Partial source separation from unknown correlation mixture for eliminating unknown periodic disturbances from random measured signals

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Separating and eliminating periodic disturbances from measured signals are a key problem to obtain original responses used for further system identification and evaluation. Actual periodic disturbances are partial unknown sources in measured signals and have certain correlation with random noise sources in time domain. In this paper, a separation problem on partial unknown sources such as periodic sources correlated with random noises is introduced. A partial unknown source separation technique is proposed by combining signal eigenspace transformation, covariance joint diagonalization and decorrelation of correlation sources. The partial source separation procedure has two main stages: obtain uncorrelated sources by eigenspace transformation and joint diagonalization; and obtain partial periodic sources correlated with random noises from the uncorrelated sources by decorrelation. The proposed partial source separation technique is supported by several theorems. Under given assumptions, the separation technique will result in accurate partial sources. The separation technique has main features such as partial unknown sources separated from measured signals, separated periodic sources correlated with random noise sources, and being suitable for dominant random noises and non-dominant periodic disturbance sources in measured signals. Numerical results are presented to illustrate the effectiveness of the separation technique.