scholarly journals A Student’s T Mixture Cardinality-Balanced Multi-Target Multi-Bernoulli Filter With Heavy-Tailed Process and Measurement Noises

IEEE Access ◽  
2018 ◽  
Vol 6 ◽  
pp. 51098-51109 ◽  
Author(s):  
Mingjie Wang ◽  
Hongbing Ji ◽  
Yongquan Zhang ◽  
Xiaolong Hu
Keyword(s):  
Bernoulli Filter ◽  
Measurement Noises ◽  
Heavy Tailed ◽  
Student’S T

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

Sensors ◽  
2019 ◽  
Vol 19 (22) ◽  
pp. 4830
Author(s):  
Dong Li ◽  
Jie Sun
Keyword(s):  
Interacting Multiple Model ◽  
Multiple Model ◽  
Student’S T Distribution ◽  
Target State ◽  
Measurement Noises ◽  
Heavy Tailed ◽  
Student’S T ◽  
Scale Matrix ◽  
Student's T Distribution ◽  
T Distribution

In maneuvering target tracking applications, the performance of the traditional interacting multiple model (IMM) filter deteriorates seriously under heavy-tailed measurement noises which are induced by outliers. 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. The mixing distributions of the target state, dof, and scale matrix are achieved through the interacting strategy of IMM filter. These mixing distributions are used for the initialization of time prediction. The posterior distributions of the target state, dof, and scale matrix conditioned on each mode are obtained by employing variational Bayesian approach. Then, the target state, dof, and scale matrix parameters are jointly estimated. A variational method is also given to estimate the mode probability. The unscented transform is utilized to solve the nonlinear estimation problem. Simulation results show that the proposed filter improves the estimation accuracy of target state and mode probability over existing filters under heavy-tailed measurement noises.

scholarly journals MULTIVARIATE HEAVY-TAILED MODELS FOR VALUE-AT-RISK ESTIMATION

2012 ◽  
Vol 15 (04) ◽  
pp. 1250029 ◽  
Author(s):  
CARLO MARINELLI ◽  
STEFANO D'ADDONA ◽  
SVETLOZAR T. RACHEV
Keyword(s):  
At Risk ◽  
Value At Risk ◽  
Stock Price ◽  
Risk Estimation ◽  
Price Data ◽  
Heavy Tailed Distributions ◽  
Derivative Instruments ◽  
Heavy Tailed ◽  
Student’S T

For purposes of Value-at-Risk estimation, we consider several multivariate families of heavy-tailed distributions, which can be seen as multidimensional versions of Paretian stable and Student's t distributions allowing different marginals to have different indices of tail thickness. After a discussion of relevant estimation and simulation issues, we conduct a backtesting study on a set of portfolios containing derivative instruments, using historical US stock price data.

scholarly journals Time series forecasting: problem of heavy-tailed distributed noise

2021 ◽  
Author(s):  
Marta Markiewicz ◽  
Agnieszka Wyłomańska
Keyword(s):  
Time Series ◽  
Regression Tree ◽  
Time Series Forecasting ◽  
Statistical Machine Learning ◽  
Practical Applications ◽  
Challenging Tasks ◽  
Heavy Tailed Distribution ◽  
Likelihood Approach ◽  
Heavy Tailed ◽  
Student’S T

AbstractTime series forecasting has been the area of intensive research for years. Statistical, machine learning or mixed approaches have been proposed to handle this one of the most challenging tasks. However, little research has been devoted to tackle the frequently appearing assumption of normality of given data. In our research, we aim to extend the time series forecasting models for heavy-tailed distribution of noise. In this paper, we focused on normal and Student’s t distributed time series. The SARIMAX model (with maximum likelihood approach) is compared with the regression tree-based method—random forest. The research covers not only forecasts but also prediction intervals, which often have hugely informative value as far as practical applications are concerned. Although our study is focused on the selected models, the presented problem is universal and the proposed approach can be discussed in the context of other systems.

scholarly journals A Novel Robust Student’s t-Based Cubature Information Filter with Heavy-Tailed Noises

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Yongtao Shui ◽  
Xiaogang Wang ◽  
Wutao Qin ◽  
Yu Wang ◽  
Baojun Pang ◽  
...  
Keyword(s):  
Information Matrix ◽  
Wishart Distribution ◽  
Gaussian Form ◽  
Information Filter ◽  
Leibler Divergence ◽  
Heavy Tailed ◽  
Bayesian Approximation ◽  
Student’S T ◽  
Scale Matrix ◽  
Fixed Point Iterations

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. At first, the predictive probability density function (PDF) and the likelihood PDF are approximated as two different Student’s t distributions. 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. Then, the predictive PDF and the likelihood PDF are transformed into a hierarchical Gaussian form to obtain the approximate solution of posterior PDF. Based on the variational Bayesian approximation method, the posterior PDF is approximated iteratively by minimizing the Kullback-Leibler divergence function. Based on the posterior PDF of the auxiliary parameters, the predicted covariance and measurement noise covariance are modified. And then the information matrix and information state are updated by summing the local information contributions, which are computed based on the modified covariance. Finally, the state, scale matrix, and posterior densities are estimated after fixed point iterations. And the simulation results for a target tracking example demonstrate the superiority of the proposed filter.

scholarly journals Distributed Consensus Student-t Filter for Sensor Networks With Heavy-Tailed Process and Measurement Noises

IEEE Access ◽  
2020 ◽  
Vol 8 ◽  
pp. 167865-167874
Author(s):  
Jinran Wang ◽  
Peng Dong ◽  
Kai Shen ◽  
Xun Song ◽  
Xiaodong Wang
Keyword(s):  
Sensor Networks ◽  
Distributed Consensus ◽  
Measurement Noises ◽  
Heavy Tailed
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