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This work describes an optical measuring device that comprises multiple laser mouse sensors to estimate 3-DOF planar motion. The linear least squares (LLS) method and nonlinear least squares (NLS) method are adopted to estimate the positions in this over-determined system. Two circular trajectories - non-orientated and self-orientated - are employed to evaluate the feasibility of the proposed device. The results are presented and validated by simulations and experimentally. For a circular trajectory with self-orientation, the estimated positions of device determined using the NLS method are associated with apparently smaller positional errors than those calculated using the LLS method. The noise at the sensor outputs has a large impact on the estimate of position. The analysis is essential to examining the error sources and increasing the accuracy of odometric measurement.