In the view of the traditional linearization of nonlinear function in the inaccurate filtering process, the second order striling polynomial interpolation method was proposed to approximate the state quantity digital characteristics. The control input was redefined in this paper. Combined with the second order interpolation, it implemented the optimal control. The entropy probability filtering algorithm mentioned in this paper provides a new idea for the filtering process applied in SLAM. The simulation experiments showed that the second order interpolation filtering algorithm had a higher filtering precision, and the new information mean and variance tended to be zero with a faster convergence rate when the system was stable. The mean of ranging and angle measured of the new information based on entropy probability with divided difference filter II (DDF II) could be reached to stability as short as in two minutes, which were controlled in 0.1 m and 0.3 m.
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