You’re in the home stretch!

This is a “focused practice” lab, meaning that:

  • It’s designed to help you figure out what you need to know as efficiently as possible; it’s up to you whether you complete it in Excel, or Matlab, or C++ (e.g. as an addition to your geomatics networks library)
  • I’ve designed it on purpose so that (in addition to reviewing what we’e already done) you can think of the doing following as the best way to prepare for your final exam:

And it’s our last lab!

Goals of this lab?

The lab has the goal of helping you efficiently review much of the material we’ve covered in the course. This includes the following in four parts.

Part 1:

  • functional modeling
  • linearization

Part 2:

  • preanalysis
  • reductions
  • gross error detection

Part 3:

  • estimation using a parametric least squares adjustment
  • checking whether to use the a-posterior variance factor

Part 4:

  • network quality measures, with a focus on precision and reliability
  • final reporting

Each of these parts is linked in the lessons below.

Situation

To keep things computationally simple, we’re just going to look at the following network:

Where I want you to imagine that:

1. The coordinates of points 1 and 2 are known and we wish to estimate the coordinates of point 5.

2. The survey has already been carried out to make this happen

3. For the ways this little network is going to be used, the semi-major axis of the point error ellipse for the new point must be less than 1.0 cm at a 95% confidence level.

4. Unfortunately, your inexperienced colleague carried out the survey and didn’t know to do both backsight and foresight measurements when turning the horizontal angles, and this and some other setup errors have resulted errors in the angular measurements that exhibit as a misalignment error, \boldsymbol{\varepsilon}. In other words, the error in all of the angular measurements can be described as follows:

angular error due to \boldsymbol{\varepsilon} = \boldsymbol{\varepsilon} x the true angle

5. Your boss has asked whether the data can be salvaged to save having to send a crew back into the field.

6. Luckily you took a class in geodetic networks, and you realize that this little issue can be thought of as having an uncalibrated instrument. You’re pretty sure you recall learning that it’s possible to estimate errors such as this as part of a network adjustment. Although this would mean coding your own little adjustment instead of using the commercial software packages at the office, you’re excited because the network’s small enough you can probably work it out in Excel or Matlab, or even as an addition to your own C++ library.

So you set to work to figure out if you can estimate \boldsymbol{\varepsilon} at the same time as estimating the coordinates of point 5, thereby avoiding the cost of sending a crew back into the field …

Notes

Keep in mind that this is a cooked up example for us to learn a few key concepts, so don’t sweat the details about where exactly the misalignment error is coming from or why they didn’t just use differential GPS in the first place.

That said, although we’re just going to assume that the combination of errors exhibits itself as the misalignment error described above, you can learn about theodolite errors in articles such as this and this and this.

Deadlines

The due dates for this work are outlined on our course page.

Assessment

As a portion of your final grade, this lab is worth the same as what Labs 2 and 3 were worth (i.e. Labs 1 and 4 are worth half as much as Labs 2, 3, and 5). Detailed rubrics will be handed out and discussed in class.