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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]

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]

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]

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]

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]

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 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]

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]

• 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]

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]

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]

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]

The object of research is the adaptive switching weighted median image filter (ASWM) algorithm. This algorithm is one of the most effective in the field of impulse noise suppression. The computational complexity and algorithmic features of this adaptive nonlinear filter make it impossible to implement a filter that works in real time on modern PLD microcircuits. The most problematic areas of the algorithm are the weight coefficient estimation cycle, which has no limit on the number of iterations and contains a large number of division operations. This does not allow implementing the filter on PLDs with a sufficiently effective method. In the course of the research, the programming model of the filter in Python was used. The performance of the algorithm was assessed using the Peak Signal-to-Noise Ratio (PSNR) and Structural Similarity Index Measure (SSIM) metrics. Modeling made it possible to find out empirically the number of iterations of the cycle for estimating the weight coefficients at different levels of noise density and to estimate the effect of artificial limitation of the maximum number of iterations on the filter performance. Regardless of the intensity of the noise impact, the algorithm performs less than 40 iterations of the evaluation cycle. Let’s also simulate the operation of the algorithm with different variants of the division module implementation. The paper considers the main of them and offers the most optimal in terms of the ratio of accuracy/hardware costs for implementation. Thus, a modified algorithm was proposed that does not have these disadvantages. Thanks to modifications of the algorithm, it is possible to implement a pipelined ASWM image filter on modern PLDs. The filter is synthesized for the main families of Intel PLDs. The implementation, which is not inferior in terms of SSIM and PSNR metrics to the original algorithm, requires less than 65,000 FPGA logical cells and allows filtering of monochrome images with FullHD resolution at 48 frames/s at a clock frequency of 100 MHz. [ABSTRACT FROM AUTHOR]

In many practical applications, the initial alignment of the strapdown inertial navigation system (SINS) must be performed under large misalignment angles. However, the error model of SINS in this situation is nonlinear, making it hard to obtain an accurate initial alignment result. Aiming at solving this problem via nonlinear filtering, an improved Markov chain Monte Carlo (MCMC)-based particle filter (PF) algorithm is designed in this article, which uses a square-root cubature Kalman filter (SCKF), PF, and MCMC algorithm synthetically. The algorithm is dedicated to extract particles from the posterior distribution of the state by the improved MCMC algorithm and avoid the particle degeneration and the particle impoverishment in a PF. This can effectively improve the performance of particle filtering for nonlinear systems. Furthermore, to solve the problem caused by the fixed number of iterations in the typical MCMC algorithm, a novel adaptive approach is introduced according to the maximum mean discrepancy. The simulation and experimental results of GPS-aided SINS in-motion initial alignment show that the proposed algorithm can provide good filtering accuracy and have good real-time performance. [ABSTRACT FROM AUTHOR]

Summary: This paper introduces two novel nonlinear stochastic attitude estimators developed on the Special Orthogonal Group SO3 with the tracking error of the normalized Euclidean distance meeting predefined transient and steady‐state characteristics. The tracking error is confined to initially start within a predetermined large set such that the transient performance is guaranteed to obey dynamically reducing boundaries and decrease smoothly and asymptotically to the origin in probability from almost any initial condition. The proposed estimators produce accurate attitude estimates with remarkable convergence properties using measurements obtained from low‐cost inertial measurement units. The estimators proposed in continuous form are complemented by their discrete versions for the implementation purposes. The simulation results illustrate the effectiveness and robustness of the proposed estimators against uncertain measurements and large initialization error, whether in continuous or discrete form. [ABSTRACT FROM AUTHOR]

The recovery of an unknown (or minimally known) physiological signal embedded in noise has been an indispensable topic drawing the attention of many researchers. Restoration of these signals through conventional linear filtering schemes induces oversmoothing effect at jump discontinuities, and most of the nonlinear filters do not perform well at large noise level. In this paper, we propose a new nonlinear filtering approach, which incorporates the majorized version of a class of nonsmooth functions integrated with Moreau envelope-based regularization. By relaxing the strict sparsifying penalty, the new algorithms balance the smoothness property and the piecewise characteristics of biosignals. We provide the optimality criterion for the proposed algorithms. These algorithms recover the source signals from their noisy measurements. The algorithms outperform the state-of-the-art methods for piecewise synthetic and real-world physiological signals corrupted by additive noise. [ABSTRACT FROM AUTHOR]

Many biophysical measurements involve source signals possessing piecewise characteristic. Recovery of the piecewise source from the noisy measurements through the linear filtering schemes fails due to the oversmoothing effect at jump discontinuities. Similarly, most of the nonlinear filters underperform at large noise level/outliers. In this paper, we propose a Huberized nonlinear filtering approach, which is penalized by the robust estimators, such as Huber, reversed-Huber (Berhu), and the total variation (TV) functions. By addressing the small residual values quadratically and large ones by their absolute errors, the effectiveness of the proposed methods is enhanced. The hidden sparsity structures of various piecewise signals are exploited. The convexity of the proposed cost functions ensures a global solution. The new approach outperforms the state-of-the-art methods by preserving the smoothness and sharp transitions of piecewise biosignals. [ABSTRACT FROM AUTHOR]

There are a variety of Gaussian sigma-point Kalman filters (GSPKF) existing in the literature which are based on different quadrature rules. Their performances are always compared with each other on accuracy and robustness from the numerical-integration perspective, where the number of the sigma points and their corresponding weights are the main reasons resulting in the different accuracy. A new perspective on the GSPKF is proposed in this paper, which is the Mahalanobis distance ellipsoid (MDE). From the MDE perspective, GSPKFs differ from each other on accuracy and robustness mainly because they enclose different probability concentrations. This characteristic is evident when using the high-degree GSPKFs to filter the low-dimensional nonlinear systems. Two classical nonlinear system examples are used to demonstrate the proposed point of this paper. Moreover, some suggestions are given on how to select an appropriate GSPKF for a given nonlinear system. [ABSTRACT FROM AUTHOR]

In order to control the orientation of a satellite, it is important to estimate the attitude accurately. Time series estimation is especially important in micro and nanosatellites, whose sensors are usually low-cost and have higher noise levels than high end sensors. Also, the algorithms should be able to run on systems with very restricted computer power. In this work, we evaluate five Kalman-type filtering algorithms for attitude estimation with 3-axis magnetometer and sun sensor measurements. The Kalman-type filters are selected so that each of them is designed to mitigate one error source for the unscented Kalman filter that is used as baseline. We investigate the distribution of the magnetometer noises and show that the Student's t-distribution is a better model for them than the Gaussian distribution. We consider filter responses in four operation modes: steady state, recovery from incorrect initial state, short-term sensor noise increment, and long-term increment. We find that a Kalman-type filter designed for Student's t sensor noises has the best combination of accuracy and computational speed for these problems, which leads to a conclusion that one can achieve more improvements in estimation accuracy by using a filter that can work with heavy tailed noise than by using a nonlinearity minimizing filter that assumes Gaussian noise. [ABSTRACT FROM AUTHOR]

In this paper, a robust unscented Kalman filter (UKF) based on the generalized maximum likelihood estimation (M-estimation) is proposed to improve the robustness of the integrated navigation system of Global Navigation Satellite System and Inertial Measurement Unit. The UKF is a variation of Kalman filter by which the Jacobian matrix calculation in a nonlinear system state model is not necessary. The proposed robust M–M unscented Kalman filter (RMUKF) applies the M-estimation principle to both functional model errors and measurement errors. Hence, this robust filter attenuates the influences of disturbances in the dynamic model and of measurement outliers without linearizing the nonlinear state space model. In addition, an equivalent weight matrix, composed of the bi-factor shrink elements, is proposed in order to keep the original correlation coefficients of the predicted state unchanged. Furthermore, a nonlinear error model is used as the dynamic equation to verify the performance of the proposed RMUKF with a simulation and field test. Compared with the conventional UKF, the impacts of measurement outliers and system disturbances on the state estimation are both controlled by RMUKF. [ABSTRACT FROM AUTHOR]

As an alternative to the Kalman filter and the particle filter, the particle flow filter has recently attracted interest for solving the curse of dimensionality of the particle filter. Compared with the particle filter, the particle flow filter can obtain a better performance in high-dimensional state spaces with fewer samples. However, for some unobservable state dimensions, the flow operation wastes computational resources. In this paper, we propose a marginalized particle flow filter to handle the unobservable sub-state estimation. In contrast to the standard particle flow filter, we only migrate those observable dimensions of each particle according to homotopy theory and estimate the unobservable dimensions using the Kalman filter. The proposed algorithm can enhance the estimation quality of the unobservable state space and reduce the runtime of the particle flow filter. We evaluate the performance of the proposed algorithm through a multi-target tracking simulation. [ABSTRACT FROM AUTHOR]

This paper makes a further foray on the study of the filtering problem for the class of Markov jump linear systems (MJLSs). The authors shall be particularly interested in the filtering problem for the Markov jump parameter (the operation mode). Previous result in the literature on this problem has been obtained by Wonham, which has derived an optimal non‐linear filter for this problem. The main hindrance with Wonham's result, in the context of the optimal control problem for MJLS with partial observation of the operation mode, is that it introduces a great deal of non‐linearity in the Hamilton–Jacobi–Belman equation, which makes it difficult to get an explicit closed solution for the control problem. Motivated, in part, by this, the main contribution of this paper is to devise an optimal linear filter for the mode operation, which they believe could be more favourable in the solution of the control problem with partial observations. In addition, relying on Murayama's stochastic numerical method and the results by Chenggui‐Yuan, they carry out simulation of Wonham's filter, and the one devised in this paper, in order to compare their performances. [ABSTRACT FROM AUTHOR]

Abstract This paper analyzes the real-time relative pose estimation and attitude prediction of a tumbling target spacecraft through a high-order numerical extended Kalman filter based on differential algebra. Indeed, in the differential algebra framework, the Taylor expansion of the phase flow is automatically available once the spacecraft dynamics is integrated and thus the need to write and integrate high-order variational equations is completely avoided making the presented solution easier to implement. To validate the technique, the ESA's e.deorbit mission, involving the Envisat satellite, is used as reference test case. The developed algorithms are implemented on a BeagleBone Black platform, as representative of the limited computational capability available on onboard processors. The performance is assessed by varying the measurement acquisition frequency and processor clock frequency, and considering various levels of uncertainties. A comparison among the different orders of the filter is carried out. Highlights • Onboard relative pose estimation using differential algebra techniques is analyzed. • Differential algebra enables an easier implementation of high-order Kalman filter. • Using orders greater than two did not improve the accuracy of the estimation. • Second order filter outperforms first order one for relatively large uncertainties. • Second order filter can be run on an ARM processor @ 100 MHz. [ABSTRACT FROM AUTHOR]

Abstract We carried out a numerical study of a sonic transverse jet into a Ma = 2.0 crossflow based on a hybrid Reynolds-averaged Navier-Stokes (RANS)/large eddy simulation (LES) method. In order to enhance the calculation accuracy, an improved high-order finite-difference scheme is introduced. This scheme consists of an eighth-order central scheme and a nonlinear dissipation filter. The filter is derived from the explicit seventh-order weighted compact nonlinear scheme (WCNS-E−7). By incorporating a local smoothness indicator and a discontinuity sensor into the nonlinear filter, we further decrease the unnecessary dissipation and increase the resolution. With the proposed scheme, the key flow features, including shock structures, large-scale vortical structures and jet-crossflow shear/mixing layers, are well captured. The simulation shows a good agreement with the experiment data in jet penetration and diffusion. Highlights • RANS/LES simulation of a transverse jet in supersonic crossflow is performed. • An improved high-order nonlinear filter scheme is introduced. • Simulation reproduces the flowfield in good agreement with experiment. [ABSTRACT FROM AUTHOR]

Processing of signals with irregular structures is a fundamental challenge to the conventional signal processing due to the complex structures. Since most of the relationships among such data from engineering applications are inherently nonlinear, those tools that do not take the nonlinearity into account may have limitations in dealing with such relationships. In this paper, a novel nonlinear polynomial graph filter (NPGF) is proposed to facilitate the nonlinear processing of signals with irregular structures. First of all, the nonlinear relationship between the input and output graph signals is constructed, which is further developed to utilize the structure information of the irregular structures (i.e., the graph shift ${\boldsymbol S}$). Specifically, the nonlinear kernels and the nonlinear input terms are both designed to be polynomials of the graph shift ${\boldsymbol S}$. Such nonlinear polynomial relationship is then defined as the NPGF. Note that shift invariance is a fundamental property in signal processing but is not straightforward in the existing nonlinear graph signal processing techniques. Due to the special expression of the NPGF, the shift-invariance is extended to our NPGF, which can conveniently facilitate the analysis and design of graph signals using NPGF and is one of the most important contributions in this paper. Numerical studies that characterize the nonlinear temperature distribution and GDP prediction based on real datasets are presented. Compared with other existing techniques, our NPGF achieves superior capability in characterizing the nonlinear relationship between the input and output graph signals, especially when only very few graph signals can be observed. [ABSTRACT FROM AUTHOR]

Modular discrete and integrated implementations of a continuous-time analog rank-order N input filter are presented that uses one operational transconductance amplifier per input. Rank is programmable for all values from k=1 (min case) to k=N (max case). The implementation is based on transconductance cells with high transconductance gain and symmetrical output current saturating characteristics. Experimental results for both discrete and CMOS integrated implementations are presented that verify functionality and the high-frequency characteristics of the proposed implementations. [ABSTRACT FROM AUTHOR]

• Differently from the existing works on connectivity-preserving consensus where the deterministic dynamics are investigated, stochastic system model is considered in this paper. • The investigated stochastic system model is more general and has more extensive research significance since unmeasured periodic disturbances are involved. • From the perspective of function approximation, a novel Fourier series expansion-fuzzy logic system function approximator is employed, which plays a vital role in dealing with periodically disturbed functions. • Unlike the most existing connectivity-preserving consensus achievements where the potential function method is adopted, error transformation method is incorporated in this paper to preserve the connectivity of communication graph. • The proposed continuous controller is developed to the event-triggered one which significantly reduces the cost of the information transmission. Differently from the existing event-triggered mechanism with static threshold, the dynamic threshold strategy is designed. Two adaptive fuzzy connectivity-preserving consensus control schemes, in continuous and event-triggered manners, are proposed for stochastic strict-feedback nonlinear multi-agent systems subject to unmeasured periodic disturbances. Differently from the existing works on connectivity-preserving consensus where the deterministic dynamics are investigated, stochastic multi-agent systems are considered. An error transformation is incorporated to preserve the initial interaction pattern determined by initial positions and communication ranges of the agents. Moreover, the stochastic system model suffers from unmeasured periodic disturbances in a nonlinear manner. By associating Fourier series expansion with fuzzy logic system, a novel function approximator is constructed to describe the packaged disturbance-dependent nonlinear functions. Meanwhile, a nonlinear filter is designed to avert the "explosion of complexity" problem in conventional backstepping recursive design procedure. In addition, the proposed continuous controller is developed to event-triggered one. Then, it is proved that the consensus is achieved and the initial connectivity of communication graph is preserved in the sense of probability. In simulations, two examples are provided to substantiate the effectiveness of the proposed consensus protocols. [ABSTRACT FROM AUTHOR]

This paper proposes a novel approach of estimating the symmetrical component into a network. The power grid development and deployment offer several advantages regarding the overall system performance of the electrical system. Currently, through the smart metering system, the symmetrical components problems can be resolved in real-time by extracting, tracking and detecting any issue related to power disturbance on the grid. An adaptive method to estimate symmetrical components in the framework of the power systems is presented. The proposed method is based on a nonlinear adaptive tracking of amplitude, phase and frequency of a non-stationary sinusoidal waveform in real-time. The method offers structural simplicity while maintaining performance robustness and controllable speed and accuracy. Experimental results are presented to verify the performance of the proposed method. The results show that the method can provide an accurate estimation of the symmetrical components in the presence of amplitude and angle variations, as well as in the presence of harmonics. The simplicity of the structure and ease of the parameter settings render the proposed method suitable for both software and hardware implementation. Two scenarios are analysed to validate the proposed algorithm. [ABSTRACT FROM AUTHOR]

The Student’s t-based nonlinear filter (STNF) can cope with the filtering problem of nonlinear systems with heavy-tailed process and measurement noises. The key problem in the design of a STNF is how to calculate the Student’s t weighted integral, and the performance of the STNF depends heavily on the used numerical integration technique. In this paper, new high-degree Student’s t spherical-radial cubature rules (STSRCRs) for the Student’s t weighted integral are proposed based on spherical-radial transformation and moment matching methods, from which new high-degree Student’s t-based cubature filters (STCFs) are developed. The proposed high-degree STSRCRs can achieve better approximation to the Student’s t weighted integral as compared with the existing third-degree Student’s t integral rules. As a result, the proposed high-degree STCFs have higher estimation accuracy than the existing STNFs. Simulation results illustrate that the proposed filters can achieve higher estimation accuracy than the existing Gaussian approximate filters, Huber-based nonlinear Kalman filters and STNFs with slightly increased computational complexities, and are computationally much more efficient than the existing Gaussian sum filter and particle filter. [ABSTRACT FROM AUTHOR]

This paper presents a density-based topology optimization approach to design compact wideband coaxial-to-waveguide transitions. The underlying optimization problem shows a strong self penalization towards binary solutions, which entails mesh-dependent designs that generally exhibit poor performance. To address the self penalization issue, we develop a filtering approach that consists of two phases. The first phase aims to relax the self penalization by using a sequence of linear filters. The second phase relies on nonlinear filters and aims to obtain binary solutions and to impose minimum-size control on the final design. We present results for optimizing compact transitions between a 50-Ohm coaxial cable and a standard WR90 waveguide operating in the X-band (8-12 GHz). [ABSTRACT FROM AUTHOR]

With the popularity of electrical vehicles, the lithium-ion battery industry is developing rapidly. To ensure battery safe usage and to reduce its average lifecycle cost, accurate state of charge (SOC) tracking algorithms for real-time implementation are required for different applications. Many SOC estimation methods have been proposed in the literature. However, only a few of them consider the real-time applicability. This paper classifies the recently proposed online SOC estimation methods into five categories. Their principal features are illustrated, and the main pros and cons are provided. The SOC estimation methods are compared and discussed in terms of accuracy, robustness, and computation burden. Afterward, as the most popular type of model-based SOC estimation algorithms, seven nonlinear filters existing in literature are compared in terms of their accuracy and execution time as a reference for online implementation. [ABSTRACT FROM AUTHOR]

The nonlinear filter based stabilization proposed in Layton et al. (J. Math. Fluid Mech. 14(2), 325-354 2012) allows to incorporate an eddy viscosity model into an existing laminar flow codes in a modular way. However, the proposed nonlinear filtering step requires the assembly of the associated matrix at each time step and solving a linear system with an indefinte matrix. We propose computationally efficient version of the filtering step that only requires the assembly once, and the solution of two symmetric, positive definite systems at each time step. We also test a new indicator function based on the entropy viscosity model of Guermond (Int. J. Numer. Meth. Fluids. 57(9), 1153-1170 2008); Guermond et al. (J. Sci. Comput. 49(1), 35-50 2011). [ABSTRACT FROM AUTHOR]

The traditional feature point detection algorithm is based on the linear scale decomposition. In the SIFT (Scale Invariant Feature Transform) algorithm, features are obtained through building the image pyramid by the Gaussian filter. SIFT has good robustness but has some flaws as well. Gaussian filter neither preserve object boundaries nor smooth the same level details and noise at all scales, which impair the accuracy and distinctiveness of the feature point positioning. Nonlinear scale decomposition can solve these problems. In this paper, a new image mosaic algorithm based on A-KAZE feature is proposed to take advantages of the A-KAZE algorithm in terms of rotation invariance, illumination invariance, speed, and stability. The optimal stitching line is obtained and the multi-resolution fusion algorithm is used to fuse the image in order to achieve a satisfactory seamless image of high resolution. The whole straightening method is applied in the image mosaic to solve the problem of the tilt of multiple image mosaic. Experimental results show that stitching algorithm in this paper is faster and more robust compared to the traditional SIFT algorithm. © 2017 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc. [ABSTRACT FROM AUTHOR]

We review some advances of the particle filtering (PF) algorithm that have been achieved in the last decade in the context of target tracking, with regard to either a single target or multiple targets in the presence of false or missing data. The first part of our review is on remarkable achievements that have been made for the single-target PF from several aspects including importance proposal, computing efficiency, particle degeneracy/impoverishment and constrained/multi-modal systems. The second part of our review is on analyzing the intractable challenges raised within the general multitarget (multi-sensor) tracking due to random target birth and termination, false alarm, misdetection, measurement-to-track (M2T) uncertainty and track uncertainty. The mainstream multitarget PF approaches consist of two main classes, one based on M2T association approaches and the other not such as the finite set statistics-based PF. In either case, significant challenges remain due to unknown tracking scenarios and integrated tracking management. [ABSTRACT FROM AUTHOR]

Purpose: Iterative image reconstruction algorithms are commonly used to optimize an objective function, especially when the objective function is nonquadratic. Generally speaking, the iterative algorithms are computationally inefficient. This paper presents a fast algorithm that has one backprojection and no forward projection. Methods: This paper derives a new method to solve an optimization problem. The nonquadratic constraint, for example, an edge-preserving denoising constraint is implemented as a nonlinear filter. The algorithm is derived based on the POCS (projections onto projections onto convex sets) approach. Awindowed FBP (filtered backprojection) algorithm enforces the data fidelity. An iterative procedure, divided into segments, enforces edge-enhancement denoising. Each segment performs nonlinear filtering. Results: The derived iterative algorithm is computationally efficient. It contains only one backprojection and no forward projection. Low-dose CT data are used for algorithm feasibility studies. The nonlinearity is implemented as an edge-enhancing noise-smoothing filter. Conclusions: The patient studies results demonstrate its effectiveness in processing low-dose x ray CT data. This fast algorithm can be used to replace many iterative algorithms. [ABSTRACT FROM AUTHOR]

With the expanding application of light-emitting diodes (LEDs), the color quality of white LEDs has attracted much attention in several color-sensitive application fields, such as museum lighting, healthcare lighting and displays. Reliability concerns for white LEDs are changing from the luminous efficiency to color quality. However, most of the current available research on the reliability of LEDs is still focused on luminous flux depreciation rather than color shift failure. The spectral power distribution (SPD), defined as the radiant power distribution emitted by a light source at a range of visible wavelength, contains the most fundamental luminescence mechanisms of a light source. SPD is used as the quantitative inference of an LED's optical characteristics, including color coordinates that are widely used to represent the color shift process. Thus, to model the color shift failure of white LEDs during aging, this paper first extracts the features of an SPD, representing the characteristics of blue LED chips and phosphors, by multi-peak curve-fitting and modeling them with statistical functions. Then, because the shift processes of extracted features in aged LEDs are always nonlinear, a nonlinear state-space model is then developed to predict the color shift failure time within a self-adaptive particle filter framework. The results show that: (1) the failure mechanisms of LEDs can be identified by analyzing the extracted features of SPD with statistical curve-fitting and (2) the developed method can dynamically and accurately predict the color coordinates, correlated color temperatures (CCTs), and color rendering indexes (CRIs) of phosphor-converted (pc)-white LEDs, and also can estimate the residual color life. [ABSTRACT FROM AUTHOR]

• We use automatic differentiation and sparse-grid integration to automate the construction of the projection filter. • We present methods for constructing projection filters for multidimensional filtering problems using a non-Gaussian parametric density. • We show that the practical performance of the filter is comparable to the particle filter and finite difference based solutions to the Kushner–Stratonovich equation. • An open-source implementation of the method is available. The projection filter is a technique for approximating the solutions of optimal filtering problems. In projection filters, the Kushner–Stratonovich stochastic partial differential equation that governs the propagation of the optimal filtering density is projected to a manifold of parametric densities, resulting in a finite-dimensional stochastic differential equation. Despite the fact that projection filters are capable of representing complicated probability densities, their current implementations are limited to Gaussian family or unidimensional filtering applications. This work considers a combination of numerical integration and automatic differentiation to construct projection filter algorithms for more generic problems. Specifically, we provide a detailed exposition of this combination for the manifold of the exponential family, and show how to apply the projection filter to multidimensional cases. We demonstrate numerically that based on comparison to a finite-difference solution to the Kushner–Stratonovich equation and a bootstrap particle filter with systematic resampling, the proposed algorithm retains an accurate approximation of the filtering density while requiring a comparatively low number of quadrature points. Due to the sparse-grid integration and automatic differentiation used to calculate the expected values of the natural statistics and the Fisher metric, the proposed filtering algorithms are highly scalable. They therefore are suitable to many applications in which the number of dimensions exceeds the practical limit of particle filters, but where the Gaussian-approximations are deemed unsatisfactory. [ABSTRACT FROM AUTHOR]

This paper studies weak continuity of nonlinear filters. It is well-known that Borel measurability of transition probabilities for problems with incomplete state observations is preserved when the original discrete-time process is replaced with the process whose states are belief probabilities. It is also known that the similar preservation may not hold for weak continuity of transition probabilities. In this paper we show that the sufficient condition for weak continuity of transition probabilities for beliefs introduced by Kara et al. (2019) is a necessary and sufficient condition for semi-uniform Feller continuity of transition probabilities. The property of semi-uniform Feller continuity was introduced recently by Feinberg et al. (2022), and the original transition probability for a Markov decision processes with incomplete information has this property if and only if the transition probability of the process, whose state is a pair consisting of the belief probability and observation, also has this property. Thus, this property implies weak continuity of nonlinear filters. This paper also reviews several necessary and sufficient conditions for semi-uniform Feller continuity. [ABSTRACT FROM AUTHOR]

We consider the nonlinear filtering problem of graph signals, where the measurements are generated based on graph topology. We propose a graph-based unscented Kalman filter (UKF) by using the decomposition of graph Laplacian matrix in the design of Kalman gain matrix. We demonstrate that the graph-based UKF reduces to the UKF for the graph Fourier transform of signals with a diagonal Kalman gain matrix, so that each vertex signal can be updated independently and more accurate results can be derived to reduce accumulation errors. Simulation results are provided to verify the effectiveness of the proposed filter. [ABSTRACT FROM AUTHOR]

The nonlinear dynamic system modeling based on the input/output relationship results from solving the approximation problem. One can distinguish two large classes: polynomials and neural networks. The different types of neural networks draw attention. The discrete time feedforward cellular neural network is suggested for filtering non-Gaussian noise, as well as the example of nonlinear filters modeling to cancel the impulse noise is represented. [ABSTRACT FROM AUTHOR]

Due to the high computational complexity required by Volterra filter, some of its practical implementations consider pipelined adaptive Volterra filter architecture with two layers structure. However, its main challenges are the poor robustness against impulsive noise, slow convergence and high computational complexity for long memory high order expansion on each module. In this paper, we firstly extend the pipelined second-order adaptive Volterra filter to its high order version. Then, to reduce the computational complexity and improve the robust performance of pipelined adaptive Volterra filter architecture, the pipelined adaptive Volterra set-membership (PAVF-SM) algorithm and its robust version (PAVF-RSM) are proposed, which are derived from the least-perturbation property and adaptive approximation principle. Due to the inherent variable step size and nonlinear selective update mechanisms, the proposed PAVF-SM and PAVF-RSM algorithms achieve lower complexity and improved convergence performance. Simulations also verify the improved performance of the PAVF-SM and PAVF-RSM algorithms under Gaussian noise and impulsive noise environments. [ABSTRACT FROM AUTHOR]

The nonlinear filter introduced by Yee et al. (1999) [27] and extensively used in the development of low dissipative well-balanced high order accurate finite-difference schemes is adapted to the finite element context of discontinuous Galerkin (DG) discretizations. The filter operator is constructed in the canonical computational domain for the standard cubical element where it is applied to the computed conservative variables in a direction per direction basis. Filtering becomes possible for all element types in unstructured meshes using collapsed coordinate transformations. The performance of the proposed nonlinear filter for DG discretizations is demonstrated and evaluated for different orders of expansions for one-dimensional and multidimensional problems with exact solutions. It is shown that for higher order discretizations discontinuity resolution within the cell is achieved and the design order of accuracy is preserved. The filter is applied for a number of standard inviscid flow test problems including strong shocks interactions to demonstrate that the proposed dissipative mechanism for DG discretizations yields superior results compared to the results obtained with the total variation bounded (TVB) limiter and high-order hierarchical limiting. The proposed approach is suitable for p -adaptivity in order to locally enhance resolution of three-dimensional flow simulations that include discontinuities and complex flow features. [ABSTRACT FROM AUTHOR]

Nonlinear filter generators are commonly used as keystream generators in stream ciphers. A nonlinear filter generator utilizes a nonlinear filtering function to combine the outputs of a linear feedback shift register (LFSR) to improve the linear complexity of keystream sequences. However, the LFSR-based stream ciphers are still potentially vulnerable to algebraic attacks that recover the key from some keystream bits. Although the known algebraic attacks only require polynomial time complexity of computations, all have their own constraints. This paper uses the linearization of nonlinear filter generators to cryptanalyze LFSR-based stream ciphers. Such a method works for any nonlinear filter generators. Viewing a nonlinear filter generator as a Boolean network that evolves as an automaton through Boolean functions, we first give its linearization representation. Compared to the linearization representation in Limniotis et al. (2008), this representation requires lower spatial complexity of computations in most cases. Based on the representation, the key recoverability is analyzed via the observability of Boolean networks. An algorithm for key recovery is given as well. Compared to the exhaustive search to recover the key, using this linearization representation requires lower time complexity of computations, though it leads to exponential time complexity. [ABSTRACT FROM AUTHOR]

In this study, a non‐linear filter named the range‐parameterised orthogonal simplex cubature Kalman filter (RPOSCKF) is proposed to further improve the accuracy of bearings‐only tracking. The filter combines the simplex spherical radial numerical rule with an orthogonal method, and thus the standard cubature points are transformed into the orthogonal simplex cubature points (OSCPs). It is proved that the filter using the OSCPs can tune the high order terms of the highly non‐linear measurement function and therefore alleviate problems due to the non‐local sampling effects. On the other hand, the fuzzy initial estimation problem is handled by an improved range‐parameterised (IRP) strategy. The IRP strategy divides the filter into some weighted orthogonal simplex CKFs each with different initial estimate, where the initial weights are based on the length of the estimate interval. Also, the sub‐filters with small updated weights will be removed and the computational complexity can be reduced. Simulations show that the proposed algorithm provides improved performance over the conventional algorithms. [ABSTRACT FROM AUTHOR]

An effective anisotropic diffusion (AD) mean filter variant is proposed for filtering of salt -and-pepper impulse noise. The implemented filter is robust to impulse noise ranging from low to high density levels. The algorithm involves a switching scheme in addition to utilizing the unsymmetric trimmed mean/median deviation to filter image noise while greatly preserving image edges, regardless of impulse noise density (ND). It operates with threshold parameters selected manually or adaptively estimated from the image statistics. It is further combined with the partial differential equations (PDE)-based AD for edge preservation at high NDs to enhance the properties of the trimmed mean filter. Based on experimental results, the proposed filter easily and consistently outperforms the median filter and its other variants ranging from simple to complex filter structures, especially the known PDE-based variants. In addition, the switching scheme and threshold calculation enables the filter to avoid smoothing an uncorrupted image, and filtering is activated only when impulse noise is present. Ultimately, the particular properties of the filter make its combination with the AD algorithm a unique and powerful edge-preservation smoothing filter at high-impulse NDs. © 2016 SPIE and IS&T [DOI: 10.1117/1.JEI.25.4.043001] [ABSTRACT FROM AUTHOR]