The first step is to develop and linearize the model needed for the problem at hand, i.e. estimating both the coordinates of point and the misalignment error .

## Step 1: Develop the functional model (or observation equations)

For the given situation, derive and write out the functional model .

## Step 2: Linearize the model

Linearize your model and write it in the form .

## Step 3: Implement your linear model

Develop a tool (Excel, Matlab, or C++) that implements the linearized model. You will be able to fill the design matrix given the following approximate values of the parameters.

For the row of corresponding to the misalignment error, be sure to account for the constants and as outlined here and as you did in Lab 2. You will need to do this.

You can also set things up for calculating the misclosure vector , although you’ll have to wait to finalize that until after you’ve reduced the distance measurements in Part 2 of this lab.

The published coordinates of points and are given in the following table:

Point (m) (m)
1223.882 -16.21
1207.456 -16.21

where means the instrument heights.

The approximate coordinate of point 5 was measured using GPS to yield:

Point (m)
1175.0

All coordinates are given in WGS84 and you can use this online tool to convert these coordinates to the UTM grid in which you’ve done your modeling and will do your adjustment. And be sure to carry enough decimal places to carry the precision through converting from DMS and to DD and to UTM.

You can approximate the misalignment error as 0.0 ppm.

And the measurements are as follows:

Measurement Value Units Notes
m no geometric reductions done
m no geometric reductions done