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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]

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]

Lately, an adaptive exponential functional link network (AEFLN) involving exponential terms integrated with trigonometric functional expansion is being introduced as a linear-in-the-parameters nonlinear filter. However, they exhibit degraded efficacy in lieu of non-Gaussian or impulsive noise interference. Therefore, to enhance the nonlinear modelling capability, here is a modified logarithmic hyperbolic sine cost function in amalgamation with the adaptive recursive exponential functional link network. In conjugation with this, a sparsity constraint motivated by a curvelet-dependent notion is employed in the suggested approach. Therefore, this paper presents an individually weighted modified logarithmic hyperbolic sine curvelet-based recursive exponential FLN (IMLSC-REF) for robust sparse nonlinear system identification. An individually weighted adaptation gain is imparted to several coefficients corresponding to the nonlinear adaptive model for accelerating the convergence rate. The weight update rule and the maximum criteria for the convergence factor are being further derived. Exhaustive simulation studies profess the effectiveness of the introduced algorithm in case of varied nonlinearity and for identifying as well as modelling the physical path of the acoustic feedback phenomenon of a behind-the-ear (BTE) hearing aid. [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 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]

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]

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]

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]

Correntropy has recently attracted great attention because of its robustness to non-Gaussian noise. Inspired by this robustness property, a spline adaptive filtering algorithm based on the maximum correntropy criterion (SAF-MCC) has been proposed. However, the steady-state convergence performance of the SAF-MCC has not been studied. This brief presents a steady-state performance analysis of the SAF-MCC for Gaussian and non-Gaussian noise. We derive and discuss the theoretical excess mean square error (EMSE) under these cases. Monte Carlo simulations are presented to corroborate the theoretical performance analysis results developed in this brief. [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]

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 non‐linear square‐root estimation scheme for brushless DC (BLDC) motors. The cubature Kalman filter (CKF) is the main estimation tool for the presented approach. The CKF is a recently proposed estimator for highly non‐linear systems and its efficacy has been verified on several applications. The square‐root version of the CKF is preferred over the conventional CKF for real‐time applications. Despite of having several advantages over other non‐linear filters, the CKF has not yet been explored for state estimation of electric drives in the electric drives community. In this study, the authors present a square‐root CKF for the speed and rotor position estimation of a highly non‐linear and high fidelity BLDC motor, these estimated speed and rotor position are then fed back to control the speed of the BLDC motor. The efficacy of the presented approach for low and high reference speeds, and in the presence of parametric uncertainties, is demonstrated by real‐time experiments. [ABSTRACT FROM AUTHOR]

• Applying an improved pipelined structure to EMF (Even Mirror Fourier)-based ANC system to reduce computational complexity. • Improvement of the noise cancellation performance by independently updating the synaptic weight vector. • A more appropriate design of system output for ANC. • Analyzing the stable conditions for the proposed system. • Considerably reducing computational complexity for EMF-based ANC system. The Even Mirror Fourier (EMF) filter is the universal approximation for nonlinear systems, which has been used in active noise control (ANC) applications, especially in scenarios where ANC contains strong nonlinearity. However, the computational burden can impede its implementation in practice. To mitigate this disadvantage, an improved pipelined EMF (IPEMF) filter has been developed and applied for the nonlinear ANC systems, in this paper. The proposed architecture uses simple small-scale EMF modules (i.e., fewer coefficients) nested in a pipelined fashion to replace the complex EMF structure, and hence has got a computational advantage. Moreover, the modules of the IPEMF are designed to update the synaptic weight vector independently, and the output of IPEMF is simplified by the sum of the local estimates of the modules. As a consequence, the nonlinear processing capability is considerably improved and the filtered-error algorithm deduced for the IPEMF controller is less complicated. Simulation results show that the proposed IPEMF controller significantly reduces the computational complexity compared to EMF, while still maintaining control performance is as equivalent as EMF and better than the pipelined EMF (PEMF), pipelined Volterra filter (PVF). [ABSTRACT FROM AUTHOR]

Abstract: A large Linear Complexity (LC) is a fundamental requirement for a binary sequence to be used in secret key cryptography. Ink this paper, a method of computing all the nonlinear filters applied to a shift register with a linear complexity LC ≥ (▪), where L is the length of the register and k the order of the filter, is proposed. The procedure is based on the handling of filtering functions by means of algebraic operations. The method formally completes the family of nonlinear filtering functions with a guaranteed large linear complexity. In cryptographic terms, it means an easy and useful way of designing sequence generators for cryptographic purposes. [Copyright &y& Elsevier]

The problem of classification of finite-dimensional estimation algebras was formally proposed by Brockett in his lecture at International Congress of Mathematicians in 1983. Due to the difficulty of the problem, in the early 1990s Brockett suggested that one should understand the low-dimensional estimation algebras first. In this article, we extend Yau and his coauthors' work of the Mitter conjecture for low-dimensional estimation algebras in nonlinear filtering problem. And, we apply the results to give classification of estimation algebras of dimension six. [ABSTRACT FROM PUBLISHER]

Abstract: The nonlinear filtering algorithm in Unscented Kalman filter (UKF) has such advantages as high estimation accuracy, fast convergence and easy implementation, but for the complex nonlinear system model, it is subject to local optimal solutions, thus leading to incorrect filtering results. In order to solve this problem, we put forward an improved UKF (IUKF) algorithm in this paper based on the strategy of seeking optimal solutions through multi-directional searches. This algorithm can search for the optimal filtering solution from different directions and locate the global optimal solution by tracing all local optimal solutions. The simulation in wireless location proves that the new method can still work normally in the situation that the original algorithm ceases to be feasible, so it also effectively expands the application scope of UKF. [Copyright &y& Elsevier]

This paper describes the design of fault diagnosis and active fault tolerant control schemes that can be developed for nonlinear systems. The methodology is based on a fault detection and diagnosis procedure relying on adaptive filters designed via the nonlinear geometric approach, which allows obtaining the disturbance de-coupling property. The controller reconfiguration exploits directly the on-line estimate of the fault signal. The classical model of an inverted pendulum on a cart is considered as an application example, in order to highlight the complete design procedure, including the mathematical aspects of the nonlinear disturbance de-coupling method based on the nonlinear differential geometry, as well as the feasibility and efficiency of the proposed approach. Extensive simulations of the benchmark process and Monte Carlo analysis are practical tools for assessing experimentally the robustness and stability properties of the developed fault tolerant control scheme, in the presence of modelling and measurement errors. The fault tolerant control method is also compared with a different approach relying on sliding mode control, in order to evaluate benefits and drawbacks of both techniques. This comparison highlights that the proposed design methodology can constitute a reliable and robust approach for application to real nonlinear processes. [ABSTRACT FROM AUTHOR]

Due to the computational complexity of the Volterra filter, there are limitations on the implementation in practice. In this paper, a novel adaptive joint process filter using pipelined feedforward second-order Volterra architecture (JPPSOV) to reduce the computational burdens of the Volterra filter is pro- posed. The proposed architecture consists of two subsections: nonlinear subsection performing a nonlinear mapping from the input space to an intermediate space by the feedforward second-order Volterra (SOY), and a linear combiner performing a linear mapping from the intermediate space to the output space. The corresponding adaptive algorithms are deduced for the non- linear and linear combiner subsections, respectively. Moreover, the analysis of theory shows that these adaptive algorithms based on the pipelined architecture are stable and convergence under a certain condition. To evaluate the performance of the JPPSOV, a series of simulation experiments are presented including nonlinear system identification and predicting of speech signals. Compared with the conventional SOY filter, adaptive JPPSOV filter exhibits a litter better convergence performance with less computational burden in terms of convergence speed and steady-state error. [ABSTRACT FROM AUTHOR]

Abstract: Different approaches for the estimation of the states of linear dynamic systems are commonly used, the most common being the Kalman filter. For nonlinear systems, variants of the Kalman filter are used. Some of these variants include the LKF (linearized Kalman filter), the EKF (extended Kalman filter), and the UKF (unscented Kalman filter). With the LKF and EKF, performance varies depending on how often Jacobians (partial derivative matrices) are updated. In other words, we see a tradeoff between computational effort and filtering performance. With the unscented Kalman filter, Jacobians are not calculated but computational effort is typically high due to the need for multiple simulations at each time step of the underlying dynamic system. Up to this point in time a number of filtering approaches have been used for aircraft turbofan engine health estimation, but a systematic comparison has not been published. This paper compares the estimation accuracy and computational effort of these filters for aircraft engine health estimation. We show in this paper that the EKF and UKF both outperform the LKF. The EKF computational effort is an order of magnitude higher than the LKF, and the UKF is another order of magnitude higher than the EKF. Overall we conclude that the EKF, with Jacobian calculations about every three flights, is the best choice for aircraft engine health estimation. [Copyright &y& Elsevier]

Recently, some methods using digital filters (Volterra filters) based on the Volterra series expansion have been proposed for the identification nonlinear systems and the elimination of their nonlinear distortions. The Volterra filters are obtained by extending the conventional linear digital filters into nonlinear, and the structures and the characteristics contain linear digital filters. Therefore, many techniques which have been developed in linear digital filters can be easily introduced into the Volterra filters. This paper introduces adaptive Volterra filters, which adjust the filter coefficients automatically. In particular, the update algorithms and problems are discussed. The future of adaptive Volterra filters is also presented. © 2000 Scripta Technica, Electron Comm Jpn Pt 3, 83(12): 51–61, 2000 [ABSTRACT FROM AUTHOR]

Linear adaptive digital filters are applied to various fields for their simplicity in the design and implementation. Considering many kinds of nonlinearities inherent to practical systems, however, nonlinear adaptive filtering will be more desirable. In this paper, we present a design method for parallel nonlinear adaptive digital filters using multilayer nonrecursive neural networks. Linear adaptive digital filters with the advantage of obtaining better accuracy of estimation. Furthermore, the nonlinear adaptive digital filter is extended to parallel nonlinear adaptive digital filters which reduce the computations of each filtering system, especially when a high-order nonlinear adaptive digital filter is necessary. [ABSTRACT FROM AUTHOR]