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When compared to the accuracy of nanoscale control, the resolution of current positioning sensors is relatively low. Because of this, the output from low-precision sensors normally includes quantization errors that could degrade control performance. As a result, in this paper, a method of quantization error estimation based on the least square method is examined. In the proposed method, estimation accuracy is improved by taking into account the effect of input disturbances. Furthermore, a bias adjustment method is proposed that is expected to satisfy the constraints on quantization error. The effectiveness of the proposed method is demonstrated by simulations and experiments.