Design of an extended LMS-type adaptive filter using semidefinite programming

Adaptive estimation mechanism makes an important role in robot control since it is necessary to estimate changes of environment of a robot for the sake of adequate control. The least mean square (LMS) algorithm is one of such adaptive estimation algorithms, and has been used as an effective and popular approach in signal processing because of its simple structure and low computational complexity. This paper proposes a design method for an LMS-type algorithm which is robust in some sense and converges faster than the conventional LMS algorithms. By means of recent robust control theory, the design problem is reduced to a semidefinite program which is an efficiently solvable optimization problem. Numerical examples are provided to illustrate the effectiveness of the proposed method.