Time and Frequency Measurements
Using the Global Positioning System
Michael A. Lombardi, Lisa M. Nelson, Andrew N. Novick,
Victor S. Zhang
National Institute of Standards and Technology
Time and Frequency Division
This paper describes how Global Positioning System (GPS) satellite signals are used in time and frequency metrology. It discusses how a GPS receiver can provide a reference signal for frequency calibrations and time synchronization. It also explains the several types of time and frequency measurements that utilize GPS signals. These include one-way or direct reception measurements, single and multi-channel commonview measurements, and carrier phase measurements. A discussion of how GPS signals can provide traceability to national and international standards is also provided.
The basic carrier-phase equation (Equation 1) shows
the parameters that must be determined in the analysis.
The analysis software makes it possible to make a good
estimate of most parameters. Generally, the number of
cycle slips and the atmospheric delays are the most
difficult parameters to determine.
R
S = g + cS - cR+ trop - ion + mult + cp + NR
S(1)
where,
= carrier wavelength, c/f, R
S = carrier phase observable for satellite S and receiver R,
g = geometric range, √((XS-XR)2+(YS-YR)2 +(ZS-ZR)2,
S = satellite clock error
R = receiver clock error
trop = propagation delay due to troposphere,
ion = propagation delay due to ionosphere,
mult = multipath error,
cp =unmodelled errors and receiver noise,
NR
S= carrier phase ambiguity or bias.
The above shows that no magic corrections are required for GPS to function, and that GPS requires reference to real and palpable national standards rather than to imaginary concerns.
The above formula is for the carrier-phase GPS that is accurate to a millimeter. That is the precision form of GPS.
Whereas the common GPS is accurate <10 meters and is the Course Acquisition GPS.
The variable symbols didn't translate symbolically to this post format..
However, the description of each variable clearly what natural parameters are required.
Whether you can find this paper on the internet I don't know.