Assessment Progress:

The following are some recommended self-assessment questions for the lesson on Linearizing the Distance Observation Equation:

Question 1:

The functional model in this example was of the following form:

    \begin{equation*} \mathbf{l}_{true} - \mathbf{F(\mathbf{x})} =\mathbf{0} \end{equation*}

a) What’s that form called? b) Why is it significant in geomatics networks?

Question 2:

Since the math behind functional models like the distance between two points is usually pretty straightforward, why do we go to the trouble of deriving their linearized forms?

Question 3:

a) Could one obtain the same linearized equation we did here using Taylor’s Theorem directly? i.e. without using the general form \mathbf{A}\boldsymbol{\delta} + \mathbf{e} + \mathbf{w} = 0? b) If yes, then why do we use that general form at all? c) If no, then why can’t it be done?

Question 4:

a) What dimensions would the misclosure vector, \mathbf{w}, be if 20 measurements had been made of the distance between the points A and B instead of one? b) And the dimensions in the same case of the design matrix, \mathbf{A}?

Question 5:

Given the information provided in Example 6 of these notes, calculate the numerical value for the misclosure vector, \mathbf{w}.

Question 6:

What are the numerical values that make up the elements of the design matrix, \mathbf{A}?

Question 7:

Using your results from questions 5 and 6 above, write the whole linearized equation using calculated numerical values.