Geometry
Which satellites can you see, and how good is their geometry?
Pick a site, a time and a mix of global navigation satellite systems (GNSS) and a low Earth orbit (LEO) layer, draw the skyline that blocks your view, and see the dilution of precision (DOP) and the position error it implies. Every number comes from the Kshana engine running in this browser. What this shows.
Advisory software, not type-approved navigation equipment (IEC 61108, IEC 61162): the operator remains responsible for the navigation of the vessel. DOP, the error ellipse and the Monte Carlo cloud are geometry under a stated error model (independent, equal, zero-mean Gaussian range errors), not a prediction of a receiver's real error, which also has biases, multipath and non-line-of-sight (NLOS) errors.
Starting the engine…
Skyplot
A representative sky, not the sky of that date at that place. The constellations are the engine's nominal presets, whose relative phases come from different reference epochs.
Zenith in the centre, the horizon on the rim, north up. Filled marks are satellites in the solution; hollow marks are hidden by the mask or the skyline, or not used.
Dilution of precision
How much the geometry multiplies the range error. Lower is better; about 1 is excellent, above 6 is poor.
Horizontal position error
The error ellipse from the geometry's covariance for the chosen σUERE, at 1-sigma and 95 % (both from the engine), over a seeded Monte Carlo cloud of least-squares solutions. East to the right, north up, in metres.
Satellites, as a table The same satellites as the skyplot.
| Constellation | Satellite | Azimuth, ° | Elevation, ° | In the solution |
|---|
What this shows
- The skyplot is the sky seen from the place: each mark is a satellite at its azimuth (compass bearing) and elevation (angle above the horizon). Colour and shape both say which constellation it belongs to.
- Dilution of precision (DOP) is how much the satellites' geometry multiplies the error of each range measurement. Satellites spread across the sky give low DOP; satellites bunched together, or all high overhead, give high DOP. GDOP is the geometric DOP (position and time), PDOP the three-dimensional position DOP, HDOP horizontal, VDOP vertical and TDOP the receiver clock (time) DOP.
- Position error ≈ σUERE × DOP. The user-equivalent range error (σUERE) is the one-sigma error of each range: satellite clock and orbit, the atmosphere, multipath and receiver noise together. Multiplying it by HDOP gives the one-sigma horizontal error, and by VDOP the vertical.
- The error ellipse is the horizontal error from the geometry's covariance, σUERE² times the east-north block of the DOP matrix: longer along the directions the satellites constrain least. It is drawn at 1-sigma and at 95 % (2.448 times larger). The Monte Carlo cloud is many least-squares solutions with seeded random range errors through the same geometry; its RMS is shown beside σUERE × HDOP, with the share of points inside the 95 % ellipse. The same seed always gives the same cloud.
- The skyline is what blocks the sky: buildings, quays, cranes or mountain sides. A satellite behind it is not used. Pick a preset (illustrative dimensions, not surveys of any real place), describe a street canyon by its width and building heights, or draw your own on the skyplot. A skyline removes satellites from the line of sight and nothing more: no reflections, diffraction or multipath.
- What it leaves out. The sky is representative: nominal constellations whose phases come from different reference epochs, not the real satellites on a date or their health. No signal strength, multipath or interference. The figures are MODELLED, not validated against a receiver at the site, and say nothing about how a real receiver will do.
- The engine runs here as WebAssembly. Nothing is fetched from another site and nothing you set is sent anywhere.