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- W3200361233 abstract "Abstract Geometric algebra (GA) is an efficient tool to deal with hypercomplex processes due to its special data structure. In this article, we introduce the affine projection algorithm (APA) in the GA domain to provide fast convergence against hypercomplex colored signals. Following the principle of minimal disturbance and the orthogonal affine subspace theory, we formulate the criterion of designing the GA-APA as a constrained optimization problem, which can be solved by the method of Lagrange Multipliers. Then, the differentiation of the cost function is calculated using geometric calculus (the extension of GA to include differentiation) to get the update formula of the GA-APA. The stability of the algorithm is analyzed based on the mean-square deviation. To avoid ill-posed problems, the regularized GA-APA is also given in the following. The simulation results show that the proposed adaptive filters, in comparison with existing methods, achieve a better convergence performance under the condition of colored input signals." @default.
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- W3200361233 date "2021-09-17" @default.
- W3200361233 modified "2023-10-15" @default.
- W3200361233 title "Geometric-algebra affine projection adaptive filter" @default.
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- W3200361233 doi "https://doi.org/10.1186/s13634-021-00790-y" @default.
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