An approach to adaptive filtering with variable step size based on geometric algebra

Recently, adaptive filtering algorithms have attracted much more attention in the field of signal processing. By studying the shortcoming of the traditional real-valued fixed step size adaptive filtering algorithm, this paper proposed the novel approach to adaptive filtering with variable step size based on Sigmoid function and geometric algebra (GA). First, the proposed approach to adaptive filtering with variable step size based on geometric algebra represents the multi-dimensional signal as a GA multi-vector for the vectorization process. Second, the proposed approach to adaptive filtering with variable step size based on geometric algebra solves the contradiction between the steady-state error and the convergence rate by establishing a non-linear function relationship between the step size and the error signal. Finally, the experimental results demonstrate that the proposed approach to adaptive filtering with variable step size based on geometric algebra achieves better performance than that of the existing adaptive filtering algorithms.