  Although the theory of constrained least squares (CLS) estimation is well
known, it is usually applied with the view that the constraints to be imposed
are unavoidable. However, there are cases in which constraints are optional.
For example, in camera color calibration, one of several possible color
processing systems is obtained if a constraint on the row sums of a desired
color correction matrix is imposed; in this example, it is not clear a priori
whether imposing the constraint leads to better system performance. In this
paper, we derive an exact expression connecting the constraint to the increase
in fitting error obtained from imposing it. As another contribution, we show
how to determine projection matrices that separate the measured data into two
components: the first component drives up the fitting error due to imposing a
constraint, and the second component is unaffected by the constraint. We
demonstrate the use of these results in the color calibration problem.
