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The fading memory filter has been proposed as a substitute for the Kalman filter when model errors exist because it discounts old data, thereby, compensating for the influence of model errors. For model errors in the form of completely unknown inputs, this paper presents computational examples for which the asymptotic error of all fading memory filters will be greater than the Kalman error. This contradicts the assumption that, when the Kalman filter is no longer optimal, there exists a fading memory filter which will achieve lower mean squared error. An explanation for this error behavior and a discussion of its implications are included.