Nonlinear Filtering With Sample-Based Approximation Under Constrained Communication:Progress, Insights and Trends

The nonlinear filtering problem has enduringly been an active research topic in both academia and industry due to its ever-growing theoretical importance and practical significance.The main objective of nonlinear filtering is to infer the states of a nonlinear dynamical system of interest based on the available noisy measurements. In recent years, the advance of network communication technology has not only popularized the networked systems with apparent advantages in terms of installation,cost and maintenance, but also brought about a series of challenges to the design of nonlinear filtering algorithms, among which the communication constraint has been recognized as a dominating concern. In this context, a great number of investigations have been launched towards the networked nonlinear filtering problem with communication constraints, and many samplebased nonlinear filters have been developed to deal with the highly nonlinear and/or non-Gaussian scenarios. The aim of this paper is to provide a timely survey about the recent advances on the sample-based networked nonlinear filtering problem from the perspective of communication constraints. More specifically, we first review three important families of sample-based filtering methods known as the unscented Kalman filter, particle filter,and maximum correntropy filter. Then, the latest developments are surveyed with stress on the topics regarding incomplete/imperfect information, limited resources and cyber security.Finally, several challenges and open problems are highlighted to shed some lights on the possible trends of future research in this realm.

Removing Random-Valued Impulse Noises by a Two-Staged Nonlinear Filtering Method

Digital images are frequently contaminated by impulse noise(IN)during acquisition and transmission.The removal of this noise from images is essential for their further processing.In this paper,a two-staged nonlinear filtering algorithm is proposed for removing random-valued impulse noise(RVIN)from digital images.Noisy pixels are identified and corrected in two cascaded stages.The statistics of two subsets of nearest neighbors are employed as the criterion for detecting noisy pixels in the first stage,while directional differences are adopted as the detector criterion in the second stage.The respective adaptive median values are taken as the replacement values for noisy pixels in each stage.The performance of the proposed method was compared with that of several existing methods.The experimental results show that the performance of the suggested algorithm is superior to those of the compared methods in terms of noise removal,edge preservation,and processing time.

Underwater four-quadrant dual-beam circumferential scanning laser fuze using nonlinear adaptive backscatter filter based on pauseable SAF-LMS algorithm

The phenomenon of a target echo peak overlapping with the backscattered echo peak significantly undermines the detection range and precision of underwater laser fuzes.To overcome this issue,we propose a four-quadrant dual-beam circumferential scanning laser fuze to distinguish various interference signals and provide more real-time data for the backscatter filtering algorithm.This enhances the algorithm loading capability of the fuze.In order to address the problem of insufficient filtering capacity in existing linear backscatter filtering algorithms,we develop a nonlinear backscattering adaptive filter based on the spline adaptive filter least mean square(SAF-LMS)algorithm.We also designed an algorithm pause module to retain the original trend of the target echo peak,improving the time discrimination accuracy and anti-interference capability of the fuze.Finally,experiments are conducted with varying signal-to-noise ratios of the original underwater target echo signals.The experimental results show that the average signal-to-noise ratio before and after filtering can be improved by more than31 d B,with an increase of up to 76%in extreme detection distance.

Quantum stochastic filters for nonlinear time-domain filtering of communication signals

Principles and performances of quantum stochastic filters are studied for nonlinear time-domain filtering of communication signals. Filtering is realized by combining neural networks with the nonlinear Schroedinger equation and the time-variant probability density function of signals is estimated by solution of the equation. It is shown that obviously different performances can be achieved by the control of weight coefficients of potential fields. Based on this characteristic, a novel filtering algorithm is proposed, and utilizing this algorithm, the nonlinear waveform distortion of output signals and the denoising capability of the filters can be compromised. This will make the application of quantum stochastic filters be greatly extended, such as in applying the filters to the processing of communication signals. The predominant performance of quantum stochastic filters is shown by simulation results.

NONLINEAR FILTERING ALGORITHM FOR IN S INITIAL ALIGNMENT

The initial alignment error equation of an INS (Inertial Navigation System) with large initial azimuth error has been derived and nonlinear characteristics are included. When azimuth error is fairly small, the nonlinear equation can be reduced to a linear one. Extended Kalman filter, iterated filter and second order filter formulas are derived for the nonlinear state equation with linear measurement equation. Simulations results show that the accuracy of azimuth error estimation using extended Kalman filter is better than that of using standard Kalman filter while the iterated filter and second order filter can give even better estimation accuracy.

Estimation of anthracnose dynamics by nonlinear filtering

In this work, we apply the nonlinear filtering theory to the estimation of the partially observed dynamics of anthracnose which is a phytopathology. The signal here is the inhi- bition rate and the observations are the fruit volume and the rotted volume. We propose stochastic models based on deterministic models studied previously in the literature, in order to represent the noise introduced by uncontrolled variations on parameters and errors on the measurements. Under the assumption of Brownian noises, we prove the well-posedness of the models in either they take into account the space variable or not. The filtering problem is solved for the nonspatial model giving Zakai and Kushner- Stratonovich equations satisfied respectively by the unnormalized and the normalized conditional distribution of the signal with respect to the observations. A prevision prob- lem and a discrete filtering problem are also studied for the realistic cases of discrete and possibly incomplete observations. We illustrate the filter behavior through figures displaying the average estimation relative error and a 95% confidence region obtained after a hundred of numerical simulations with initial conditions taken randomly with respect to uniform law.

Applying nonlinear filtering in reverberation time measurement under strong background noise

Nonlinear filtering of impulse response obtained by M-sequence correlation method under strong background noise is presented. The research shows that the new method works very efficiently without the need to cut off impulse response data. Even if the ratio of signal to noise is below -15 dB, the same decay curve ranges can still be obtained as when S/N > 40 dB

Nonlinear H_∞ filtering for interconnected Markovian jump systems

The problem of nonlinear H∞ filtering for interconnected Markovian jump systems is discussed. The aim of this note is the design of a nonlinear Markovian jump filter such that the resulting error system is exponentially meansquare stable and ensures a prescribed H∞ performance. A sufficient condition for the solvability of this problem is given in terms of linear matrix inequalities（LMIs）. A simulation example is presented to demonstrate the effectiveness of the proposed design approach.

An Optimized Implementation of a Novel Nonlinear Filter for Color Image Restoration

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

Nonlinear Teager-Kaiser Infomax Boost Clustering Algorithm for Brain Tumor Detection Technique

Brain tumor detection and division is a difficult tedious undertaking in clinical image preparation.When it comes to the new technology that enables accurate identification of the mysterious tissues of the brain,magnetic resonance imaging(MRI)is a great tool.It is possible to alter the tumor’s size and shape at any time for any number of patients by using the Brain picture.Radiologists have a difficult time sorting and classifying tumors from multiple images.Brain tumors may be accurately detected using a new approach called Nonlinear Teager-Kaiser Iterative Infomax Boost Clustering-Based Image Segmentation(NTKFIBC-IS).Teager-Kaiser filtering is used to reduce noise artifacts and improve the quality of images before they are processed.Different clinical characteristics are then retrieved and analyzed statistically to identify brain tumors.The use of a BraTS2015 database enables the proposed approach to be used for both qualitative and quantitative research.This dataset was used to do experimental evaluations on several metrics such as peak signal-to-noise ratios,illness detection accuracy,and false-positive rates as well as disease detection time as a function of a picture count.This segmentation delivers greater accuracy in detecting brain tumors with minimal time consumption and false-positive rates than current stateof-the-art approaches.

Modified unscented particle filter for nonlinear Bayesian tracking

A modified unscented particle filtering scheme for nonlinear tracking is proposed, in view of the potential drawbacks （such as, particle impoverishment and numerical sensitivity in calculating the prior） of the conventional unscented particle filter （UPF） confronted in practice. Specifically, a different derivation of the importance weight is presented in detail. The proposed method can avoid the calculation of the prior and reduce the effects of the impoverishment problem caused by sampling from the proposal distribution, Simulations have been performed using two illustrative examples and results have been provided to demonstrate the validity of the modified UPF as well as its improved performance over the conventional one.

Major Development Under Gaussian Filtering Since Unscented Kalman Filter

Filtering is a recursive estimation of hidden states of a dynamic system from noisy measurements.Such problems appear in several branches of science and technology,ranging from target tracking to biomedical monitoring.A commonly practiced approach of filtering with nonlinear systems is Gaussian filtering.The early Gaussian filters used a derivative-based implementation,and suffered from several drawbacks,such as the smoothness requirements of system models and poor stability.A derivative-free numerical approximation-based Gaussian filter,named the unscented Kalman filter(UKF),was introduced in the nineties,which offered several advantages over the derivativebased Gaussian filters.Since the proposition of UKF,derivativefree Gaussian filtering has been a highly active research area.This paper reviews significant developments made under Gaussian filtering since the proposition of UKF.The review is particularly focused on three categories of developments:i)advancing the numerical approximation methods;ii)modifying the conventional Gaussian approach to further improve the filtering performance;and iii)constrained filtering to address the problem of discrete-time formulation of process dynamics.This review highlights the computational aspect of recent developments in all three categories.The performance of various filters are analyzed by simulating them with real-life target tracking problems.

Simplified unscented particle filter for nonlinear/non-Gaussian Bayesian estimation

Particle filters have been widely used in nonlinear/non- Gaussian Bayesian state estimation problems. However, efficient distribution of the limited number of particles （n state space remains a critical issue in designing a particle filter. A simplified unscented particle filter （SUPF） is presented, where particles are drawn partly from the transition prior density （TPD） and partly from the Gaussian approximate posterior density （GAPD） obtained by a unscented Kalman filter. The ratio of the number of particles drawn from TPD to the number of particles drawn from GAPD is adaptively determined by the maximum likelihood ratio （MLR）. The MLR is defined to measure how well the particles, drawn from the TPD, match the likelihood model. It is shown that the particle set generated by this sampling strategy is more close to the significant region in state space and tends to yield more accurate results. Simulation results demonstrate that the versatility and es- timation accuracy of SUPF exceed that of standard particle filter, extended Kalman particle filter and unscented particle filter.

NONLINEAR ESTIMATION METHODS FOR AUTONOMOUS TRACKED VEHICLE WITH SLIP

In order to achieve precise,robust autonomous guidance and control of a tracked vehicle,a kinematic model with longitudinal and lateral slip is established,Four different nonlinear filters are used to estimate both state vector and time-varying parameter vector of the created model jointly.The first filter is the well-known extended Kalman filter.The second filter is an unscented version of the Kalman filter.The third one is a particle filter using the unscented Kalman filter to generate the importance proposal distribution.The last one is a novel and guaranteed filter that uses a linear set-membership estimator and can give an ellipsoid set in which the true state lies.The four different approaches have different complexities,behavior and advantages that are surveyed and compared.

A Review of Nonlinear Kalman Filter Appling to Sensorless Control for AC Motor Drives

Sensorless control of AC motor drives,which takes the advantages of cost saving,higher reliability,and less hardware,has been developed for several decades.Among the existing speed sensorless control methods,nonlinear Kalman filter-based one has attached widespread attention due to its superb estimation accuracy and inherent resistibility to noise.However,the determination of noise covariance matrix and robustness of model uncertainties are still open issues in practice.A great number of studies try to solve these problems in resent years.This paper reviews the application of extended Kalman filter(EKF),unscented Kalman filter(UKF),and cubature Kalman filter(CKF)in speed sensorless control for AC motor drives.As an iterative algorithm,EKF has advantages in processor implementation.However,EKF suffers from the linearization error and model uncertainties when applying to sensorless control system.This paper presents the predominant improvements of EKF which is also applicative in UKF and CKF mostly.

Skew t Distribution-Based Nonlinear Filter with Asymmetric Measurement Noise Using Variational Bayesian Inference

This paper is focused on the state estimation problem for nonlinear systems with unknown statistics of measurement noise.Based on the cubature Kalman filter,we propose a new nonlinear filtering 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 filter can perform satisfactorily in the presence of unknown statistics of measurement noise and outperform than the existing state-of-the-art nonlinear filters.

Particle Filter Object Tracking Algorithm Based on Sparse Representation and Nonlinear Resampling

Object tracking with abrupt motion is an important research topic and has attracted wide attention.To obtain accurate tracking results,an improved particle filter tracking algorithm based on sparse representation and nonlinear resampling is proposed in this paper. First,the sparse representation is used to compute particle weights by considering the fact that the weights are sparse when the object moves abruptly,so the potential object region can be predicted more precisely. Then,a nonlinear resampling process is proposed by utilizing the nonlinear sorting strategy,which can solve the problem of particle diversity impoverishment caused by traditional resampling methods. Experimental results based on videos containing objects with various abrupt motions have demonstrated the effectiveness of the proposed algorithm.

Optimal State Estimation and Fault Diagnosis for a Class of Nonlinear Systems

This study proposes a scheme for state estimation and,consequently,fault diagnosis in nonlinear systems.Initially,an optimal nonlinear observer is designed for nonlinear systems subject to an actuator or plant fault.By utilizing Lyapunov's direct method,the observer is proved to be optimal with respect to a performance function,including the magnitude of the observer gain and the convergence time.The observer gain is obtained by using approximation of Hamilton-Jacobi-Bellman(HJB)equation.The approximation is determined via an online trained neural network(NN).Next a class of affine nonlinear systems is considered which is subject to unknown disturbances in addition to fault signals.In this case,for each fault the original system is transformed to a new form in which the proposed optimal observer can be applied for state estimation and fault detection and isolation(FDI).Simulation results of a singlelink flexible joint robot(SLFJR)electric drive system show the effectiveness of the proposed methodology.

New Kalman Filtering Algorithm for Narrowband Interference Suppression in Spread Spectrum Systems

A new Kalman filtering algorithm based on estimation of spread spectrum signal before suppression of narrowband interference （NBI） in spread spectrum systems, using the dependence of autoregressive （AR） interference, is presented compared with performance of the ACM nonlinear filtering algorithm, simulation results show that the proposed algorithm has preferable performance, there is about 5 dB SNR improvement in average.

A Hybrid Nonlinear Active Noise Control Method Using Chebyshev Nonlinear Filter

Investigations into active noise control(ANC)technique have been conducted with the aim of effective control of the low-frequency noise.In practice,however,the performance of currently available ANC systems degrades due to the effects of nonlinearity in the primary and secondary paths,primary noise and louder speaker.This paper proposes a hybrid control structure of nonlinear ANC system to control the non-stationary noise produced by the rotating machinery on the nonlinear primary path.A fast version of ensemble empirical mode decomposition is used to decompose the non-stationary primary noise into intrinsic mode functions,which are expanded using the second-order Chebyshev nonlinear filter and then individually controlled.The convergence of the nonlinear ANC system is also discussed.Simulation results demonstrate that proposed method outperforms the FSLMS and VFXLMS algorithms with respect to noise reduction and convergence rate.