A system and method of determining a filter to cancel feedback signals from input signals in a hearing assistance device includes determining feedback signals for a plurality of feedback paths associated with the device, and determining a model of the plurality of feedback paths, with the model having an invariant portion and a time varying portion. A probable structure of the invariant portion is determined to generate a structural constraint to constrain the plurality of feedback paths, and probability distributions to impose the structural constraint on the invariant portion are determined. During an iterative process, the invariant portion is iteratively determined using the determined probability distributions and the feedback path measurements. A measurement noise variance representative of model mismatch is updated, for each iteration, to reduce a probability of a non-desirable determination of an invariant filter, and the invariant filter is determined in response to a criterion for ending the iterative process being satisfied.