AEROSTATOPEN AIRSPACE INTELLIGENCE
Manually refreshed OpenSky dashboard and geodesic-deviation analysis

Aerostat
flightgeometry

Jonathan R. Landers

Aerostat combines a credit-safe live aircraft globe with mathematical analysis of geodesic-deviation patterns across a captured one-hour OpenSky state series, including theoretical guarantees that distinguish ordinary route-scale variation from the 53 near-geodesic boundary tracks and estimate when that split becomes detectable.

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What this project contains

The live dashboard and the analytical experiment are deliberately separated. Runtime code protects OpenSky credits and secrets; experiment code turns bounded captures into static visualizations and a reproducible paper on geodesic-deviation pattern analysis.

Live aircraft globe

A Python standard-library local server, vendored globe assets, and a CloudFront-backed deployed site. Aircraft data is refreshed manually, never through browser polling.

static/app.jsapp.py

AWS deployment path

CloudFormation, Lambda, S3, CloudFront, DynamoDB, SQS, and a local collector bridge. Real credentials and deployment state stay in ignored local files.

infrastructurescripts

Geodesic-deviation experiment

A bounded one-hour historical pull of OpenSky state vectors, compact browser-ready datasets, and a main path-deviation analysis from endpoint great-circle arcs, with traversals and altitude included as simple baseline checks.

experimentsvisualizations
Main mathematical results

Path-deviation patterns across live flight tracks

The paper starts with spherical cross-track deviation, proves when route-scale variation makes deviation histograms look lognormal, uses the failed lower tail to separate the 53 near-geodesic aircraft from the rest of the cohort, and derives how long the split takes to detect from partial tracks.

Deviation factorization

Each route's RMS deviation is modeled as D = A Q, where A is the route-scale variable and Q is the RMS functional of an endpoint-pinned standardized bridge.

Lognormal smoothing

If log-scale variation dominates bridge-shape variation, the product law becomes close to lognormal. The theorem makes that smoothing quantitative in Wasserstein distance.

Exact cumulant attenuation

For Gaussian log-scale log A, every standardized cumulant of order three or higher is inherited from log Q and divided by the total log-variance scale.

Brownian-bridge threshold

The Brownian bridge baseline gives SD(log Q) about 0.385. A route-scale spread near sigma_A = 0.50 already makes residual skew and excess kurtosis small.

53-aircraft boundary

The quality-filtered cohort has sample log-skewness near -2.40 and log-excess-kurtosis near 8.11, concentrated in 53 tracks at or below 0.1 km RMS deviation.

Sequential boundary test

Prefix residual energy and a Wasserstein separation check estimate when a single observed aircraft is credibly part of the near-geodesic boundary population: the differing physics of the two populations becomes visible after about 41 elapsed minutes in the current hour.

Paper

Geodesic-Deviation Pattern Analysis

This five-page paper develops the scale-shape model, proves the smoothing and cumulant identities, calibrates a Brownian-bridge baseline, and uses the observed lower-tail failure to motivate a boundary-mixture model for nearly geodesic tracks.

The main result is a diagnostic separation: ordinary aircraft tracks can produce a lognormal-looking center through route-scale variation, while the 53 near-geodesic tracks form a boundary population with different underlying constraints or physics. The sequential result then derives how much of a track is needed before that distinction is visible in the data.

Open PDF Read TeX source Experiment README
Main experiment and checks

Primary path-geometry experiment

The primary experiment is the geodesic-deviation analysis. The animated traversals and altitude distribution are currently simple baseline checks on the captured OpenSky state series.