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Uncertainty-Aware Conflict Detection Against Operator-Conditioned Weather Hazards

Balram Kandoria, Seulki Kim, Aryaman Singh Samyal

arXiv:2609.12095v1cs.RO

TL;DR

AAM pre-flight validation must assess conflicts when uncertain arrival times meet transient weather hazards. The paper combines Kalman-based trajectory uncertainty, operator-conditioned weather polyhedra, and temporal overlap analysis; a 139-second uncertainty shift turns a deterministic non-conflict into a detected conflict. [But no citations in lead; remove marker]

  • Problem

    AAM flight-plan validation must assess conflicts under trajectory and hazard uncertainty, particularly when arrival-time deviations coincide with transient weather during constrained, pre-departure operations.

    Source: A. Motivation · p. 1, B. Problem Statement · p. 2

  • Method

    The framework propagates trajectory uncertainty, converts weather grids into operator-conditioned polyhedra, and checks uncertainty-conditioned trajectories for spatial and temporal conflict.

    Source: B. Problem Statement · p. 2, C. Sigmoid-Blended Measurement Noise… · p. 5, C. Polyhedra Construction · p. 9

  • Results

    139 s of cumulative RTA variance extended the segment-0 arrival time to 739 s, shifting it into hazard group C’s active window and producing a detected conflict where deterministic validation found none.

    Source: §2 · pp. 15–16

  • Takeaways & Limitations

    For AAM missions, deterministic validation alone is insufficient when temporal uncertainty occurs on the same timescale as transient low-altitude weather.

    Source: §VI · p. 17

    The evaluation is limited to a single route and uses a constant-velocity process model that omits climb, descent, and turning dynamics.

    Source: §VI · p. 17

Abstract

from arXiv · show

Strategic flight plan validation in Advanced Air Mobility (AAM) environments requires robust methods for predicting aircraft state uncertainty and detecting potential conflicts with dynamic airspace hazards. This paper presents a novel framework for uncertainty-conditioned trajectory prediction combined with polyhedra hazard representation for pre-flight conflict detection. We introduce a closed-form uncertainty estimation method that couples non-uniform rational B-spline (NURBS) curve fitting for kinematic trajectory generation with a Kalman Filter for state covariance propagation. Drawing from the Light Propagation Algorithm (LPA) paradigm, we employ a sigmoid-blended measurement noise model that captures the uncertainty reduction behavior of flight management systems approaching the required time of arrival (RTA) for waypoints. The resulting temporal uncertainty bounds are derived through a velocity-to-time variance transformation, enabling probabilistic assessment of arrival time deviations along the flight path. For hazard representation, we develop an operator-conditioned classification scheme that transforms gridded environmental data, specifically weather phenomena, into three-dimensional polyhedra volumes with intensity-based stratification. These hazard polyhedra incorporate aircraft-specific safety buffers computed from vehicle performance characteristics. Conflict detection is performed through mesh intersection algorithms operating on the spatial uncertainty tube surrounding the mean trajectory against the hazard polyhedra and temporal overlap. The framework enables the continuous strategic validation of flight plans throughout the pre-flight planning time horizon as environmental conditions evolve.

I. Introduction

AAM flight-plan validation must assess conflict probability under aircraft and hazard uncertainty, especially because arrival-time deviations can overlap transient weather in constrained corridors. The section frames pre-flight uncertainty propagation and operator-specific hazard characterization as core requirements.

B. Problem Statement

A. Motivation

  • AAM missions’ 2–3-minute arrival-time uncertainty can coincide with transient weather, making temporal overlap central in constrained corridors requiring pre-departure deconfliction.The cited discussion places this uncertainty at 5–15% of a typical 15–45-minute mission and notes limited spatial rerouting flexibility.Source: A. Motivation · p. 1

B. Problem Statement

  • Weather severity must reflect aircraft- and operator-specific tolerance, while validation propagates trajectory uncertainty, represents hazards in 3D, and checks conflicts within confidence bounds.Source: B. Problem Statement · p. 2

1. Uncertainty Propagation in Trajectory Prediction

  • Prior approaches include unbounded linear uncertainty growth, bounded but fixed-rate LPA behavior, and NURBS-based velocity-to-time propagation requiring empirical variances.Pre-flight methods have also modeled wind uncertainty and estimated wind fields with Gaussian processes.Source: §1 · p. 2

3. Weather Hazard Characterization

Existing weather-hazard methods largely focus on convective hazards or flow-level risk, leaving a need for geometric hazard volumes with severity tied to aircraft performance. The paper combines uncertainty propagation and operator-conditioned weather volumes in strategic conflict detection.

3. Weather Hazard Characterization

  • Prior weather methods largely represent convective hazards, while AAM hazards such as wind and visibility require severity decisions tied to aircraft performance and operator thresholds.The paper identifies a gap in geometric hazard volumes and multi-level severity linked to specific performance envelopes.Source: §3 · p. 3

D. Contributions

  • The framework constructs 3D weather polyhedra with advisory, caution, and warning levels, then integrates temporal uncertainty to detect conflicts within confidence bounds.Source: §3 · p. 3, D. Contributions · p. 3

A. Kinematic Profile from NURBS Curves

B. Kalman Filter Formulation

  • A Kalman Filter propagates uncertainty using a six-dimensional position-velocity state, NURBS-derived velocity control, constant-velocity dynamics with acceleration noise, and position-only measurements.The filter is initialized at the first waypoint with zero velocity and covariance reflecting GPS and velocity-estimation uncertainty.Source: B. Kalman Filter Formulation · p. 4

C. Sigmoid-Blended Measurement Noise Model

A progress-dependent sigmoid measurement-noise covariance models FMS-like uncertainty reduction without discrete mode switching. In this implementation, updates run continuously while their corrective strength increases as the aircraft approaches a waypoint.

C. Sigmoid-Blended Measurement Noise Model

  • The progress-dependent measurement-noise covariance is introduced to capture FMS uncertainty reduction without discrete switching.Source: C. Sigmoid-Blended Measurement Noise… · p. 5
  • The model uses waypoint progress p, threshold p_LPA, and sharpness k; experiments selected p_LPA = 0 for the smoothest blend, keeping updates continuously active.The cited LPA convention typically places the activation threshold at 2/3, whereas the experiments found continuous updating provided the smoothest blending.Source: C. Sigmoid-Blended Measurement Noise… · p. 5
  • Early in a segment, high measurement noise yields minimal Kalman gain and allows uncertainty to grow; near the waypoint, low noise strengthens correction and reduces uncertainty.Source: C. Sigmoid-Blended Measurement Noise… · p. 5

D. Temporal Uncertainty Derivation

The method converts propagated velocity uncertainty into cumulative arrival-time uncertainty, then models waypoint arrival time probabilistically for comparison with hazard validity windows.

D. Temporal Uncertainty Derivation

E. Wind Uncertainty Integration

Wind uncertainty is incorporated into trajectory propagation using spatially varying Gaussian-process predictions. Weather hazards are classified using operator-defined thresholds and an aggregate level for compound conditions.

E. Wind Uncertainty Integration

  • Gaussian-process wind predictions provide mean wind and covariance, which enter propagation as an additive control input and augment process noise.This lets uncertainty propagation adapt to spatially varying wind rather than assume uniform disturbance characteristics.Source: E. Wind Uncertainty Integration · p. 6

A. Hazard Classification

  • Weather attributes are evaluated against three operator-defined levels: Advisory, Caution, and Warning.The attributes considered include temperature, visibility, precipitation rate, and wind speed.Source: A. Hazard Classification · pp. 6–7
  • The AAM thresholds used in evaluation are preliminary representative values calibrated for one aircraft profile and may vary across vehicles.The paper says operators should establish platform-specific thresholds through flight testing and manufacturer guidance before deployment.Source: A. Hazard Classification · p. 7
  • The aggregate hazard level captures cells where multiple weather attributes simultaneously exceed their thresholds.The passage gives high wind speed and low visibility as an example of compound conditions.Source: A. Hazard Classification · p. 8

1. Single-Attribute Clustering

Weather cells are clustered spatially to form the basis for hazard polyhedra. Aggregate clusters preserve differences in the contributing attributes and their hazard levels.

1. Single-Attribute Clustering

  • Single-attribute hazard cells are grouped when spatially adjacent and at the same intensity, using breadth-first search with 26-neighborhood connectivity.The resulting clusters form the basis for polyhedra construction.Source: §1 · p. 8

2. Aggregate Clustering

  • Aggregate cells join the same cluster only when adjacent cells share both their active attribute set and each attribute’s hazard level.This keeps regions with different hazard compositions separate even if their aggregate levels coincide.Source: §2 · p. 9
  • Cells with wind-speed and visibility levels [2, 1] and [1, 2] form separate clusters despite sharing aggregate level 2.Their per-attribute levels differ.Source: §2 · p. 9

C. Polyhedra Construction

Weather clusters are represented as vertically extruded convex polyhedra with temporal validity and intensity metadata. The polyhedra are expanded using aircraft-specific safety buffers before mesh-based use.

C. Polyhedra Construction

  • Each cluster’s horizontal convex hull is extruded across its minimum-to-maximum altitude range to form a polyhedron.The resulting volume has vertices and triangular faces.Source: C. Polyhedra Construction · p. 9

D. Temporal Validity and Hazard Metadata

  • Hazard metadata records geometric extent, altitude bounds, temporal validity, intensity, and hazard type for spatial and temporal filtering.Weather validity windows follow forecast timestamps; regulatory hazards can provide explicit start and end times.Source: D. Temporal Validity and Hazard Metadata · p. 9

E. Aircraft-Specific Safety Buffers

  • Aircraft-specific safety buffers expand hazard polyhedra before they are discretized into triangular meshes.The lateral safety radius depends on aircraft category, and the expansion uses lateral and vertical buffers.Source: E. Aircraft-Specific Safety Buffers · pp. 9–10

IV. Conflict Detection

The Kalman Filter-FMS method predicted real-aircraft performance in approximately 70% of simulations without specific knowledge of the flight environment. Conflict assessment combines spatial intersection of trajectory and hazard meshes with temporal overlap against hazard validity windows.

A. Trajectory Uncertainty Tube

  • A three-dimensional tube around the mean trajectory represents spatial uncertainty and is discretized into a triangular mesh.Its radius is derived from position covariance and a fixed loss-of-separation radius.Source: A. Trajectory Uncertainty Tube · p. 10

B. Mesh Intersection Algorithm

  • A non-zero-volume intersection between the trajectory tube mesh and a hazard polyhedron indicates a spatial conflict.The intersection points identify the spatial extent of the conflict region.Source: B. Mesh Intersection Algorithm · p. 10

C. Temporal Conflict Assessment

  • For spatially intersecting segments, temporal conflict is assessed by comparing RTA bounds with hazard validity windows.The bounds use a selected number of standard deviations for the desired confidence level.Source: C. Temporal Conflict Assessment · p. 10

A. Trajectory Forecast Uncertainty Validation

  • Approximately 70% of simulations predicted real-aircraft performance with the Kalman Filter-FMS method without specific knowledge of the flight environment.The paper attributes inaccurate cases to tactical deviations from filed plans and expects autonomous AAM flights to adhere more strictly to planned trajectories.Source: A. Trajectory Forecast Uncertainty… · pp. 10–11

B. Uncertainty-Conditioned Conflict Detection

The Houston experiment tests whether arrival-time uncertainty reveals weather conflicts missed by deterministic validation, using a Kalman Filter trajectory pipeline and operator-conditioned hazard volumes. Its setup combines HRRR weather data, aircraft-specific buffering, and temporal hazard windows.

B. Uncertainty-Conditioned Conflict Detection

  • In Houston scenarios, incorporating Kalman Filter RTA uncertainty into conflict detection reveals conflicts that deterministic validation misses.For a 30-minute mission, a 2σ arrival window spans about 10 minutes, comparable to the active lifetime of some low-altitude weather phenomena.Source: B. Uncertainty-Conditioned Conflict… · p. 11

1. Experiment Design

  • 69.6% accuracy across 23 Kalman Filter verification flights (16 passed, 7 failed).Table 4 reports the verification results.Source: Table 4 · p. 12
  • HRRR weather hazards are threshold-classified, spatially clustered, extruded into polyhedra, and expanded using an aircraft-specific buffer; Fig. 4 shows intensity classes and Fig. 5 shows buffered polygons.The reported expansion is approximately 787 m laterally and ±500 ft vertically.Source: §1 · p. 13, Figure 4 · p. 13, Figure 5 · p. 14
  • 33 Houston hazard polygons comprise 15 single-attribute and 18 aggregate hazards, with their intensity distribution summarized in Table 5.The table is titled “Weather Hazard Distribution over Houston.”Source: §1 · p. 13, Table 5 · p. 14
  • Visibility and wind hazards have 5–30 minute validity windows, while temperature-dominated hazards persist across the full forecast hour.The passage notes that narrow-window hazards are particularly susceptible to being missed by deterministic validation but caught when temporal uncertainty is included.Source: §1 · p. 14
  • The experiment processes a route through Houston hazards using NURBS path fitting, Kalman Filter covariance propagation, velocity-to-RTA uncertainty conversion, and deterministic and uncertainty-conditioned checks.The route is evaluated against hazards generated from HRRR data covering Houston at 3 km horizontal resolution.Source: §1 · pp. 11, 12, 14

2. Results

In the Houston route test, adding cumulative RTA variance shifted segment 0’s arrival into hazard group C and revealed a confirmed 3D conflict missed by deterministic validation. The conclusion reports a 69.6% uncertainty capture rate across 23 real flights and identifies model and evaluation-scope limitations.

2. Results

  • 12 of 33 hazards passed the first-pass altitude filter, forming four groups by active time window.The table distinguishes temporal overlap from confirmed 3D conflicts and temporal overlap without spatial intersection.Source: §2 · p. 15, Table 6 · p. 16
  • 139 seconds of cumulative RTA variance shifted segment 0’s arrival into hazard group C’s active window, revealing a confirmed 3D conflict missed by deterministic validation.The nominal RTA was 600 s; uncertainty extended arrival to 739 s, within the hazard’s 600–1500 s active window.Source: §2 · p. 15, Figure 7 · p. 16, Table 6 · p. 16
  • The other segments had temporal overlap with hazards but no 3D intersection because the AAM flight ceiling was below the hazards’ lowest extrusion point.Those segments passed under both nominal and uncertainty-conditioned evaluation.Source: §2 · pp. 15–16

VI. Conclusion

  • 69.6% capture rate was achieved by the trajectory uncertainty model across 23 real flights; Houston HRRR data produced 33 operator-conditioned polyhedra at three intensity levels.The hazard volumes used aircraft performance-conditioned safety buffers of approximately 787 m.Source: §VI · p. 16
  • The evaluation is limited by a constant-velocity process model that omits climb, descent, and turning dynamics, convex-hull overestimation, and single-route scope.The paper identifies higher-fidelity dynamics, non-convex hazard representations, and multi-flight scaling as future work.Source: §VI · p. 17
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