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}. Now I want you to do a little preanalysis, reduce the measurements, and take a look at blunder detection.

Step 1: Carry out a quick preanalysis

The survey has already been carried out in this example, but I want you to get into the practice of taking a quick look at the \mathbf{C}_{\hat{\mathbf{x}}} matrix before doing a full adjustment. Plus, you’re going to need to the same calculation anyway when you do the adjustment. For this, as you know, you will need to create a variance-covariance matrix for the observations. The following are thought to be correct: \sigma_{distances} = 0.003 m \sigma_{angles} = 1.0 arc seconds Errors are uncorrelated. Be sure to convert to units that are compatible with what you assumed for and put into your \mathbf{A} matrix.

Step 2: Check whether the specs can be met

I gave you the specifications for the coordinate of point 5 when describing the situation. Given your \mathbf{C}_{\hat{\mathbf{x}}}, do you expect your survey to meet those specs? Describe this finding in your report.

Step 3: Reduce the distances to the mapping plane

The distance measurements you were given in Part 1 of this lab are slope distances, i.e. measured from instrument to instrument. Use the coordinate information you were given and the following instrument heights to reduce the distances to the mapping plane: \Delta\textit{h}_{1} = 1.441 m \Delta\textit{h}_{2} = 1.553 m \Delta\textit{h}_{5} = 1.661 m And use the radius of curvature R = 6365227.8281 m. Document your reduced measurements in your report. Also comment on how big a difference the reductions make in this case where the points are close together geographically. Note that I have already reduced the angles to the mapping plane for you, i.e. the angular measurements given were on the mapping plane.

Step 4: Pre-screening

We know your colleague made some human errors that led to a specific kind of systematic error in the angular measurements. It sure would be nice to know if he also made any gross errors. But can you do gross error detection for the measured distances in this situation? Can you do it for the measured angles? In answering both of these questions in your report indicated clearly why or why not. And if it’s possible to do it, then do so and document the results in your report.

Move to Part 3

Now you’re ready to carry out your adjustment.