This paper presents a novel approach to reconstruct the output of linear systems in the case where the measured output is uniformly quantized. By fitting the quantized measurements with polynomials in a moving horizon manner, a smooth signal is reconstructed by solving a convex optimization problem with ℓ1-norm regularization. The quantization feature and the system models are taken into account in the optimization. A numerical example is given to show the excellent reconstruction performance of the proposed method. In addition, the proposed method is implemented in a high-precision linear stage through DSP, and its effectiveness is verified through experiments using a real positioning system.
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