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The positioning mean square error (MSE) prediction theory for dual Mach-Zehnder interferometric vibration sensor is proposed. The cross-correlation algorithm is considered. By taking into account the general noise time delay model, the impact of each noise term in output interference signal to ultimate positioning MSE is to our knowledge the first time be analyzed. An equivalent signal to noise ratio term for general noise time delay model is derived. It shows that incoherent phase noise (coming from polarization fading effect) makes an equivalent contribution to positioning MSE as additive noise under assumptions. In practical prediction, cross-correlation coefficient between two channel signals can be used to estimate positioning MSE. Simulation as well as experimental results are presented to corroborate the theory.