Analysis of Least Stochastic Entropy Adaptive Filters for Noncircular Gaussian Signals

Zhang, Xing; Dees, Bruno Scalzo; Li, Chunguo; Xia, Yili; Yang, Luxi; Mandic, Danilo P.

doi:10.1109/tcsii.2019.2936767

Cited by 11 publications

(5 citation statements)

References 17 publications

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“…d-Derivation of the gain matrix K 1 i (k +1) (first recursion): Substituting from (37) into (32) while using (12), (13) and (36), the gain matrix K 1 i (k + 1) is given by:…”

Section: The Recursive Formula Of the Filtered Estimatormentioning

confidence: 99%

“…Substituting from (40) into (39) while using (12), (13) and (32), then after simple mathematical manipulation, it is easy to get: j (k + 1|k + 1 ) is given by:…”

Section: The Recursive Formula Of the Filtered Estimatormentioning

confidence: 99%

“…Many algorithms were developed in the literature for state estimation of nonlinear systems [1]- [13]. These algorithms include various Kalman Filter (KF) variants such as: the extended Kalman filter (EKF) [1]- [4], the unscented Kalman filter (UKF) [5], [6], the ensemble Kalman filter (EnKF) [7], cubature Kalman Filer [8], central difference Kalman Filer [9], etc.…”

Section: Introduction a Literature Reviewmentioning

confidence: 99%

“…These algorithms include various Kalman Filter (KF) variants such as: the extended Kalman filter (EKF) [1]- [4], the unscented Kalman filter (UKF) [5], [6], the ensemble Kalman filter (EnKF) [7], cubature Kalman Filer [8], central difference Kalman Filer [9], etc. Other examples of nonlinear estimators include the Moving Horizon estimator (MHE) [10], the particle filter [11], the iterated gain-based filter [12], and recently the least stochastic entropy adaptive filter [13]. In many applications, some equality and/or inequality constraints are imposed on the states of the system due to physical or practical considerations.…”

Section: Introduction a Literature Reviewmentioning

confidence: 99%

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A Generalized Decomposed State Estimation Approach for Uncertain Constrained Stochastic Nonlinear Systems

Hassan

2020

IEEE Access

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In this paper, a decomposed state estimator is developed for stochastic constrained nonlinear discrete-time dynamical systems with uncertain parameters. The proposed estimator can deal with general nonlinear uncertain stochastic systems without any pre-defined specifications on the system structure and/or the measurement model. Moreover, it can handle estimation problems for nonlinear stochastic systems subject to a set of imposed linear and/or nonlinear equality and/or inequality constraints. The mathematical structure of the proposed estimator is developed using multiple projection approach and its performance is analyzed and compared with the global (un-decomposed) structure. The main features of the proposed estimator are: it reduces the processing time, it can handle estimation problems with bad initial conditions of the estimator, it can be implemented on modern parallel processing facilities to further reduce the processing time, and last but not least, it minimizes the rounding off errors and hence improves the numerical stability of the algorithm. Simulations results on different real applications are presented to show the effectiveness of the developed approach, and its improved performance when compared with other techniques reported in the literature. INDEX TERMS Constrained stochastic uncertain nonlinear systems, decomposed state estimation, extended Kalman filter, large scale systems, performance analysis.

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“…d-Derivation of the gain matrix K 1 i (k +1) (first recursion): Substituting from (37) into (32) while using (12), (13) and (36), the gain matrix K 1 i (k + 1) is given by:…”

Section: The Recursive Formula Of the Filtered Estimatormentioning

confidence: 99%

“…Substituting from (40) into (39) while using (12), (13) and (32), then after simple mathematical manipulation, it is easy to get: j (k + 1|k + 1 ) is given by:…”

Section: The Recursive Formula Of the Filtered Estimatormentioning

confidence: 99%

Section: Introduction a Literature Reviewmentioning

confidence: 99%

Section: Introduction a Literature Reviewmentioning

confidence: 99%

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A Generalized Decomposed State Estimation Approach for Uncertain Constrained Stochastic Nonlinear Systems

Hassan

2020

IEEE Access

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“…Correntropy can be regarded as a natural higher order extension of the standard, second order, correlation measure which accounts for higher order moments of the probability distribution function of the data [11]. Owing to its ability to model higher order moments of non-Gaussian signals [9,12,13], correntropy is a suitable candidate as a reward function for robust optimisation, adaptive filtering [14,15], and machine learning, within the so called maximum correntropy criterion (MCC) paradigm [16,9].…”

Section: Introductionmentioning

confidence: 99%

Robust PCA Through Maximum Correntropy Power Iterations

Chereau

Scalzo

Mandic

2021

ICASSP 2021 - 2021 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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Principal component analysis (PCA) is considered a quintessential data analysis technique when it comes to describing linear relationships between the features of a dataset. However, the well-known lack of robustness of PCA for non-Gaussian data and/or outliers often makes its practical use unreliable. To this end, we introduce a robust formulation of PCA based on the maximum correntropy criterion (MCC). By virtue of MCC, robust operation is achieved by maximising the expected likelihood of Gaussian distributed reconstruction errors. The analysis shows that the proposed solution reduces to a generalised power iteration, whereby: (i) robust estimates of the principal components are obtained even in the presence of outliers; (ii) the number of principal components need not be specified in advance; and (iii) the entire set of principal components can be obtained, unlike existing approaches. The advantages of the proposed maximum correntropy power iteration (MCPI) are demonstrated through an intuitive numerical example.

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A full second-order statistical analysis of strictly linear and widely linear estimators with MSE and Gaussian entropy criteria

Zhang

Xia

et al. 2022

Signal Processing

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Analysis of Least Stochastic Entropy Adaptive Filters for Noncircular Gaussian Signals

Cited by 11 publications

References 17 publications

A Generalized Decomposed State Estimation Approach for Uncertain Constrained Stochastic Nonlinear Systems

A Generalized Decomposed State Estimation Approach for Uncertain Constrained Stochastic Nonlinear Systems

Robust PCA Through Maximum Correntropy Power Iterations

A full second-order statistical analysis of strictly linear and widely linear estimators with MSE and Gaussian entropy criteria

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