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Urooj A, Dak A, Ristic B, Radhakrishnan R. 2D and 3D Angles-Only Target Tracking Based on Maximum Correntropy Kalman Filters. SENSORS 2022; 22:s22155625. [PMID: 35957180 PMCID: PMC9370889 DOI: 10.3390/s22155625] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 06/15/2022] [Revised: 07/21/2022] [Accepted: 07/22/2022] [Indexed: 02/01/2023]
Abstract
In this paper, angles-only target tracking (AoT) problem is investigated in the non Gaussian environment. Since the conventional minimum mean square error criterion based estimators tend to give poor accuracy in the presence of large outliers or impulsive noises in measurement, a maximum correntropy criterion (MCC) based framework is presented. Accordingly, three new estimation algorithms are developed for AoT problems based on the conventional sigma point filters, termed as MC-UKF-CK, MC-NSKF-GK and MC-NSKF-CK. Here MC-NSKF-GK represents the maximum correntropy new sigma point Kalman filter realized using Gaussian kernel and MC-NSKF-CK represents realization using Cauchy kernel. Similarly, based on the unscented Kalman filter, MC-UKF-CK has been developed. The performance of all these estimators is evaluated in terms of root-mean-square error (RMSE) in position and % track loss. The simulations were carried out for 2D as well as 3D AoT scenarios and it was inferred that, the developed algorithms performed with improved estimation accuracy than the conventional ones, in the presence of non Gaussian measurement noise.
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Affiliation(s)
- Asfia Urooj
- Department of Electrical Engineering, Sardar Vallabhbhai National Institute of Technology, Surat 395007, India; (A.U.); (A.D.); (R.R.)
| | - Aastha Dak
- Department of Electrical Engineering, Sardar Vallabhbhai National Institute of Technology, Surat 395007, India; (A.U.); (A.D.); (R.R.)
| | - Branko Ristic
- School of Engineering, RMIT University, Melbourne, VIC 3000, Australia
- Correspondence:
| | - Rahul Radhakrishnan
- Department of Electrical Engineering, Sardar Vallabhbhai National Institute of Technology, Surat 395007, India; (A.U.); (A.D.); (R.R.)
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2
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Variational Bayesian-Based Improved Maximum Mixture Correntropy Kalman Filter for Non-Gaussian Noise. ENTROPY 2022; 24:e24010117. [PMID: 35052143 PMCID: PMC8775028 DOI: 10.3390/e24010117] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 11/29/2021] [Revised: 01/07/2022] [Accepted: 01/10/2022] [Indexed: 11/28/2022]
Abstract
The maximum correntropy Kalman filter (MCKF) is an effective algorithm that was proposed to solve the non-Gaussian filtering problem for linear systems. Compared with the original Kalman filter (KF), the MCKF is a sub-optimal filter with Gaussian correntropy objective function, which has been demonstrated to have excellent robustness to non-Gaussian noise. However, the performance of MCKF is affected by its kernel bandwidth parameter, and a constant kernel bandwidth may lead to severe accuracy degradation in non-stationary noises. In order to solve this problem, the mixture correntropy method is further explored in this work, and an improved maximum mixture correntropy KF (IMMCKF) is proposed. By derivation, the random variables that obey Beta-Bernoulli distribution are taken as intermediate parameters, and a new hierarchical Gaussian state-space model was established. Finally, the unknown mixing probability and state estimation vector at each moment are inferred via a variational Bayesian approach, which provides an effective solution to improve the applicability of MCKFs in non-stationary noises. Performance evaluations demonstrate that the proposed filter significantly improves the existing MCKFs in non-stationary noises.
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Shaukat N, Moinuddin M, Otero P. Underwater Vehicle Positioning by Correntropy-Based Fuzzy Multi-Sensor Fusion. SENSORS (BASEL, SWITZERLAND) 2021; 21:6165. [PMID: 34577372 PMCID: PMC8470692 DOI: 10.3390/s21186165] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 08/10/2021] [Revised: 09/06/2021] [Accepted: 09/10/2021] [Indexed: 11/16/2022]
Abstract
The ability of the underwater vehicle to determine its precise position is vital to completing a mission successfully. Multi-sensor fusion methods for underwater vehicle positioning are commonly based on Kalman filtering, which requires the knowledge of process and measurement noise covariance. As the underwater conditions are continuously changing, incorrect process and measurement noise covariance affect the accuracy of position estimation and sometimes cause divergence. Furthermore, the underwater multi-path effect and nonlinearity cause outliers that have a significant impact on positional accuracy. These non-Gaussian outliers are difficult to handle with conventional Kalman-based methods and their fuzzy variants. To address these issues, this paper presents a new and improved adaptive multi-sensor fusion method by using information-theoretic, learning-based fuzzy rules for Kalman filter covariance adaptation in the presence of outliers. Two novel metrics are proposed by utilizing correntropy Gaussian and Versoria kernels for matching theoretical and actual covariance. Using correntropy-based metrics and fuzzy logic together makes the algorithm robust against outliers in nonlinear dynamic underwater conditions. The performance of the proposed sensor fusion technique is compared and evaluated using Monte-Carlo simulations, and substantial improvements in underwater position estimation are obtained.
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Affiliation(s)
- Nabil Shaukat
- Institute of Oceanic Engineering Research, University of Malaga, 29010 Malaga, Spain;
| | - Muhammad Moinuddin
- Department of Electrical and Computer Engineering, King Abdulaziz University, Jeddah 21589, Saudi Arabia;
- Center of Excellence in Intelligent Engineering Systems, King Abdulaziz University, Jeddah 21589, Saudi Arabia
| | - Pablo Otero
- Institute of Oceanic Engineering Research, University of Malaga, 29010 Malaga, Spain;
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Wang L, Wang S, Yang W. Adaptive federated filter for multi-sensor nonlinear system with cross-correlated noises. PLoS One 2021; 16:e0246680. [PMID: 33606738 PMCID: PMC7895398 DOI: 10.1371/journal.pone.0246680] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/15/2020] [Accepted: 01/22/2021] [Indexed: 11/23/2022] Open
Abstract
This paper presents an adaptive approach to the federated filter for multi-sensor nonlinear systems with cross-correlations between process noise and local measurement noise. The adaptive Gaussian filter is used as the local filter of the federated filter for the first time, which overcomes the performance degradation caused by the cross-correlated noises. Two kinds of adaptive federated filters are proposed, one uses a de-correlation framework as local filter, and the subfilter of the other one is defined as a Gaussian filter with correlated noises at the same-epoch, and much effort is made to verify the theoretical equivalence of the two algorithms in the nonlinear fusion system. Simulation results show that the proposed algorithms are superior to the traditional federated filter and Gaussian filter with same-paced correlated noises, and the equivalence between the proposed algorithms and high degree cubature federated filter is also demonstrated.
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Affiliation(s)
- Lijun Wang
- School of Navigation, Guangdong Ocean University, Zhanjiang, China
- Hubei Key Laboratory of Inland Shipping Technology, Wuhan, China
| | - Sisi Wang
- School of Navigation, Guangdong Ocean University, Zhanjiang, China
- * E-mail:
| | - Wenzhi Yang
- School of Navigation, Guangdong Ocean University, Zhanjiang, China
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Ali A, Qadri S, Khan Mashwani W, Kumam W, Kumam P, Naeem S, Goktas A, Jamal F, Chesneau C, Anam S, Sulaiman M. Machine Learning Based Automated Segmentation and Hybrid Feature Analysis for Diabetic Retinopathy Classification Using Fundus Image. ENTROPY 2020; 22:e22050567. [PMID: 33286339 PMCID: PMC7517087 DOI: 10.3390/e22050567] [Citation(s) in RCA: 17] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 03/23/2020] [Revised: 04/23/2020] [Accepted: 04/23/2020] [Indexed: 11/16/2022]
Abstract
The object of this study was to demonstrate the ability of machine learning (ML) methods for the segmentation and classification of diabetic retinopathy (DR). Two-dimensional (2D) retinal fundus (RF) images were used. The datasets of DR-that is, the mild, moderate, non-proliferative, proliferative, and normal human eye ones-were acquired from 500 patients at Bahawal Victoria Hospital (BVH), Bahawalpur, Pakistan. Five hundred RF datasets (sized 256 × 256) for each DR stage and a total of 2500 (500 × 5) datasets of the five DR stages were acquired. This research introduces the novel clustering-based automated region growing framework. For texture analysis, four types of features-histogram (H), wavelet (W), co-occurrence matrix (COM) and run-length matrix (RLM)-were extracted, and various ML classifiers were employed, achieving 77.67%, 80%, 89.87%, and 96.33% classification accuracies, respectively. To improve classification accuracy, a fused hybrid-feature dataset was generated by applying the data fusion approach. From each image, 245 pieces of hybrid feature data (H, W, COM, and RLM) were observed, while 13 optimized features were selected after applying four different feature selection techniques, namely Fisher, correlation-based feature selection, mutual information, and probability of error plus average correlation. Five ML classifiers named sequential minimal optimization (SMO), logistic (Lg), multi-layer perceptron (MLP), logistic model tree (LMT), and simple logistic (SLg) were deployed on selected optimized features (using 10-fold cross-validation), and they showed considerably high classification accuracies of 98.53%, 99%, 99.66%, 99.73%, and 99.73%, respectively.
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Affiliation(s)
- Aqib Ali
- Department of Computer Science & IT, The Islamia University of Bahawalpur, Bahawalpur 61300, Pakistan; (A.A.); (S.Q.); (S.N.)
| | - Salman Qadri
- Department of Computer Science & IT, The Islamia University of Bahawalpur, Bahawalpur 61300, Pakistan; (A.A.); (S.Q.); (S.N.)
| | - Wali Khan Mashwani
- Institute of Numerical Sciences, Kohat University of Sciences & Technology, Kohat 26000, Pakistan;
| | - Wiyada Kumam
- Program in Applied Statistics, Department of Mathematics and Computer Science, Faculty of Science and Technology, Rajamangala University of Technology Thanyaburi (RMUTT), Thanyaburi, Pathumthani 12110, Thailand
- Correspondence: (W.K.); (P.K.)
| | - Poom Kumam
- Center of Excellence in Theoretical and Computational Science (TaCS-CoE) & KMUTT Fixed Point Research Laboratory, Room SCL 802 Fixed Point Laboratory, Science Laboratory Building, Departments of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, Thailand
- Department of Medical Research, China Medical University Hospital, Taichung 40402, Taiwan
- Correspondence: (W.K.); (P.K.)
| | - Samreen Naeem
- Department of Computer Science & IT, The Islamia University of Bahawalpur, Bahawalpur 61300, Pakistan; (A.A.); (S.Q.); (S.N.)
| | - Atila Goktas
- Department of Statistics, Mugla Sıtkı Koçman University, Mugla 48000, Turkey;
| | - Farrukh Jamal
- Department of Statistics, Govt S.A Post Graduate College Dera Nawab Sahib, Bahawalpur 63351, Pakistan;
| | - Christophe Chesneau
- Department of Mathematics, Université de Caen, LMNO, Campus II, Science 3, 14032 Caen, France;
| | - Sania Anam
- Department of Computer Science, Govt Degree College for Women Ahmadpur East, Bahawalpur 63350, Pakistan;
| | - Muhammad Sulaiman
- Department of Mathematics, Abdul Wali Khan University Mardan, Mardan 23200, Pakistan;
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Li D, Sun J. Robust Interacting Multiple Model Filter Based on Student's t-Distribution for Heavy-Tailed Measurement Noises. SENSORS 2019; 19:s19224830. [PMID: 31698779 PMCID: PMC6891737 DOI: 10.3390/s19224830] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 09/08/2019] [Revised: 11/03/2019] [Accepted: 11/04/2019] [Indexed: 11/16/2022]
Abstract
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.
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Affiliation(s)
- Dong Li
- Unit 94, PLA 91550, Dalian 116023, China
- Correspondence: ; Tel.: +86-0411-8085-8444
| | - Jie Sun
- Unit 93, PLA 91550, Dalian 116023, China;
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Adaptive Extended Kalman Filter with Correntropy Loss for Robust Power System State Estimation. ENTROPY 2019; 21:e21030293. [PMID: 33267008 PMCID: PMC7514774 DOI: 10.3390/e21030293] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 01/25/2019] [Revised: 03/12/2019] [Accepted: 03/13/2019] [Indexed: 11/17/2022]
Abstract
Monitoring the current operation status of the power system plays an essential role in the enhancement of the power grid for future requirements. Therefore, the real-time state estimation (SE) of the power system has been of widely-held concern. The Kalman filter is an outstanding method for the SE, and the noise in the system is generally assumed to be Gaussian noise. In the actual power system however, these measurements are usually disturbed by non-Gaussian noises in practice. Furthermore, it is hard to get the statistics of the state noise and measurement noise. As a result, a novel adaptive extended Kalman filter with correntropy loss is proposed and applied for power system SE in this paper. Firstly, correntropy is used to improve the robustness of the EKF algorithm in the presence of non-Gaussian noises and outliers. In addition, an adaptive update mechanism of the covariance matrixes of the measurement and process noises is introduced into the EKF with correntropy loss to enhance the accuracy of the algorithm. Extensive simulations are carried out on IEEE 14-bus and IEEE 30-bus test systems to verify the feasibility and robustness of the proposed algorithm.
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