Building your practice in linearization

In the mini course functional math modeling for geomatics networks you developed and understood the concept of the functional math model \mathbf{F}(\mathbf{x},\mathbf{l}_{true}) = \mathbf{0} and how it relates our desired parameters, \mathbf{x}, to our observed quantities, \mathbf{l}_{true}.

Now we need to discuss how to go about linearizing that relationship because it turns out that practical estimation techniques require that our models be linear.

You need to use this mini course to understand where the following linearized form of the same equation come from:

    \begin{equation*} \mathbf{A}\boldsymbol{\delta} - \mathbf{e} + \mathbf{w} = 0 \end{equation*}

And to get good at using the key concepts and equations to linearize any model in the form \mathbf{F}(\mathbf{x},\mathbf{l}_{true}) = \mathbf{0} .

We’ll consider the process of linearization, we’ll look at the outcome for each of the types of functional model seen earlier, and we’ll summarize the situation in an handy table.

Directions

Just work your way through lessons (under “Resource content”) below.