08.06.2013 Views

Bernese GPS Software Version 5.0 - Bernese GNSS Software

Bernese GPS Software Version 5.0 - Bernese GNSS Software

Bernese GPS Software Version 5.0 - Bernese GNSS Software

SHOW MORE
SHOW LESS

You also want an ePaper? Increase the reach of your titles

YUMPU automatically turns print PDFs into web optimized ePapers that Google loves.

7. Parameter Estimation<br />

The equation shows, that we may superpose the terms H ⊤ P hH and H ⊤ P hh to the original<br />

normal equation system to incorporate a priori information on the parameters.<br />

Constraints may be introduced in <strong>GPS</strong>EST and ADDNEQ2 for the following parameter<br />

types:<br />

• coordinates: absolute constraints (station constraining), station fixing, free network<br />

constraints (only ADDNEQ2), relative constraints (between stations, only ADDNEQ2),<br />

• velocities: absolute and relative (concerning sites) constraints (only ADDNEQ2), relative<br />

constraints (between stations, only ADDNEQ2),<br />

• kinematic coordinates: absolute constraints with respect to a priori trajectory,<br />

• troposphere: absolute and relative (in time) constraints for zenith path delays and<br />

gradient parameters,<br />

• global ionosphere models: absolute for and relative constraints between model coefficients<br />

and single-layer height parameters,<br />

• stochastic ionosphere parameters: absolute and relative (in time) constraints,<br />

• differential code biases: absolute constraints for station and satellite parameters,<br />

• orbit: absolute constraints for Keplerian, dynamical, stochastic parameters,<br />

• geocenter coordinates: absolute constraints,<br />

• Earth orientation parameters: absolute constraints (UT1 and nutation absolute values<br />

have to be constrained to VLBI values) and continuity constraints (only in <strong>GPS</strong>EST),<br />

• receiver and satellite antenna offsets and patterns: absolute constraints.<br />

For some of the parameters, e.g., clock parameters and differential code biases zero-mean<br />

conditions for the estimate corrections can be applied.<br />

Constraints are always removed before saving a normal equation. Therefore, whatever<br />

constraints were defined in <strong>GPS</strong>EST, new constraints may always be defined in program<br />

ADDNEQ2.<br />

In the following we detail the implementation of parameter constraining in <strong>Bernese</strong> <strong>GPS</strong><br />

<strong>Software</strong>.<br />

7.5.4.1 Absolute Constraining<br />

Any parameter may be constrained to its a priori value by constraining the parameter<br />

improvement to zero (absolute constraint) using the fictitious observation in the form<br />

Such a fictitious observation has the weight<br />

pi = 0 . (7.26)<br />

Pi = σ2 0<br />

σ 2 i<br />

, (7.27)<br />

where both, σ2 0 (a priori variance of unit weight, option “A priori sigma” in panel “<strong>GPS</strong>EST 3.1:<br />

General Options 1”) and σ2 i , are input parameters of the program. This type of constraining<br />

Page 150 AIUB

Hooray! Your file is uploaded and ready to be published.

Saved successfully!

Ooh no, something went wrong!