This technical note is aimed to derive the Chandrasekhar-type recursion for the maximum correntropy criterion (MCC) Kalman filtering (KF). For the classical KF, the first Chandrasekhar difference ...equation was proposed at the beginning of 1970s. This is the alternative to the traditionally used Riccati recursion and it yields the so-called fast implementations known as the Morf-Sidhu-Kailath-Sayed KF algorithms. They are proved to be computationally cheap because of propagating the matrices of a smaller size than n × n error covariance matrix in the Riccati recursion. The problem of deriving the Chandrasekhar-type recursion within the MCC estimation methodology has never been raised yet in engineering literature. In this technical note, we do the first step and derive the Chandrasekhar MCC-KF estimators for the case of adaptive kernel size selection strategy, which implies a constant scalar adjusting weight. Numerical examples substantiate a practical feasibility of the newly suggested MCC-KF implementations and correctness of the presented theoretical derivations.
This article aims at presenting novel square-root unscented Kalman filters (UKFs) for treating various continuous-discrete nonlinear stochastic systems, including target tracking scenarios. These new ...methods are grounded in the commonly used singular value decomposition (SVD), that is, they propagate not the covariance matrix itself but its SVD factors instead. The SVD based on orthogonal transforms is applicable to any UKF with only nonnegative weights, whereas the remaining ones, which can enjoy negative weights as well, are treated by means of the hyperbolic SVD based on <inline-formula><tex-math notation="LaTeX">J</tex-math></inline-formula>-orthogonal transforms. The filters constructed are presented in a concise algorithmic form, which is convenient for practical utilization. Their two particular versions grounded in the classical and cubature UKF parameterizations and derived with use of the It<inline-formula><tex-math notation="LaTeX">\hat{\rm o}</tex-math></inline-formula>-Taylor discretization are examined in severe conditions of tackling a seven-dimensional radar tracking problem, where an aircraft executes a coordinated turn, in the presence of ill-conditioned measurements.
In this paper, we propose a data-driven parameters' adaptation technique for Stochastic Dynamic Neural Field (SDNF) models with finite signal transmission rate modeled by a distance-dependent delay. ...Our approach integrates nonlinear Bayesian filtering methods into mathematical neuroscience by establishing the state-space representation for the SDNF models with the delays. This allows to formulate the filtering problem in order to reconstruct the average membrane potential from incomplete data available from measurement devices. Additionally, when the state-space model is set up, the unknown system parameters can be estimated in a systematic way, for example, by using the method of maximum likelihood. In this paper, we derive for the first time the SDNF-oriented adaptive Extended Kalman filter (EKF) with the space-dependent delays in order to calibrate the SDNF models and to reconstruct the average membrane potential from incomplete data collected. The main benefit of the novel methodology is that both problems-the state and parameter estimation-are solved in parallel. The numerical experiments are provided to illustrate a performance of the novel methodology.
The first two Chandrasekhar recursions for the maximum correntropy criterion (MCC) Kalman filter (KF) have been recently derived for constant discrete-time linear systems. Their key feature is a ...mathematical re-formulation of the underlying MCC-based Riccati-type difference equation in terms of the involved error covariance matrix increment. Thus, the Chandrasekhar recursion-based solution is proved to yield a significant reduction of the computational complexity. This letter discusses the existence of a stable square-root solution for Chandrasekhar-type MCC-KF estimators, i.e. their computational reliability issue in a finite precision arithmetic. Two square-root solutions are proposed in terms of covariance quantities, namely within the Cholesky factorization and singular value decomposition.
In this paper, a singular value decomposition (SVD) approach is developed for implementing the cubature Kalman filter. The discussed estimator is one of the most popular and widely used method for ...solving nonlinear Bayesian filtering problem in practice. To improve its numerical stability (with respect to roundoff errors) and practical reliability of computations, the SVD-based methodology recently proposed for the classical Kalman filter is generalized on the nonlinear filtering problem. More precisely, we suggest the SVD-based solution for the continuous–discrete cubature Kalman filter and design two estimators: (i) the filter based on the traditionally used Euler–Maruyama discretization scheme; (ii) the estimator based on advanced Itô-Taylor expansion for discretizing the underlying stochastic differential equations. Both estimators are formulated in terms of SVD factors of the filter error covariance matrix and belong to the class of stable factored-form (square-root) algorithms. The new methods are tested on a radar tracking problem.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UILJ, UL, UM, UPCLJ, UPUK, ZAGLJ, ZRSKP
This paper addresses the problem of designing the continuous–discrete unscented Kalman filter (UKF) implementation methods. More precisely, the aim is to propose the MATLAB-based UKF algorithms for ...accurate and robust state estimation of stochastic dynamic systems. The accuracy of the continuous–discrete nonlinear filters heavily depends on how the implementation method manages the discretization error arisen at the filter prediction step. We suggest the elegant and accurate implementation framework for tracking the hidden states by utilizing the MATLAB built-in numerical integration schemes developed for solving ordinary differential equations (ODEs). The accuracy is boosted by the discretization error control involved in all MATLAB ODE solvers. This keeps the discretization error below the tolerance value provided by users, automatically. Meanwhile, the robustness of the UKF filtering methods is examined in terms of the stability to roundoff. In contrast to the pseudo-square-root UKF implementations established in engineering literature, which are based on the one-rank Cholesky updates, we derive the stable square-root methods by utilizing the J-orthogonal transformations for calculating the Cholesky square-root factors.
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This paper elaborates the Accurate Continuous-Discrete Extended Kalman Filter grounded in an ODE solver with global error control and its comparison to the Continuous-Discrete Cubature and Unscented ...Kalman Filters. All these state estimators are examined in severe conditions of tackling a seven-dimensional radar tracking problem, where an aircraft executes a coordinated turn. The latter is considered to be a challenging one for testing nonlinear filtering algorithms. Our numerical results show that all the methods can be used for practical target tracking, but the Accurate Continuous-Discrete Extended Kalman Filter is more flexible and robust. It treats successfully (and without any manual tuning) the air traffic control scenario for various initial data and for a range of sampling times.
Objective
IgG4‐related disease (IgG4‐RD) is an immune‐mediated fibroinflammatory condition that can affect nearly any organ. Prior studies have focused on individual cases of IgG4‐RD or small case ...series. This study was undertaken to report detailed clinical and laboratory findings in a larger group of patients with IgG4‐RD whose diagnosis was established by strict clinicopathologic correlation.
Methods
The baseline features of 125 patients with biopsy‐proven IgG4‐RD were reviewed. The diagnosis was confirmed by pathologists’ review, based on consensus diagnostic criteria and correlation with clinicopathologic features. Disease activity and damage were assessed using the IgG4‐RD Responder Index (RI). Flow cytometry was used to assess levels of circulating plasmablasts.
Results
Of the 125 patients, 107 had active disease and 86 were not receiving treatment for IgG4‐RD. Only 51% of the patients with active disease had elevated serum IgG4 concentrations. However, patients with active disease and elevated serum IgG4 concentrations were older, had a higher IgG4‐RD RI score, a greater number of organs involved, lower complement levels, higher absolute eosinophil counts, and higher IgE levels compared to those with active disease but normal serum IgG4 concentrations (P < 0.01 for all comparisons). The correlation between IgG4+ plasmablast levels and the IgG4‐RD RI of disease activity (Spearman's ρ = 0.45, P = 0.003) was stronger than the correlation between total plasmablast levels and the IgG4‐RD RI. Seventy‐six (61%) of the patients were male, but no significant differences according to sex were observed with regard to disease severity, organ involvement, or serum IgG4 concentrations. Treatment with glucocorticoids failed to produce sustained remission in 77% of patients.
Conclusion
Nearly 50% of this patient cohort with biopsy‐proven, clinically active IgG4‐RD had normal serum IgG4 concentrations. Elevations in the serum IgG4 concentration appeared to identify a subset of patients with a more severe disease phenotype. In addition, the levels of IgG4+ plasmablasts correlated well with the extent of disease activity.
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BFBNIB, FZAB, GIS, IJS, KILJ, NLZOH, NUK, OILJ, SBCE, SBMB, UL, UM, UPUK
The problem of numerical instability of the classical Kalman filter (KF) still remains one of the most important topics in engineering literature. For improving its robustness with respect to ...roundoff errors, the singular value decomposition (SVD) methodology has been proposed for implementing the underlying classical KF Riccati recursion. In this study, SVD-based filtering is derived for an alternative KF mechanisation that is based on the so-called Chandrasekhar recursion and yields a family of fast KF implementations. The new methodology involves hyperbolic SVD (HSVD) factorisation rather than usual SVD utilised in the Riccati-based filtering. The results of numerical study indicate that the HSVD-based filtering strategy outperforms the conventional Chandrasekhar-based KF while solving ill-conditioned state estimation problem. Together with the existed Cholesky-based algorithms, they are the preferred implementations when solving applications with high reliability requirements within the class of fast Chandrasekhar-based KF implementations.
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FZAB, GIS, IJS, KILJ, NLZOH, NUK, OILJ, SBCE, SBMB, UL, UM, UPUK
Recent research in nonlinear filtering and signal processing has suggested an efficient derivative-free Extended Kalman filter (EKF) designed for discrete-time stochastic systems. Such approach, ...however, has failed to address the estimation problem for continuous-discrete models. In this paper, we develop a novel continuous-discrete derivative-free EKF methodology by deriving the related moment differential equations (MDEs) and sample point differential equations (SPDEs). Additionally, we derive their Cholesky-based square-root MDEs and SPDEs and obtain several numerically stable derivative-free EKF methods. Finally, we propose the MATLAB-oriented implementations for all continuous-discrete derivative-free EKF algorithms derived. They are easy to implement because of the built-in fashion of the MATLAB numerical integrators utilized for solving either the MDEs or SPDEs in use, which are the ordinary differential equations (ODEs). More importantly, these are accurate derivative-free EKF implementations because any built-in MATLAB ODE solver includes the discretization error control that bounds the discretization error arisen and makes the implementation methods accurate. Besides, this is done in automatic way and no extra coding is required from users. The new filters are particularly effective for working with stochastic systems with highly nonlinear and/or nondifferentiable drift and observation functions, i.e. when the calculation of Jacobian matrices are either problematical or questionable. The performance of the novel filtering methods is demonstrated on several numerical tests.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UILJ, UL, UM, UPCLJ, UPUK, ZAGLJ, ZRSKP
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