I. Introduction
Adaptive notch filtering is well known as a useful technique for detecting, removing, enhancing and retrieving sinusoidal signals of unknown frequency from additive broad-band noise. It is widely applied in digital communications, control, radar, sonar, biomedical engineering, active noise control, and so on [1]–[3]. Adaptive notch digital filters can mainly be classified into two classes of filters such as the direct-form filters with constrained poles and zeros [4]–[10] or the lattice-based filters [11]–[14]. The former usually possesses biased frequency estimate [6], [8], [10], whereas the latter yields unbiased frequency estimate for a single sinusoid [11], [12]. It is noted that a simplified iterative algorithm was used in [11], [14], an ordinary differential equation approach was employed in [12], and the affine combination of Regalia's simplified lattice algorithm and lattice gradient algorithm was utilized in [13].