This talk offers an algorithmic appproach to constrained least squares estimation. Thus our primary objects of interest are rather the algorithms that allow one to solve least squares estimation tasks and not so much the existence and uniqueness results for the concrete estimation tasks. The nature of such numerical algorithms is strongly influenced by two basic aspects:

1. the geometry and parametrization of the constraint set and
2. the type of dynamics underlying the algorithms.

In this talk we show how such aspects can be used to analyze and tune least squares estimation tasks in quantum control. No knowledge on quantum control is assumed and we review the necessary background.