Estimation of the dominant singular values for svd based noise reduction methods

In this paper we present an algorithm for the estimation of the dominant singular values or respectively the noise floor for Singular Value Decomposition (SVD) based noise reduction methods. The algorithm presented here uses the SVD of the trajectory matrix, is based on matrix perturbation analysis, and is applied for a noise filtering method based on time-varying state-space modeling. The efficiency of the algorithm is then studied by the estimation of the correlation integral and, respectively, the correlation dimension of noisy and filtered time series. For testing of the filtering method with the noise floor estimation algorithm integrated, the Lorenz equations, which have a chaotic attractor, were used. To determine the effects of the noise and the noise reduction method, Gaussian random noise was added to the simulated system as a measurement error. The proposed noise floor estimation algorithm turns out to be well suited for SVD based noise filtering methods where the number of dominant singular values is not known a priori.