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Error Sources

Error Sources

Principle sources of GNSS errors
Figure 1: Principle sources of GNSS errors

Pseudorange Calculation

Multiple issues affect the calculation of the pseudorange:

  • satellite clock offset (known).
  • receiver clock offset (unknown).
  • ionosphere delay (unknown).
  • other errors, such as multipath (unknown).

The calculation is very sensible since \(c \approx 3 \times 10^8 \, \text{m/s}\), and a 1 µs error will cause a 300 m error in the calculated distance, since we have:

\[ p_{r,s} = r_{r,s} + c \cdot (\delta t_s - \delta t_r) \]

where:

  • \(p_{r,s}\): pseudorange
  • \(r_{r,s}\): actual range
  • \(\delta t_s\): satellite clock offset
  • \(\delta t_r\): receiver clock offset

Ionosphere Delay

Ionospheric delay:

  • Is due to free electrons in the ionosphere.
  • Is highly variable (depends on time and space).
  • Ranges from a few meters to hundreds of meters.
  • Is maximum near geomagnetic equator, around local noon and during solar maxima.
  • Is proportional to \(1 / \text{frequency}^2\).
  • Can be estimated using two frequencies. This is why satellites emit at L1 (1575.42 MHz) and L2 (1227.60 MHz).

Masking Angle

GNSS receivers ignore signals from below a certain elevation, making them prone to errors (typically between 5° and 15°).

Errors due to terrain, buildings, and elevation angle
Figure 2: Errors due to terrain, buildings, and elevation angle

GNSS Augmentation Systems

GNSS augmentation systems supply differential corrections and integrity alerts that meet the needs of safety-critical applications. There are two types:

Criteria Space-based augmentation systems (SBAS) Ground-based augmentation systems (GBAS)
Coverage Large country or small continent Local area (e.g. an airfield)
Broadcast Geostationary satellites Ground-based transmitters
Precision Lower than GBAS Higher than SBAS