Robust Student’s t-Based Stochastic Cubature Kalman Filter with Heavy-Tailed Noises and Randomly Delayed Measurements

LU Chun-guang; ZHANG Yong-shun; LI Zhi-hui; GE Qi-chao

doi:10.3969/j.issn.0372-2112.2019.09.003

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Robust Student’s t-Based Stochastic Cubature Kalman Filter with Heavy-Tailed Noises and Randomly Delayed Measurements

更新时间：2025-07-16

- Robust Student’s t-Based Stochastic Cubature Kalman Filter with Heavy-Tailed Noises and Randomly Delayed Measurements
- Acta Electronica Sinica Vol. 47, Issue 9, Pages: 1830-1840(2019)
- 作者机构：
  
  1. 空军工程大学防空反导学院,陕西,西安,710051
  2. 信息感知技术协同创新中心,陕西,西安,710077
  3. 空军工程大学防空反导学院,陕西,西安,710051
  4. 信息感知技术协同创新中心,陕西,西安,710077
- 作者简介：
- 基金信息：
  
  National Natural Science Foundation of China (No.61571459)
- DOI：10.3969/j.issn.0372-2112.2019.09.003
  CLC： TN97
- Published Online：25 September 2019，
  
  Published：2019
- 稿件说明：
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LU Chun-guang, ZHANG Yong-shun, LI Zhi-hui, et al. Robust Student’s t-Based Stochastic Cubature Kalman Filter with Heavy-Tailed Noises and Randomly Delayed Measurements[J]. Acta Electronica Sinica, 2019, 47(9): 1830-1840.
DOI：

LU Chun-guang, ZHANG Yong-shun, LI Zhi-hui, et al. Robust Student’s t-Based Stochastic Cubature Kalman Filter with Heavy-Tailed Noises and Randomly Delayed Measurements[J]. Acta Electronica Sinica, 2019, 47(9): 1830-1840. DOI： 10.3969/j.issn.0372-2112.2019.09.003.

摘要

针对量测随机延迟下带厚尾过程噪声和量测噪声的非线性状态估计问题，本文通过充分考虑量测一步随机延迟特性及过程噪声和量测噪声的厚尾特性，推导了一种新的鲁棒Student's t滤波器框架，并采用随机Student's t-球面相径容积规则近似计算Student's t权值积分，从而设计了一种新的鲁棒Student's t随机容积滤波器.首先，采用一组服从伯努利分布的随机序列来描述系统中可能存在的量测一步随机延迟现象，并采用Student's t分布刻画过程噪声和量测噪声中存在的厚尾特性；其次，从理论上证明了当自由度参数趋于无穷以及随机延迟概率为零时，该鲁棒Student's t滤波器就自动地降为标准的非线性高斯近似滤波器；最后，采用随机Student's t-球面相径容积规则给出了一种新的鲁棒Student's t随机容积滤波器，并通过协同转弯模型验证了该滤波器的有效性和优越性.

Abstract

Aiming at the nonlinear state estimation problem with heavy-tailed process measurement noise and randomly delayed measurements

this paper deduces a new robust student's t filter framework by taking into one-step random delay characteristics and heavy-tailed characteristics of process noise and measurement noise account fully. Meanwhile

this paper proposes a new robust Student's t-based stochastic cubature filter(RSTCF)by approximately calculating the Student's t weight integral using stochastic Student's t-spherical radial cubature rule. Firstly

this paper uses a set of stochastic sequences obeying the Bernoulli distribution to describe the possible one-step random delay phenomenon in the system

what's more

this paper also uses the student's t distribution to characterize the heavy-tailed characteristics of the process noise and measurement noise. Secondly

it's theoretically proved that the robust Student's t filter automatically will be reduced to a standard nonlinear Gaussian approximation filter when the degrees of freedom in the posterior probability density function of the state and measurement noise are increasing continuously and randomly delay probability is equal to zero. Finally

this paper presentes a new robust Student's t-based stochastic cubature filter by use of stochastic Student's t-spherical radial cubature rule. The effectiveness and superiority of the filter are verified by the coordinated turn maneuvers model.

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