Development and Application of Dual Form Conic Formulation of Multichannel Active Noise Control Filter Design Problem in Frequency Domain

Active noise control filter design methods can be categorized as time-domain or frequencydomain methods. When multiple frequency-dependent constraints need to be specified, such as the enhancement constraint, stability constraint and robustness constraint, the optimal filter coe cients can be obtained more conveniently by solving a constrained optimization problem formulated using frequency-domain methods. However, the computational load for searching the global optimal solution is significantly high, if the number of channels, filter coe cients, or constraints is large. To improve computational e ciency, some previous work relaxed the traditional formulation to a convex problem, and then reformulated it to a cone programming problem. After this reformulation, e cient algorithms for cone programming problem, e.g., the primal-dual interior-point methods, can be applied to solve the filter design problem. However, some numerical issues may occur when solving the reformulated standard conic form directly. In this paper, the numerical instability issue for active noise control filter design problem is investigated. The original conic form was rearranged via dual formulation and different treatments of free variables are discussed. It is demonstrated that the proposed approach result is equivalent to the standard conic form but numerically more stable.