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.

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.

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.

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.

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.

Study of nonlinear filter methods: particle filter

Extended Kalman filter （EKF） is one of the most widely used methods for nonlinear system estimation. A new filtering algorithm, called particle filtering （PF） is introduced. PF can yield better performance than that of EKF, because PF does not involve the linearization approximating to nonlinear systems, that is required by the EKF. PF has been shown to be a superior alternative to the EKF in a variety of applications. The base idea of PF is the approximation of relevant probabifity distributions using the concepts of sequential importance sampling and approximation of probability distributions using a set of discrete random samples with associated weights. PF methods still need to be improved in the aspects of accuracy and calculating speed.

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.

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.

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 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

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.

Interference-Driven Designs of Nonlinear-Phase FIR Filter with Application in FBMC System

In the forthcoming 5G systems, new technologies, such as amorphous networks and non-orthogonal filter bank multicarriers(FBMC), provide an effective way to accommodate high-rate transmissions. Meanwhile, the prototype filter affects the adjacent channel interference, and therefore is important for FBMC systems. Besides, once the amorphous network is taken into account, the requirement for interference controlmust be much stricter. Accordingly, this paper focuses on the design of prototype filter with better ability of interference controlling, where we exploit the nonlinear phase FIR filter(NLPFF) instead of traditional linear phase FIR filter(LPFF) to achieve more optimization spaces under a small sacrifice of linear phase. In ourdesigns, both the amplitude and phase responsesare handled independently to approach the stopband performance enhancements, in while the nearly perfect reconstruction(NPR) conditionsare relaxed by pre-specified thresholds. Computer simulations confirm the effectiveness of the NLPFF designs, and demonstrate the advantages of the proposed NLPFF in FBMC applications.

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.

A New Particle Filter for Nonlinear Tracking Problems

A new particle filter is presented for nonlinear tracking problems. Inpractice, maneuvering target-tracking systems are usually nonlinear and incompletely observed, andthe main difficulty of maneuvering target-tracking problem lies in the fact that the maneuverabilityat every step is of high uncertainties. Here a new smoothing particle filter algorithm is proposed,which combines the particle filter to tackle the non-linear and non-Gaussian peculiarities of theproblem, together with smoothing of the PDF of system modes and thus settles the estimate problem ofthe target maneuverability. The simulation comparison with the auxiliary particle filters showsthat the approach has superiority and yields performance improvements in solving nonlinear trackingproblems.

Nonlinear Bayesian Estimation： From Kalman Filtering to a Broader Horizon

This article presents an up-to-date tutorial review of nonlinear Bayesian estimation. State estimation for nonlinear systems has been a challenge encountered in a wide range of engineering fields, attracting decades of research effort. To date,one of the most promising and popular approaches is to view and address the problem from a Bayesian probabilistic perspective,which enables estimation of the unknown state variables by tracking their probabilistic distribution or statistics(e.g., mean and covariance) conditioned on a system's measurement data.This article offers a systematic introduction to the Bayesian state estimation framework and reviews various Kalman filtering(KF)techniques, progressively from the standard KF for linear systems to extended KF, unscented KF and ensemble KF for nonlinear systems. It also overviews other prominent or emerging Bayesian estimation methods including Gaussian filtering, Gaussian-sum filtering, particle filtering and moving horizon estimation and extends the discussion of state estimation to more complicated problems such as simultaneous state and parameter/input estimation.

Particle filter for nonlinear systems with multi-sensor asynchronous random delays

This paper is concerned with the recursive filtering problem for a class of discrete-time nonlinear stochastic systems in the presence of multi-sensor measurement delay. The delay occurs in a multi-step and asynchronous manner, and the delay probability of each sensor is assumed to be known or unknown. Firstly, a new model is constructed to describe the measurement process, based on which a new particle filter is developed with the ability to fuse multi-sensor information in the case of known delay probability.In addition, an online delay probability estimation module is introduced in the particle filtering framework, which leads to another new filter that can be implemented without the prior knowledge of delay probability. More importantly, since there is no complex iterative operation, the resulting filter can be implemented recursively and is suitable for many real-time applications. Simulation results show the effectiveness of the proposed filters.

Ensemble-based Kalman Filters in Strongly Nonlinear Dynamics

This study examines the effectiveness of ensemble Kalman filters in data assimilation with the strongly nonlinear dynamics of the Lorenz-63 model, and in particular their use in predicting the regime transition that occurs when the model jumps from one basin of attraction to the other. Four configurations of the ensemble-based Kalman filtering data assimilation techniques, including the ensemble Kalman filter, en- semble adjustment Kalman filter, ensemble square root filter and ensemble transform Kalman filter, are evaluated with their ability in predicting the regime transition （also called phase transition） and also are compared in terms of their sensitivity to both observational and sampling errors. The sensitivity of each ensemble-based filter to the size of the ensemble is also examined.