Primary Noise Reduction Efficiency for Detecting Chaos in High Noisy Pseudoperiodic Time Series

Abstract

The deterministic structure from a high noisy pseudoperiodic time series is detecting by using the different noise reduction methods based on principal component analysis for a primary noise reduction and algorithm for detecting chaos is described. The correlation coefficient as a measure of the distance between closest embedding vectors is used and averaged diverging slope, as an indicator of chaos, is calculated according modifying well known Rosenstein method for largest Lyapunov exponents calculating. It is concluded, that the global phase space singular value decomposition method gives better results for pseudoperiodic signal with high level of additive white noise (the noise is comparable with signals) than local phase space projection method. But commonly the prefiltering of high noisy pseudoperiodic time series gives limited advantage – by using global phase space method for noisy signal prefiltering we can reliably distinguish chaos from regular sinusoidal signal in the presence of additive white noise at a signal-noise ratio up to 6 dB. The proposed algorithm for chaos detecting performed reasonably well for SNR up to 10 dB without prefiltering for time series data exhibiting strong pseudoperiodic behavior. Ill 3, bibl. 13 (in English; summaries in English, Russian and Lithuanian).