lkd-aerospace
Inside GNSS: Engineering Solutions from the Global Navigation Satellite System Community
GPS Galileo Glonass BeiDou Regional/Augmentation
NovAtel
essp
unicore
Inside Unmanned Systems
Inside Unmanned Systems
Thought Leadership Series
GNSS Sol Header_0_0.jpg

The Math of Ambiguity

“GNSS Solutions” is a regular column featuring questions and answers about technical aspects of GNSS. Readers are invited to send their questions to the columnist, Dr. Mark Petovello, Department of Geomatics Engineering, University of Calgary, who will find experts to answer them. mark.petovello@ucalgary.ca

Share via: SlashdotSlashdot   TechnoratiTechnorati   The Math of Ambiguity (Inside GNSS)TwitterTwitter   FacebookFacebook

Q: What is the acquisition ambiguity function and how is it expressed mathematically?

A: One of the main tasks of a GNSS receiver is the acquisition of the signals-in-space (SISs) of all the satellites in view. This operation is based on the evaluation of a 2-D correlation function, called the ambiguity function (AF), which allows both the satellite detection and estimation of the received signal parameters, namely the code phase offset (code offset) and Doppler frequency/shift.

The AF is evaluated for each PRN code across all possible combinations of local code offset  and Doppler shift. This concept was well described in Michael Braasch’s “GNSS Solutions” contribution in the March-April 2007 issue of Inside GNSS.

In order to decide on the presence or absence of the searched satellite, the maximum absolute value of the resulting AF is then compared with a predefined threshold. In fact, if the PRN code sought is present in the SIS the AF exhibits a well-defined peak.

. . .

At this point a number of questions arise. What is the validity region of this approximation in the plane (∆τ,∆f)? Is it possible to have a closed-form expression valid in the whole plane (∆τ,∆f)? It is possible to obtain a similar formula for the cross-correlation terms?

Why do we ask these questions? The fact is that new scenarios with new applications are appearing every day within the satellite navigation world. Most of these require very demanding receiver performance (for example, the capability of dealing with degraded scenarios, indoor navigation, and so forth) and new block processing techniques.

In some cases we can approach the study of these new scenarios with a variety of theoretical tools, and the results can eventually be validated by simulation or by real-life experiments. In these cases to have a closed-form expression of the AF, together with its quality of approximation, would greatly help the study — and thus solution — of the problem.

(For Letizia Lo Presti and Beatrice Motella’s complete answer to this question, including formulas and tables, please download the full article using the pdf link above.)

Copyright © 2017 Gibbons Media & Research LLC, all rights reserved.

China Satellite Navigation Conference
Signals
Trimble
Trimble
Sensonor
NavtechGPS
Spectracom
Summit
CAST
NovAtel
globe Copyright © Inside GNSS Media & Research LLC. All rights reserved.
157 Broad Street, Suite 318 | Red Bank, New Jersey USA 07701
Telephone (732) 741-1964

Problems viewing this page? Contact our webmaster.