This topic is a quick but practical introductory treatment of: 1) geospatial estimation using least squares; and 2) using Excel to make quick work of the basic estimation process.
By the time you’re done, you will have what you need to solve a whole bunch of practical parametric geospatial estimation problems on your own.
What I’m sharing here is one of the most practical bits of my toolbox and I hope it helps you as much as it’s helped me.
Just give me the equations I need!
Here are the basic questions you need to do parametric least squares estimation happen …
Now show me how to implement them efficiently in Excel!
Here’s an example and some guidance on how to implement this kind of thing efficiently in Excel. I use Excel like this all the time – it’s like having a glorified geospatial estimation calculator right at my fingertips
You’ll notice that the example I chose here follows from the drone location problem featured in an earlier practice quiz. In that quiz, the goal was to set up the models needed for estimation. The goal here is to actually do the estimation itself, i.e. to implement the equations introduced above in order to get a quick estimate of the coordinates of the drone from the measurements provided.
The problem statement here might be something like this:
Given the situation outlined in the above-linked drone location problem, estimate the coordinates of the drone and the uncertainty in your estimated coordinates. Assume that the measurements provided all have a known standard deviation of 2.5 cm and that the uncertainty in any one measurement is uncorrelated with the uncertainty in the others.
The idea that the standard deviation of the measurements is known can be interpreted to mean that the distance sensors being used in this situation are known to have that precision, perhaps based on reliable manufacturer specs or from extensive a-priori calibration work. And the information about the uncorrelated nature of the measurements might also be stated as saying that the measurements are independent of each other; an error in one has no impact or bearing on the error in any other.
There’s more to least squares estimation than we’ve covered here, but this gives you a great and very practical start.