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An adaptive filtering algorithm using an orthogonal projection to an affine subspace and its properties
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1984
Year
Adaptive FilterAdaptive Filtering AlgorithmEngineeringFiltering TechniqueAffine Projection AlgorithmAdaptive ModulationOrthogonal ProjectionAffine SubspaceAdaptive ControlLms AlgorithmInverse ProblemsAdaptive AlgorithmSpatial FilteringLearning IdentificationSystem IdentificationApproximation TheorySignal Processing
The LMS algorithm and learning identification, common adaptive algorithms, can suffer greatly reduced convergence speed depending on input signal properties. The paper aims to avoid this slowdown by geometrically analyzing its cause and proposing a new adaptive algorithm. The authors develop a new adaptive algorithm derived from a geometrical analysis of the LMS defect and extend it to the affine projection algorithm (APA) family, encompassing the original algorithm and learning identification. Numerical experiments show the proposed algorithm and APA achieve markedly faster convergence than learning identification, with APA’s coefficient vector converging monotonically and its speed independent of input amplitude, and the study also clarifies noise effects and filter order adequacy.
Abstract The LMS algorithm and learning identification, which presently are typical adaptive algorithms, have a problem in that the speed of convergence may decrease greatly depending on the property of the input signal. To avoid this problem, this paper presents a geometrical discussion as to the origin of that defect, and proposes a new adaptive algorithm based on the result of the investigation. Comparing the convergence speeds of the proposed algorithm and the learning identification by numerical experiment by computer, great improvement was verified. The algorithm is extended to a group of algorithms which includes the original algorithm and the learning identification, which are called APA (affine projection algorithm). It is shown that APA has some desirable properties, such as, the coefficient vector approaches the true value monotonically and the convergence speed is independent of the amplitude of the input signal. Clear conclusions are also obtained for the problem as to what noise is included in the output signal when an external disturbance is impressed or the degree of the adaptive filter is not sufficient.