In the first part of this lab you developed and linearized the model needed to estimate both the coordinates of point 5 and the misalignment error \boldsymbol{\varepsilon}. And in the second part you did a preanalysis, reduced the measurements, and took a look at blunder detection. Now I would like you to estimate the unknown parameters.

Step 1: Adjust your network

You’ve done a lot of the work for this already, but now I want you to carry out the required parametric least squares adjustment using the approach we discussed in this course. And document the results in your report.

Step 2: Calculate and test the a-posteriori variance factor

Calculate the a-posteriori variance factor \hat{\sigma}_0^2. This was also discussed at the link provided in the last step. Then, assuming that the a-priori variance factor \sigma_0^2 is 1.0, carry out an appropriate statistical test to learn whether your variance-covariance matrices need to be scaled by \hat{\sigma}_0^2. We discussed this statistical test in class. If they do need scaling, then scale them. Document the results of this in your report too and provide your final estimates of the unknown parameters and the key variance-covariance matrices. (Note: I built my solution to this lab in a spreadsheet. So to test this notion of scaling I just made a copy of my adjustment tab and then scaled the input \mathbf{C}_{l} matrix up – by scaling the standard deviations of my observations by \sqrt{\hat{\sigma}_0^2} – and my spreadsheet took care of everything else for me. However you implemented things, you can do this too just by running your adjustment again using the different input standard deviations (scaled by\sqrt{\hat{\sigma}_0^2}) or different input \mathbf{C}_{l} (scaled by \hat{\sigma}_0^2). All you need for this step is to scale the variance-covariance matrices, but it is very interesting to compare the output of the adjustment before and after scaling \mathbf{C}_{l} and it can be just as quick.)

Move to Part 4

Now you’re ready to assess the quality of your network in the last part of this lab.