Exact quantification of the variance of estimated zeros

This paper is concerned with quantification of noise induced errors in estimates of zeros of dynamic systems. Preceding work on this problem has provided variance expressions that are asymptotic in data length and model order for non-minimum phase zeros. This paper presents expressions that are asymptotic only in data length and they are therefore `exact´ for arbitrarily small true model orders. These expressions are also valid for both minimum phase and non-minimum phase zeros. A key insight is that the variance error quantification problem is equivalent to deriving a reproducing kernel for a space that depends on the employed model structure.