All demonstrationsMULTI-OBSERVER TRACKS / RUST CPU

Where do the sightlines meet?

Combine timed angular observations from different locations to estimate a moving object’s 3D position and velocity, with residuals and explicit uncertainty limits.

triangulate_tracksTry the real call

Concept artwork · not calculation evidence

01 / UNDERSTAND THE METHOD

Make sight lines tangible.

ILLUSTRATION · NOT A CALCULATION

INPUT SIGHT LINES · NO FIT YETPerspective

Preparing the interactive view…

Drag to orbit · pinch or scroll to zoom · right-drag to pan. Camera rotation does not advance time. The input preview sweeps through each supplied angle sequence independently. It does not align clocks or fit a trajectory. Ray lengths are illustrative; no range is estimated here. Observer markers are enlarged for visibility.

Teaching animation only · no MCP request

02 / ASK THE ACTUAL TOOL

Make it your experiment.

SYNTHETIC OBSERVATION CASES

Change the geometry or clock assumption. Selecting a case loads its inputs; run it to see the actual verdict.

Complete tool arguments

{
  "observers": [
    {
      "lat": 48.85,
      "lon": 2.35,
      "elevation_m": 35,
      "clock_offset_s": 0,
      "sigma_az_deg": 0.2,
      "sigma_el_deg": 0.2,
      "samples": [
        {
          "t_s": 0,
          "azimuth_deg": 101.991260935,
          "elevation_deg": 14.447682585
        },
        {
          "t_s": 10,
          "azimuth_deg": 93.467590277,
          "elevation_deg": 14.732612639
        },
        {
          "t_s": 20,
          "azimuth_deg": 84.786897815,
          "elevation_deg": 14.70245413
        },
        {
          "t_s": 30,
          "azimuth_deg": 76.336410848,
          "elevation_deg": 14.362974947
        },
        {
          "t_s": 40,
          "azimuth_deg": 68.446289854,
          "elevation_deg": 13.773863939
        },
        {
          "t_s": 50,
          "azimuth_deg": 61.324990456,
          "elevation_deg": 13.022637731
        },
        {
          "t_s": 60,
          "azimuth_deg": 55.051414611,
          "elevation_deg": 12.194843666
        },
        {
          "t_s": 70,
          "azimuth_deg": 49.607028444,
          "elevation_deg": 11.356342386
        },
        {
          "t_s": 80,
          "azimuth_deg": 44.917906873,
          "elevation_deg": 10.549458666
        },
        {
          "t_s": 90,
          "azimuth_deg": 40.888140057,
          "elevation_deg": 9.79700007
        },
        {
          "t_s": 100,
          "azimuth_deg": 37.420214884,
          "elevation_deg": 9.108372913
        }
      ]
    },
    {
      "lat": 48.85,
      "lon": 2.45,
      "elevation_m": 35,
      "clock_offset_s": 0,
      "sigma_az_deg": 0.2,
      "sigma_el_deg": 0.2,
      "samples": [
        {
          "t_s": 0,
          "azimuth_deg": 258.008739065,
          "elevation_deg": 14.447682585
        },
        {
          "t_s": 10,
          "azimuth_deg": 266.532409723,
          "elevation_deg": 14.732612639
        },
        {
          "t_s": 20,
          "azimuth_deg": 275.213102185,
          "elevation_deg": 14.70245413
        },
        {
          "t_s": 30,
          "azimuth_deg": 283.663589152,
          "elevation_deg": 14.362974947
        },
        {
          "t_s": 40,
          "azimuth_deg": 291.553710146,
          "elevation_deg": 13.773863939
        },
        {
          "t_s": 50,
          "azimuth_deg": 298.675009544,
          "elevation_deg": 13.022637731
        },
        {
          "t_s": 60,
          "azimuth_deg": 304.948585389,
          "elevation_deg": 12.194843666
        },
        {
          "t_s": 70,
          "azimuth_deg": 310.392971556,
          "elevation_deg": 11.356342386
        },
        {
          "t_s": 80,
          "azimuth_deg": 315.082093127,
          "elevation_deg": 10.549458666
        },
        {
          "t_s": 90,
          "azimuth_deg": 319.111859943,
          "elevation_deg": 9.79700007
        },
        {
          "t_s": 100,
          "azimuth_deg": 322.579785116,
          "elevation_deg": 9.108372913
        }
      ]
    }
  ]
}

Arrays, coordinates and nested contracts remain editable here. Units and limits are checked by the real tool.

Runs only when you press the button. Input edits discard the previous displayed result. Public compute limits apply.

KNOW WHAT THE RESULT MEANS

Useful evidence needs boundaries.

Stationary observers and constant velocity on a 6371.0088 km spherical Earth are explicit assumptions. These are supplied angle measurements, not automatic video or photo analysis.
Refraction is not modelled; low-elevation samples are flagged. Clock offsets must be supplied, and systematic biases can be partly absorbed by a two-observer fit.
Reported standard deviations are local, model-based approximations using the declared errors. They do not include unmodelled refraction, sensor bias or clock error and are not independently calibrated accuracy guarantees.
The reduced chi-square cutoff of 9 is an explicit screening convention. Inconsistent concerns the supplied single-object motion model, never an accusation or a conclusion about origin.

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