On frequency tracking properties of a generalized adaptive notch filter

The paper presents results of local performance analysis of a generalized adaptive notch filter (GANF). Generalized adaptive notch filters are used for identification/tracking of quasi-periodically varying dynamic systems and can be considered extension, to the system case, of classical adaptive notch filters. The frequency tracking properties of the algorithm are studied analytically using a direct averaging approach and an approximating linear filter (ALF) technique. Even though restricted to a single frequency case, the presented analysis provides valuable insights into the tracking mechanisms of GANF, including the associated speed/accuracy tradeoffs, the achievable performance bounds, and tracking limitations. Additionally, it allows one to formulate some useful rules of thumb for choosing design parameters. We show that under the conditions of the ALF approximation, the optimally tuned GANF is a statistically efficient estimator of a slowly drifting system frequency.