Time-Varying Noise Statistic Estimator Based Adaptive Simplex Cubature Kalman Filter

To address the problem that filtering accuracy is reduced with the inaccurate time-varying noise statistic in conventional cubature Kalman filter, a noise statistic estimator based adaptive simplex cubature Kalman filter is put forward in this paper. First, the simplex cubature rule is adopted to approximate the intractable nonlinear Gaussian weighted integral in the filter. Secondly, a suboptimal unbiased constant noise statistic estimator is derived based on the maximum a posteriori estimation criterion. For the time-varying noise, the above estimator is modified using an exponential weighted attenuation method to realize the oblivion of stale data which results in a fading memory estimator, which has the ability to estimate the time-varying noise statistic to revise the filter online. The simulation results indicate that the proposed filter can achieve higher accuracy than conventional filters with inaccurate noise statistic.