# Variance-covariance matrix for a network adjustment

Hallo Micha,

I would like to do a local tie analysis including calculations of vectors between invariant points of a VLBI antenna, a SLR telescope and several GNSS pillars.
My problem arises using JAG3D when I want to include the centers of the VLBI and SLR instruments in the variance-covariance matrix estimation.

My data include:

1) 236 level measurements between 16 altimetric marks (and some auxiliar points) in different instruments or concrete platforms in our Observatory. We placed the instrument in 13 diferent positions so I treated every position as independent sets.
Based on the used instrument (Leica LS15), I defined an uncertainty of 0.1 mm for each measurement in the properties tab.

2) Measurements of an horizontal network (directions and horizontal distancies) composed of 10 sites that have forced centering bases. 6 of these points materialize the main axis of GNSS instruments, while the others are located on the concrete platforms of the VLBI and the SLR instrument. Like height measurements, each position of the total station was taken independently.

3) Measurements of marks sticked to the VLBI and SLR instruments. In each concrete platform, we placed a total station (Leica TS60) and a theodolite in front of each other and from both intrument we take measurements to at least two fix marks located on platforms and several measurements of a rotating mark linked to the intrument of interest. Last measurements describe two circles and the centers of those circles define the main and secondary instrument axes.

4) GNSS continuous measurement in 6 pillars for the campaign days. One of this pillar represents the main GNSS station of the observatory and is a IGS station. The other pillars conform the GNSS control network. The observatory occupies an area of ​​around 40x40m.

So, my question is, knowing the precision of each measurements of points that make up the circles around the axes, is it possible to do a network adjustment and determine a variance-covariance matrix that includes the invariant points of VLBI and SLR?

Romina

## Variance-covariance matrix for a network adjustment

Hello Romina,

So, my question is, knowing the precision of each measurements of points that make up the circles around the axes, is it possible to do a network adjustment and determine a variance-covariance matrix that includes the invariant points of VLBI and SLR?

JAG3D is a network adjustment application. You are able to estimate all points that are connected by (terrestrial) observations. The invariant points of the telescopes are - to my understanding - not part of you observation procedure and therefore not part of the network adjustment. You can export the fully populated covariance matrix of the network and can thread this matrix as well as the circle-arc points as incoming in a further analysis step (outside from JAG3D). Please take a look to Figure 1 to get an impression of the procedure we used so far.

Kind regards
Micha

--
applied-geodesy.org - OpenSource Least-Squares Adjustment Software for Geodetic Sciences

## Variance-covariance matrix for a network adjustment

The LINZ pyaxis software does include estimation and covariance of the antenna invariant point. It is a python software and much cruder than JAG3D, but it does provide this feature. It was written specifically for local tie surveys. Details at:

https://github.com/linz/python-linz-pyaxis

Regards
Chris Crook

## Variance-covariance matrix for a network adjustment

Hello Chris,

It was written specifically for local tie surveys.

Thanks for the hint. It is a suitable way of analyzing the data in the frame work of local-ties.

All the best
Micha

--
applied-geodesy.org - OpenSource Least-Squares Adjustment Software for Geodetic Sciences