Unbiased equation error adaptive IIR notch filter

Abstract

This paper presents the unbiased gradient algorithm for the equation error adaptive IIR notch filter (UEANF). The proposed algorithm employs the bias removal technique to remove the bias existing in the estimated parameter, resulting in obtaining good estimate of the parameter. Moreover, the convergence property is improved as compared with the conventional adaptive IIR notch filter (ANF). The computer simulations are provided to confirm the performances of the proposed technique.

A novel adaptive IIR notch filter for frequency estimation and tracking

“…And the relationships between pole radius and MSE after convergence are shown in Fig.3. The fixed step size adaptive algorithm presented in [8] has a high MSE compared with another algorithms, but it can be seen that its MSE is not sensitive to the change of pole radius. Proposed algorithm is not the best one when weighed by MSE performance, its performance is in the middle of other two variable algorithms.…”

“…In this part, some typical simulation results are shown to demonstrate the performance of proposed adaptive IIR notch filter compared with algorithm presented by [6]- [8]. References [6]- [7] are variable step size algorithms while [8]is fixed.…”

“…By substituting the (6) and (7) into (5), it can be obtained (8) It is clear to see that the global minimum of f(a) occurs when a is _ (A2 I(A2 + 2(j�»2cos%, compared with the expecting value -2cos%, it convergences to a biased estimation impacted by the amplitude ofx(n) and the input noise variance. In order to eliminate the bias exists in f (a) , here defined J(a) by subtracting (j�(2 + a2) in (8), so J(a) expressed by (9) According to adaptive signal processing theory, the algorithm which controls the update of parameter a can be shown as follow…”

“…Firstly, the equation error formulation based on bias removal technique developed by R.Punchalard in [5] is applied in proposed notch filter. Secondly, the step size of the adaptive algorithm is not fixed, and it uses the estimation of the instantaneous output signal autocorrelation to update the step size, which can reduce the impact of the [8]. The performance of the filter is also discussed here.…”