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Mathematical Models and GNSS Interference

GNSS Solutions is a regular column featuring questions and answers about technical aspects of GNSS. Readers are invited to send their questions to the columnists, Professor Gérard Lachapelle ( and Assistant Professor Mark Petovello (, Department of Geomatics Engineering, University of Calgary, who will find experts to answer them.

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Q: What does “geometry-based” and “geometry-free” mean in the context of GNSS?

A: The geometry-based model is the usual mathematical model for solving high-precision positions from phase (and code) data using a relative GNSS receiver setup.

The relative receiver-satellite geometry plays a crucial role and has a significant effect on the precision of the parameters to be determined, which are, among others, the carrier phase ambiguities and the relative receiver position.

The geometry-free model dispenses this receiver-satellite geometry: it solves for the receiver-satellite ranges instead of positions. However, ambiguity resolution is still possible using this model.

(For the rest of Dennis Odijk's answer to this question, including figures and graphs, please download the complete article using the pdf link above.)

Q:What are the main classes of interference that can degrade the GNSS signals? What are the possible countermeasures?

A: The extremely low received power of a GNSS signal makes it vulnerable to different kinds of interference, such as spurious and out-of-band emissions. These emissions can originate from telecommunication and electronic systems, either operating in adjacent bands or working at frequencies relatively far from the GNSS bands.

Interference can be intentional or unintentional. Intentional interference can be generated easily by GNSS jammers that adopt different strategies for jamming GNSS receivers, such as the emission of strong continuous waves (CW) or strong Gaussian noise occupying the same frequencies as the GNSS signal. Unintentional interference can be generated by a variety of sources, because every electronic device potentiallys emit strong electromagnetic signals that can jam the GNSS receiver.

Examples of unintentional interference are UHF and VHF television, VOR (VHF omnidirectional radio-range), and ILS (instrument landing system) harmonics and spurious signals caused by power amplifiers working in their non-linear region or by oscillators present in many electronic devices. Regardless of their source, interfering signals can generally be classified as pulsed, continuous wave, or swept. . .

. . . For each kind of interference, an appropriate countermeasure exists that exploits the time-frequency characteristics of the disturbing signal. One such method is based on spatial diversity, which effectively mitigates interference but is not discussed in detail here. Briefly, however, these techniques exploit the correlation between the received signals at different spatially separated antennas in order to minimize the interference impact. A short introduction to this topic can be found in “GNSS Solutions” of April 2006.

Aside from spatial diversity, interference mitigation techniques can be divided into time, frequency, and time-frequency algorithms according to the specific domain in which they operate.

(For the rest of Daniele Borio's and Letizia Lo Presti's answer to this question,including
figures and graphs, please download the complete article using the pdf link above.)

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