Circuits, Systems, and Signal Processing

, Volume 37, Issue 5, pp 2206–2225 | Cite as

Design of High-Degree Student’s t-Based Cubature Filters

  • Yulong Huang
  • Yonggang Zhang
Short Paper


The Student’s t-based nonlinear filter (STNF) can cope with the filtering problem of nonlinear systems with heavy-tailed process and measurement noises. The key problem in the design of a STNF is how to calculate the Student’s t weighted integral, and the performance of the STNF depends heavily on the used numerical integration technique. In this paper, new high-degree Student’s t spherical-radial cubature rules (STSRCRs) for the Student’s t weighted integral are proposed based on spherical-radial transformation and moment matching methods, from which new high-degree Student’s t-based cubature filters (STCFs) are developed. The proposed high-degree STSRCRs can achieve better approximation to the Student’s t weighted integral as compared with the existing third-degree Student’s t integral rules. As a result, the proposed high-degree STCFs have higher estimation accuracy than the existing STNFs. Simulation results illustrate that the proposed filters can achieve higher estimation accuracy than the existing Gaussian approximate filters, Huber-based nonlinear Kalman filters and STNFs with slightly increased computational complexities, and are computationally much more efficient than the existing Gaussian sum filter and particle filter.


Nonlinear filter Student’s t weighted integral Outlier State estimation Nonlinear system 


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Copyright information

© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  1. 1.College of AutomationHarbin Engineering UniversityHarbinPeople’s Republic of China

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