A posteriori reference variance

by Micha ⌂ @, Tuesday, May 28, 2019, 15:10 (19 days ago) @ a2pac

Hello Antonio,

Firstly, in the initial adjustment steps, JAG3D calculates the weight matrix P of all observations. Weights of all observations are calculated based on the given a-priori uncertainty (e.g. a-priori uncertainty of horizontal distance) and a-priori reference variance σ.

Yes, you are right.

The default value of the a-priori reference variance σ is 1, and can't be changed in JAG3D. Are the stated facts correct?

Yes, the (a-priori) variance of the unit weight is set to σ = 1. The variance of the unit weight does not affect the estimates (parameters and dispersion).

Furthermore, during the adjustment procedure JAG3D calculates the a-posteriori reference variance factor and uses it to calculate all confidence measures defined by the adjustment model. Where does JAG3D directly shows the calculated a-posteriori reference variance factor?

The estimated variance of the unit weight is part of the variance-component estimation (vce). Thus, results are presented in the Table of the vce.

Next, after the adjustment of two consecutive epochs, during the deformation analysis, does JAG3D calculates and shows the displacement vector between the points of the two measured epochs?

Yes. The 2D displacement vectors are shown, see for instance Fig. 3 in this contribution.

And finally, let's say I have a 2D geodetic network measured in two consecutive epochs. The network is adjusted as a free network (the minimum trace datum is defined). My goal is to determine if unstable points exist in the network (between epochs) and to calculate the deformation vector of the unstable points. What would be the general workflow (main steps) in JAG3D to accomplish the above stated goal?

Please take a look on this example project. The reference point number 3 is unstable. The next step is to duplicate point 3 and to rename the points, e.g. 3_E1 and 3_E2 for reference and control epoch, respectively. Move 3_E1 and 3_E2 to a new point group (point 3 is unstable and should not define the datum). Introduce the new point names in the corresponding observation groups (,i.e., rename the point 3 by 3_E1 in reference epoch and rename the point by 3_E2 in control epoch. Define a "link" 3_E1 - 3_E2 to estimate the teststatistics of the displacement.

Kind regards

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

JAG3D, deformation analysis, congruence analysis, variance of the unit weight

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