Recent developments in the realm of state estimation of stochastic dynamic systems in the presence of non-Gaussian noise have induced a new methodology called the maximum correntropy filtering. The ...filters designed under the maximum correntropy criterion (MCC) utilize a similarity measure (or correntropy) between two random variables as a cost function. They are shown to improve the estimators’ robustness against outliers or impulsive noises. In this paper we explore the numerical stability of linear filtering technique proposed recently under the MCC approach. The resulted estimator is called the maximum correntropy criterion Kalman filter (MCC-KF). The purpose of this study is two-fold. First, the previously derived MCC-KF equations are revised and the related Kalman-like equality conditions are proved. Based on this theoretical finding, we improve the MCC-KF technique in the sense that the new method possesses a better estimation quality with the reduced computational cost compared with the previously proposed MCC-KF variant. Second, we devise some square-root implementations for the newly-designed improved estimator. The square-root algorithms are well known to be inherently more stable than the conventional Kalman-like implementations, which process the full error covariance matrix in each iteration step of the filter. Additionally, following the latest achievements in the KF community, all square-root algorithms are formulated here in the so-called array form. It implies the use of orthogonal transformations for recursive update of the required filtering quantities and, thereby, no loss of accuracy is incurred. Apart from the numerical stability benefits, the array form also makes the modern Kalman-like filters better suited to parallel implementation and to very large scale integration (VLSI) implementation. All the MCC-KF variants developed in this paper are demonstrated to outperform the previously proposed MCC-KF version in two numerical examples.
During recent years there has been a growing interest in stochastic dynamic neural fields employed for modeling and predictions in biomedical and technical systems. In this paper, given some ...incomplete noisy data available from sensors, we propose and explore a state estimation method for fast restorations of membrane potential in the cortex based on such measurements and the Amari equation used for simulations of neural population activity in a stochastic setting. Our novel technique relies upon a Galerkin-type spectral approximation utilized within the conventional state-space approach. Translating a stochastic system into its state-space form creates a straightforward and fruitful way to the data-driven parameter estimation, filtering, prediction and smoothing. The present study is particularly focused on establishing a nonlinear stochastic Galerkin-spectral-approximation-induced system of large size, which is further estimated by the traditional extended Kalman filter (EKF). The efficiency of calculations is the main purpose of our research. That is why the fast filtering solution devised is based on processing the incoming data incrementally, that is, by processing measurements one at a time, rather than handling them as a unified high-dimensional vector. Such sequential filters suit well for dealing with large data sets as well as with real-time on-line computations. Also, their derivation and substantiation is of great interest in the context of neural network training because of large stochastic systems arisen there. In comparison to the batch filtering, our novel algorithm reduces the computational cost of membrane potential reconstructions in terms of the amount of grid nodes N accepted in the underlying spacial discretization, significantly. Apart from its computation efficiency, this sequential method is more robust to round-off errors committed within a computer-based finite precision arithmetics than the classical EKF because of the (N × N)-matrix inversion elimination from such membrane potential calculations. The superior performance of our technique is examined and confirmed in comparison to the batch one on two known scenarios in the dynamic neural field modeling.
•The problem of reconstructing the membrane potential in the cerebral cortex from incomplete noisy measurements is explored.•The superiority of the sequential filter towards the traditional batch one is confirmed on two examples in neuroscience.•The membrane potential reconstruction accuracies of the sequential and batch filters are studied in simulated applications.•The stochastic simulations suggest the excellent accuracy and stability of the newly-devised sequential filtering method.
Summary
This paper presents novel square‐root accurate continuous‐discrete extended‐unscented Kalman filtering (ACD‐EUKF) algorithms for treating continuous‐time stochastic systems with discrete ...measurements. The time updates in such methods are fulfilled as those in the extended Kalman filter whereas their measurement updates are copied from the unscented Kalman filter. All this allows accurate predictions of the state mean and covariance to be combined with accurate measurement updates. The main weakness of this technique is the need for the Cholesky decomposition of predicted covariances derived in time‐update steps. Such a factorization is highly sensitive to numerical integration and round‐off errors committed, which may result in losing the covariance's positivity and, hence, failing the Cholesky decomposition. The latter problem is usually solved in the form of square‐root filtering implementations, which propagate not the covariance matrix but its square root instead. Here, we devise square‐root ACD‐EUKF methods grounded in the singular value decomposition (SVD). The SVD rooted in orthogonal transforms is applicable to any ACD‐EUKF with nonnegative weights, whereas the remaining ones, which can enjoy negative weights as well, are treated by means of the hyperbolic SVD based on J‐orthogonal transforms. The filters constructed are presented in a concise algorithmic form, which is convenient for practical use. Their two particular versions grounded in the classical and cubature unscented Kalman filtering parameterizations are examined in severe conditions of tackling a radar tracking problem, where an aircraft executes a coordinated turn. These are also compared to their non‐square‐root predecessor and other methods within the target tracking scenario with ill‐conditioned measurements.
Using the array form of numerically stable square-root implementation methods for Kalman filtering formulas, we construct a new square-root algorithm for the log-likelihood gradient (score) ...evaluation. This avoids the use of the conventional Kalman filter with its inherent numerical instabilities and improves the robustness of computations against roundoff errors. The new algorithm is developed in terms of covariance quantities and based on the ldquocondensed formrdquo of the array square-root filter.
A stable square-root approach has been recently proposed for the unscented Kalman filter (UKF) and fifth-degree cubature Kalman filter (5D-CKF) as well as for the mixed-type methods consisting of the ...extended Kalman filter (EKF) time update and the UKF/5D-CKF measurement update steps. The mixed-type estimators provide a good balance in trading between estimation accuracy and computational demand because of the EKF moment differential equations involved. The key benefit is a consolidation of reliable state mean and error covariance propagation by using delicate discretization error control while solving the EKF moment differential equations and an accurate measurement update according to the advanced UKF and/or 5D-CKF filtering strategies. Meanwhile the drawback of the previously proposed estimators is an utilization of sophisticated numerical integration scheme with the built-in discretization error control that is, in fact, a complicated and computationally costly tool. In contrast, we design here the mixed-type methods that keep the same estimation quality but reduce a computational time significantly. The novel estimators elegantly utilize any MATLAB-based numerical integration scheme developed for solving ordinary differential equations (ODEs) with the required accuracy tolerance pre-defined by users. In summary, a simplicity of the suggested estimators, their numerical robustness with respect to roundoff due to the square-root form utilized as well as their estimation accuracy due to the MATLAB ODEs solvers with discretization error control involved are the attractive features of the novel estimators. The numerical experiments are provided for illustrating a performance of the suggested methods in comparison with the existing ones.
We previously showed that glyceraldehyde-3-phosphate dehydrogenase (GAPDH) is S-glutathionylated in the presence of H2O2 and GSH. S-glutathionylation was shown to result in the formation of a ...disulfide bridge in the active site of the protein. In the present work, the possible biological significance of the disulfide bridge was investigated.
Human recombinant GAPDH with the mutation C156S (hGAPDH_C156S) was obtained to prevent the formation of the disulfide bridge. Properties of S-glutathionylated hGAPDH_C156S were studied in comparison with those of the wild-type protein hGAPDH.
S-glutathionylation of hGAPDH and hGAPDH_C156S results in the reversible inactivation of the proteins. In both cases, the modification results in corresponding mixed disulfides between the catalytic Cys152 and GSH. In the case of hGAPDH, the mixed disulfide breaks down yielding Cys152-Cys156 disulfide bridge in the active site. In hGAPDH_C156S, the mixed disulfide is stable. Differential scanning calorimetry method showed that S-glutathionylation leads to destabilization of hGAPDH molecule, but does not affect significantly hGAPDH_C156S. Reactivation of S-glutathionylated hGAPDH in the presence of GSH and glutaredoxin 1 is approximately two-fold more efficient compared to that of hGAPDH_C156S.
S-glutathionylation induces the formation of Cys152-Cys156 disulfide bond in the active site of hGAPDH, which results in structural changes of the protein molecule. Cys156 is important for reactivation of S-glutathionylated GAPDH by glutaredoxin 1.
The described mechanism may be important for interaction between GAPDH and other proteins and ligands, involved in cell signaling.
•Human recombinant GAPDH is S-glutathionylated in the presence of H2O2 and GSH.•Formation of mixed disulfide between the catalytic Cys152 and GSH inactivates GAPDH.•GAPDH-SSG reacts with adjacent Cys156 to form Cys152-Cys156 disulfide bond.•The mutation C156S prevents the disulfide bond formation and breakdown of GAPDH-SSG.•The mutation C156S decelerate reactivation of S-glutathionylated GAPDH by GSH and Grx.
This article considers the catalytic and physicochemical properties of composite materials obtained by the heat treatment of nickel nitrate immobilized on polyvinyl alcohol (PVA). The effects of the ...composite formation temperature on the phase composition of the metal-containing particles and their size were studied. The composite material obtained was found to be an active catalyst for the hydrogenation of carbon monoxide without a pre-activation step. The following synthesis parameters were achieved: 29% carbon monoxide conversion under conditions for catalytic hydrogenation and 28 g/m3 methane yield. Hypotheses were offered concerning the effect of particle size on the activity of the synthesized composite and an effect of the volume velocity on the carbon monoxide hydrogenation process parameters was demonstrated.
Summary
This paper presents a case study investigation of numerical robustness of extended Kalman filters used for estimation of stochastic chemical systems with ill‐conditioned measurements. Here, ...we consider both a batch reactor model and that of a continuously stirred tank reactor. Our purpose is to explore performance of extended Kalman filtering–based state estimators when the measurement model becomes increasingly ill conditioned. In this way, we determine numerically robust methods, which are suitable for accurate estimation of stochastic chemical systems in the presence of round‐off and other disturbances. We examine both conventional filters and their square‐root forms. All these algorithms are implemented by means of the conventional matrix inversion used in their measurement update steps and the Moore‐Penrose pseudoinversion as well. Furthermore, the square‐root filters under investigation are obtained in two ways, namely, by solving square‐root moment differential equations and by square rooting the filter itself. We show that only the square‐root filters grounded in the second approach (with use of stable orthogonal decompositions) are numerically robust and provide the excellent estimation accuracy within all our ill‐conditioned stochastic chemical system scenarios considered in this paper. In addition, the convectional filters and the square‐root variants based on solving moment equations are rather sensitive to round‐off and may be useful and accurate if the chemical system at hand is rather well conditioned.
This paper presents three state estimators grounded in the variable-stepsize Gauss- and Lobatto-type Nested Implicit Runge–Kutta (NIRK) formulas of orders 4 and 6 and designed for treating ...continuous-time stochastic systems arisen in radar tracking. Our filters are built within the Extended Kalman Filtering (EKF) framework and based on accurate numerical integrations of the corresponding Moment Differential Equations (MDEs). Automatic local and global error regulation mechanisms implemented in these methods allow the committed discretization error to be under control and made negligible in automatic mode. The latter raises the state estimation accuracy of the constructed filters, significantly. This also leads to the advanced notion of Accurate Continuous–Discrete Extended Kalman Filtering (ACD-EKF) developed by Kulikov and Kulikova in 2013–2016. Our novel methods are constructed within the same approach, but possess the improved accuracy and efficiency in comparison to their predecessors due to both more effective error control mechanisms implemented for integrating MDEs and more accurate iterations used for treating arisen nonlinear equations in the revised filters. Numerical experiments with the updated state estimators and their comparison to the cited earlier-designed ACD-EKFs are fulfilled in severe conditions of tackling a seven-dimensional radar tracking problem, where an aircraft executes a coordinated turn, in Matlab. This examination suggests that the novel state estimation algorithms outperform their predecessors and possess a promising potential for solving target tracking tasks in real-world applications.
•The novel accurate continuous–discrete unscented Kalman filter is devised for treating stochastic models in radar tracking.•The accurate continuous–discrete extended Kalman filter is revised for ...accurate estimation of stochastic models in radar tracking.•The mixed-type accurate continuous–discrete extended-unscented Kalman filter is updated for raising its efficiency for radar tracking models.•The accurate continuous–discrete extended and unscented Kalman filters are examined in estimating an aircraft executing a coordinated turn.
This paper presents a new state estimation technology grounded in the unscented Kalman filtering for nonlinear continuous-time stochastic systems. The resulting accurate continuous–discrete unscented Kalman filter is based on adaptive solvers with automatic global error control for treating numerically the moment differential equations arising in the mean and covariance calculation of propagated Gaussian density. It is intended for an accurate and robust state estimation in nonlinear continuous–discrete stochastic systems of various sorts, including in radar tracking models. This new filter is 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. For comparison, we also examine such efficient state estimators as the accurate continuous–discrete extended Kalman filter, the continuous–discrete unscented Kalman filter and the mixed-type accurate continuous–discrete extended-unscented Kalman filter designed earlier, but further modified in the present study. The comparison is fulfilled in terms of accuracy and efficiency of estimating the state in the mentioned air traffic control scenario.
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