DYNAMICS LAB · ENGINE01

Probabilistic Flight Modeling Benchmark

Study context

Problem addressed
Which motion estimates perform best on the same held-out historical flights?
Contribution relative to existing methods
The benchmark puts established methods and a validation-fitted ensemble under one protocol.
Potential commercial use
Select candidate estimators for offline evaluation on a civil fleet’s own telemetry.

Market context and value assumptions on the engine page

DME-001

Experiment conclusions

On nine test flights, Kalman had the lowest mean displacement error at 9.12 m, slightly ahead of CRW at 9.27 m. The ensemble had the lowest RMSE, 15.12 m, while its mean error was 9.60 m. Model choice therefore depends on the error measure that matters.

Study limits. The flights share a platform and circuit. GNSS is a noisy reference and the ranking may differ on other flights.

Model-by-model results
RW
Random-walk reference: 34.80 m mean error, above constant velocity.
CV
Constant velocity: 12.74 m mean error, a useful simple baseline.
CA
Constant acceleration: 18.13 m mean error, above CV in this test.
KF
Kalman: lowest mean error, 9.12 m.
CRW
Correlated random walk: 9.27 m mean error, close to Kalman.
OU
Ornstein–Uhlenbeck: highest mean error, 180.27 m. High coverage did not offset poor accuracy.
Ensemble
Model combination: lowest RMSE, 15.12 m.
HMM
Groups motion patterns into descriptive states. The states have no verified intent labels.
EKF
Extended Kalman filter: available in the core, without a measured result in DME-001.
Particle Filter
Available in the core, without a measured result in DME-001.
Monte Carlo
In DME-003, 100 synthetic random-walk replicates produced a distribution of final outcomes.

DME-001 · REAL EXPERIMENTAL DATA

Computed 2026-11-06T10:25:09.902316+00:00 · reproducible scientific prototype

Objective & dataset

Compare six motion models and a validation-fitted ensemble on held-out civil flight observations.

{
  "flights_imported": 30,
  "valid_source_observations": 75510,
  "excluded_source_rows": 0,
  "development_flights": 12,
  "validation_flights": 9,
  "test_flights": 9,
  "validation_origins": 450,
  "test_origins": 439,
  "test_forecast_points_per_model": 1317,
  "individual_models": 6,
  "ensemble_models": 1
}

Measured and computed results

modelADE_mFDE_mRMSE_mMAE_coordinate_mcoverage95
RW34.79599357.40528241.42632820.4674110.96096
CV12.74391920.82719422.1855878.2067630.90653
CA18.12908935.42205529.65208211.4919210.883761
KF9.12169517.24209815.832155.7986830.904366
CRW9.27140817.24023515.4396845.926360.909744
OU180.270339237.539602208.814684116.086710.98021
ENSEMBLE9.5996117.40035515.115736.1198570.926349
Six individual methods and validation-fitted ensemble, identical held-out origins. GNSS is a noisy reference.
Six individual methods and validation-fitted ensemble, identical held-out origins. GNSS is a noisy reference.
Actual coverage of nominal Gaussian95percent regions; validation fitting does not guarantee test coverage.
Actual coverage of nominal Gaussian95percent regions; validation fitting does not guarantee test coverage.
Public display uses relative ENU and stride only; observations are not simulation truth.
Public display uses relative ENU and stride only; observations are not simulation truth.

Paired comparison and uncertainty

modelreferencemean_ADE_difference_mtwo_sided_exact_signflip_punitsholm_adjusted_p
RWCV22.0520750.00390690.023438
CACV5.3851710.00390690.023438
KFCV-3.6222230.00390690.023438
CRWCV-3.4725110.00390690.023438
OUCV167.526420.00390690.023438
ENSEMBLECV-3.1443080.00390690.023438

Intervals resample whole flight files; shared platform/circuit and unknown recording days limit independence. More complex methods and the ensemble are not assumed superior.

{
  "RW": {
    "ADE_interval95": {
      "lower": 33.394518634683514,
      "upper": 36.45540032492981,
      "resampling_unit": "whole flight file, equal weight",
      "replicates": 999,
      "seed": 20261106,
      "n_units": 9,
      "assumption": "Flight-file exchangeability/independence not guaranteed across unreported day groups; conditional interval, limited external generalization"
    },
    "coverage_interval95": {
      "lower": 0.951194561727825,
      "upper": 0.9719819626723475,
      "resampling_unit": "whole flight file, equal weight",
      "replicates": 999,
      "seed": 20261106,
      "n_units": 9,
      "assumption": "Flight-file exchangeability/independence not guaranteed across unreported day groups; conditional interval, limited external generalization"
    }
  },
  "CV": {
    "ADE_interval95": {
      "lower": 11.970185251147065,
      "upper": 13.572510260043504,
      "resampling_unit": "whole flight file, equal weight",
      "replicates": 999,
      "seed": 20261106,
      "n_units": 9,
      "assumption": "Flight-file exchangeability/independence not guaranteed across unreported day groups; conditional interval, limited external generalization"
    },
    "coverage_interval95": {
      "lower": 0.8928219540634288,
      "upper": 0.9195976862564671,
      "resampling_unit": "whole flight file, equal weight",
      "replicates": 999,
      "seed": 20261106,
      "n_units": 9,
      "assumption": "Flight-file exchangeability/independence not guaranteed across unreported day groups; conditional interval, limited external generalization"
    }
  },
  "CA": {
    "ADE_interval95": {
      "lower": 17.09672790656177,
      "upper": 19.133507993257894,
      "resampling_unit": "whole flight file, equal weight",
      "replicates": 999,
      "seed": 20261106,
      "n_units": 9,
      "assumption": "Flight-file exchangeability/independence not guaranteed across unreported day groups; conditional interval, limited external generalization"
    },
    "coverage_interval95": {
      "lower": 0.8665181003860317,
      "upper": 0.9010038011240665,
      "resampling_unit": "whole flight file, equal weight",
      "replicates": 999,
      "seed": 20261106,
      "n_units": 9,
      "assumption": "Flight-file exchangeability/independence not guaranteed across unreported day groups; conditional interval, limited external generalization"
    }
  },
  "KF": {
    "ADE_interval95": {
      "lower": 8.588941941202101,
      "upper": 9.715699860802555,
      "resampling_unit": "whole flight file, equal weight",
      "replicates": 999,
      "seed": 20261106,
      "n_units": 9,
      "assumption": "Flight-file exchangeability/independence not guaranteed across unreported day groups; conditional interval, limited external generalization"
    },
    "coverage_interval95": {
      "lower": 0.8873652966285815,
      "upper": 0.9187859249856266,
      "resampling_unit": "whole flight file, equal weight",
      "replicates": 999,
      "seed": 20261106,
      "n_units": 9,
      "assumption": "Flight-file exchangeability/independence not guaranteed across unreported day groups; conditional interval, limited external generalization"
    }
  },
  "CRW": {
    "ADE_interval95": {
      "lower": 8.723924360992173,
      "upper": 9.903148689362789,
      "resampling_unit": "whole flight file, equal weight",
      "replicates": 999,
      "seed": 20261106,
      "n_units": 9,
      "assumption": "Flight-file exchangeability/independence not guaranteed across unreported day groups; conditional interval, limited external generalization"
    },
    "coverage_interval95": {
      "lower": 0.8889613997153427,
      "upper": 0.9265915633254418,
      "resampling_unit": "whole flight file, equal weight",
      "replicates": 999,
      "seed": 20261106,
      "n_units": 9,
      "assumption": "Flight-file exchangeability/independence not guaranteed across unreported day groups; conditional interval, limited external generalization"
    }
  },
  "OU": {
    "ADE_interval95": {
      "lower": 170.895326803684,
      "upper": 190.87843474957631,
      "resampling_unit": "whole flight file, equal weight",
      "replicates": 999,
      "seed": 20261106,
      "n_units": 9,
      "assumption": "Flight-file exchangeability/independence not guaranteed across unreported day groups; conditional interval, limited external generalization"
    },
    "coverage_interval95": {
      "lower": 0.9689552046405913,
      "upper": 0.989076369213609,
      "resampling_unit": "whole flight file, equal weight",
      "replicates": 999,
      "seed": 20261106,
      "n_units": 9,
      "assumption": "Flight-file exchangeability/independence not guaranteed across unreported day groups; conditional interval, limited external generalization"
    }
  },
  "ENSEMBLE": {
    "ADE_interval95": {
      "lower": 9.085326886795325,
      "upper": 10.193450729001109,
      "resampling_unit": "whole flight file, equal weight",
      "replicates": 999,
      "seed": 20261106,
      "n_units": 9,
      "assumption": "Flight-file exchangeability/independence not guaranteed across unreported day groups; conditional interval, limited external generalization"
    },
    "coverage_interval95": {
      "lower": 0.9147342511883979,
      "upper": 0.9352277884893583,
      "resampling_unit": "whole flight file, equal weight",
      "replicates": 999,
      "seed": 20261106,
      "n_units": 9,
      "assumption": "Flight-file exchangeability/independence not guaranteed across unreported day groups; conditional interval, limited external generalization"
    }
  }
}

Robustness

conditionmodelADE_mmatched_baseline_ADE_morigins
context_noise2mRW34.98976134.795993439
context_noise2mCV13.18690412.743919439
context_noise2mCA23.08131318.129089439
context_noise2mKF23.9340849.121695439
context_noise2mCRW23.2605769.271408439
context_noise2mOU180.268998180.270339439
context_noise2mENSEMBLE22.6866699.59961439
context_missing30percentRW35.76946234.874378435
context_missing30percentCV12.86528712.78599435
context_missing30percentCA18.33421818.112987435
context_missing30percentKF9.2439759.115594435
context_missing30percentCRW9.5046229.270341435
context_missing30percentOU182.589058179.941936435
context_missing30percentENSEMBLE9.8308669.594352435

Method & parameters

# DME-001 — method

Kind: REAL EXPERIMENTAL DATA. Algorithm: dme-flight-1.0.

First30 sorted source GPS files; first12development, next9validation, last9test. File-disjoint, not recording-day-independent. Twenty past samples per origin, stride50; nearest observed targets1/3/5s within120ms; source gaps>2s rejected. WGS84 ECEF→local ENU horizontal, no altitude or Euclidean degrees. Six methods share identical origins and targets. q∈{.01,1,100}, R∈{1,10}, validationADE/NLL tie-break only. Covariance scale=validation equal-flight mean Mahalanobis²/2. Ensemble simplex minimizes validation equal-flight MSE; total covariance includes within-model and between-mean dispersion. ADE/FDE/RMSE/MAE/coverage aggregate equally over nine test files. Nominal95percent Gaussian ellipse (χ²₂), empirical coverage and999 whole-file bootstrap samples. Exact paired sign-flip512patterns, Holm correction over6comparisons. Robustness adds2m context noise or30percent missingness with untouched held-out reference and matched-origin baseline. HMM3 descriptive states fit development only on offline speed/acceleration/turn-rate features; not causal intent inference.

## Limits
- Recorded GNSS is a noisy reference, not known true state. Physical sensor calibration is unavailable.
- Flights share platform and circuit; recording-day groups are unavailable. File-disjoint splits prevent row leakage but do not prove external generalization or independent days.
- Gaussian nominal regions and validation scaling are empirically evaluated, not guaranteed confidence coverage.
- ADE averages sampled1/3/5second horizons, actual timestamp offsets recorded; no interpolation.
- All parameter and ensemble fitting use development/validation only; test outcomes are not tuning inputs.

## Source
{
  "source": "Zenodo IDF_DS",
  "doi": "10.5281/zenodo.16992976",
  "version": "v1.0",
  "archive_url": "https://zenodo.org/api/records/16992976/files/Speedybee%20DataSet.zip/content",
  "archive_total_bytes": 580834225,
  "archive_declared_md5_not_whole_verified": "md5:fa6210078d8f615118027a5310dfc99c",
  "whole_archive_downloaded": false,
  "license": "CC-BY-4.0",
  "authors": [
    "García Gascón, César"
  ],
  "concept_dataset_flights_claimed": 240,
  "readme_speedybee_flights_claimed": 120,
  "actual_gps_members": 111,
  "selected_by_rule": "First30lexicographically sorted GPS files before values; no outcome selection",
  "members": [
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  "excluded": [],
  "source_metadata_sha256": "61f648b3f9e0cebd3b40da4aa0f937fdaf376bb65b9d6c46239a69aa6c0a5a01",
  "imported_flights": 30,
  "raw_source_bytes": 7416149,
  "documentation_caveat": "Speedybee README describes120flights; actual archive has111GPS files. Do not conflate archive layouts or claim all240flights analyzed."
}

Validation and reproducibility

# Reproduce DME-001

Use Python3.12 and the pinned lock. From the distribution root:

    python -m dynamics.cli run DME-001 --data /your/local/dynamics-data
    python -m dynamics.cli reproduce JOB_UUID --data /your/local/dynamics-data

The second command rehashes every acquired source object, reparses original selected ZIP bytes and recomputes mathematical results offline, with the original manifest parameters. Missing or altered cached bytes fail explicitly; a new download is a new acquisition, not substitution for an old vintage. The results_sha256 excludes measured execution timing but includes all scientific results and source identities. Public source packages do not contain multi-GB third-party archives. Dataset source availability may change. All seeds/parameters/dependency versions and source hashes are in the manifest.

Scientific result SHA-256: 1f0238e055f9f9a1d601982e68e3e6406f6148a4e768ca17fd0cdfed30427280. Numerical correctness is evaluated with independent controls and source replay; scientific validity remains bounded by source quality and model assumptions.

Limits

Recorded GNSS is a noisy reference, not known true state. Physical sensor calibration is unavailable.
Flights share platform and circuit; recording-day groups are unavailable. File-disjoint splits prevent row leakage but do not prove external generalization or independent days.
Gaussian nominal regions and validation scaling are empirically evaluated, not guaranteed confidence coverage.
ADE averages sampled1/3/5second horizons, actual timestamp offsets recorded; no interpolation.
All parameter and ensemble fitting use development/validation only; test outcomes are not tuning inputs.

Sources & attribution

{
  "source": "Zenodo IDF_DS",
  "doi": "10.5281/zenodo.16992976",
  "version": "v1.0",
  "archive_url": "https://zenodo.org/api/records/16992976/files/Speedybee%20DataSet.zip/content",
  "archive_total_bytes": 580834225,
  "archive_declared_md5_not_whole_verified": "md5:fa6210078d8f615118027a5310dfc99c",
  "whole_archive_downloaded": false,
  "license": "CC-BY-4.0",
  "authors": [
    "García Gascón, César"
  ],
  "concept_dataset_flights_claimed": 240,
  "readme_speedybee_flights_claimed": 120,
  "actual_gps_members": 111,
  "selected_by_rule": "First30lexicographically sorted GPS files before values; no outcome selection",
  "members": [
    {
      "name": "Speedybee DataSet/processed/GPS/Lap001_gps.csv",
      "bytes": 228258,
      "crc32": "2edff5e8",
      "sha256": "611f2d9417f94eaf6399d77bb971cd0dd2eba6c7dac9a8fce8e34bc87474a22e"
    },
    {
      "name": "Speedybee DataSet/processed/GPS/Lap002_gps.csv",
      "bytes": 231394,
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  "source_metadata_sha256": "61f648b3f9e0cebd3b40da4aa0f937fdaf376bb65b9d6c46239a69aa6c0a5a01",
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  "documentation_caveat": "Speedybee README describes120flights; actual archive has111GPS files. Do not conflate archive layouts or claim all240flights analyzed."
}

Execution evidence

{
  "acquisition_seconds": 0.2941706250421703,
  "analysis_seconds": 36.02503625000827,
  "models": {
    "RW": {
      "test_forecast_seconds": 0.03504662500927225,
      "forecast_points": 1317
    },
    "CV": {
      "test_forecast_seconds": 0.07636908302083611,
      "forecast_points": 1317
    },
    "CA": {
      "test_forecast_seconds": 0.08068858296610415,
      "forecast_points": 1317
    },
    "KF": {
      "test_forecast_seconds": 0.9414666250231676,
      "forecast_points": 1317
    },
    "CRW": {
      "test_forecast_seconds": 0.9354272079654038,
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    },
    "OU": {
      "test_forecast_seconds": 0.7737172080087475,
      "forecast_points": 1317
    }
  },
  "total_seconds": 36.638933082984295,
  "network_bytes_this_run": 0,
  "source_response_bytes": 2153015,
  "process_peak_rss_bytes": 227229696,
  "rss_scope": "Whole process lifetime peak; no unmeasured hard RSS guarantee"
}