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Student's $t$ -Filters for Noise Scale Estimation

Filip Tronarp, Toni Karvonen, Simo Sarkka
2019 IEEE Signal Processing Letters  
We analyse certain Student's t-filters for linear Gaussian systems with misspecified noise covariances.  ...  If the noise covariances are misscaled by a common scalar, then the re-scaling is asymptotically exact. We also compare the Student's t-filter scale estimates to the maximum likelihood estimates.  ...  FILTERING FOR LINEAR SYSTEMS We begin by introducing the classical Kalman filter [24] , [25, Ch. 4] and Student's t-filter as it appears in [11] , [12] .  ... 
doi:10.1109/lsp.2018.2889440 fatcat:xbeckk6lp5eqnb5ecq6olqhrny

A Novel Kullback-Leilber Divergence Minimization-Based Adaptive Student's t-Filter

Yulong Huang, Yonggang Zhang, Jonathon Chambers
2019 IEEE Transactions on Signal Processing  
To improve the Student's t-modelling accuracy, a novel KLD minimization-based adaptive method is then proposed to estimate the scale matrices of Student's t-distributions, in which the modified evidence  ...  A novel KLD minimization-based adaptive Student's t-filter is derived via combining the proposed Student's t-matching technique and the adaptive method.  ...  Godsill, at the Engineering Department of University of Cambridge, for providing comments and suggestions on the manuscript.  ... 
doi:10.1109/tsp.2019.2939079 fatcat:gvis5py3wvbdlcg4isj2jjpd2e

A Novel Robust Student's t-Based Kalman Filter

Yulong Huang, Yonggang Zhang, Ning Li, Zhemin Wu, Jonathon A. Chambers
2017 IEEE Transactions on Aerospace and Electronic Systems  
A novel robust Student's t based Kalman filter.  ...  Abstract-A novel robust Student's t based Kalman filter is proposed by using the variational Bayesian approach, which provides a Gaussian approximation to the posterior distribution.  ...  The problem of state estimation for a linear state space model with heavy-tailed process and measurement noises is transformed into the problem of state estimation for a Student's t based hierarchical  ... 
doi:10.1109/taes.2017.2651684 fatcat:kv7k3usn3nfa3fxbcdj7aubl5i

An Improved Invariant Kalman Filter for Lie Groups Attitude Dynamics with Heavy-Tailed Process Noise

Jiaolong Wang, Chengxi Zhang, Jin Wu, Ming Liu
2021 Machines  
of state prediction is defined based on student's t distribution, while the conjugate prior distributions of the scale matrix and degrees of freedom (dofs) parameter are respectively formulated as the  ...  To address the attitude estimation problem with heavy-tailed process noise, this paper proposes a hierarchical Gaussian state-space model for invariant Kalman filtering: The probability density function  ...  Robust Student's t Based Invariant Kalman Filter for Attitude Estimation on SO(3) Probability View of Attitude Estimation with Heavy-Tailed Process Noise For attitude estimation, if the process noise  ... 
doi:10.3390/machines9090182 fatcat:oio5m2ta4vgr3n2hqcbon2f6ya

Robust Student's $t$ -Based Cooperative Navigation for Autonomous Underwater Vehicles

Qian Li, Yueyang Ben, Syed Mohsen Naqvi, Jeffrey A. Neasham, Jonathon A. Chambers
2018 IEEE Transactions on Instrumentation and Measurement  
A robust leader-slave cooperative navigation (CN) algorithm for autonomous underwater vehicles (AUVs) based on the Student's t extended Kalman filter (SEKF) is proposed.  ...  Compared with the conventional EKF based on a Gaussian distributed noise assumption, which has been widely used in the field of CN, the Student's t-based filtering algorithms show an improved robustness  ...  With the assumption that both the process noise and measurement noise admit a Student's t distribution, a robust Student's t filter for a linear system is derived by approximating the posterior probability  ... 
doi:10.1109/tim.2018.2809139 fatcat:txybpgkowrhc5hqecyijji4cii

Robust student's t based nonlinear filter and smoother

Yulong Huang, Yonggang Zhang, Ning Li, Jonathon Chambers
2016 IEEE Transactions on Aerospace and Electronic Systems  
Index Terms-State estimation, heavy tailed noise, Student's t based approximate filter, Student's t based approximate smoother, Student's t weighted integral, unscented transform  ...  Novel Student's t based approaches for formulating a filter and smoother, which utilize heavy tailed process and measurement noise models, are found through approximations of the associated posterior probability  ...  Although this linear Student's t based filter can be used to achieve the filtering estimate for nonlinear systems with heavy tailed process and measurement noises based on the first order linearisation  ... 
doi:10.1109/taes.2016.150722 fatcat:bohjw34krvfifpfnqphoh75ktu

Robust Interacting Multiple Model Filter Based on Student's t-Distribution for Heavy-Tailed Measurement Noises

Dong Li, Jie Sun
2019 Sensors  
A robust IMM filter utilizing Student's t-distribution is proposed to handle the heavy-tailed measurement noises in this paper.  ...  The measurement noises are treated as Student's t-distribution, whose degrees of freedom (dof) and scale matrix are assumed to be governed by gamma and inverse Wishart distributions, respectively.  ...  That is because the scale matrix of Student's t-distribution is required to be estimated additionally for the proposed filter, while the scale matrix is known exactly for IMMVBStdF.  ... 
doi:10.3390/s19224830 fatcat:zd3arjcajzgebmdxvyor64t7n4

A New Outlier-Robust Student's t Based Gaussian Approximate Filter for Cooperative Localization

Yulong Huang, Yonggang Zhang, Bo Xu, Zhemin Wu, Jonathon Chambers
2017 IEEE/ASME transactions on mechatronics  
The state vector, scale matrices and degrees of freedom (dof) parameters are estimated based on the variational Bayesian approach by using the constructed Student's t based hierarchical Gaussian statespace  ...  In this paper, a new outlier-robust Student's t based Gaussian approximate filter is proposed to address the heavytailed process and measurement noises induced by the outlier measurements of velocity and  ...  A reasonable approach to improve the estimation accuracy is employing the Student's t distribution to model the heavytailed non-Gaussian noises.  ... 
doi:10.1109/tmech.2017.2744651 fatcat:v5vl4chymbe7hgnekiwvlpxkga

Robust Student's t based Stochastic Cubature Filter for Nonlinear Systems with Heavy-tailed Process and Measurement Noises [article]

Yulong Huang, Yonggang Zhang
2017 arXiv   pre-print
In this paper, a new robust Student's t based stochastic cubature filter (RSTSCF) is proposed for nonlinear state-space model with heavy-tailed process and measurement noises.  ...  correntropy criterion based Kalman filter, and robust Student's t based nonlinear filters, and is computationally much more efficient than the existing particle filter.  ...  The PF can model the process and measurement noises as arbitrary distributions, such as the Student's t distributions for heavy-tailed non-Gaussian noises [14] , [15] .  ... 
arXiv:1704.00040v1 fatcat:xexfr4hqabdkfmpvltbaof44qi

Multi-sensor Suboptimal Fusion Student's t Filter [article]

Tiancheng Li, Zheng Hu, Zhunga Liu, Xiaoxu Wang
2022 arXiv   pre-print
A multi-sensor fusion Student's t filter is proposed for time-series recursive estimation in the presence of heavy-tailed process and measurement noises.  ...  Driven from an information-theoretic optimization, the approach extends the single sensor Student's t Kalman filter based on the suboptimal arithmetic average (AA) fusion approach.  ...  The process and measurement noises are approximated by Student's t noise with the normal mean and covariance/scale parameters as specified, and with dof ν Q = ν R = 3.  ... 
arXiv:2204.11098v1 fatcat:7vpxks3ryfdkxjtiti4yjggq4i

A Novel Robust Student's t-Based Cubature Information Filter with Heavy-Tailed Noises

Yongtao Shui, Xiaogang Wang, Wutao Qin, Yu Wang, Baojun Pang, Naigang Cui
2020 International Journal of Aerospace Engineering  
In this paper, a novel robust Student's t-based cubature information filter is proposed for a nonlinear multisensor system with heavy-tailed process and measurement noises.  ...  To avoid the process uncertainty induced by the heavy-tailed process noise, the scale matrix of the predictive PDF is modeled as an inverse Wishart distribution and estimated dynamically.  ...  Since the Student's t distribution is a reasonable model of the heavy-tailed noise, some Student's t-based Kalman filters (STKF) have been proposed by modeling the heavy-tailed noises as the Student's  ... 
doi:10.1155/2020/7075037 fatcat:oojvhnlytvdgtlxbmcgklnwy3y

On-line Bayesian estimation of signals in symmetric /spl alpha/-stable noise

M.J. Lombardi, S.J. Godsill
2006 IEEE Transactions on Signal Processing  
We describe how the method can be used for estimation of TVAR signals buried in symmetric α-stable noise, efficiently implemented using an adaptation to an existing Rao-Blackwellised particle filter.  ...  In this paper we describe on-line Bayesian filtering methods for time series models with heavy-tailed α-stable noise.  ...  In particular, the Student's t and the power exponential distribution are especially appreciated in the setting of noise modelling; the densities that should be employed for the scale factor λ are reported  ... 
doi:10.1109/tsp.2005.861886 fatcat:jvk5ey6wonfaxi5tgjny2q5pca

A Student's t Mixture Probability Hypothesis Density Filter for Multi-Target Tracking with Outliers

Zhuowei Liu, Shuxin Chen, Hao Wu, Renke He, Lin Hao
2018 Sensors  
The proposed filter models the heavy-tailed process noise and measurement noise as a Student's t distribution as well as approximates the multi-target intensity as a mixture of Student's t components to  ...  Under the Bayesian filtering framework, the Student's t approximation-based closed form recursions are obtained for the linear system [18] .  ...  follow zero-mean Student's t distribution with scale matrix Q k−1 and R k , respectively.  ... 
doi:10.3390/s18041095 pmid:29617348 pmcid:PMC5948621 fatcat:75lmry2c5jgrpc45snqy6sulmu

Robust Bayesian Filtering and Smoothing Using Student's t Distribution [article]

Michael Roth, Tohid Ardeshiri, Emre Özkan, Fredrik Gustafsson
2017 arXiv   pre-print
After a discussion of Student's t distribution, exact filtering in linear state-space models with t noise is analyzed.  ...  Therefore, this paper describes the use of Student's t distribution to develop robust, scalable, and simple filtering and smoothing algorithms.  ...  Acknowledgment This work was supported by the project Scalable Kalman Filters granted by the Swedish Research Council (VR).  ... 
arXiv:1703.02428v1 fatcat:3escwhgiq5avxghn3vnugamjra

Improved Student's t-Based Unscented Filter and its Application to Trajectory Estimation for Maneuvering Target

Wu, Ma
2019 Applied Sciences  
To estimate the systems with one-step randomly delayed measurement and time-correlated heavy-tailed measurement noises, on the basis of robust Student's t based unscented filter (RSTUF), an improved Student's  ...  t based unscented filter (ISTUF) is proposed.  ...  Table 2 , we can find the estimation accuracy is higher than that in Reference [8] because the scale of noise affected the estimation accuracy of filters, and the scale of noise in this paper was less  ... 
doi:10.3390/app9112186 fatcat:jheacdaxbzarvbcx6ijy743cxi
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