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Preprocessing & Geometry 🛰️

This stage transforms raw observations into high-quality, geometrically-referenced time series, determining exactly where the ionospheric observations took place.

Ephemeris Preparation 📐

The first step is filtering global navigation messages and preparing ephemerides. Beyond preparing data for orbital propagation, this function enriches the GNSSContext with GLONASS frequency_channels (if R is among the requested constellations).

from pytecgg.satellites import prepare_ephemeris

ephem_dict = prepare_ephemeris(nav_dict, ctx=ctx)

Signal Processing 🔎

Starting from the basic observables and given a GNSSContext, PyTECGg can compute the following linear combinations, useful for removing biases or isolating physical effects:

  • Geometry-Free Linear Combination (GFLC), sensitive to ionospheric effects.
  • Ionosphere-Free Linear Combination (IFLC), used to eliminate the ionospheric delay.
  • Melbourne-Wübbena (MW) combination, useful for cycle-slip detection and ambiguity resolution.
from pytecgg.linear_combinations import calculate_linear_combinations
from pytecgg.tec_calibration import extract_arcs

# Compute selected linear combinations
df_lc = calculate_linear_combinations(
    df_obs,
    ctx=ctx,
    combinations=["gflc_phase", "gflc_code", "mw"]
)

# Identify continuous arcs, detect cycle slips
# and loss-of-lock events
df_arcs = extract_arcs(
    df=df_lc,
    ctx=ctx,
    threshold_abs=10,
    threshold_std=10,
    threshold_jump=5
)

Processing parameters and options:

  • combinations: defines which signals to compute. Options include GFLC (gflc_phase, gflc_code), IFLC (iflc_phase, iflc_code), and MW (mw).
  • extract_arcs: outputs a Polars DataFrame containing unique arc identifiers (id_arc_valid) and arc-levelled GFLC values, essential for accurate bias estimation.
  • threshold_abs & threshold_std: absolute and standard deviation thresholds used on the MW combination to detect cycle slips.
  • threshold_jump: tolerance for detecting and correcting residual jumps within an arc.
  • max_gap: an be explicitly set or automatically inferred from the data; if the time gap between consecutive epochs becomes too large, a loss-of-lock is declared

Orbital Propagation 🌍

To locate the ionospheric samples, we must first compute the satellite positions in the ECEF frame.

from pytecgg.satellites import satellite_coordinates

# Compute satellitess ECEF coordinates
df_coords = satellite_coordinates(
    sv_ids=df_arcs["sv"],
    epochs=df_arcs["epoch"],
    ephem_dict=ephem_dict
)

# Join coordinates with the observation data
df_geom = df_arcs.join(df_coords, on=["sv", "epoch"], how="left")

satellite_coordinates provides the X, Y, Z positions of each satellite for every observed epoch.

Ionospheric Pierce Point (IPP) 📌

The IPP is the theoretical intersection between the satellite–receiver line of sight and a thin-shell ionospheric model at the altitude defined in the GNSSContext (default: 350 km).

from pytecgg.satellites import calculate_ipp

df_final = calculate_ipp(df_geom, ctx=ctx, min_elevation=20)

This function appends geographic coordinates (lat_ipp, lon_ipp) and the mapping function values to the Polars DataFrame. The min_elevation argument sets a cut-off angle (in degrees) to filter satellites elevation.

Elevation Masking

Filtering out elevations below 20° is highly recommended to feed cleaner data to the calibration model, as low-elevation signals are more susceptible to multipath and noise.

Wrapping up 🏁

After completing all the preprocessing steps, your DataFrame is ready for the calibration engine: it now contains a rich set of features, that you can inspect using Polars selection methods.

As an example, we may want to inspect arc metadata, like the unique identifier for each continuous observation sequence (id_arc_valid); the corrected and levelled GFLC (gflc_levelled, in TECu); and some geometric features, like the geographic IPP location (lat_ipp, lon_ipp) and the viewing geometry from the station (azi, ele).

import polars as pl

df_final.filter(
    pl.col("id_arc_valid").is_not_null()
).select(
    [
        "epoch",
        "sv",
        "id_arc_valid",
        "gflc_levelled",
        "lat_ipp",
        "lon_ipp",
        "azi",
        "ele",
    ]
).head()
epoch sv id_arc_valid gflc_levelled lat_ipp lon_ipp azi ele
00:00:00 E02 "bneu_e02_001" 42.39 20.40 96.31 257.73 26.55
00:00:00 E03 "bneu_e03_001" 42.11 23.51 99.84 314.36 47.16
00:00:00 E05 "bneu_e05_001" 44.97 20.75 101.93 179.50 73.10
00:00:00 E16 "bneu_e16_001" 11.03 23.88 102.24 27.57 52.26
00:00:00 E25 "bneu_e25_001" 34.64 22.97 100.76 321.15 59.68