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Error Sources

Error Sources

Pseudorange Calculation

Multiple issues affect the calculation of the pseudorange:

  • the satellite clock has an offset, which is known (part of the navigation message)
  • the receiver clock has an offset, which is unknown
  • the ionosphere causes a delay (due to a lower speed of light), which is unknown
  • there might be other errors, such as multipath, which are unknown

Any of these issues will cause the calculated pseudorange to be inaccurate. 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

One of the major error sources in GPS is due to the ionosphere, which contains free electrons that cause the speed of light to be lower than in vacuum.

The ionospheric delay may be highly variable, as a function of both time and space. In terms of distance ranging, it can go from a few meter to hundreds of meters, and is maximum round the geomagnetic equator around local noon, and during solar maxima.

The ionosphere delay scales, to a very good approximation, with the inverse of the square of the radio frequency of the signal, so using two different frequencies allows to create the so­-called ionosphere-­free range measurements. This is why GPS satellites were originally designed to transmit ranging signals on both the L1 (1575.42 MHz) and L2 (1227.60 MHz) frequency.

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 1: 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