The following are some recommended applied self-assessment questions for the lesson called Linearizing the parametric functional model. They’re intended for you to work through to test your own understanding of the key concepts we covered there.
If you have the following functional model:
What is the corresponding linearized form if:
Because there is only one measurement here, what I’m really asking for is for you to write out (which is the same as ), i.e. the work here is in obtaining numerical values for and . Please show your work.
Imagine the following situation where we want to estimate the unknown coordinates of point 4:
Imagine that we know the coordinates of the other points to be as follows:
And we know the measured distances to be as follows:
a) In this situation, what are , , and ?
b) What is the functional model that applies for each row of the vector function , i.e. for each measurement? Write this in terms of general points A and B as we did in the example in the topic video.
c) Is this linear or non-linear in ?
d) What is the full linearized form of the functional model in a)? This should have the form: and should be written out as set of vectors and matrices into which you could plug in and compute the numerical values.
e) Write out the same linearized model, but now with the numerical values corresponding to the given situation. Here you can use the following approximate coordinates for point 4:
I get the following linearized form of this functional model:
which doesn’t need to be but could also be written more explicitly as follows (I just find expanding the terms helpful as a reminder of what they mean):
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