It is common to need to estimate the frequency
response of a system from observed input-output data.
This paper uses integral constraints to characterise the
undermodelling induced errors involved in solving this problem via
parametric least squares methods. This is achieved by exploiting
the Hilbert Space structure inherent in the least squares solution
in order to provide a
geometric interpretation of the nature of frequency domain errors.
The result is that an intuitive process can be
applied in which for a given data collection method and model
structure, one identifies the
sides of a right triangle, and then by noting the hypotenuse to be the
longest side, integral constraints on magnitude estimation error are
obtained. By also noting that the triangle sides both lie in a
particular plane, integral constraints on phase estimation error are derived.
This geometric approach is in contrast to earlier work in this area
which has relied on
algebraic manipulation.