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Mathematical Problems in Engineering
Volume 2017, Article ID 5349879, 8 pages
Research Article

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

1Graduate School, Academy of Equipment, Beijing 101416, China
2Department of Optical and Electrical Equipment, Academy of Equipment, Beijing 101416, China

Correspondence should be addressed to Zhaoming Li; moc.361@yxbzgnimoahzil

Received 25 September 2017; Accepted 26 November 2017; Published 14 December 2017

Academic Editor: Ton D. Do

Copyright © 2017 Zhaoming Li et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.