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Bernese GPS Software Version 5.0 - Bernese GNSS Software

Bernese GPS Software Version 5.0 - Bernese GNSS Software

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7. Parameter Estimation<br />

7.1 Introduction<br />

Parameter estimation in the <strong>Bernese</strong> <strong>GPS</strong> <strong>Software</strong> is based on Least-Squares Estimation<br />

(LSE). The two main programs in the software package allowing for the adjustment of<br />

model parameters to <strong>GNSS</strong> observations are <strong>GPS</strong>EST (”Menu>Processing>Parameter estimation”)<br />

and ADDNEQ2 (”Menu>Processing>Normal equation stacking”). The first of the two programs processes<br />

the observations. It sets up the observation equations and solves the normal equation<br />

(NEQ) while ADDNEQ2 manipulates and combines solutions on the normal equation level.<br />

ADDNEQ2 is discussed in more detail in Chapter 9. This chapter provides general information<br />

for program <strong>GPS</strong>EST, details on the estimation of the various parameters available in<br />

the <strong>Bernese</strong> <strong>GPS</strong> <strong>Software</strong> may be found in the following chapters.<br />

<strong>GPS</strong>EST offers many processing options. Additional options are available in program<br />

ADDNEQ2 such as datum definition by means of free network condition, writing of coordinate<br />

SINEX file, or estimation of station velocities. On the other hand a number of<br />

parameters are only supported by <strong>GPS</strong>EST, in particular epoch parameters (clock corrections,<br />

kinematic coordinates, stochastic ionosphere parameters) and phase ambiguities. An<br />

overview on the availability of the parameters supported by the <strong>Bernese</strong> <strong>GPS</strong> <strong>Software</strong>,<br />

<strong>Version</strong> <strong>5.0</strong> is given in Table 1.1.<br />

As all programs in the <strong>Bernese</strong> <strong>GPS</strong> <strong>Software</strong>, <strong>GPS</strong>EST is running in batch mode, i.e., it<br />

assumes that all observations are available in files. No real-time or data-streaming mode is<br />

supported. The program furthermore assumes that good a priori values for all parameters are<br />

available. The program does not iterate but computes the improvements of the parameters<br />

from the linearized observation equations. If iteration is necessary the program has to be<br />

run again using the improved parameters as a priori values.<br />

7.2 Basic Theory of Least-Squares Estimation<br />

The (linearized) observation equations in the Gauss-Markoff Model of full rank are given,<br />

e.g., by [Koch, 1988]<br />

E(y) = Ap ; D(y) = σ 2 P −1<br />

(7.1)<br />

with<br />

n,u number of observations, number of unknowns,<br />

A n × u matrix of given coefficients with full rank rank A = u; A is also called design<br />

matrix,<br />

<strong>Bernese</strong> <strong>GPS</strong> <strong>Software</strong> <strong>Version</strong> <strong>5.0</strong> Page 139

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