Aircraft Trajectory Uncertainty Evaluation Using Polynomial Chaos
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Solution Overview
Problem
Current aircraft trajectory prediction techniques are deterministic and computationally demanding, making it ineffective to quantify uncertainty propagation in real-time air traffic management, which is essential for advanced Decision Support Tools and Air Traffic Controllers.
Innovation Solution
The use of uni-variable and multi-variable polynomial chaos expansions to analytically quantify uncertainty in aircraft trajectory predictions, allowing for a faster and more efficient characterization of uncertainty propagation without significant computational overhead, by decoupling and modeling random variability in sources such as weather, aircraft performance, and intent.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If Monte Carlo simulations are used to quantify uncertainty in trajectory prediction, then measurement precision is improved, but productivity deteriorates due to high computational demand and slow results
Solution Approach 1:
The patent transforms the computational approach by changing the mathematical parameters and methods used. Instead of running thousands of Monte Carlo simulations, the invention uses polynomial chaos expansions with a small number of deterministic trajectory predictions to analytically compute uncertainty metrics. This parameter change in the computational methodology achieves both high precision uncertainty quantification and fast computational speed, resolving the contradiction between measurement precision and productivity.
2Measurement precision
If sensitivity analyses are performed using Monte Carlo simulations, then measurement precision is improved, but loss of time increases due to requiring multiple separate simulations
Solution Approach 1:
The patent merges multiple sensitivity analysis tasks into a single unified computational framework. By using polynomial chaos expansions, the system can evaluate the sensitivity to multiple uncertainty sources simultaneously from just a few deterministic predictions, whereas traditional Monte Carlo methods would require separate simulations for each sensitivity analysis. This merging approach dramatically reduces the time required while maintaining high measurement precision.
3Productivity
If deterministic trajectory prediction is used, then productivity is improved, but measurement precision deteriorates due to inability to quantify uncertainty
Solution Approach 1:
The patent segments the prediction process into two independent components: a deterministic trajectory prediction component and an uncertainty quantification component. The deterministic part maintains high productivity by using efficient prediction models, while the uncertainty component uses polynomial chaos expansions to analytically compute uncertainty metrics from the deterministic predictions. This segmentation allows both productivity and measurement precision to coexist, as each component optimizes for its specific function without compromising the other.
Data Source
AI summary
A system and a computer-implemented method for evaluating uncertainty of a predicted trajectory infrastructure is disclosed The method comprises collecting a plurality of data sets from a predicted trajectory: comprising providing an aircraft intent description based on the predicted trajectory; selecting both a point in time and one or more variables among the collected plurality of data sets as sources of uncertainty; representing each selected variable at the selected point in time as a uni-variable polynomial expansion; representing each non-selected variable by a single point; and combining selected and non-selected variables into a multi-variable polynomial chaos expansion representing a stochastic prediction of the aircraft's trajectory at the selected point in time and a measurement of a sensitivity of the prediction to each of the selected one or more sources of uncertainty.