An Estimation-Based Approach to the Design of Adaptive IIR Filters - American Control Conference, 1998. Proceedings of the 1998

is one approach which uses a separate feedkjack within the adaptive controller to cancel-the effect of the undesired feedback [6]. This scheme, however, requires special care in the implementation to avoid the cancellation of the reference signal all together (see [4] for details). Looking at feedback neutralization from a different point of view, it is clear that this algorithm generates poles as well as zeros for the overall adaptive filter. In other words, the overall adaptive controller is an IIR filter in general (and hence stability of the overall system should be closely monitored). Observing this fact, there have been several attempts to directly design an adaptive IIR filter in such circumstances. Filtered-U recursive LMS algorithm is one such approach. In this technique, the feedback path is We present an estimation-based approach to the design of adaptive IIR filters. We also use this approach to design adaptive filters when a feedback signal from the output of the adaptive filter contaminates the reference signal. We use an H , criterion to cast the problem as a nonlinear H , filtering problem, and present an approximate linear H , filtering solution. This linear filtering solution is then used to adapt the adaptive IIR Filter. The presentation of the proposed adaptive algorithm is done in the context of an adaptive Active Noise Cancellation (ANC) problem. Simulations are used to examine the performance of the proposed estimation-based adaptive algorithm. explicitly treated as part of the plant, [7], and the derivation involves approximations that rely on slow adaptation. Furthermore, there are many concerns about the convergence properties of this scheme [4]. It is also noted that the optimal solution can be extremely ill-conditioned if a large number of controller coefficients are used or the structure of feedback path is complicated. This paper's estimation-based approach to the design of adaptive IIR filters, in essence meets a disturbance attenuation criterion (to be defined shortly), and hence provides a framework in which the questions about convergence and stability of the adaptive algorithm can be systematically addressed. Moreover, the estimation-based approach easily extends to the case where the reference signal available to the adaptive algorithm is contaminated with the feedback from the output of the adaptive filter. This paper is organized as follows. Section 2 presents the estimation-based formulation for the adaptive filter design. Section 3 discusses the H,-optimal solution to the formulated estimation problem. Section 4 outlines our proposed implementation scheme for the adaptive algorithm. Section 5 contains simulation results. Section 6 concludes this paper with a summary and final remarks. 2 Problem Formulation we discuss the estimation-based approach to the design of an adaptlve IIR filter (with and the presence of a feedback path) in the context of the ANC problem of ~i~~~~ 1. this section we first concentrate on the caSe where there is no feedback path. The with feedback path is then an The objective of ANC is to generate a control signal u ( k ) such that the output of the secondary path, Y(k), is In some measure (to be specified later) close enough to the output of the primary path, d(le). For this to materialize, the series connection of the IIR filter (for some optipath must appropriately approximate the unknown pri