Bernese GPS Software Version 5.0 - Bernese GNSS Software

7. Parameter Estimation
7.1 Introduction
Parameter estimation in the Bernese GPS Software is based on Least-Squares Estimation
(LSE). The two main programs in the software package allowing for the adjustment of
model parameters to GNSS observations are GPSEST (”Menu>Processing>Parameter estimation”)
and ADDNEQ2 (”Menu>Processing>Normal equation stacking”). The first of the two programs processes
the observations. It sets up the observation equations and solves the normal equation
(NEQ) while ADDNEQ2 manipulates and combines solutions on the normal equation level.
ADDNEQ2 is discussed in more detail in Chapter 9. This chapter provides general information
for program GPSEST, details on the estimation of the various parameters available in
the Bernese GPS Software may be found in the following chapters.
GPSEST offers many processing options. Additional options are available in program
ADDNEQ2 such as datum definition by means of free network condition, writing of coordinate
SINEX file, or estimation of station velocities. On the other hand a number of
parameters are only supported by GPSEST, in particular epoch parameters (clock corrections,
kinematic coordinates, stochastic ionosphere parameters) and phase ambiguities. An
overview on the availability of the parameters supported by the Bernese GPS Software,
Version 5.0 is given in Table 1.1.
As all programs in the Bernese GPS Software, GPSEST is running in batch mode, i.e., it
assumes that all observations are available in files. No real-time or data-streaming mode is
supported. The program furthermore assumes that good a priori values for all parameters are
available. The program does not iterate but computes the improvements of the parameters
from the linearized observation equations. If iteration is necessary the program has to be
run again using the improved parameters as a priori values.
7.2 Basic Theory of Least-Squares Estimation
The (linearized) observation equations in the Gauss-Markoff Model of full rank are given,
e.g., by [Koch, 1988]
E(y) = Ap ; D(y) = σ 2 P −1
(7.1)
with
n,u number of observations, number of unknowns,
A n × u matrix of given coefficients with full rank rank A = u; A is also called design
matrix,
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