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This paper presents a new approach for system identification of rapidly time varying systems with applications to echo-cancellation in a cabin environment. These situations arise when the coherence time is significant relative to the system time-scale. Under these conditions it is not meaningful to track the system dynamics exactly as this would lead to significant variability in performance. The novelty of our approach relies on deliberately undermodeling the system in a lower complexity model class and reliably tracking the reduced order model. From a theoretical standpoint, under-modeling requires dealing with residual dynamics in addition to measurement noise. A novel technique based on first annihilating the residual error by exploiting the inherent 'orthogonal' decomposition between model class and unmodeled dynamics is obtained. We quantify the estimation error as a function of the rate of variation, complexity of the model class and the undermodeling error.