is more conservative than Cases 2 and Case 3 for longitudinal calculation.In order to calculate the longitudinal risk in a more conservative way,we only integrate Case 1 into the CREAM software.However,longitudinal risk with respect to those three cases are all analyzed in this study for research purposes.

3.6.Research assumptions

3.7.TSD expansion method

In order to investigate the RSM and their impact on horizontal risk with respect to future traffic demand,we develop a simple yet efficient method to expand the TSD.The developed method is presented in Algorithm 1.

Algorithm 1.Proposed method for TSD expansion for a given ATS route Input: TSD_Org – original TSD for a given route Output: TSD_New – new TSD for the focal route 1.TSD_New = [];2.For ALT = 290:10:410 a)TSD_Org1 = TSD_Org(find(TSD_Org.FL == ALT);b)TSD_Org1 = SortByEntryTime(TSD_Org1, ’ascend’);c)For i = 1 to length(TSD_Org1)–1 i.t =TSD_Org1(i+1).EntryTime-TSD_Org1(i).EntryTime;//time difference between the entry time of two consecutive aircraft at the same FL ii.If t >= 30 min A.n_ac = floor(t/15–1); // number of intermediate aircraft that can be allocated B.delta = t/(n_ac + 1); // time interval of intermediate aircraft C.For j = 1 to n_ac●TSD_cpy = TSD_Org1(i);●TSD_cpy.FixTime = TSD_cpy.FixTime + delta*j;●TSD_New = [TSD_New; TSD_cpy]D.End For iii.End If d)End For 3.End For

As can be discovered from Algorithm 1,the underlying principle of the algorithm is that new traffic data will be generated between two consecutive flights from the original TSD as long as the difference between the time the two flights hit the entry fix is no smaller than 30 min.When interpolating the intermediate aircraft,the time duration for determining the maximum number of aircraft that can be allocated is set to be 15 min in a conservative way to ensure the traffic safety.

Table 3 Research assumptions of the critical components/parameters and their typical values pertaining to the horizontal collision risk models.

4.Experimental settings

In order to validate the feasibility of applying RSM to procedural airspaces and analyze its corresponding impact on the collision risk, in the experimental section we will carry out a case study on the procedural airspace of Singapore FIR which has a large separation in place.This section presents the experimental settings for subsequent analysis.

4.1.Procedural airspace of Singapore FIR

Fig.8 visualizes the procedural airspace of Singapore FIR.As shown in the figure,there are four ATS routes which are N892,L625, N884, and M767.For Singapore FIR, the lateral and longitudinal separation minima in use for the aircraft flying in the procedural airspace are all 50 NM.

In Fig.8, the arrows indicate the directions of the routes.As shown in Fig.8, the two pairs of parallel routes are unidirectional.Note that due to the unique directions of those routes,there is only opposite-direction occupancy when calculating the lateral risk.

4.2.Traffic sample data

TSD is the main data that is required to estimate the collision risk.The information given in the TSD includes the date, call sign, aircraft registration number, PBN approval type, aircraft type, original aerodrome, destination aerodrome, entry fix into the airspace, time at entry fix (UTC),flight level at entry fix, route after entry fix, exit fix from airspace, time at exit fix (UTC), flight level at exit fix and route before exit fix.

The TSD used in this study is for December 2018.It records the en-route flight movements in Singapore FIR.A simplified version of the TSD containing the key information for 10 aircraft is shown in Table 4.Based on the TSD, we filter out the flights on the four studied routes for subsequent analysis.‘‘Fix#1–4”are the names of the waypoints.

4.3.Data pre-processing

In order to facilitate the collision risk estimation process,data pre-processing process is needed to clean the original TSD due to the noise contained in the data.Specifically, the following criteria are adopted to remove flights from the TSD.

(1)Flights that do not have valid aircraft dimensions(each aircraft will be retrieved from a database containing the dimension information for diverse kinds of aircraft).

(2) Flights that only carry-one waypoint information.

(3) Flights that do not have any waypoints within Singapore FIR.

(4) Flights that have no flight path information.

(5)Flights that have zero travel time(for some flights,it has been found that the traveling time durations between two consecutive waypoints are zero due to anthropogenic errors).

(6) Flights that have abnormal ground speed (in the analysis, as long as the ground speed of a flight on an airway segment is outside of the range [210, 600] knot, then the flight is removed from the TSD).

For the studied TSD, there are a total of 44215 flights.After the cleaning process based upon the above criteria,33366 flights are kept for subsequent collision risk estimation.It should be pointed out that although around 25 % of the flights have been removed, those flights have little impact on the collision risk calculation.For one thing, the majority of the removed flights are flights outside Singapore airspace.Those flights contribute nil to the collision risk calculation for Singapore FIR.For another thing, the remaining flights that have been removed are mainly flights without dimension information (flights that cannot be retrieved from the flight database)and abnormal flights(zero flight time and abnormal ground speed).These flights are unsuitable for collision risk calculation.

Fig.8 Visualization of procedural airspace of Singapore FIR and four parallel ATS routes.

Table 4 Example of simplified TSD with 10 flights (F1-F10).

Table 5 Values of the key parameters involved in the horizontal collision risk models.

4.4.Parameter settings

Based on those assumptions listed in Table 3,we further work out the values of other components/parameters that relay on those assumptions.Table 5 records the values of the key parameters involved in the horizontal risk models.Most of the values are derived from the cleaned one-month TSD for Singapore FIR.

5.Impact of RSM on collision risk

This section demonstrates the case study on the procedural airspace of Singapore FIR with respect to reduced horizontal separation minima.The collision risk with respect to current separation minima and new separation minima will be analyzed based on one-month traffic data provided by the Civil Aviation Authority of Singapore (CAAS).

5.1.RSM and lateral risk with current demand

For Singapore FIR,the lateral separation minimum in use for the aircraft flying in the procedural airspace is 50 NM.In order to investigate how the lateral separation minimum affects the lateral collision risk,a wide range of[20,50]NM for the lateral separation minimum is set.

Regarding the lateral collision risk, there are two types of occupancy, namely same direction occupancy and opposite direction.However,the two pairs of parallel routes in the procedural airspace of Singapore FIR, as shown in Fig.8, are in opposite directions.So only the opposite occupancy is required to be computed.

Figs.9(a)and(b)demonstrate the comparisons of the lateral collision risk with respect to different lateral separation standards and RNP specifications.It can be clearly seen from Fig.9(b)that the lateral risk is quite close to the TLS with current procedures (Sy=50 NM, RNP 10) when model M1 is considered for calculating the lateral overlap probability.Model M2 can lead to smaller lateral risk, as can be seen from Fig.9.Fig.9(b)also shows that the lateral risk with respect to model M1 exceeds the TLS if Sydecreases,which indicates that the lateral separation cannot be further reduced with current procedures.

Fig.9 Lateral risk with respect to different Sy.

With advanced CNS technologies,RNP 4 can be applied to en-route airspace.Fig.9(a) and 9(b) clearly show that the lateral collision risk can be further reduced with RNP 4.The lateral risk will surpass the TLS if the lateral separation minimum is smaller than 22 NM.The above analysis indicates that, if RNP 4 is to be implemented, then the lateral separation minimum can be within the range of [22, 50] NM with respect to the current traffic scenario.

5.2.RSM and longitudinal risk with current demand

For the longitudinal separation minimum, a range of [20, 50]NM has also been set to explore the promising range of RSM in the longitudinal plane.In order to estimate the longitudinal risk, it is needed to figure out the distribution of the longitudinal separation.

5.2.1.Distributions of longitudinal separation

Figs.6 and 7 show how to derive the separations from a given TSD.Based on the derived separations,curve fitting technique is introduced to estimate the distribution of the longitudinal separations.In this study, four distributions, i.e., Gamma(GMA), Log-normal (LGN), Normal (NML) and Weibull(WBL),are introduced,and below are their probability density functions.

Fig.10 Distributions of longitudinal separations derived from TSD with respect to Case 1 and Case 2.

Fig.11 Distributions of longitudinal separations derived from TSD with respect to Case 3 under different time intervals.

In Eq.(7),k and θ are the shape and scale parameters,while Γ（k ）is the Gamma function.In Eqs.(8) and (9), μ and σ are the mean and standard deviation, respectively.In Eq.(10), λ and k are the scale and shape parameters.

The initial inter-pair longitudinal separation distribution derived from the Singapore TSD with respect to Case 2 is presented in Fig.10 together with the curve fitting results.Fig.10 shows that the log-normal distribution has the best fit as it has the highest R2value and lowest RMSE as compared to other distributions, where f represents frequency.

It should be noted that the distribution of the separation derived from the TSD with respect to Case 2 does not seem to follow any distribution, as the R2values as shown in Fig.10 are quite small.Since the R2value with respect to the Gamma distribution is the largest amongst the three density functions, in the subsequent analysis we take it that the longitudinal separation distribution follows the Gamma distribution.In what follows the distribution with respect to Case 3 will be analyzed.

Fig.11 demonstrates the distributions of longitudinal separations with respect to Case 3 under different time intervals.The curve fitting results indicate that the distribution of the longitudinal separations follows the log-normal distribution with respect to Case 3.The parameters involved in the lognormal distribution with respect to different time intervals are:

(1) δ=1 min;σ=0.38818;μ=5.02800; see Fig.11(a).

(2) δ=3 min;σ=0.37930;μ=5.06172;see Fig.11(b).

(3) δ=5 min;σ=0.37720;μ=5.04284;see Fig.11(c).

(4) δ=10 min;σ=0.37650;μ=5.04388; see Fig.11(d).

(5) δ=15 min;σ=0.37831;μ=5.04120; see Fig.11(e).

(6) δ=20 min;σ=0.37439;μ=5.03975.see Fig.11(f).

Fig.12 Longitudinal risk under Cases 1, 2 and 3 with respect to different separation standards and intervention models.

5.2.2.Longitudinal risk under the three cases

Based on the three cases,the longitudinal risk is calculated with respect to different Sxand intervention models shown in Fig.4 and Fig.5.Fig.12 presents the estimated longitudinal risk under Case 1,Case 2,and Case 3.Note that RNP 10 is considered in Fig.12(a) while RNP 4 is considered in Fig.12(b).

Case 1 is very conservative.This is why the corresponding risk recorded in Fig.12 are higher than those with respect to Case 2.The results shown in Fig.12 indicate that the longitudinal risk under current control procedures are below the TLS under Cases 1 and 2.Fig.12(a) suggests that the longitudinal separation can be reduced to 35 NM given the current control procedures, while Fig.12(b) indicates that a further reduced separation of 20 NM can be implemented with advanced CNS.

For Case 3,it is obvious from Fig.12 that the collision risk with respect to Case 3 is below the TLS with current control procedures.When new CNS technologies are employed, then the longitudinal separation for the procedural airspace of Singapore FIR can be reduced to 20 NM under Case 3,while the collision risk still can meet the TLS.

As can be seen from the above experiments,advanced CNS technologies both affect the RSM and the corresponding collision risk.Advanced communication techniques, such as improved CPDLC services, can help controllers reduce the intervention time for conflict resolution.Improved navigation specifications such as RNP 4 can reduce aircraft lateral deviation frequencies, while better surveillance services such as space-based ADS-B, can reduce horizontal overlap probabilities.Regarding the horizontal collision risk, advanced CNS technologies affect the values of components, such asSy,Sx,etc.,involved in the collision risk models.A min

i

ma lateral/longitudinal separation therefore can be derived by setting the upper limit of the resultant collision risk to be the TLS.

5.3.Future demand simulation

The above section investigates the impact of RSM on horizontal risk with respect to current traffic demand.Intuitively, if the separation minima are reduced, then the traffic demand can be increased.The following sections aim to investigate the impact of RSM on the horizontal risk with respect to future traffic demand.

5.3.1.Data-driven demand analysis

Fig.13 Hourly demands on four routes derived from one-month TSD.

In order to investigate the impact of RSM on the horizontal risk under future demand, the first thing that we need to do is to generate new TSD that can simulate future demand based on current TSD.To do so, we first present a holistic view of current demand with respect to the available TSD.A datadriven method for deriving the traffic demand from the TSD is therefore developed.

For the studied procedural airspace, there are four routes,viz., N892, L625, N884, and M767.Hereafter, we represent them by R1, R2, R3, and R4, respectively, for simplicity.For a given route, say R1, we first filter out all the flights that pass through R1 from the one-month TSD.We then sort all the filtered flights in ascending order based on the first time points pertaining to the flights’flying profile.Finally,we count the number of flights passing through route R1 per hour.We set the starting time point to be 00:00 UTC.The average flight rate over 31 days (because the TSD is for every December) is then taken as the demand on the studied route.

Based on the one-month TSD,we obtain the demands of the four studies routes using the method described above.Fig.13 shows the corresponding results.As can be seen from Fig.13,the hourly demands on the four routes vary a lot.Route R4 and route R1 are the busiest routes as they serve 28.81% and 27.19 % of the traffic, respectively, while routes R2 and R3 accommodate 25.82%and 18.18%of the traffic,respectively.Based on Fig.13,we get the average demands on R1,R2,R3 and R4, which are DR1=2.85 ac/h, DR2=3.10 ac/h,DR3=2.93 ac/h, DR4=3.66 ac/h (ac represents aircraft)respectively.The starting time point is 00:00 am UTC.

5.3.2.Expanded TSD

Fig.13 clearly shows that the average demands on the four studied routes are quite below their peaks.This indicates that there is large space to expand the TSD to simulate the future traffic demand.This is the main reason why we develop Algorithm 1 to expand the TSD.

Note that Algorithm 1 is for a single route.We apply Algorithm 1 to each of the four studied routes and therefore obtain four expanded TSD denoted by TSD_R1,TSD_R2,TSD_R3,and TSD_R4.Fig.14 shows the hourly demands on the four routes based on the expanded TSD using the data-driven demand analysis method presented above.As compared to Fig.13, the expanded TSD have hourly demands which are roughly-nine times of the original demands.Based on Fig.14, we get the average demands on R1, R2, R3 and R4,which are DR1=21.92 ac/h; DR2=40.11 ac/h; DR3=48.66 ac/h; DR4=25.70 ac/h, respectively.Note that the demands shown in Fig.13 and Fig.14 are for all the 13 flight levels from FL290 to FL410.Therefore, an hourly demand of 80 aircraft on a single route is feasible.

Fig.14 Hourly demands on four routes derived from expanded TSD, i.e., TSD_R1, TSD_R2, TSD_R3, and TSD_R4.

We can clearly observe from Figs.13 and 14 that the newly obtained TSD has more flights than the original TSD does.This phenomenon is mainly due to the fact that we observe from the original TSD that there is no flight (zero values as shown in Fig.13) on each of the routes for certain time periods.We further observe that those time periods are as long as several days,as can be seen from Fig.13.As a consequence,Algorithm 1 will generate the flying profiles for a large number of flights during those periods.

5.4.RSM and lateral risk with future demand

As can be inferred from Fig.14, the expanded TSD has much higher demands than the original TSD.Recall the results presented in Fig.9 which indicate that Sycan be reduced to 24 NM with current demand under RNP 4.In this section, we would like to see the minima Sywith respect to increased demands.

Fig.15 Lateral risk with respect to varying separation standards Syand different portions (10 %-200 % at an interval of 10 %) of increased traffic demands when applied to procedural airspace of Singapore FIR.

Fig.15 visualizes the distributions of Naywith respect to varying Syand p.For a given value of p,we do the TSD sampling 50 times since the expanded TSD is quite large in size.We can see from Fig.15 that when the demand is increased by 0.2 times, the minimum Sybecomes 23 NM, while the Naystill meets the TLS standard.Fig.15 also shows that if the demand is doubled (1.0x), then Sycan be reduced from 50 NM to 25 NM.Fig.15 further indicates that when we increase the demand by 2x (two times), the minimum Sycan be reduced to 31 NM.

The results recorded in Fig.15 are quite valuable to ANSPs.Fig.15 provides scientific insights for ANSPs to understand the relationship between increased traffic demands and the resultant lateral risk, thereby assisting network managers with their decision makings for airspace and/or traffic management.

5.5.RSM and longitudinal risk with future demand

The above section investigates the lateral collision risk under future demand.This section therefore investigates the longitudinal risk under future demand with respect to different longitudinal separations.Note that the calculation of Naxis time consuming.During the analysis, we therefore only consider Case 1 as discussed in subsection 3.5.1.Case 1 is a conservative way for estimating the longitudinal risk.

As presented in section 3,the longitudinal risk calculation is related to the specific controller intervention model.The results demonstrated in Fig.12(a) indicate that the longitudinal separation Sxcan be reduced to from 50 NM to 36 NM with respect to current demand and intervention model when a uniform distribution of Sxis assumed.

As shown in Fig.12(b), if new intervention model is adopted, then Sxcan be reduced to 20 NM under current demand while Naxis still below the TLS.In view of this, we analyze the longitudinal risk under future demands with respect to the two intervention models.The corresponding results are recorded in Table 6.

Table 6 clearly shows that when p increases, the longitudinal risk also increases.However, the increment of Naxis quite small.When the current intervention model is considered, the traffic demand can be increased by two times without the need to alter the longitudinal separation minimum.The results shown in the last column of the table even suggest that the longitudinal separation can be slightly reduced (larger than 45 NM)as Naxis small than the TLS.When the new intervention model is considered, then we can observe from Table 6 that Naxhas been largely decreased.Even though we increase the demand by two times, the longitudinal separation still can be reduced to 20 NM, while the risk is about 1.6×10-9fapfh.

6.Conclusions

Air transport is an indispensable part of the domestic as well as the international transportation systems due to its significant contribution to the economy.With the projected increase in demand for both passengers and air cargo in a post-COVID-19 scenario, airspace may encounter unprecedented traffic movements.In order to maintain the safety of air traffic operations, stringent air traffic separation standards are in place where aircraft are separated vertically and horizontally based on certain separation minima to avoid mid-air collisions.

Note that the separation minima for aircraft flying in procedural airspace covered by limited CNS services are normally larger than those for non-procedural airspace.With the advancement of CNS technologies for air traffic such as space-based ADS-B, large separation minima may be reduced and can significantly contribute to counterbalancing the imbalance between the limited airspace capacity and increasing air traffic demand.The reduction in separation minima will affect the collision risk of the traffic within a given volume of air-space.It is of great significance to ANSPs to explore the extent to which the reduced separation minima can be achieved while still maintaining an acceptable level of traffic collision risk.

Table 6 Longitudinal risk with respect to varying separation standards Sxand different portions(20%-180%at an interval of 20%)of increased traffic demands when applied to the procedural airspace of Singapore FIR.

This paper aims to investigate the feasibility of reduced horizontal separation minima to procedural airspace and the corresponding impact on traffic collision risk.To do so,this paper first presented the CREAM software developed by the authors.The CREAM software exempts aviation decision makers from complicated collision risk models by providing a user-friendly collision risk estimation interface.Meanwhile, the CREAM software is able to estimate collision risk at fine grained levels, i.e., waypoints and airway segments, which provides visual clues regarding collision risk for decision makers.Then this paper presented the adoptions of the horizontal collision risk models with respect to advanced CNS techniques.At last, this paper carried out a case study on the procedural airspace of Singapore FIR in which the lateral and longitudinal separation standards are both 50 NM.The horizontal risk with respect to a one-month TSD had been analyzed with respect to different control procedures(different separation minima, different CNS specifications,and different traffic scenarios).The results indicated that,with current control procedures, the lateral and longitudinal collision risk all meet the TLS standards.The results further indicated that, if RNP 4 is implemented in the Singapore procedural airspace, the current lateral and longitudinal separation minima can be reduced from 50 NM to 22 NM and 20 NM, respectively, while the corresponding collision risk still meets the TLS.

Note that the traffic demand is envisaged to increase in the future.It would be very helpful if the collision risk with respect to future demands also can be estimated.In view of this, the paper developed a simple algorithm to expand the existing traffic data to simulate future traffic demands.The horizontal risk with respect to increased traffic demands was analyzed.A parameter p was introduced to control the increment of the traffic demand.The horizontal risk with respect to p varying from 10 % to 200 % was estimated and the corresponding minimum separation standards were identified.It was discovered that when the demand was increased by two times,the lateral and longitudinal separations could be reduced to 31 NM and 20 NM respectively,while the corresponding risk was still below the TLS.

Note that the research findings revealed in this study are based upon certain assumptions.Regarding the collision risk estimation,many assumptions like the double exponential distributions are adopted in order to estimate the collision risk.One may also try to adopt other assumptions or even pure data-driven methods to estimate the key components and parameters involved in the collision risk models.As a consequence,the final horizontal risk could slightly differ from what is reported in this study and the feasible separation minima could also vary.

Author contribution

Q.Cai, H.Ang and S.Alam conceived the research idea.Q.Cai and H.Ang conducted the analysis.All the authors wrote the paper and reviewed the paper.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgement

The authors would like to thank the Civil Aviation Authority of Singapore (CAAS) POCs for their useful discussions and feedback.This research is supported by the National Research Foundation, Singapore, and the CAAS, under the Aviation Transformation Programme.Any opinions, findings and conclusions or recommendations expressed in this material are those of the author(s)and do not reflect the views of National Research Foundation, Singapore and the CAAS.

Appendix A

in which α represents the percentage of aircraft that experience anomalies caused by aircraft navigation system errors.

In the above equation, the value of α is estimated as α=1-0.051/nwith n being the annual number of flights.49The parameter a1is determined by the RNP specification and is estimated as a1=-RNP/log20.05, while parameter a2is estimated as a2=Sy.

in which M is defined as the cumulative 12-month traffic counts.λ（k ）is the intensity parameter and is dependent on parameter k which is the cumulative 12-month total number of incidents of large lateral deviation.The relationship between λ and k is as follows:

In this research,the parameter of M is set to be 72,250 and the cumulative 12-months total number of large lateral deviations is 4,i.e., k=4, based on the lateral deviation report for 2018.A detailed derivation of the formula used can be found in Ref.53.

(2) Calculation of vertical overlap probability.

The probability of vertical overlap of aircraft nominally flying at the same flight level on laterally adjacent flight paths,viz., Pz（0 ）, is calculated as

(3) Calculation of Occupancy.

There are two types of occupancy, namely same direction occupancy and opposite direction occupancy.To determine the occupancy, the number of proximate aircraft pairs for pairs of parallel routes have to be determined first.Every flight on its route is compared with other flights that are on the adjacent parallel route by using the reporting points.The reporting points used must be points that are at a right angle to the plane of the parallel routes so as to compare the passing time of aircraft on one route to the passing time of aircraft on the other route and they can be the waypoints or interpolated points between the waypoints that have timestamps.For Singapore procedural airspace, the reporting points used for parallel route pair N892-L625 are MABLI and LUSMO and the reporting points used for parallel route pair N884-M767 are LAXOR and TEGID.

If two flights are at the same flight level, then they are counted as an approximate pair as long as the time difference between any two reporting points for those two flights is less than or equal to 15 min (a time duration taken by a flight to fly Sx).

(5) Distribution of speed variation

The notations of f1（V1）and f2（V2）in the longitudinal risk model are the probability distribution functions for the aircraft speed variations.It is assumed that both f1（V1）and f2（V2）follow a double exponential distribution with scale parameter λv=5.82 knot.The assumed average aircraft ground speed of 480 knots is used as the location parameter V0.The double exponential distribution is truncated at 100 knots on either side of the location parameter, and then normalized to equal 1.Thus, f1（V1）and f2（V2）have the same form as follows