Broadcast-ephemeris accuracy: compare a broadcast navigation product against a precise SP3 product over a window.

This is the standard broadcast-orbit / clock accuracy check (the orbit and clock pieces of the signal-in-space range error, SISRE). For each satellite at each epoch it differences the broadcast-evaluated ECEF position and clock against the precise SP3 values, decomposes the position error into radial / along-track / cross-track (RAC) components, and summarizes the differences as RMS and maximum statistics per satellite and overall.

Both products are evaluated through Orbis.GNSS.Ephemeris, so the frame (ITRF/IGS ECEF, meters), the time scale (GPST), and the clock sign convention (positive = satellite clock ahead of system time) are exactly as documented there. Only epochs where both sources return a valid state contribute to the statistics; an epoch missing from either product is skipped, never extrapolated.

RAC frame

The radial/along-track/cross-track unit vectors are built from the precise state: radial along the position vector, cross-track along the orbital angular momentum r x v, and along-track completing the right-handed triad. The SP3 position/clock interpolation does not expose a velocity, so the velocity is derived by a centered finite difference of the precise position ((r(t+dt) - r(t-dt)) / 2dt, falling back to a one-sided difference at a window edge). The position-difference vector broadcast - precise is projected onto this triad.

Expected magnitudes

GPS LNAV broadcast orbits differ from IGS precise orbits at roughly the 1-2 m RMS level (3D), dominated by the along-track and radial components; Galileo and BeiDou MEO are comparable. A result far outside this band (tens of meters or more) indicates a parse or evaluation defect rather than normal broadcast error.

The broadcast models follow IS-GPS-200 (GPS LNAV), the Galileo OS-SIS-ICD, and the BeiDou BDS-SIS-ICD; the precise product is SP3-c / SP3-d (IGS).

Example

{:ok, broadcast} = Orbis.GNSS.Broadcast.load("BRDC.rnx")
{:ok, sp3} = Orbis.GNSS.SP3.load("igs.sp3")

report =
  Orbis.GNSS.BroadcastComparison.compare(broadcast, sp3, ["G01", "E11"], %{
    from: ~N[2020-06-25 02:00:00],
    to: ~N[2020-06-25 04:00:00],
    step_s: 300
  })

report.overall.orbit_3d_rms_m   # 3D orbit RMS over all satellites, meters
report.per_satellite["G01"].radial_rms_m

Broadcast-vs-precise on a sample day

Comparing the GPS LNAV broadcast message against the GBM precise SP3 product for 2020 day-of-year 177 — all GPS satellites over a multi-hour window at a 15 min step — gives an overall 3D orbit RMS of about 1.5 m (max ~4 m), split as roughly 1.1 m radial / 0.9 m along-track / 0.5 m cross-track, the expected GPS broadcast accuracy. The raw clock differences (clock_rms_m) are larger (several meters) because the broadcast and precise clocks are referenced to different time datums, which differ by a common per-epoch offset that drifts over the day. clock_datum_removed_rms_m removes that common offset (the per-epoch median over satellites) and reports the actual signal-in-space clock error, which is several times smaller. The same call works against a broadcast product with no change of shape, so mix gnss.broadcast_diff --nav BRDC.rnx --sp3 igs.sp3 --from ... --to ... prints this table from the command line.