Filtering Error Research Articles

The efficiency of using wavelet transforms for filtering noise in the signals of measuring transducers

Methods of wavelet filtering of noise in signals of measuring transducers using the threshold method of discrete wavelet transform are considered. To study the methods of wavelet filtering of noise, special model signals were used to estimate the filtering errors. A method has been developed for determining the parameters of wavelet filtering of noise with a threshold for all levels of decomposition, which makes it possible to determine the wavelet function, threshold function and filtering threshold of the detailing coefficients of the discrete wavelet decomposition. The influence of the parameters of the noise distribution, the noise level, the number of vanishing moments of the Daubechies wavelet function, the nature of the threshold function and the threshold value on the filtering error caused by the noises of non-stationary measuring signals has been investigated by the method of a computational experiment. The results of the study of six threshold functions are given with the addition of noise to the measuring signal with nonstationary amplitude, frequency and duty cycle of rectangular pulses. The signal of the Doppler sensors is investigated, the wavelet filtering parameters are calculated, which provide the minimum error. The obtained parameters are used to construct graphs of signals before and after filtering directly in the time domain using the inverse wavelet transform.

Distributed filtering for delayed nonlinear system with random sensor saturation: a dynamic event-triggered approach

This paper is concerned with the distributed filtering problem for a class of delayed nonlinear systems with random sensor saturation (RSS) under a dynamic event-triggered mechanism. The nonlinear function is assumed to satisfy the Lipschitz condition. A dynamic event-triggered mechanism is employed to further reduce the innovation transmission frequencies among the adjacent nodes. Both the Bernoulli distributed random variables and saturation function are employed to model the phenomenon of RSS. The aim of this paper is to design a sub-optimal filter such that the covariance of the filtering error has an upper bound, which is minimized by appropriately computing the filter gain. Furthermore, the error boundedness is analysed and a sufficient criterion is presented to ensure that the filtering error is mean-square bounded. Finally, a numerical example is provided to verify the effectiveness of the proposed filtering algorithm.

Mode-Dependent Event-Triggered Fault Detection for Nonlinear Semi-Markov Jump Systems With Quantization: Application to Robotic Manipulator

This paper is studied with fault detection issue for nonlinear semi-Markov jump systems. In particular, the mode-dependent mechanism of event-triggered transmission is developed for improving communication efficiency. Furthermore, the mode-dependent quantization method is utilized to cope with the limited network bandwidth. These strategies are chosen for more effective utilization of system mode information with less conservatism. Mode-dependent filter type fault detectors are constructed and sufficient conditions are established by Lyapunov-Krasovskii functionals, such that the filter error system can achieve the desired dissipative performance. In the end, the designed fault detection method is verified through a practical example of robotic manipulator.

An adaptive multi-sensor resource allocation algorithm based on efficiency function

In this paper, combined with the Kalman filtering algorithm, the linear weighted sum of the normalized prediction information increment DI and the norm of target filter error covariance matrix ║ cP ║ is used to represent the pairing function of the target-sensor combination and the assignment and automatic updating of the pairing function between sensor and target are realized. Based on the analytic hierarchy process (AHP), an adaptive sensor resource allocation algorithm is proposed. The simulation results show that the algorithm can effectively integrate various evaluation factors and is compatible with different types of targets. The algorithm has simple structure and good versatility. The limited sensor resources can be dynamically adjusted according to the priority of targets, making the sensor allocation strategy more reasonable and effective.

Quantized passive filtering for switched delayed neural networks

The issue of quantized passive filtering for switched delayed neural networks with noise interference is studied in this paper. Both arbitrary and semi-Markov switching rules are taken into account. By choosing Lyapunov functionals and applying several inequality techniques, sufficient conditions are proposed to ensure the filter error system to be not only exponentially stable, but also exponentially passive from the noise interference to the output error. The gain matrix for the proposed quantized passive filter is able to be determined through the feasible solution of linear matrix inequalities, which are computationally tractable with the help of some popular convex optimization tools. Finally, two numerical examples are given to illustrate the usefulness of the quantized passive filter design methods.

Research on the Package Feature Selection of Talent Attracting Factors in International Trade in Guangdong-Hong Kong-Macao Greater Bay Area

This paper designs a survey questionnaire based on the Guangdong-Hong Kong-Macao Greater Bay Area’s demand for talents in international trade, adds job types, filters through package features, and performs feature filtering with the error filter criteria set in this paper, and conducts logistic regression analysis on talent types, so as to realize the classification and dynamic analysis of talents. The dynamic needs of various types of talents in international trade in the Guangdong-Hong Kong-Macao Greater Bay Area are drawn, and specific measures such as increasing salaries and benefits, reducing living costs, providing housing subsidies, solving children's employment problems, and ensuring quality of life are proposed for the development of international trade talents. Reducing the cost of talent migration can promote them to make more contributions to the Guangdong-Hong Kong-Macao Greater Bay Area. This will help the Guangdong-Hong Kong-Macao Greater Bay Area government to attract outstanding international trade talents and formulate detailed and feasible strategies, which has certain reference significance.

Real-Time Artifact Removal System for Surface EMG Processing During Ten-Fold Frequency Electrical Stimulation

In this paper, three easily implemented hardware algorithms, including the adaptive prediction error filter based on the Gram-Schmidt algorithm (GS-APEF), the least mean square adaptive filter and the comb filter, are extensively investigated for artifact denoising on a constructed semi-simulated database with varied ten-fold frequency stimulation. By implementing the GS-APEF in the field-programmable gate array (FPGA) and using the edge noise mitigating technique, a stimulation artifact denoising system is designed to realize real-time stimulation artifact removal under varied ten-fold frequency functional electrical stimulation. Good performance of the artifact denoising is demonstrated in proof-of-concept experiments on able-bodied subjects with a mean correlation coefficient between the root mean square profile of denoised surface electromyography and volitional force of 0.94, verifying the validity of the proposed prototype.

New approach to finite frequency Filter Design for two-dimensional T-S fuzzy systems

This paper considers the problem of filter design for two-dimensional (2D) discrete-time non-linear systems in Takagi-Sugeno (T-S) fuzzy mode. The problem to be solved in the paper is to find a H∞ filter model such that the filtering error system is asymptotically stable. A numerical example is employed to illustrate the validity of the proposed methods.

Event-triggered distributed filtering for discrete-time systems with integral measurements

This paper handles the event-triggered distributed filtering problem for a class of discrete-time systems with integral measurements over sensor networks (SNs). First of all, a plant is monitored by an SN formulated by a digraph. The integral measurement phenomenon is modelled for each node to account for the interval time taken by sample collection. Next, to mitigate the communication burden of network, an event generator function is introduced for each node to regulate the data transmission to its neighbouring nodes. This paper aims to find the suitable filter gains for each node such that the filtering error dynamics satisfies the exponentially ultimately boundedness. Via the Lyapunov stability theory, a sufficient condition is established which ensures the existence of the distributed filter under the desirable performance index. Moreover, the ultimate bound in the performance index is minimized via the robust optimization method. Then, the filter gains are acquired by solving a linear matrix inequality with the YALMIP toolbox. Finally, a numerical simulation example is employed to verify the usefulness of the distributed filtering algorithm developed in this paper.

Neural Network Command Filtered Control of Fractional-Order Chaotic Systems.

An adaptive neural network (NN) backstepping control method based on command filtering is proposed for a class of fractional-order chaotic systems (FOCSs) in this paper. In order to solve the problem of the item explosion in the classical backstepping method, a command filter method is adopted and the error compensation mechanism is introduced to overcome the shortcomings of the dynamic surface method. Moreover, an adaptive neural network method for unknown FOCSs is proposed. Compared with the existing control methods, the advantage of the proposed control method is that the design of the compensation signals eliminates the filtering errors, which makes the control effect of the actual system improve well. Finally, two examples are given to prove the effectiveness and potential of the proposed method.

Reservoir prediction of shallow braided delta front by Comprehensive Prediction Error Filtering Analysis

For a more accurate reservoir prediction of braided delta front, the method of High Resolution Sequence Stratigraphy was adopted in Moxizhuang Oil Field with the assistance of Comprehensive Prediction Error Filter Analysis. J1s2 was divided into 2 fifth-order base-level cycles, 5 sixth-order base-level cycles, with the turnaround surfaces of base-level rise to fall, and time-equal correlation of shallow braided delta front was achieved. Through study of microfacies correlation in High Resolution Sequence Stratigraphy frame, it is apparent that base-level cycles control microfacies distribution, and furthermore reservoir distribution: reservoirs around turnaround surface of base-level falling to rising are thick and laterally connected, while reservoirs near the middle of base-level falling and base-level rising are relatively thinner and less laterally connected, and reservoirs close to the beginning of base-level falling and the end of base-level rising are undeveloped.

Event-triggered L1 filtering for uncertain networked control systems with multiple sensor fault modes

Considering the influence of sensor fault modes on the system performance in communication network, under the discrete event-triggered communication scheme (DETCS), the problems of the robust [Formula: see text] filtering for a class of uncertain networked control systems (NCSs) with multiple sensor fault modes and persistent and amplitude-bounded disturbance constraints are investigated. A set of stochastic variables are adopted to describe the sensor faults, the filtering error system is established, which characterizes the effects of sensor faults and DETCS. By constructing an appropriate delay-dependent Lyapunov-Krasovskii functional, new results on stability and robust [Formula: see text] performance are proposed for the filtering error system according to Lyapunov theory and the integral inequality method, and the co-design method for gaining the desired [Formula: see text] filter parameters and event-triggering parameters is given in terms of linear matrix inequalities (LMIs). We notice that with the structrue of Lyapunov-Krasovskii functional which considers the piecewise-linear sawtooth structure characteristic of transmission delay, a less conservative result is obtained. Finally, three examples are provided to illustrate the feasibility of the proposed method.

Command filtering-based adaptive control for chaotic permanent magnet synchronous motors considering practical considerations

In this paper, an efficient adaptive control is designed for chaotic Permanent Magnet Synchronous Motors (PMSMs) with full-state asymmetric time-varying constraints in the input saturation presence. The strategy that is suggested in this work is equipped with the command filtering for addressing the problem of the “explosion of complexity” available in the common backstepping method. In addition, the filtering errors are incorporated into the control design procedure for improving the control system performance. During the control design, the asymmetric barrier Lyapunov functions (BLFs) are employed so that the restriction of state variables in the given intervals is guaranteed. In the suggested control method, for approximating unknown nonlinear functions, the Bessel series is utilized as a simple but effective function approximation approach as a universal approximator. The presented design provides this advantage that by considering practical considerations, a reduced-order observer is also designed so that there is no need to mount the physical sensors to measure the position and the velocity of the chaotic PMSM. The Lyapunov stability theory is used to establish the boundedness of all the closed-loop signals. According to the comparative results obtained with neural networks, the presented control design is able to suppress the chaotic behavior of the PMSM drive system while ensuring an excellent tracking performance.

Event-Triggered H ∞ Filtering for Markovian Jump Neural Networks under Random Missing Measurements and Deception Attacks

This paper concentrates on the event-triggered H ∞ filter design for the discrete-time Markovian jump neural networks under random missing measurements and cyber attacks. Considering that the controlled system and the filtering can exchange information over a shared communication network which is vulnerable to the cyber attacks and has limited bandwidth, the event-triggered mechanism is proposed to relieve the communication burden of data transmission. A variable conforming to Bernoulli distribution is exploited to describe the stochastic phenomenon since the missing measurements occur with random probability. Furthermore, seeing that the communication networks are vulnerable to external malicious attacks, the transferred information via the shared communication network may be changed by the injected false information from the attackers. Based on the above consideration, sufficient conditions for the filtering error system to maintain asymptotically stable are provided with predefined H ∞ performance. In the end, three numerical examples are given to verify the proposed theoretical results.

Input-Output Finite-Time Generalized Dissipative Filter of Discrete Time-Varying Systems With Quantization and Adaptive Event-Triggered Mechanism.

This article discusses the issue of input-output finite-time generalized dissipative filter design for a class of discrete time-varying systems. First, an adaptive event-triggered mechanism (AETM) with an adaptive law is proposed to adjust the threshold in the AETM according to the error between the system states and the filter states. Such an AETM determines whether the measurement output should be transmitted or not, which is more effective to economize the communication resources comparing with the traditional event-triggered mechanism. Second, in view of network-induced delays, the quantization and the AETM, a time-varying filter error system (TV-FES) is modeled. Then, a new augmented time-varying Lyapunov functional containing triple sum terms is provided. Based on the new finite-sum inequality and improved reciprocally convex combination lemma, delay-dependent conditions are obtained, which can ensure the TV-FES to be input-output finite-time stable and satisfy the given generalized dissipative performance. Moreover, the recursive linear matrix inequalities are presented to obtain the desired filter gains. Finally, numerical examples demonstrate the superiority and feasibility of the proposed method in this article.

On the Relation Between Smooth Variable Structure and Adaptive Kalman Filter

This article is addressed to the topic of robust state estimation of uncertain nonlinear systems. In particular, the smooth variable structure filter (SVSF) and its relation to the Kalman filter is studied. An adaptive Kalman filter is obtained from the SVSF approach by replacing the gain of the original filter. Boundedness of the estimation error of the adaptive filter is proven. The SVSF approach and the adaptive Kalman filter achieve improved robustness against model uncertainties if filter parameters are suitably optimized. Therefore, a parameter optimization process is developed and the estimation performance is studied.

Robust Attitude Stabilization of Spacecraft Under Constrained Network With Hysteresis Quantizer

This article investigates the application of hysteresis quantizer for the spacecraft regulation problem under a constrained network. The hysteresis quantizer helps in quantizing the continuous control command at a lower rate of communication while avoiding the chattering in the quantized signal. The proposed scheme employs robust adaptive control law along with a filter error similar to the terminal sliding surface. Two separate adaptive laws are implemented to avoid the overestimation problem. The filter error is specially designed owing to the fact that the quaternion-based attitude representation faces the problem of unwinding. The theoretical analysis of the proposed scheme guarantees the uniformly ultimately bounded (UUB) stability of the closed-loop system, which is subjected to the quantization error, inertial uncertainties, and external disturbances. Moreover, it is also proved that the unwinding problem does not arrive in the proposed strategy. The validation of theoretical results is tested through extensive numerical simulation. Furthermore, the comparative analysis with the existing results shows the efficacy of the proposed approach.

Adaptive fault-tolerant control for switched nonlinear systems based on command filter technique

This article put forward an adaptive neural fault-tolerant control strategy for a class of switched nonlinear systems subject to actuator fault by means of the command filter approach. By using neural networks, the unknown nonlinear functions of the system under consideration are approximated, while its unmeasurable states are estimated by establishing a switched observer. Furthermore, the “explosion of complexity” issue, which arises from the derivatives of virtual controllers, is addressed with the command filter method. In order to reduce filter errors and overcome the drawbacks of the most traditional approaches, such as the ones based on dynamic surface control techniques, an error compensation mechanism was developed. In summary, by taking advantage of the command filter approach, backstepping algorithm, and average dwell time method, an adaptive NNs fault-tolerant controller is established for the system under consideration. Finally, the designed controller has the ability to make the reference signal which can be tracked by the output of the system as close as possible and the boundness of all signals within the closed-loop system can be guaranteed. The usefulness of the designed controller is illustrated by the simulation example.

Adaptive neural network finite-time command filtered tracking control of fractional-order permanent magnet synchronous motor with input saturation

In this paper, the finite-time position tracking control for the fractional-order permanent magnet synchronous motor with input saturation, load disturbance and parameter uncertainties is considered. Based on the command filtered backstepping method, a novel adaptive neural network finite-time controller is presented. First, the neural network is introduced to approximate the uncertain function. Then, by using a command filter at the output side of the virtual signal, the issue of “explosion of complexity” is avoided. In addition, an adaptive law is applied to eliminate the approximation error and filtering error. Meanwhile, by utilizing the terminal sliding mode control technique, the finite-time signal tracking is achieved. Furthermore, an auxiliary design system is constructed to cope with the input saturation constraint. The proposed scheme not only possesses the superiorities of the classical command filtered backstepping, but also holds quick finite-time convergence property. Numerical simulations and experiment results are included to reveal the validity of the proposed design.

On the Stability Bounds of Kalman Filters for Linear Deterministic Discrete-Time Systems

In this article, we prove input-to-state stability of the estimation error of the discrete-time Kalman filter under suitable assumptions. Input-to-state stability is an important prerequisite for the use of many contemporary analysis tools for cascaded and interconnected systems. In this way, this article provides a missing link for the rigorous analysis of systems, of which the Kalman filter is a subsystem, using these tools.