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The interference of impulsive noise is very common in the identification of nonlinear systems. The spline prioritization optimization generalized maximum correntropy criterion adaptive filtering (SPOAF-GMCC) algorithm is an online identification method for nonlinear systems that can effectively suppress the interference of impulsive noise. However, as the number of FIR filter weights increases, the computational complexity of the SPOAF-GMCC algorithm in the adaptive process will increase drastically. To improve the computational efficiency of the SPOAF-GMCC algorithm, a nonlinear frequency domain SPOAF-GMCC (FDSPOAF-GMCC) algorithm is proposed in this paper. The range of learning rates when the proposed FDSPOAF-GMCC algorithm converges is theoretically analyzed. In addition, to further improve the convergence speed and reduce the error in the adaptive process, a frequency domain spline prioritization optimization generalized maximum correntropy criterion evolved momentum adaptive filtering (FDSPOAF-GMCC-LMON) algorithm by introducing the evolved momentum (LMON) algorithm is proposed in this paper. Numerical simulations have confirmed that the proposed FDSPOAF-GMCC-LMON algorithm has better robustness to impulsive noise and higher computational efficiency than the frequency domain spline adaptive filtering algorithm. [ABSTRACT FROM AUTHOR]

In this paper, we consider a nonlinear filtering model with observations driven by correlated Wiener processes and point processes. We first derive a Zakai equation whose solution is an unnormalized probability density function of the filter solution. Then, we apply a splitting-up technique to decompose the Zakai equation into three stochastic differential equations, based on which we construct a splitting-up approximate solution and prove its half-order convergence. Furthermore, we apply a finite difference method to construct a time semi-discrete approximate solution to the splitting-up system and prove its half-order convergence to the exact solution of the Zakai equation. Finally, we present some numerical experiments to demonstrate the theoretical analysis. [ABSTRACT FROM AUTHOR]

This paper proposes an efficient extension of functional links artificial neural networks (EE-FLANN) for the active noise control (ANC) application. The developed EE-FLANN controller can upgrade the model accuracy with the actual system thanks to adding the cross-terms to the trigonometric function. Unlike the method in the generalized FLANN (GFLANN) controller, the EE-FLANN exploits include cross-term symmetry. However, this causes the computational burden to increase remarkably. To reduce this disadvantage, we truncate the cross-terms appropriately based on the simplified strategy. Furthermore, the adaptive algorithm is designed to partially update the filter coefficients appropriately. Specifically, the cross-terms that do not satisfy certain magnitude conditions will be omitted during the update process to reduce costs. Experiments have shown that the proposed EE-FLANN controller can achieve comparable performance to the GFLANN controller but the complexity is reduced by up to 20%. [ABSTRACT FROM AUTHOR]

• An adaptive backstepping controller based on nonlinear filter Lyapunov function is designed. • Integration of body control objectives and hard constraints into one control variable. • An adaptive backstepping bottom controller based on nonlinear disturbance observer is designed. • Conduct stability analyses of zero-power systems to ensure that safety performance indicators are bounded. • Backstepping dynamic surface control is used to avoid the derivative explosion phenomenon. In order to improve the ride comfort and handling stability of the electro-hydraulic active suspension system, a hierarchical control strategy is proposed. For the active suspension system with body mass uncertainty and safety constraints, an enhanced constraint adaptive backstepping controller is designed to generate the target force of body vertical motion. When dealing with constraints, nonlinear filters are introduced, backstepping technology and quadratic Lyapunov function are used to combine the control target and domain constraints, and the vertical displacement of the body and the suspension deflection control index are synthesized into a single controlled variable, so that the control variable converging to zero meets the suspension dynamic displacement limit. The ride comfort and safety of the active suspension system are improved. Secondly, stability analysis is conducted on the zero dynamic error system to ensure that all safety performance indicators are bounded. The effects of external disturbances, parameter uncertainties and modelling errors on the force tracking accuracy of asymmetric cylinder electrohydraulic systems are addressed. A backstepping dynamic surface control method based on a nonlinear perturbation observer is proposed, which estimates the composite perturbation terms such as modelling error and external perturbation, and uses the estimated value of the nonlinear observer to design a feedforward compensating control term to offset the effect of the composite perturbation on the system performance. In addition, the dynamic surface control method is used to calculate the derivative of the target force input, which avoids the derivative explosion phenomenon and reduces the computational complexity of the system. Simulation test results show that this method reduces the computational complexity of the system and improves the control performance. And under random and bumpy road conditions, the root-mean-square value of sprung mass acceleration performance index is reduced by 48.354 % and 72.677 % compared with passive suspension, which improves the ride comfort of the vehicle. [ABSTRACT FROM AUTHOR]

Summary: Most of the existing adaptive filter algorithms pay more attention to improving performance while ignoring the computational complexity and the impact of the impulsive environment. When encountering the impulsive noise environments, the performance of traditional nonlinear adaptive filter may be significantly reduced and usually needs high computational cost. Therefore, this article proposes a hyperbolic tangent Leclerc robust nonlinear adaptive filter based on the low complexity decomposable Volterra model (HTLNAF‐DVM). The filter is implemented by imposing a rank‐one structure on the full Volterra model to get a product of linear filters, and employs a hyperbolic tangent Leclerc function as a robust norm to effectively improve the robustness against the impulsive noise. In addition, we give the theoretical analyses of the steady‐state mean‐square performance of the proposed HTLNAF‐DVM. Finally, the simulation results prove that the proposed HTLNAF‐DVM algorithm has better performance than the existing algorithms and fit well with the theory. [ABSTRACT FROM AUTHOR]

A nonlinear filter is presented by using a formal linearization method and the Extended Kalman Filter (EKF) approach in this paper. Defining a linearization function that consists of polynomials, a given nonlinear dynamic system is transformed into an augmented linear one with respect to this linearization function. Introducing a new augmented measurement vector that consists of polynomials of measurement data for a given measurement equation, this equation is also transformed into an augmented linear one with respect to the linearization function in the same way. As a result, the EKF theory can be applied to these augmented linearized systems and a nonlinear filter is synthesized. In order to show the performance of the method, numerical experiments are carried out by comparing with the EKF as a conventional method. [ABSTRACT FROM AUTHOR]

This paper introduces an innovative adaptive control approach utilizing a nonlinear filter for a specific subset of nonlinear discrete-time systems, considering the presence of both input and output noise. The system can be transformed into a nonlinear autoregressive moving average with exogenous inputs (NARMAX) model. The concept of discrete Nussbaum gain is introduced to address the theoretical constraint associated with unknown directions of feed-forward or control gains, and the extended adaptive tuning sequence is introduced to facilitate the acceleration of parameter updating. In the case of no noise, asymptotical output tracking and global stability are achieved with the adaptive control. Further, in the presence of input noise and output noise, a novel nonlinear filter is designed to generate a more accurate filtered output, which improves the control system's ability to adapt and track accurately. Finally, examples are provided to showcase the effectiveness and precision of the method. [ABSTRACT FROM AUTHOR]

In this work, an adaptive fuzzy backstepping fault-tolerant control (FTC) issue is tackled for uncertain fractional-order (FO) nonlinear systems with sensor and actuator faults. A fuzzy logic system is exploited to manage unknown nonlinearity. In addition, a novel FO nonlinear filter-based dynamic surface control (DSC) method is constructed, effectively avoiding the inherent complexity explosion problem in the backstepping recursive process, and in the light of the construction of auxiliary functions, compensating the coupling term introduced by faults. On account of certain assumptions, the stability criterion of the FO Lyapunov function is applied to guarantee the stability of the closed-loop system. Finally, the simulation example verifies the validity of the presented control strategy. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Zhengzhou University: Engineering Science is the property of Editorial Office of Journal of Zhengzhou University: Engineering Science and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

This paper proposes a maximum-ratio combining sensor fusion scheme for using an extended Kalman filter in the underwater vehicle positioning task by means of communication devices (buoys) providing location information using a slant-range mechanism, inertial sensors, a Doppler velocity log, and a pressure sensor in the absence of bearing angle data. The parameter estimation methods for all navigation system components are described. The results of simulation modeling with corresponding quality metrics are presented. The outcomes were supported by conducted field experiments. The results obtained allowed us to obtain a position determination model for the underwater vehicle, which is still a relevant and complex task for seabed explorers. [ABSTRACT FROM AUTHOR]

This study is devoted to a nonlinear filter-based adaptive fuzzy output-feedback control scheme for uncertain fractional-order (FO) nonlinear systems with unknown external disturbance. Fuzzy logic systems (FLSs) are applied to estimate unknown nonlinear dynamics, and a new FO fuzzy state observer based on a nonlinear disturbance observer is established for simultaneously estimating the unmeasurable states and mixed disturbance. Then, with the aid of auxiliary functions, a novel FO nonlinear filter is given to approximately replace the virtual control functions, together with the corresponding fractional derivative, which not only erases the inherent complexity explosion problem under the framework of backstepping, but also completely compensates for the effects of the boundary errors induced by the constructed filters compared to the previous FO linear filter method. Under certain assumptions, and in line with the FO stability criterion, the stability of the controlled system is ensured. An FO Chua–Hartley simulation study is presented to verify the validity of the proposed method. [ABSTRACT FROM AUTHOR]

A nonlinear filter is presented by using a formal linearization method and the extended Kalman filter (EKF) approach in this paper. A given nonlinear system is transformed into an augmented nonlinear system by considering the higher‐order polynomial terms of state as new additional states. And then, the EKF theory is applied to it well. Numerical experiments show the effectiveness of this new filter. © 2023 Institute of Electrical Engineer of Japan and Wiley Periodicals LLC. [ABSTRACT FROM AUTHOR]

Image processing is becoming more popular because images are being used increasingly in medical diagnosis, biometric monitoring, and character recognition. But these images are frequently contaminated with noise, which can corrupt subsequent image processing stages. Therefore, in this paper, we propose a novel nonlinear filter for removing "salt and pepper" impulsive noise from a complex color image. The new filter is called the Modified Vector Directional Filter (MVDF). The suggested method is based on the traditional Vector Directional Filter (VDF). However, before the candidate pixel is processed by the VDF, theMVDF employs a threshold and the neighboring pixels of the candidate pixel in a 3×3 filter window to determine whether it is noise-corrupted or noise-free. Several reference color images corrupted by impulsive noise with intensities ranging from 3% to 20% are used to assess theMVDF's effectiveness. The results of the experiments show that theMVDF is better than the VDF and the Generalized VDF (GVDF) in terms of the PSNR (Peak Signal-to-Noise Ratio), NCD (Normalized Color Difference), and execution time for the denoised image. In fact, the PSNR is increased by 6.554% and 12.624%, the NCD is decreased by 20.273% and 44.147%, and the execution time is reduced by approximately a factor of 3 for the MVDF relative to the VDF and GVDF, respectively. These results prove the efficiency of the proposed filter. Furthermore, a hardware design is proposed for the MVDF using the High-Level Synthesis (HLS) flow in order to increase its performance. This design, which is implemented on the Xilinx ZynqXCZU9EG Field-ProgrammableGate Array (FPGA), allows the restoration of a 256×256-pixel image in 2 milliseconds (ms) only. [ABSTRACT FROM AUTHOR]

In order to mitigate the interference of impulsive noises in the identification of nonlinear systems using spline prioritization optimization adaptive filtering (SPOAF) algorithm, an enhanced SPOAF based on generalized hyperbolic secant (GHS) function, named SPOAF–GHS, is proposed in this paper. The convergence property of the proposed algorithm has been theoretically analyzed. Two improvements have been made in the proposed algorithm. On the one hand, to improve the convergence speed in the adaptive process, the momentum Nesterov accelerated gradient optimization algorithm has been introduced. In addition, a frequency domain filtering architecture model has been proposed to address the high computational complexity of the filtering algorithm caused by the presence of bigger number of taps during the filtering process. Several numerical experiments are conducted, and the results show that the proposed GHS-type algorithms have superior performance compared to existing spline interpolation filtering algorithms. [ABSTRACT FROM AUTHOR]

The highly accurate state estimation of nonlinear systems is needed in many different application fields. In many existing nonlinear filters, the uncompensated nonlinear approximation error and widely used numerical sampling methods both seriously affect the estimation accuracy and numerical stability. In this paper, based on the variational Bayesian framework, a novel iterative nonlinear filter consisting of forward modeling and inverse estimation is proposed. In the forward modeling stage, a linear Gaussian regression process with distributed variational parameters (VPs) is designed to fit the whole nonlinear measurement likelihood. The distributed VPs consider both first and second moments information, so as to compensate for approximation error from the whole likelihood perspective, instead of only the nonlinear function approximation, which can further improve the accuracy of Bayesian posterior update. In the linear Gaussian regression process, the original nonlinear measurement function (NMF) is just viewed as a prior and no longer directly participates in the modeling of the measurement likelihood. Hence, in the inverse estimation stage, when maximizing the evidence lower bound to update the posteriors of the state and VPs, we can obtain closed‐form solutions without numerical sampling methods to approximate the integral of NMF required in many existing methods, which can guarantee numerical stability. Moreover, to avoid the random setting of hyperparameters and to block the propagation of the accumulated error, we propose two rules, estimation and lower bound consistencies, to conduct the hyperparameters' initialization at the beginning of iteration at each sampling time and also derive an optimization method to update hyperparameters during iteration. Finally, the performance of our proposed method is demonstrated in the nonlinear orbital estimation problems. [ABSTRACT FROM AUTHOR]

This paper presents the machine learning-based ensemble conditional mean filter (ML-EnCMF) -- a filtering method based on the conditional mean filter (CMF) previously introduced in the literature. The updated mean of the CMF matches that of the posterior, obtained by applying Bayes' rule on the filter's forecast distribution. Moreover, we show that the CMF's updated covariance coincides with the expected conditional covariance. Implementing the EnCMF requires computing the conditional mean (CM). A likelihoodbased estimator is prone to significant errors for small ensemble sizes, causing the filter divergence. We develop a systematical methodology for integrating machine learning into the EnCMF based on the CM's orthogonal projection property. First, we use a combination of an artificial neural network (ANN) and a linear function, obtained based on the ensemble Kalman filter (EnKF), to approximate the CM, enabling the ML-EnCMF to inherit EnKF's advantages. Secondly, we apply a suitable variance reduction technique to reduce statistical errors when estimating loss function. Lastly, we propose a model selection procedure for element-wisely selecting the applied filter, i.e., either the EnKF or ML-EnCMF, at each updating step. We demonstrate the MLEnCMF performance using the Lorenz-63 and Lorenz-96 systems and show that the ML-EnCMF outperforms the EnKF and the likelihood-based EnCMF. [ABSTRACT FROM AUTHOR]

Copyright of Journal of South China University of Technology (Natural Science Edition) is the property of South China University of Technology and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The navigation and positioning of multi-autonomous underwater vehicles (AUVs) in the complex and variable marine environment is a significant and much-needed area of attention, especially considering the fact that cooperative navigation technology is the essential method for multiple AUVs to solve positioning problems. When the extended Kalman filter (EKF) is applied for underwater cooperative localization, the outliers in the sensor observations cause unknown errors in the measurement system due to deep-sea environmental factors, which are difficult to calibrate and cause a significant reduction in the co-location accuracy of AUVs, and can even cause problems with a divergence of estimation error. In this paper, we proposed a cooperative navigation method of the EKF algorithm based on the combined observation of multiple AUVs. Firstly, the corresponding cooperative navigation model is established, and the corresponding measurement model is designed. Then, the EKF model based on combined observation is designed and constructed, and the unknown error is eliminated by introducing a previously measured value. Finally, simulation tests and lake experiments are designed to verify the effectiveness of the algorithm. The results indicate that the EKF algorithm based on combined observation can approximately eliminate errors and improve the accuracy of cooperative localization when the unknown measurement error cannot be calibrated by common EKF methods. The effect of state estimation is improved, and the accuracy of co-location can be effectively improved to avoid serious declines in—and divergence of—estimation accuracy. [ABSTRACT FROM AUTHOR]

In this article, we develop a second‐order nonlinear filter based stabilization scheme for high Reynolds number flows. We prove the unconditional stability of the method, establish the second order consistency and discuss the dynamical tuning of the relaxation parameter. The scheme is then validated against experimental data for an isothermal turbulent flow in a Staggered Tube Bundle at Reynolds number of 18,000. Numerical results are found to be in an overall good qualitative and quantitative agreement with the benchmark results. [ABSTRACT FROM AUTHOR]

This paper is concerned with a nonlinear filter for a general class of nonlinear time-varying systems, by making use of a pseudo-formal linearization method and Kalman filter approach. The given nonlinear time-varying dynamic and measurement equations are piecewisely linearized by the formal linearization method using Taylor expansion so that Kalman filter can be applied for each linearized time-varying equations. Then the resulting filters are smoothly united into a single nonlinear filter by an automatic choosing function. The efficiency of this filter is shown through numerical examples. [ABSTRACT FROM AUTHOR]

In this work, an adaptive fuzzy backstepping fault-tolerant control (FTC) issue is tackled for uncertain fractional-order (FO) nonlinear systems with sensor and actuator faults. A fuzzy logic system is exploited to manage unknown nonlinearity. In addition, a novel FO nonlinear filter-based dynamic surface control (DSC) method is constructed, effectively avoiding the inherent complexity explosion problem in the backstepping recursive process, and in the light of the construction of auxiliary functions, compensating the coupling term introduced by faults. On account of certain assumptions, the stability criterion of the FO Lyapunov function is applied to guarantee the stability of the closed-loop system. Finally, the simulation example verifies the validity of the presented control strategy.

Eliminating noise from a color image represents an essential task in image processing, given that noise can markedly diminish visual quality and impact the precision of subsequent analyses or applications (such as visual quality inspection, medical image analysis, etc.). In this study, we introduce an innovative approach designed to remove noise while preserving the edges and fine details of a color image. This method is based on Laplacian operators, threshold values for identifying potentially corrupted pixels due to noise, and the Vector Directional Filter (VDF) for substituting noisy pixels. Consequently, this technique is termed Laplacian VDF (LVDF). Additionally, a Hardware/Software (HW/SW) design is formulated for the real-time implementation of the LVDF filter. The hardware architecture is designed through the High-Level Synthesis (HLS) flow, while the software component is executed using the ARM Cortex-A53 hardcore processor. Furthermore, five Direct Memory Access (DMAs) are employed to enhance data throughput between the hardware coprocessor and Double Data Rate (DDR) memory. Performance evaluations conducted on the ZCU102 kit reveal that the LVDF HW/SW design facilitates the restoration of 74 images per second, resulting in a 94 % reduction in execution time compared to the software implementation, all while maintaining consistent objective and subjective image quality. [ABSTRACT FROM AUTHOR]

This paper proposes a maximum-ratio combining sensor fusion scheme for using an extended Kalman filter in the underwater vehicle positioning task by means of communication devices (buoys) providing location information using a slant-range mechanism, inertial sensors, a Doppler velocity log, and a pressure sensor in the absence of bearing angle data. The parameter estimation methods for all navigation system components are described. The results of simulation modeling with corresponding quality metrics are presented. The outcomes were supported by conducted field experiments. The results obtained allowed us to obtain a position determination model for the underwater vehicle, which is still a relevant and complex task for seabed explorers.

This study is devoted to a nonlinear filter-based adaptive fuzzy output-feedback control scheme for uncertain fractional-order (FO) nonlinear systems with unknown external disturbance. Fuzzy logic systems (FLSs) are applied to estimate unknown nonlinear dynamics, and a new FO fuzzy state observer based on a nonlinear disturbance observer is established for simultaneously estimating the unmeasurable states and mixed disturbance. Then, with the aid of auxiliary functions, a novel FO nonlinear filter is given to approximately replace the virtual control functions, together with the corresponding fractional derivative, which not only erases the inherent complexity explosion problem under the framework of backstepping, but also completely compensates for the effects of the boundary errors induced by the constructed filters compared to the previous FO linear filter method. Under certain assumptions, and in line with the FO stability criterion, the stability of the controlled system is ensured. An FO Chua–Hartley simulation study is presented to verify the validity of the proposed method.

Video sequences are frequently contaminated by noise throughout the acquisition process, resulting in considerable degradation of video display quality. In this paper, we present a novel method of video filtering. The proposed filter is developed from an optimization problem in which a Bayesian term and a noisy video sequence prior distribution are combined. The method begins by segmenting the video sequence into space-time blocks and then substituting each noisy block by a weighted average of non-local neighbor blocks. Gradient-based weights are used to dynamically adjust the edge preservation and smoothness of the reference block. The obtained formulation enables nonlinear filtering and, hence, preserving key features such as edges and corners while using the intrinsic Bayesian filtering framework. Experiments on different video sequences with varying degrees of noise show that the proposed method performs better than state-of-the-art video filtering approaches.

In the framework of Kalman filtering, the key points is the estimation of the covariance of prediction error which is used to calculate the Kalman filter gain. For the traditional algorithm, e.g. extended Kalman filter, the priori information is obtained on the basis of the Taylor expansion approximation of the nonlinear system. Because the linear propagation approximation of prior information cannot truly reflect the evolution of the probability distribution of the prediction errors in nonlinear systems, however, the traditional method affects the estimation accuracy of the extended Kalman filter. To solve these problems and be easy to apply to high-dimensional nonlinear systems, this paper improves the SPKF algorithm. Firstly, the prediction error propagation model is re-established to eliminate the approximation error of Taylor expansion in the derivation of the probability density function of the prediction error. Then, a Fisher matrix calculation method that is easier for high-dimensional system is obtained by defining the calculation method of Hilbert inner product of vector and matrix function. To illustrate the merits of the novel algorithm, this paper took the oxygen generation system by using electrolytic water in space station as a case study and conducted the state estimation by respectively using the extended Kalman filter, unscented Kalman filter and high-dimensional stochastic projection Kalman filter. The simulation results shown that the new algorithm can obtain higher estimation precision than the traditional algorithm. • The improve algorithm does not need to linearize the nonlinear system through the Taylor method. The influence of linearization error on estimation accuracy is directly avoided. • The improve algorithm gives the calculation method of the Fisher matrix for a high-dimensional nonlinear system. It can easy to apply on a high-dimensional nonlinear system. • The improve algorithm does not need to obtain the analytic solution of the Kushner-Stratonovich equation. Thus, it is suitable for the real-time state estimation of the nonlinear system. [ABSTRACT FROM AUTHOR]

This paper deals with a design of a nonlinear filter using a pseudo‐formal linearization method based on Chebyshev expansion with constant filter gains. The given nonlinear dynamic and measurement equations are piecewisely linearized by a formal linearization method using Chebyshev expansion, therefore the steady‐state Kalman filter can be applied for each linearized system. Then the resulting filters are smoothly united into a single nonlinear filter by an automatic choosing function. We demonstrate the proposed method in nonlinear systems to verify the effectiveness. © 2022 Institute of Electrical Engineers of Japan. Published by Wiley Periodicals LLC. [ABSTRACT FROM AUTHOR]

This paper is concerned with the designing a nonlinear filter making use of a pseudo-formal linearization method and Kalman filter approach of constant-gains type for nonlinear systems. We piece-wisely linearize the given nonlinear dynamic and measurement equations by a formal linearization method and design linear filters. They are smoothly united into a single nonlinear filter. The efficacy of this filter is shown through numerical examples. [ABSTRACT FROM AUTHOR]

In this paper, we present an inverse optimal tracking controller for a class of Euler–-Lagrange systems having uncertainties in their dynamical terms under the restriction that only the output state (i.e. position for robotic systems) is available for measurement. Specifically, a nonlinear filter is used to generate a velocity substitute, then a controller formulation ensuring a globally asymptotically stable closed-loop system while minimizing a performance index despite the presence of parametric uncertainty, is proposed. The stability proof is established using a Lyapunov analysis of the system with proposed optimal output feedback controller. Inverse optimality is derived via designing a meaningful cost function utilizing the control Lyapunov function. Numerical simulations are presented to illustrate the viability and performance of the derived controller. [ABSTRACT FROM AUTHOR]

This paper is focused on the state estimation problem for nonlinear systems with unknown statistics of measurement noise. Based on the cubature Kalman after, we propose a new nonlinear alltering algorithm that employs a skew t distribution to characterize the asymmetry of the measurement noise. The system states and the statistics of skew t noise distribution, including the shape matrix, the scale matrix, and the degree of freedom (DOF) are estimated jointly by employing variational Bayesian (VB) inference. The proposed method is validated in a target tracking example. Results of the simulation indicate that the proposed nonlinear after can perform satisfactorily in the presence of unknown statistics of measurement noise and outperform than the existing state-of-the-art nonlinear filters. [ABSTRACT FROM AUTHOR]

This paper focuses on deriving the projection filter equation for a class of stochastic differential equations that incorporate correlated state and measurement noises, where the measurement process covariances depend on the state. To effectively implement the projection filter algorithm for exponential families, it is crucial to compute not only the expectation and variance of the natural statistics but also higher-dimensional statistics. However, computing these high-dimensional statistics can be computationally intensive and potentially compromise the numerical stability of the projection filter. To tackle this challenge, this study proposes a method for the careful selection of natural statistics. We shows that, subject to specific technical conditions, it is feasible to compute all the required statistics by utilizing only partial differentiation of an approximated cumulant-generating function. Notably, this approach eliminates the need to increase the parameter dimension, which was previously required in Emzir et al. (2023). • We generalize the projection filter the class of SDEs with correlated noise. • If applied to the exponential family, the filter equation can be computed efficiently. • We show the efficiency of the new method on three filtering problems. • The accompanying code is available at. [ABSTRACT FROM AUTHOR]

The navigation and positioning of multi-autonomous underwater vehicles (AUVs) in the complex and variable marine environment is a significant and much-needed area of attention, especially considering the fact that cooperative navigation technology is the essential method for multiple AUVs to solve positioning problems. When the extended Kalman filter (EKF) is applied for underwater cooperative localization, the outliers in the sensor observations cause unknown errors in the measurement system due to deep-sea environmental factors, which are difficult to calibrate and cause a significant reduction in the co-location accuracy of AUVs, and can even cause problems with a divergence of estimation error. In this paper, we proposed a cooperative navigation method of the EKF algorithm based on the combined observation of multiple AUVs. Firstly, the corresponding cooperative navigation model is established, and the corresponding measurement model is designed. Then, the EKF model based on combined observation is designed and constructed, and the unknown error is eliminated by introducing a previously measured value. Finally, simulation tests and lake experiments are designed to verify the effectiveness of the algorithm. The results indicate that the EKF algorithm based on combined observation can approximately eliminate errors and improve the accuracy of cooperative localization when the unknown measurement error cannot be calibrated by common EKF methods. The effect of state estimation is improved, and the accuracy of co-location can be effectively improved to avoid serious declines in—and divergence of—estimation accuracy.

To lower the high computational burden of nonlinear filter in the practical applications, the previous paper has proposed the adaptive algorithm based on the joint process filter using pipelined feedforward second-order Volterra architecture (JPPSOV). Even though the JPPSOV adaptive filter has been common used for nonlinear systems identification, nonlinear active noise controller (ANC) and nonlinear acoustic echo cancellers (AEC), there is currently no literature that gives the steady state analysis of JPPSOV. Therefore, we analyze the steady state performance of the LMS adaptive algorithm of the JPPSOV filter for nonlinear system identification in this brief. Finally, the simulated results are in good agreement with the theoretical results. [ABSTRACT FROM AUTHOR]

This brief proposes a novel perspective for solving single input and multiple output (SIMO) nonlinear systems with multi-cost function adaptive algorithm. Based on Euler polynomials, the Euler filter with finite memory is proposed to construct a filter bank, which realizes the accurate identification of high-dimensional nonlinear systems. To improve the algorithm performance, a multi-cost function is proposed. Moreover, the mean-square stability and steady-state performance of the proposed method are rigorously analyzed. The typical FitzHugh-Nagumo (FHN) system, which fiercely exhibits chaotic dynamics, is considered for justifying the performance of this new algorithm. Numerical results highlight the solution accuracy via comparison with existing approaches. [ABSTRACT FROM AUTHOR]

We propose a new extension of Kalman filtering for continuous-discrete systems with nonlinear state-space models that we name as the level set Kalman filter (LSKF). The LSKF assumes the probability distribution can be approximated as a Gaussian and updates the Gaussian distribution through a time-update step and a measurement-update step. The LSKF improves the time-update step compared to existing methods, such as the continuous-discrete cubature Kalman filter (CD-CKF), by reformulating the underlying Fokker-Planck equation as an ordinary differential equation for the Gaussian, thereby avoiding the need for the explicit expression of the higher derivatives. Together with a carefully picked measurement-update method, numerical experiments show that the LSKF has a consistent performance improvement over the CD-CKF for a range of parameters. Meanwhile, the LSKF simplifies implementation, as no user-defined timestep subdivisions between measurements are required, and the spatial derivatives of the drift function are not explicitly needed. [ABSTRACT FROM AUTHOR]

The nonlinear filtering problem is a hot spot in robot navigation research. As an advanced method that can effectively improve the robustness and accuracy of the system, the progressive Gaussian approximate filter with variable step size (PGAFVS) still has some shortcomings, how to resolve the nonlinear filtering problem in the application of tightly coupled integration under the premise of the prior uncertainty and further promote robustness high measurement accuracy, which becomes the purpose of this paper. This paper formulates the processing of trajectory tracking measurement noise problem as a Kalman filtering procedure and the measurement noise covariance matrix in controller, is jointly estimated based on the progressive Gaussian approximate filter (PGAF), after that, PGAFVS can be deduced. Then we proposed an adaptive fuzzy and backpropagation neural network controller based on PGAFVS (AFNPGA-VS) that can improve the application of tightly coupled integration under the premise of the prior uncertainty and further promote robustness high measurement accuracy. The simulation results show that the proposed algorithm outperforms the state-of-the-art methods. [ABSTRACT FROM AUTHOR]

Video sequences are frequently contaminated by noise throughout the acquisition process, resulting in considerable degradation of video display quality. In this paper, we present a novel method of video filtering. The proposed filter is developed from an optimization problem in which a Bayesian term and a noisy video sequence prior distribution are combined. The method begins by segmenting the video sequence into space-time blocks and then substituting each noisy block by a weighted average of non-local neighbor blocks. Gradient-based weights are used to dynamically adjust the edge preservation and smoothness of the reference block. The obtained formulation enables nonlinear filtering and, hence, preserving key features such as edges and corners while using the intrinsic Bayesian filtering framework. Experiments on different video sequences with varying degrees of noise show that the proposed method performs better than state-of-the-art video filtering approaches. [ABSTRACT FROM AUTHOR]

For the nonlinear systems with uncertain system parameters, based on the recursive linear minimum variance estimation framework, the effect of the system parameters on the mean squared error (MSE) is analyzed, that is, the greater the system parameters deviation (whether they are positive or negative deviation) is, the greater the MSE is. Based on the analysis results and prior probability statistics (probability distributions or sampling distributions), an innovative robust estimation algorithm is proposed for nonlinear systems with uncertain system parameters. Three examples verify the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

In this paper, we propose a filter structure whose output satisfies the velocity and acceleration constraints for any input signals. In the field of factory automation, step signals are sometimes converted into trapezoidal waves to satisfy the intended velocity limitations. This helps the operators avoid overload in industrial robots. In some cases, physical protection of the equipment, safety, and ride quality can be ensured by limiting the characteristics of input signals in actual plants. A signal-limitation filter is proposed for the input signal to satisfy the intended signal limit. In the previous study, a signal-limitation filter structure was provided as a simple unit-feedback control with a saturation function. The filter structure in the previous study had a delay between the input and output signals because it is difficult to design gains considering both the saturating and non-saturating cases. To solve this problem, we propose a novel filter structure that includes feedforward and feedback components. Applying this filter structure with feedforward terms including saturation enables us to fulfill the desired limitations for arbitrary input signals. We evaluated the proposed structure in a signal-limitation filter that simultaneously limits the velocity and acceleration. The simulation results demonstrate the effectiveness of our proposed filter.

This paper first proposes nonlinear spline adaptive filter based on the robust Geman-McClure estimator (SAF-RGM). The proposed algorithm is obtained by minimizing the cost function relied on the Geman-McClure estimator. Since the Geman-McClure estimator can remove outliers with large amplitude from dataset, the proposed algorithm can obtain the excellent performance in the impulsive noise. Moreover, the mean and mean square behaviors of the SAF-RGM algorithm are analyzed. Simulations are conducted to confirm that the proposed SAF-RGM algorithm achieves better performance than the existing spline nonlinear adaptive filtering algorithms. Besides, simulation results validate the theoretical conclusions.

This paper investigates a neural network (NN) adaptive fixed‐time stabilization control problem for high‐order nonlinear systems. Radial basis function NNs (RBFNNs) are used to approximate unknown nonlinear function. A nonlinear filter is designed to solve the issue of “explosion of complexity.” Combining adaptive backstepping design and adding a power integrator, an adaptive NN fixed‐time control method is developed. It is proved that all the signals of the closed‐loop system are bounded in fixed time. Finally, simulation example is provided to confirm the effectiveness of the presented control method. [ABSTRACT FROM AUTHOR]

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The applicability of adaptive Volterra filter is greatly limited by the high computational complexity and notable performance degradation when encountering the impulsive noise. Although the existing interpolated adaptive Volterra filter has reduced the computational complexity, its performance is still significantly degraded while the impulsive noise occurs. This brief proposes a robust fully arctangent adaptive fully interpolated Volterra (RFAAFIV) filtering algorithm by using the novel arctangent function. The proposed algorithm can effectively improve the robustness against impulsive noise while requiring the low computational cost. Moreover, the computational complexity and the steady-state mean square performance of the proposed RFAAFIV algorithm are analyzed. Simulations on nonlinear system identification further evaluate the effectiveness of the RFAAFIV algorithm against impulsive noise and verify the theoretical analysis. [ABSTRACT FROM AUTHOR]

In this paper, a new variational Gaussian regression filter (VGRF) is proposed by constructing the linear parametric Gaussian regression (LPGR) process including variational parameters. Through modeling the measurement likelihood by LPGR to implement the Bayesian update, the nonlinear measurement function will not be directly involved in the state estimation. The complex Monte Carlo computation used in traditional methods is also avoided well. Hence, in PVFF, the inference of state posteriori and variational parameters can be achieved tractably and simply by using variational Bayesian inference approach. Secondly, a filtering evidence lower bound (F-ELBO) is proposed as a quantitative evaluation rule of different filters. Compared with traditional methods, the higher estimation accuracy of VGRF can be explained by the F-ELBO. Thirdly, a relationship between F-ELBO and the monitored ELBO (M-ELBO) is found, i.e., F-ELBO is always larger than M-ELBO. Based on this finding, the accuracy performance improvement of VGRF can be theoretically explained. Finally, three numerical examples are employed to illustrate the effectiveness of VGRF. [ABSTRACT FROM AUTHOR]

We consider a simultaneous small noise limit for a singularly perturbed coupled diffusion described by d X t ε = b (X t ε , Y t ε) d t + ε α d B t , d Y t ε = - 1 ε ∇ y U (X t ε , Y t ε) d t + s (ε) ε d W t , where B t , W t are independent Brownian motions on R d and R m respectively, b : R d × R m → R d , U : R d × R m → R and s : (0 , ∞) → (0 , ∞) . We impose regularity assumptions on b, U and let 0 < α < 1. When s (ε) goes to zero slower than a prescribed rate as ε → 0 , we characterize all weak limit points of X ε , as ε → 0 , as solutions to a differential equation driven by a measurable vector field. Under an additional assumption on the behaviour of U (x , ·) at its global minima we characterize all limit points as Filippov solutions to the differential equation. [ABSTRACT FROM AUTHOR]

In this paper, a nonlinear low-pass filter is presented, which produces significantly less phase lag than linear and some nonlinear filters. The proposed filter employs a saturation function to enhance the linear filter's performance. The gain and phase responses of the filter are derived analytically using a modified describing function, and the efficiency of the proposed method is examined through numerical examples. Based on the required cut-off frequency and noise to signal ratio, a rule of thumb is given to set the filter's parameters. In the frequency domain, simulation results show that the filter's gain response is near 0 dB in the pass-band, and the noise attenuation rate is − 40 dB ∕ dec , while the phase lag is three times lesser compared to 2nd order Butterworth low-pass filter. Moreover, comparing with Jin et al.'s parabolic sliding mode filter and feed-forwarded parabolic sliding mode filter the gain and phase of the proposed filter are closer to zero in the pass-band and before cut-off frequency. Furthermore, the filter's performance is also evaluated in case of different noise color and concluded that the proposed filter is superior to linear and nonlinear filters in case of white, blue, or purple noise Finally, the filter's effectiveness and the tuning guideline are validated by simulating a precision motion control system in the discrete-time domain. • Achieving unity gain and zero phase lag in the passband. • Noise attenuation rate of − 40 dB ∕ dec in the stopband. • Deriving frequency response of the filter based on a modified describing function. • Presenting tuning guideline based on approximate noise to signal ratio. [ABSTRACT FROM AUTHOR]

• A variational Bayesian based cubature Kalman filter (VBCKF-R) is derived. • An adaptive robust nonlinear filtering framework is proposed based on the variational Bayesian (VB) method and generalized maximum likelihood estimation (GM estimation). • The VBCEECKF algorithm is developed by applying the CEE criteria to the proposed adaptive robust nonlinear filtering framework. • The proposed VBCEECKF algorithm has high precision in target tracking under non-ideal measurement situations. An adaptive robust nonlinear filtering framework is proposed based on the variational Bayesian (VB) method and generalized maximum likelihood estimation (GM estimation) to simultaneously handle the outliers and uncertain measurement noise covariance matrix (MNCM) for state estimation. This framework utilizes the cubature criterion to solve nonlinear integration problems. By embedding GM estimation in the VB method, the uncertain MNCM is modified while robust estimation is performed. The modified MNCM also provides more accurate model parameters for GM estimation, achieving the unity of adaptability and robustness. The VBCEECKF algorithm was obtained by applying the strong robust centered error entropy criterion to the adaptive robust nonlinear filtering framework. The simulation results of target tracking under different noise conditions verify the superiority of the adaptive robust filter compared to existing methods. [ABSTRACT FROM AUTHOR]

The article is devoted to the problem of improving the quality of images recorded using low-resolution optical instruments, including diffraction-based cameras. A two-stage image correction technology is proposed. At the first stage, the correction is carried out using a linear FIR filter with a centrally symmetric frequency response in the form of quadratic and exponential functions. The resulting image is then processed with a non-linear filter that performs computer retouching of image areas characterized by a noticeable brightness difference. This procedure is only performed on those pixels in which the absolute value of gradients in different directions is sufficiently high, that is, they are located on the borders of areas with different intensity levels. This allows us to avoid noise amplification in the background, which is typical of traditional filters. The examples of the implementation are provided, showing the possibility of achieving high sharpness and illustrating how the filter can be adjusted by visual perception.

We propose an Iterative Mean Filter (IMF) to eliminate the salt-and-pepper noise. IMF uses the mean of gray values of noise-free pixels in a fixed-size window. Unlike other nonlinear filters, IMF does not enlarge the window size. A large size reduces the accuracy of noise removal. Therefore, IMF only uses a window with a size of $3\times3$ . This feature is helpful for IMF to be able to more precisely evaluate a new gray value for the center pixel. To process high-density noise effectively, we propose an iterative procedure for IMF. In the experiments, we operationalize Peak Signal-to-Noise Ratio (PSNR), Visual Information Fidelity, Image Enhancement Factor, Structural Similarity (SSIM), and Multiscale Structure Similarity to assess image quality. Furthermore, we compare denoising results of IMF with ones of the other state-of-the-art methods. A comprehensive comparison of execution time is also provided. The qualitative results by PSNR and SSIM showed that IMF outperforms the other methods such as Based-on Pixel Density Filter (BPDF), Decision-Based Algorithm (DBA), Modified Decision-Based Untrimmed Median Filter (MDBUTMF), Noise Adaptive Fuzzy Switching Median Filter (NAFSMF), Adaptive Weighted Mean Filter (AWMF), Different Applied Median Filter (DAMF), Adaptive Type-2 Fuzzy Filter (FDS): for the IMAGESTEST dataset - BPDF (25.36/0.756), DBA (28.72/0.8426), MDBUTMF (25.93/0.8426), NAFSMF (29.32/0.8735), AWMF (32.25/0.9177), DAMF (31.65/0.9154), FDS (27.98/0.8338), and IMF (33.67/0.9252); and for the BSDS dataset - BPDF (24.95/0.7469), DBA (26.84/0.8061), MDBUTMF (26.25/0.7732), NAFSMF (27.26/0.8191), AWMF (28.89/0.8672), DAMF (29.11/0.8667), FDS (26.85/0.8095), and IMF (30.04/0.8753).