Adaptive step size EASI algorithm based on nonlinear correlation for on-line separation of satellite micro-vibration sources

The on-line blind separation of satellite micro-vibration source signals can provide the basis for the on-line suppression of satellite micro-vibration from the perspective of vibration source control, which has important academic significance and remarkable engineering application value for improving the performance of satellite positioning accuracy. Focusing on the inherent contradiction between convergence rate and steady-state error in on-line separation, a novel adaptive step size EASI (Equivariant Adaptive Separation via Independence) algorithm is proposed. Since nonlinear uncorrelation of Blind Source Separation (BSS) results displays its independence equivalently, minimizing nonlinear correlation also marks the optimal state of separation. According to this basic BSS estimation principle, a separation index based on nonlinear correlation coefficients is constructed to represent the separation degree, and on-line updating equations of separation index is derived by time average technique. Then, a suitable nonlinear monotone function is adopted to map separation index to the step size, and the step size can be adaptively adjusted according to separation degree. Finally, the novel adaptive blind separation algorithm in this paper is formed by introducing the adaptive step size to traditional EASI algorithm. Compared with fixed step size EASI algorithm (FS-EASI) and several variable step size EASI algorithms, the proposed algorithm greatly improves convergence rate while ensuring high separation accuracy. Effectiveness and superiority of the proposed algorithm are verified by simulation case analysis and satellite cabin structure experimental study.