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We apply the independent component analysis (ICA) algorithm to uncover intrinsic noise in the beam position monitor (BPM) system. Numerical simulations found that ICA is efficient in the BPM noise estimation. The ICA algorithm is applied to the turn-by-turn data at the Relativistic Heavy Ion Collider. We found the distribution of the BPM noise level, which is consistent with the Johnson-Nyquist thermal noise model. The ICA analysis of turn-by-turn data can be used in neuronetwork feasibility of monitoring a storage ring parasitically.