Sect_8.1.1

8.1.1 GPS Baseline Processing

INTRODUCTION

A GPS campaign generally involves the use of several GPS receivers deployed over a network of points for a number of observation sessions.

This chapter will focus on single baseline processing as this is the fundamental unit of a GPS solution. Most commercial GPS data processing software will accept only the simultaneous phase data collected by two GPS receivers. This is because the observable modelling necessary for GPS phase data reduction involves two stations -- defining a baseline. This is obvious for the double-differenced and triple-differenced phase models, but perhaps less obviously for the case of the undifferenced model. It is however stated, without proof, that in order to estimate the clock parameters, appearing explicitly in the undifferenced observation eqns (6.1-13), data from several sites to several satellites must be collected and processed together. In section 6.1.1 comments were made regarding the equivalence of the "undifferenced data processing approach" and the "double-differenced data processing approach" to GPS phase data reduction. (It is beyond the scope of these notes to algebraically prove that the result is exactly equivalent to processing double-differenced data.) To differentiate between the two approaches, the former may be referred to as involving implicit differencing (carried out in the solution algorithm), while the conventional double- and triple-differences are generated by explicit differencing.

As many of the remarks about double-differenced data (baseline) solutions hold equally whether the differencing is "implicit" or "explicit", it is not necessary to distinguish between undifferenced and double-differenced data models for baseline solutions. They will be simply referred to as the double-differenced mode of data processing to differentiate it from the triple-differenced solution mode.

An entire network may be built up either from a large number of independently processed baselines, or, more efficiently, in a simultaneous adjustment in which the set of differenced observations is generated in a mathematically correlated fashion. This aspect of GPS data reduction will be discussed in Chapter 9. An understanding of the nature of a single baseline solution is nevertheless vital as many of the concepts, for example "ambiguity resolution", are central even to network solutions.

Section 7.3 described some of the data pre-processing procedures. It will now be assumed that all the data is "clean", and free of cycle slips. The next step is the phase data processing in single baseline mode. The main steps of a baseline solution using phase data are:

SETUP

Preparation: apriori coordinates, ephemeris file to be used, baseline to be processed (if more than one observed in a session), data file names, antenna height and offsets, etc.
Selection of parameters: this is dependent on the baseline to be processed, the ambiguity model used in the software, differencing scheme adopted, etc.
Selection of options: apriori standard deviation of parameters and observations, criteria for data rejection, data reduction flags, whether correlations are to be considered, elevation cutoff, satellites to be excluded from solution, differencing strategy to be used, etc.

PROCESSING There are three types of phase solutions:

provides good apriori baseTriple-Difference Solution:line solution even in the presence of cycle slips in the phase data.
where the ambiguity parameters are "free" Double-Difference Solution (Ambiguity-free):to take whatever values the Least Squares solution gives.
Double-Difference Solution (Ambiguity-fixed): where the ambiguity parameter values are fixed to integer values (and in the process converting ambiguous phase data to range data).

OUTPUT

Coordinate parameters as: Cartesian (x,y,z) or geodetic (,,h) values in the WGS84 datum, baseline components, for ground mark and/or antenna centres.
Estimated standard deviation and correlation matrix (or VCV matrix) of parameters.
Indicators of quality of the solution.

Although each of these will be discussed further in subsequent sections and chapters, it is necessary to first make a clear distinction between an ambiguity-free and an ambiguity-fixed solution.

There are two types of double-difference phase data solutions:

AMBIGUITY-FREE SOLUTION (also known as a bias or ambiguity "float" solution), in which the parameters to be estimated are the non-reference coordinates (one end of a baseline) and the ambiguity parameters.
AMBIGUITY-FIXED SOLUTION (or "bias-fixed" solution), in which some or all the ambiguity parameters have been "resolved" to their integer values.

The AMBIGUITY-FREE solution is generally the first step. If after this solution the values of the ambiguity parameters (which theoretically should be integers) may be close to integer values (but not exactly due to the presence of residual biases such as atmospheric refraction, orbit error, multipath, etc.).

If the correct ambiguity values are identified, they can be held fixed in the subsequent AMBIGUITY-FIXED solution. Such a solution is very strong as it only contains the station coordinate parameters (hence it is equivalent to processing unambiguous and precise ranges).

Note: it may not always be possible to attempt the ambiguity-fixed solution!

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© Chris Rizos, SNAP-UNSW, 1999