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This paper presents tracking analysis of a gradient-based simplified algorithm for an allpass filter-based adaptive infinite impulse response (IIR) notch filter with a linear chirp input signal. A first-order difference equation with respect to steady-state instantaneous frequency tracking error is derived first. Then tracking error mean, variance and mean square error (MSE) are derived from the difference equation using the power spectral density (PSD) method. Computer simulation results are presented to validate the analysis.