The assumption of linear least squares
is that there is a linear relationship between our measurements
and the variables to be estimated
![]() |
(1) |
For this example let us assume that our measurements are given in Table 1 and you can see them plotted in Figure 1.
x | -3.0 | -2.5 | -2.0 | -1.5 | -1.0 | -0.5 | 0.0 | 0.5 | 1.0 | 1.5 |
z | -1.0 | -0.25 | 0.0 | 0.25 | 0.4 | 0.7 | 1.0 | 1.1 | 1.4 | 1.8 |
The linear least squares solution to fit the given data is given by the equation
![]() |
(2) |
The only not so obvious step before using a tool like Matlab, is to form the
matrix, which is a combination of an identity
vector
and
as column vectors, such that
This is clarified by looking at the example code in Matlab, LinearLeastSquares.m. A plot of fitting the measurement data with a line such that it minimizes the the mean square of the error is shown in Figure 1.
The equation of the line to fit this data is then
As of this snapshot date, this entry was owned by bloftin.