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 An Adaptive Filter for Nonlinear Multi-Sensor Systems with Heavy-Tailed Noise

Sensors ◽  
2020 ◽  
Vol 20 (23) ◽  
pp. 6757
Author(s):  
Xiangxiang Dong ◽  
Luigi Chisci ◽  
Yunze Cai
Keyword(s):  
Information Fusion ◽  
Joint Estimation ◽  
Information Feedback ◽  
Auxiliary Parameter ◽  
Variational Bayesian ◽  
Information Filter ◽  
Scenarios Simulation ◽  
Heavy Tailed ◽  
Student’S T ◽  
Scale Matrix

Aiming towards state estimation and information fusion for nonlinear systems with heavy-tailed measurement noise, a variational Bayesian Student’s t-based cubature information filter (VBST-CIF) is designed. Furthermore, a multi-sensor variational Bayesian Student’s t-based cubature information feedback fusion (VBST-CIFF) algorithm is also derived. In the proposed VBST-CIF, the spherical-radial cubature (SRC) rule is embedded into the variational Bayes (VB) method for a joint estimation of states and scale matrix, degree-of-freedom (DOF) parameter, as well as an auxiliary parameter in the nonlinear system with heavy-tailed noise. The designed VBST-CIF facilitates multi-sensor fusion, allowing to derive a VBST-CIFF algorithm based on multi-sensor information feedback fusion. The performance of the proposed algorithms is assessed in target tracking scenarios. Simulation results demonstrate that the proposed VBST-CIF/VBST-CIFF outperform the conventional cubature information filter (CIF) and cubature information feedback fusion (CIFF) algorithms.

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 A Robust SMC-PHD Filter for Multi-Target Tracking with Unknown Heavy-Tailed Measurement Noise

Sensors ◽  
2021 ◽  
Vol 21 (11) ◽  
pp. 3611
Author(s):  
Yang Gong ◽  
Chen Cui
Keyword(s):  
Target Tracking ◽  
Sequential Monte Carlo ◽  
Measurement Noise ◽  
Particle Simulation ◽  
Target Number ◽  
Student T Distribution ◽  
Multi Target Tracking ◽  
Heavy Tailed ◽  
Scale Matrix ◽  
T Distribution

In multi-target tracking, the sequential Monte Carlo probability hypothesis density (SMC-PHD) filter is a practical algorithm. Influenced by outliers under unknown heavy-tailed measurement noise, the SMC-PHD filter suffers severe performance degradation. In this paper, a robust SMC-PHD (RSMC-PHD) filter is proposed. In the proposed filter, Student-t distribution is introduced to describe the unknown heavy-tailed measurement noise where the degrees of freedom (DOF) and the scale matrix of the Student-t distribution are respectively modeled as a Gamma distribution and an inverse Wishart distribution. Furthermore, the variational Bayesian (VB) technique is employed to infer the unknown DOF and scale matrix parameters while the recursion estimation framework of the RSMC-PHD filter is derived. In addition, considering that the introduced Student- t distribution might lead to an overestimation of the target number, a strategy is applied to modify the updated weight of each particle. Simulation results demonstrate that the proposed filter is effective with unknown heavy-tailed measurement noise.

Improved square-root cubature information filter

2016 ◽  
Vol 39 (4) ◽  
pp. 579-588 ◽  
Author(s):  
Yulong Huang ◽  
Yonggang Zhang ◽  
Ning Li ◽  
Lin Zhao
Keyword(s):  
Large Scale ◽  
Estimation Error ◽  
Sampling Interval ◽  
Prediction Errors ◽  
Square Root ◽  
Sigma Point ◽  
Theoretical Comparison ◽  
Error Covariance ◽  
Information Filter ◽  
Scale Matrix

In this paper, a theoretical comparison between existing the sigma-point information filter (SPIF) framework and the unscented information filter (UIF) framework is presented. It is shown that the SPIF framework is identical to the sigma-point Kalman filter (SPKF). However, the UIF framework is not identical to the classical SPKF due to the neglect of one-step prediction errors of measurements in the calculation of state estimation error covariance matrix. Thus SPIF framework is more reasonable as compared with UIF framework. According to the theoretical comparison, an improved cubature information filter (CIF) is derived based on the superior SPIF framework. Square-root CIF (SRCIF) is also developed to improve the numerical accuracy and stability of the proposed CIF. The proposed SRCIF is applied to a target tracking problem with large sampling interval and high turn rate, and its performance is compared with the existing SRCIF. The results show that the proposed SRCIF is more reliable and stable as compared with the existing SRCIF. Note that it is impractical for information filters in large-scale applications due to the enormous computational complexity of large-scale matrix inversion, and advanced techniques need to be further considered.

scholarly journals AN INDOOR SLAM METHOD BASED ON KINECT AND MULTI-FEATURE EXTENDED INFORMATION FILTER

2017 ◽  
Vol XLII-2/W7 ◽  
pp. 327-332
Author(s):  
M. Chang ◽  
Z. Kang
Keyword(s):  
Point Cloud ◽  
Information Matrix ◽  
Depth Image ◽  
Point Cloud Data ◽  
A Posteriori ◽  
Cloud Data ◽  
Information Filter ◽  
Error Accumulation ◽  
Priori Information ◽  
Information Vector

Based on the frame of ORB-SLAM in this paper the transformation parameters between adjacent Kinect image frames are computed using ORB keypoints, from which priori information matrix and information vector are calculated. The motion update of multi-feature extended information filter is then realized. According to the point cloud data formed by depth image, ICP algorithm was used to extract the point features of the point cloud data in the scene and built an observation model while calculating a-posteriori information matrix and information vector, and weakening the influences caused by the error accumulation in the positioning process. Furthermore, this paper applied ORB-SLAM frame to realize autonomous positioning in real time in interior unknown environment. In the end, Lidar was used to get data in the scene in order to estimate positioning accuracy put forward in this paper.

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 An Improved Extended Information Filter SLAM Algorithm Based on Omnidirectional Vision

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Jingchuan Wang ◽  
Weidong Chen
Keyword(s):  
High Reliability ◽  
Information Matrix ◽  
Omnidirectional Vision ◽  
Great Efficiency ◽  
Repeated Observations ◽  
Global Correlation ◽  
Information Filter ◽  
Wide Scale ◽  
Slam Algorithm ◽  
Omnidirectional Images

In the SLAM application, omnidirectional vision extracts wide scale information and more features from environments. Traditional algorithms bring enormous computational complexity to omnidirectional vision SLAM. An improved extended information filter SLAM algorithm based on omnidirectional vision is presented in this paper. Based on the analysis of structure a characteristics of the information matrix, this algorithm improves computational efficiency. Considering the characteristics of omnidirectional images, an improved sparsification rule is also proposed. The sparse observation information has been utilized and the strongest global correlation has been maintained. So the accuracy of the estimated result is ensured by using proper sparsification of the information matrix. Then, through the error analysis, the error caused by sparsification can be eliminated by a relocation method. The results of experiments show that this method makes full use of the characteristic of repeated observations for landmarks in omnidirectional vision and maintains great efficiency and high reliability in mapping and localization.

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 Revisit the Wishart Distributionm

2020 ◽  
Vol 9 (5) ◽  
pp. 79
Author(s):  
Emilly A. Obuya ◽  
Prakash C. Joshi ◽  
Thomas A. Gray ◽  
Thomas C. Keane ◽  
Wayne E. Jones Jr.
Keyword(s):  
Standard Form ◽  
Wishart Distribution ◽  
Degree Of Freedom ◽  
Data Matrix ◽  
Alternative Proof ◽  
Scale Matrix ◽  
Unit Normal

If S_pxp can be written as S=X' X , where X_nxp is a data matrix from N_p(0,V) , then S is said to have a Wishart distribution with scale matrix V of degree of freedom parameter n. We write S~W_p(V,n). When V=I,  the distribution is said to be in standard form. When p=1, the W_1(σ^2, n)  distribution is found to be Σ^n_i=1(x^2_i) , where the elements of x_i  are identically independently distributed unit normal variables; being the σ^2(x_n)^2 distribution. Although Anderson (1984, p248~249) has presented two theorems for the Wishart distribution. In the following we give an alternative proof.

scholarly journals Adaptive Consensus-Based Unscented Information Filter for Tracking Target with Maneuver and Colored Noise

Sensors ◽  
2019 ◽  
Vol 19 (14) ◽  
pp. 3069 ◽  
Author(s):  
Li ◽  
Wang ◽  
Zheng
Keyword(s):  
State Estimation ◽  
Situation Awareness ◽  
Information Matrix ◽  
Estimation Method ◽  
Measurement Noise ◽  
Distributed State Estimation ◽  
Information Filter ◽  
Fading Factor ◽  
Stability And Accuracy ◽  
The Impact

Distributed state estimation plays a key role in space situation awareness via a sensor network. This paper proposes two adaptive consensus-based unscented information filters for tracking target with maneuver and colored measurement noise. The proposed filters can fulfill the distributed estimation for non-linear systems with the aid of a consensus strategy, and can reduce the impact of colored measurement noise by employing the state augmentation and measurement differencing methods. In addition, a fading factor that shrinks the predicted information state and information matrix can suppress the impact of dynamical model error induced by target maneuvers. The performances of the proposed algorithms are investigated by considering a target tracking problem using a space-based radar network. This shows that the proposed algorithms outperform the traditional consensus-based distributed state estimation method in aspects of tracking stability and accuracy.

Sign in / Sign up

Export Citation Format

Share Document