Mixed H2/ H∞ algorithm for exponentially windowed adaptive filtering

The RLS or its equivalent H2 algorithms achieve the best average performance. But these suffer from poor worst case performance. Stochastic gradient based algorithms (like LMS) achieve best worst case performance, but a poor average performance. In this paper we propose switching criteria for acquiring advantages of both of these algorithms. The proposed algorithm uses a nonlinear combination of H2 optimal and H∞ optimal estimation. We present a mixed H2/H∞ algorithm employing an exponential window and the achievable bound for this estimation strategy.