Kernel adaptive filter algorithm based on function expansion

Abstract

The invention provides a kernel adaptive filter algorithm based on function expansion. Through an orthogonal basis function expansion model, original input data is subjected to dimension expansion, then a kernel minimum squared error algorithm is used to carry out filtering, and the output of a filter is obtained, wherein the orthogonal basis function expansion model is formed by a Chebyshev orthogonal polynomial or a Legendre orthogonal polynomial. The invention provides the kernel adaptive filter algorithm based on function expansion, through a function expansion model, the input data is subjected to dimension expansion and then is taken as an input of a kernel least squares algorithm, the minimum squared error algorithm is used to carry out adaptive filtering, the algorithm performance can be improved further, a reasonable embedding dimension is given, since only the dimension of an input space is increased in the function expansion model, the computational complexity is not significantly increased, the convergence performance of the filter can be significantly improved under the premise of not significantly increasing the computational complexity, and the algorithm has an important research significance and a wide practical engineering value.

Description

technical field [0001] The invention belongs to method research in the field of signal processing, and relates to a kernel adaptive filter algorithm of function expansion. Background technique [0002] At present, online learning plays an important role in many fields, including tracking, filtering, and system identification in the field of control, filtering, visual tracking in computer vision, denoising, prediction, etc. in the field of signal processing. [0003] In recent years, the research on online kernel methods is also common. Kernel methods are gradually applied to many practical engineering problems relying on their powerful nonlinear capabilities and related mathematical theory support. The Mercel kernel can map nonlinear data to ultra-high-dimensional space or even infinite-dimensional space through kernel functions, and then use linear methods to process data in high-dimensional space. Support vector machines and kernel adaptive filtering are methods widely us...

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These perturbations are usually not measurable, they may be deterministic or random...

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