In the first part of this lab you developed and linearized the model needed to estimate both the coordinates of point and the misalignment error . Then in the second part you did a preanalysis, reduced the measurements, and took a look at blunder detection. Then in the third part you estimated the unknown parameters and assessed whether or not to scale the variance-covariance matrices. Now let’s wrap things up.

Step 1: Check the precision of your coordinate against the spec again

If you did have to scale the variance-covariance matrices in Step 2 of the third part of this lab, then I would like you to check the precision of the coordinates of point against the spec given earlier. This would mean using the scaled to calculate the semi-major axis at a 95% confidence level again.

Is your estimate of the unknown parameters any different? Does the network still meet spec in your estimation?

Reflect upon and document the situation in your report.

Step 2: Finish assessing the precision

You just looked again at the semi-major axis of the error ellipse of the unknown coordinate.

Now I want you to calculate the semi-minor axis (also at a 95% confidence level), as well as the angle .

Document the results in your report and provide a sketch of the error ellipse to scale and oriented properly. Essentially, in doing this you will have diagonalized the variance-covariance matrix of your estimated parameters, a process also called eigenvalue decomposition or principle component analysis. Use your results to comment on this and why it’s important to do it in the case of a survey network.

Also calculate an appropriate measure of the precision of the estimated misalignment error in ppm at a 95% confidence level.

Step 3: Assess the reliability of your network

Use the matrix equation we saw in class to calculate the total reliability of your network and the individual redundancy and absorption numbers.

Document the results of this in your report.

Step 4: Studying the reliability for another look at network design

1. Which measurement do the redundancy numbers suggest is the “most important” to your adjusted solution?

2. Which is the least important?

3. Even with having to estimate the misalignment error in your network, this survey had two more measurements than unknowns. What would the semi-major axis of your unknown coordinate look like if you removed the two “least important” measurements? Did those measurements make a big difference?

• Note: Although it’ll mess with the redundancy numbers, a very quick way to do this is to re-run your adjustment using a very low weight (high standard deviation) for the measurements in question.

4. If you could go back in time and “undo” two measurements and replace them with two others in order to strengthen the network design, what would you recommend? (You don’t need to do a full pre-analysis here – I’m just looking for your intuition based on the geometry of the situation and what the measures of precision and reliability are telling you.)