Real Time Aircraft Conflict Detection

Hybrid Vector Based Ground System for Real Time Aircraft Conflict Detection

1. Abstract

This concept describes a ground based conflict detection engine that continuously evaluates all cooperative aircraft in a terminal or approach airspace using explicit three dimensional vector mechanics and a hybrid risk scoring method that combines relative motion calculations with learned patterns from historical traffic and crash data. The system, named vCAS (vector based Conflict Alert System), operates directly on surveillance derived state vectors of all aircraft in the monitored region, rather than only on filed flight plans or altitude thresholds, and provides graded alerts to controllers based on time to conflict and composite risk. The method is intended as a research framework that extends and complements existing tools such as STCA, MTCD, and on board ACAS, particularly in complex mixed instrument and visual environments.

2. Motivation and Novelty Compared to Existing Systems

2.1 Gap in Current Operational Tools

The typical safety layers in use today include:

• On board TCAS and ACAS X which rely on relative altitude, range, and closure between ownship and intruders and which mainly provide vertical resolution advisories based on pairwise logic inside the aircraft.
• Short Term Conflict Alert (STCA) in the ground ATM system, which usually applies simple geometric predictions with short lookahead and triggers when predicted separation falls below configured minima in the next tens of seconds.
• Medium Term Conflict Detection (MTCD) which uses filed flight plans and route structures to identify potential conflicts minutes ahead in the en route and upper airspace environment.

These mechanisms are effective within their design envelopes but they have limitations when traffic mixes instrument approaches, visual approaches, vectoring, and non standard paths in dense terminal airspace. Typical limitations include:

• Limited use of full three dimensional relative motion between all aircraft in a terminal volume in a continuous fashion.
• Strong dependence on filed flight plans for MTCD which may not capture tactical vectors or visual maneuvering near the aerodrome.
• On board systems that cannot see the full picture of every aircraft in a sector but only traffic within transponder and sensor range around one aircraft.

2.2 What vCAS Adds

The vCAS concept adds the following:

• Continuous computation of relative position vectors and relative velocity vectors for every aircraft pair inside a dynamically defined time based sample space in the terminal region, using explicit Newtonian kinematics in three dimensions.
• Time to conflict based filtering, where the primary screening variable is estimated time to loss of separation rather than only instantaneous distance. This enables very early warning when closing trajectories exist, including at eight minutes or more before minimum separation would be breached.
• A two level conflict thread structure. One thread for developing conflicts with medium term risk and another for imminent conflicts with short term risk, each with its own escalation and exit rules tied to both geometric closure and a composite risk score.
• A hybrid risk score that combines three components. A flight path based component derived from planned trajectories, a kinematic component derived from relative motion, and a machine learning component trained on historical crash and near miss patterns in four dimensional space.
• A database centric architecture that preserves high resolution histories for each interacting pair, allowing full reconstruction of why an alert was raised or cancelled.

The novelty is not a single equation. It is the specific combination of:

• Explicit use of relative velocity vectors, closing speed along the line of centers, and time to closest point of approach as first class variables in a ground system for all aircraft, not only in on board hardware.
• Structured thread based promotion and tracking logic driven by time to conflict and persistent closing trends, rather than only distance thresholds.
• An integrated weighted risk score that can be tuned and validated, with the physics layer acting as a conservative baseline and the learning layer refining sensitivity based on real historical events.

3. Coordinate System and Basic Mechanics

3.1 Local Cartesian Frame for a Terminal Area

Surveillance data arrives as latitude, longitude, and altitude. To apply vector mechanics, vCAS defines a local Cartesian frame centered on a reference aerodrome or terminal control area center. Let:

• φ be latitude in radians.
• λ be longitude in radians.
• h be geometric or barometric altitude in meters referenced to mean sea level.
• R be an effective Earth radius, for example approximately 6 371 000 meters.
• φ0, λ0 be the latitude and longitude of the terminal reference point.

For a limited region around the aerodrome, a small angle approximation is sufficient:

x ≈ R · (λ − λ0) · cos(φ0)
y ≈ R · (φ − φ0)
z = h

Each aircraft i then has a three dimensional position vector:

rᵢ = (xᵢ, yᵢ, zᵢ)

Velocity in the local Cartesian frame is derived from ground speed and track, or directly from successive position updates:

vᵢ = (vₓᵢ, v_yᵢ, v_zᵢ)

This is a classical Newtonian kinematics framework in a Euclidean three dimensional coordinate system.

3.2 Relative Position and Relative Velocity

For two aircraft, indexed 1 and 2, the core quantities are:

Δr = r₂ − r₁          relative position vector
Δv = v₂ − v₁          relative velocity vector

This is standard relative motion in a Galilean frame. Under the assumption of piecewise constant velocity during short prediction windows, the relative position as a function of time is:

Δr(t) = Δr₀ + Δv · t

The Euclidean distance between the aircraft is:

d(t) = ∥Δr(t)∥ = sqrt( (Δr₀ + Δv t) · (Δr₀ + Δv t) )

The unit vector pointing from aircraft 1 to aircraft 2 at the current time is:

ê = Δr₀ / ∥Δr₀∥

The scalar projection of the relative velocity along this line is:

v_cl = − Δv · ê

This is the closing speed along the line of centers. It is a direct application of the dot product projection concept from vector calculus. When v_cl is positive, the aircraft are advancing toward each other along the direct line joining them. When v_cl is negative, they are increasing their separation along that line.

3.3 Time to Conflict and Closest Approach

If there is a protected radius R_protected representing required horizontal separation and the current separation is greater than this radius, a first estimate of time until the centers approach that radius is:

T_c ≈ (∥Δr₀∥ − R_protected) / v_cl   for v_cl > 0

This is a simple one dimensional kinematic calculation along the line of centers. To find the exact time of closest point of approach (CPA) in three dimensions, the system minimises d²(t):

d²(t) = (Δr₀ + Δv t) · (Δr₀ + Δv t)
       = Δr₀ · Δr₀ + 2 (Δr₀ · Δv) t + (Δv · Δv) t²

Taking the derivative with respect to time and setting it to zero gives:

∂(d²)/∂t = 2 (Δr₀ · Δv) + 2 (Δv · Δv) t_min = 0

t_min = − (Δr₀ · Δv) / (Δv · Δv)

This is the classical result for the time of closest approach between two points moving with constant relative velocity. If t_min is positive and lies within the time horizon of interest, the minimum separation distance can be computed as:

d_min = ∥Δr₀ + Δv t_min∥

Horizontal and vertical components are separated by:

d_horizontal(t) = sqrt( (Δx(t))² + (Δy(t))² )
Δz(t)            = z₂(t) − z₁(t)

Loss of separation is declared inside a prediction window if there exists some t where:

d_horizontal(t) ≤ R_protected
|Δz(t)| ≤ H_protected

where H_protected is the vertical minimum. This is standard separation geometry written explicitly in vector form.

4. Dynamic Sample Space and Thread 1

4.1 Monitoring Volume

The terminal region has a baseline recommended monitoring radius R_base around the aerodrome. vCAS uses a configurable factor k_R to define the outer volume where initial computations are performed:

R_monitor = k_R · R_base

Typical values of k_R are between 2 and 3. Only aircraft with:

∥rᵢ∥ ≤ R_monitor

are included in the Thread 1 candidate set. This removes distant aircraft that cannot interact with the terminal sequence in the near future.

4.2 Time Based Inclusion Criterion

Thread 1 runs on every surveillance update, for example at 1 Hz. It generates all pairs of aircraft inside the monitoring volume and evaluates a first estimate of time to conflict. It uses the three dimensional relative motion described earlier and checks the following condition for each pair:

0 < T_c ≤ T_threshold_1

where T_threshold_1 is a configurable value such as eight minutes. The physics used here is simple but explicit Newtonian constant velocity motion. Pairs that satisfy the condition are retained as candidates and written to a real time state store together with:

• Their current relative position and velocity.
• The current estimate of T_c and d_min.
• Short history arrays of travelled distance and time to conflict for trend analysis.

Pairs that do not satisfy the condition are not passed to higher level threads, which limits the computational load.

4.3 Distance and Time Histories

For each candidate pair, vCAS stores sliding window arrays:

D_pair(t_k)   = d(t_k)       for k = 0 … n
Tc_pair(t_k)  = T_c(t_k)

These arrays are bounded by configuration. For example a 10 minute window at 1 Hz results in 600 samples. When new samples are appended, the oldest entries are dropped. These sequences are used by Thread 2 to detect persistent closing or opening patterns beyond single sample noise.

5. Conflict Threads 2A and 2B

5.1 Separation of Roles

Thread 2 is split into:

• Thread 2A for imminent conflicts that require immediate controller attention.
• Thread 2B for developing conflicts that are not yet imminent but show consistent risk build up.

Thread 1 writes raw geometric values and minimal derived fields into a shared state store. Threads 2A and 2B then work off that store without having their conflict specific tracking variables overwritten.

5.2 Thread 2A: Imminent Conflicts

A pair enters Thread 2A when any of the following is true:

• The estimated time to conflict T_c is less than a short horizon threshold such as 300 seconds.
• The composite risk score P_total described later exceeds a high threshold such as 0.70.

Thread 2A runs at high frequency, for example once per second. For each tracked pair it:

• Recomputes the exact time of closest point of approach t_min and corresponding d_min using the formulas in section 3.
• Checks if, within the lookahead window, horizontal separation and vertical separation minima can be breached.
• Maintains detailed histories of distance, time to conflict, and risk score for post event analysis.

Exit criteria for Thread 2A include:

• One aircraft has landed, altitude remains at or near zero for a sustained period (for example 60 seconds), and no further conflict geometry exists with the other aircraft.
• The conflict geometry disappears, with no predicted separation loss in the lookahead window for a continuous period such as 60 seconds.

5.3 Thread 2B: Developing Conflicts

Thread 2B receives pairs that have non trivial risk but are not yet imminent. Typical entry conditions include:

• T_threshold_2A ≤ T_c ≤ T_threshold_1, for example between 5 minutes and 8 minutes.
• P_total between 0.50 and 0.70.
• Consistent decreasing trend in the distance history, even if T_c is still somewhat large.

Thread 2B keeps for each pair:

D_pair(t_k)
Tc_pair(t_k)
Trend_sign(t_k) = sign( D_pair(t_k) − D_pair(t_{k−1}) )
Persist_closing = number of consecutive seconds with Trend_sign < 0

The main logic is:

• If T_c drops below T_threshold_2A, or if P_total rises above 0.70, promote the pair to Thread 2A.
• If the distance has been strictly decreasing for at least a configured number of seconds (for example 15) and remains inside an envelope such as a certain multiple of the protected radius, promote as well even if T_c is marginally above the short horizon threshold.
• If, for a full window such as 60 seconds, distance is stable or increasing and there is no predicted loss of separation in the horizon, drop the pair from Thread 2B and log the completion of the interaction.

6. Data Model and Relationship Handling

6.1 Primary Key Structure

Aircraft specific state can be stored with a composite primary key:

aerodrome_id
timestamp_utc
aircraft_id

Core state fields include local Cartesian position, velocity components, heading, ground speed, and phase of flight. To represent conflicts, the schema does not create separate rows for each pair. Instead, per aircraft, it maintains structured fields that are lists of attributes per conflict partner:

conflict_partner_ids   = [id₂, id₃, …]
conflict_Tc            = [T_c(1,2), T_c(1,3), …]
conflict_dmin          = [d_min(1,2), d_min(1,3), …]
conflict_P_total       = [P_total(1,2), P_total(1,3), …]

When a conflict pair is first inserted, vCAS writes the relationship in both directions. If aircraft 1 is in conflict with aircraft 2, the entry for aircraft 2 also contains aircraft 1 as a partner with matching arrays. This ensures consistency when generating controller displays that may be anchored on either aircraft.

6.2 Thread Specific Logs

Separate log tables such as thread1_log, thread2A_log, and thread2B_log record snapshots at entry and exit of each thread together with compressed histories. For example a Thread 2A log record for a pair can contain:

pair_id
entry_time
exit_time
D_pair_history
Tc_pair_history
P_total_history
minimum_recorded_distance
minimum_recorded_vertical_separation

These logs allow after the fact review of why and how the system behaved for specific interactions, including potential incidents and near misses.

7. Hybrid Risk Scoring

7.1 Components of the Risk Function

The composite risk score P_total for an ordered pair of aircraft is built from three components:

• P_fp: risk derived from planned four dimensional flight path data such as route, altitude constraints, and scheduled crossing points.
• P_phys: risk derived from deterministic vector calculations using relative position, relative velocity, closing speed, time to conflict, and minimum predicted separation.
• P_ml: risk derived from a machine learning model trained on historical trajectory data, including known accidents and serious incidents, in a four dimensional representation.

A simple linear combination is:

P_total = w_fp · P_fp + w_phys · P_phys + w_ml · P_ml

with example weights:

w_fp   = 0.20
w_phys = 0.30
w_ml   = 0.50

The exact values are to be tuned. The key idea is that the deterministic mechanics layer provides a strict lower bound on risk, while the learning layer can increase sensitivity in patterns that historically led to loss of separation, including curved approaches and complex visual maneuvers.

7.2 Risk Buckets and Interface Mapping

For practical controller interfaces the continuous risk is mapped into three buckets:

• High risk where P_total ≥ 0.70. These pairs are managed by Thread 2A and presented with strong visual and aural indications.
• Medium risk where 0.50 ≤ P_total < 0.70. These pairs are managed by Thread 2B and shown on a medium priority panel for early awareness.
• Low risk where P_total < 0.50. These pairs are logged and optionally displayed in a low priority list so the controller can see which trajectories the system is watching without generating attention demanding alerts.

The mapping between the physics based time to conflict thresholds and these buckets is configurable. For example any pair with T_c below 120 seconds could be forced into the high risk bucket regardless of the machine learning score, to avoid over reliance on statistical models in very short horizons.

8. Use of Historical Trajectories and Crash Data

To derive P_ml, vCAS models each interacting pair as a time series of relative state vectors:

State(t) = [Δx(t), Δy(t), Δz(t), ∥Δv(t)∥, bearing_rel(t), T_c(t)]

where:

• Δx, Δy, Δz are relative Cartesian coordinates.
• ∥Δv(t)∥ is the magnitude of the relative velocity vector.
• bearing_rel(t) is the angle of aircraft 2 relative to aircraft 1 in the horizontal plane.
• T_c(t) is the physics based time to conflict estimate at time t.

This sequence can be fed to a recurrent neural network, a long short term memory network, or a transformer configured for time series data. Labels are derived from known outcomes:

• Sequences that led to collision or serious loss of separation are labelled as high risk.
• Sequences that did not result in a conflict, despite initial proximity, are labelled as low risk.

The trained model outputs a probability P_ml that the current sequence, if left unmitigated, will result in a serious conflict. In operation, the model is used in inference mode only, and its output is combined with flight path and deterministic kinematic risk.

9. Comparison to Existing Research

Several strands of existing research explore medium term conflict detection with flight plan based prediction and also trajectory prediction using machine learning. The vCAS concept differentiates itself by:

• Applying relative motion calculations at high frequency for all aircraft pairs inside a time based sample space in the terminal region, instead of using flight plans alone for medium term horizons.
• Embedding the Newtonian relative motion model explicitly in the risk computation chain, including relative velocity vectors, closing speed projections, and time to closest approach.
• Defining an explicit two stage thread architecture tied to time thresholds and persistence of closing trends that can be directly mapped to controller workflows.
• Integrating a learned component that can capture patterns beyond straight line segments, while still anchored by deterministic vector calculations that can be independently audited.

This combination of continuous all pair kinematics, structured promotion logic, and hybrid risk scoring appears less represented in published work and is intended as a candidate foundation for a research paper or conference contribution in the air traffic management and safety domain.

10. Computational Considerations

The number of aircraft in a terminal area is finite but can be high. If there are N aircraft inside the monitoring volume, a naive all pairs evaluation would need roughly N (N − 1) / 2 relative motion computations each second. vCAS reduces this burden through:

• Restricting evaluation to aircraft within R_monitor.
• Using simple spatial indexing, for example hashing into three dimensional grid cells, to generate only nearby pairs instead of all combinations.
• Discarding pairs whose first estimate of T_c is larger than T_threshold_1 so that only pairs with potential conflict in the next several minutes are passed to higher layers.
• Applying the more expensive Thread 2A and 2B logic, and any machine learning inference, only to the small subset of pairs that have already passed the Thread 1 screening.

The core mathematical operations in Thread 1 are vector additions, dot products, and square roots. These are low cost. Machine learning inference can be batched and placed on dedicated hardware if required. With careful engineering, the architecture is consistent with real time operation at update rates of one Hertz or higher for realistic numbers of aircraft in a terminal control area.

11. Limitations and Future Extensions

Limitations of the concept include:

• Assumption of constant velocity during prediction windows. Significant turns, level offs, or speed changes inside the horizon reduce accuracy. Use of flight path data and adaptive segmenting can mitigate this somewhat.
• Dependence on cooperative surveillance sources. Non cooperative traffic and sensor anomalies can cause both deterministic and learned components to misjudge risk. Conservative thresholds and integrity monitoring are necessary.
• The need for extensive validation. Any candidate implementation must be tested in high fidelity simulation with real traffic recordings and known events before it can be considered for operational use.

Potential extensions include:

• Feeding vCAS outputs to augmented reality head mounted displays in the cockpit, so that predicted conflict points can be visualised relative to pilot head position, while still controlled and certified as ground side decision support.
• Producing sector level conflict density maps for use in flow management and arrival spacing tools.
• Incorporating meteorological vector fields such as wind and turbulence that can influence likely deviations from planned paths.

12. Conclusion

The vCAS concept describes a hybrid system in which classical vector mechanics and modern machine learning are combined in a ground based engine for real time conflict detection in terminal airspace. The system maintains a local Cartesian representation of each aircraft, uses relative position and relative velocity to compute closing speed, time to conflict, and minimum separation, tracks these quantities in time, and promotes aircraft pairs through a structured thread architecture based on time thresholds and risk scores. A composite risk function merges flight path information, deterministic kinematic risk, and learned patterns from historical data into a single figure used to drive graded alerts. This approach is intended to close a gap between current medium term and short term tools, especially in mixed instrument and visual environments, and to provide a technical foundation for further research and potential publication.

License and Usage Restriction

All algorithms, equations, concepts, workflows, data structures, and descriptive text in this document are the original intellectual property of Sri Surya Sameer Vaddhiparthy (the Author). No part of this work may be copied, reproduced, stored, transmitted, adapted, implemented, simulated, or used in any personal, academic, research, commercial, or governmental system without the Author's prior explicit written consent.

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