This paper gives a precise meaning to the robustness of risk-sensitive filters for problems in which one is uncertain as to the exact value of the probability model. It is shown that risk-sensitive estimators (including filters) enjoy an error bound which is the sum of two terms, the first of which coincides with an upper bound on the error that one would obtain if one knew exactly the underlying probability model, while the second term is a measure of the distance between the true and design probability models. The paper includes a discussion of several approaches to estimation, including H/sub /spl infin// filtering.