Nonlinear Filtering Research Articles

Second Order Extended Ensemble Filter for Non-linear Filtering

Whenever the state of a system must be estimated from noisy information, a state estimator is employed to fuse the data with the model to produce an accurate estimate of the state. When the system dynamics and observation models are linear, the Kalman Filter which is optimal, is used. However, in most applications of interest the system dynamics and observations equations are not- linear and suitable extensions of the Kalman Filter have been developed; for example, the Extended Kalman Filter(EKF). The Extended Kalman Filter is based on linearization by the Taylor series expansion about the mean of the state. This filtering process is however computationally expensive especially in high dimensional data. The cause for this is the high cost of integrating the equation of evolution of covariances. Due to this complexity in integration, new methods were sought known as the particle filters. It replaces linearization of non-linearities with Monte Carlo methods. The particle filter formed a basis for Ensemble Kalman Filter (EnKF) an extension of Kalman filter to non-linear filtering. The EnKF reduced the computational cost but its innovation process does not capture information sufficiently hence there is need to improve its performance. This study has developed a new filter, Second order Extended Ensemble Filter (SoEEF).We derived it from stochastic state models by expansion of expected values to the second order by use of Taylor series together with Monte Carlo method and Matlab. We used Lorenz 63 system of ordinary equations and differential Matlab to test the performance of the new filter. Then we compared its performance with four other filters like Bootstrap Particle Filter (BPF), First order Kalman Bucy Filter (FoEKBF),Second order Kalman Bucy Filter (SoKBF) and First order Extended Ensemble Filter (FoEEF). SoEEKF performs much better than the other four filters.

Gaussian Denoising for the First Image from The James Webb Space Telescope “Carina Nebula” using Non-Linear Filters

Noise, including Gaussian noise, distorts images during transition or acquisition process, reducing required information. Removing or reducing this noise is crucial in image processing. The James Webb Space Telescope (JWST) is a vital tool for enhancing our understanding of the universe, providing valuable scientific data and inspiring global interest. In this paper we introduce several nonlinear (Non-Local Mean, Bilateral, and classical) filters to remove the Gaussian noise from the Carina Nebula Image, the first image taken by (JWST) on 12 July 2022. These nonlinear filters were therefore selected to highlight the significance of selecting the right technique that can handle, process, and preserve as many details as possible. They also serve to elucidate the degree of advancement achieved in the field of denoising and the distinction between the classical filters and the more sophisticated filters that have evolved to handle finer details. Classic filters deal with the pixels themselves and their neighbors and then perform the desired statistical process. While advanced filters consider the similarities and distances between the central pixel and its neighbors, they preserve the edges of the image as advanced features. Based on quality measurements (PSNR) and (SSIM), the filter results were compared. The results show that the Bilateral filter gives high performance in restoring images under different Gaussian noise densities compared with the other denoising filters where it gives values of (30.65) and (0.93) for (PSNR) and (SSIM) respectively Which is higher than the results of the filters. Paper type :Research paper.

Mid-infrared edge-enhanced imaging via angle-selective nonlinear filtering

Mid-infrared edge-enhanced imaging via angle-selective nonlinear filtering

Adaptive nonlinear filtering algorithms for removal of non-stationary noise in electronystagmographic signals

Non-stationary physiological noise poses significant difficulties due to its time-varying and previously unknown characteristics. When processing electronystagmographic signals, linear filtering can distort diagnostically significant rapid changes caused by saccadic eye movements. In such cases, nonlinear filters based on robust estimators are more appropriate, whereas linear filtering effectively reduces white noise in parts of a signal with linear behaviour. Therefore, an adaptive signal processing approach that varies in nonlinearity from highly nonlinear robust estimation to linear averaging and combines their benefits appears promising. We have proposed a low-complexity adaptive method for switching filter sets and relevant filter parameter settings based on the estimated noise level and local signal behaviour. This method does not require time for filter parameter modification and does not need prior information on the signal model and noise variance. Based on this method, we have designed adaptive nonlinear filtering algorithms to exploit the advantages of both the nonlinear robust and linear averaging estimators. We have evaluated the filtering quality statistically using the minimum mean square error criteria and the maximum signal-to-noise ratio for a model signal with different levels of additive Gaussian noise. The proposed real-time adaptive filtering algorithms demonstrate a significant efficiency improvement compared to the commonly used filters. The proposed adaptive myriad algorithm achieves the highest efficiency by adjusting a sample myriad linearity parameter depending on the local estimate of a signal scale and changing the sliding window length and the coefficient affecting the linearity parameter.

A Comprehensive Analysis of Traditional and Advanced Approaches of Image Restoration Techniques

Introduction: Tremendous developments in multimedia technology have promoted a massive amount of research in image and video processing. As imaging technologies are rapidly increasing, it is becoming essential to use images in almost every application in our day-today life. Materials and Method: This paper presents a comparative analysis of various image restoration approaches, ranging from fundamental methods to advanced techniques. These approaches aim to improve the quality of images that have been degraded during acquisition or transmission. A brief overview of the image restoration approaches is mentioned in the paper, which are as follows: Wiener Filter: The Wiener filter is a classical approach used for image restoration. It is a linear filter that minimizes the mean square error between the original image and the restored image. Inverse Filter: The inverse filter is another traditional restoration technique. It attempts to invert the degradation process to recover the original image. However, inverse filtering is highly sensitive to noise and tends to amplify noise artifacts. Linear and Nonlinear Filtering: These methods involve applying linear or nonlinear filters to the degraded image to enhance its quality. Linear filters, such as Gaussian filters, can effectively reduce noise but may blur the image. Nonlinear filters, such as median filters, can preserve edges while reducing noise. Compressive Sensing (CS) Restoration Approaches: Compressive sensing is a signal processing technique that exploits the sparsity of signals or images to reconstruct them from fewer measurements. CS-based restoration methods aim to recover high-quality images from compressed or incomplete measurements. Neural Networks Approaches: With the advancements in deep learning, neural networks have been widely used for image restoration tasks. Convolutional neural networks (CNNs) and generative adversarial networks (GANs) have shown promising results in restoring degraded images by learning from large datasets. Result: The paper likely provides a detailed analysis and comparison of these approaches, highlighting their strengths, weaknesses, and performance in different scenarios. Conclusion: This paper aims to improve the quality of restored images. Several image restoration approaches have been compared, and they have exhibited enhanced performance compared to several existing image restoration approaches.

Innovation Adaptive UKF Train Location Method Based on Kinematic Constraints

To address the issue of reduced positioning accuracy caused by satellite signal interruptions when trains pass through long tunnels, a novel train positioning method based on an innovative adaptive unscented Kalman filter (UKF) under kinematic constraints is proposed. This method aims to improve the accuracy of the location of trains during operation. By considering the dynamic characteristics of the train, a dynamic kinematic-constrained inertial navigation system (INS)/odometer (ODO) combination positioning system is established. This system utilizes kinematic constraints to correct the accumulated errors of the INS. Additionally, the algorithm incorporates real-time estimation of the measurement noise covariance using innovation sequences. The updated adaptive estimation algorithm is applied within the UKF framework for nonlinear filtering, forming the innovative adaptive UKF algorithm. At each time step, the difference between the ODO sensor data and the INS output is used as the measurement input for the innovative adaptive UKF algorithm, enabling global estimation. This process ultimately yields the actual positioning result for the train. Simulation results demonstrate that the innovative adaptive UKF train positioning method, incorporating kinematic constraints, effectively mitigates the impact of satellite signal interruptions. Compared with the traditional INS/ODO positioning method, the innovative adaptive UKF method reduces position errors by 34.35% and speed errors by 36.33%. Overall, this method enhances navigation accuracy, minimizes train positioning errors, and meets the requirements of modern train positioning systems.

Realization of global audio telepresence via a learning-based model-matching approach with an acoustic array system

A Global Audio Telepresence (GOAT) system requires a microphone array to capture the spatial audio signals in the far end and a loudspeaker array to reconstruct the sound field in the near end. This seamlessly immerses near-end users in remote audio scenes with full ambience. In this paper, we use a learning-based GOAT system (L-GOAT) based on the model-matching principle, where a deep neural network (DNN) acts as non-linear filters for the GOAT system. The network training attempts to minimize the matching error between the signals reproduced by the DNN and the desired signals filtered by the far-end acoustic transfer functions (ATFs). Extensive simulations were carried out for multi-source scenarios in two different rooms with different reverberation times. To implement the L-GOAT system, a five-microphone linear array was adopted in the far-end room, while a six-loudspeaker array was utilized in the near-end room. The objective evaluation matrices, including the Perceptual Evaluation of Speech Quality (PESQ), Short-Time Objective Intelligibility (STOI), and the matching errors, were conducted to validate the efficacy of the GOAT systems. The proposed learning-based approach has demonstrated superior performance compared to a conventional digital signal processing (DSP)-based method.

A probabilistic framework for identifying anomalies in urban air quality data.

Just as the value of crude oil is unlocked through refining, the true potential of air quality data is realized through systematic processing, analysis, and application. This refined data is critical for making informed decisions that may protect health and the environment. Perhaps ground-based air quality monitoring data often face quality control issues, notably outliers. The outliers in air quality data are reported as error and event-based. The error-based outliers are due to instrument failure, self-calibration, sensor drift over time, and the event based focused on the sudden change in meteorological conditions. The event-based outliers are meaningful while error-based outliers are noise that needs to be eliminated and replaced post-detection. In this study, we address error-based outlier detection in air quality data, particularly targeting particulate pollutants (PM2.5 and PM10) across various monitoring sites in Delhi. Our research specifically examines data from sites with less than 5% missing values and identifies four distinct types of error-based outliers: extreme values due to measurement errors, consecutive constant readings and low variance due to instrument malfunction, periodic outliers from self-calibration exceptions, and anomalies in the PM2.5/PM10 ratio indicative of issues with the instruments' dryer unit. We developed a robust methodology for outlier detection by fitting a non-linear filter to the data, calculating residuals between observed and predicted values, and then assessing these residuals using a standardized Z-score to determine their probability. Outliers are flagged based on a probability threshold established through sensitivity testing. This approach helps distinguish normal data points from suspicious ones, ensuring the refined quality of data necessary for accurate air quality modeling. This method is essential for improving the reliability of statistical and machine learning models that depend on high-quality environmental data.

Adaptive Distributed Control of Nonlinear Multiagent Systems With Event-Triggered for Communication Faults and Dead-Zone Inputs.

This article studies the containment control problem of nonlinear multiagent systems (MASs) subjected to communication link faults and dead-zone inputs. In case of an unknown fault in the communication link, there is no constant Laplacian matrix anymore and each follower agent cannot be informed of the global information simultaneously. To deal with this problem, an adaptive compensating estimator is constructed to estimate the signal spanned by the leaders. Instead of using the linear filter, a nonlinear filter is employed, which both solves the classical complexity explosion in the traditional backstepping method and flushes out the usefulness of the boundary layer error. Considering the dead zone input, we propose two event-triggered schemes, that is, the update-triggered scheme and the transmit-triggered scheme. In the former, the threshold function involves the tracking errors and additional dynamic variable, which can provide the desirable tradeoff between the containment control performance of the considered MASs and saving communication resources. In the latter, the triggered condition is designed according to the characteristic of dead zone, which makes the communication burden be reduced further. Following the backstepping design framework, an adaptive containment control is constructed, it is shown that the containment error can converge to an adjustable residual set even if MASs are subjected to the unknown and bounded communication link faults and dead-zone inputs. Finally, an example is given to show the effectiveness of the proposed results.

Predefined Accuracy Adaptive Tracking Control for Nonlinear Multiagent Systems With Unmodeled Dynamics.

This article focuses on an adaptive dynamic surface tracking control issue of nonlinear multiagent systems (MASs) with unmodeled dynamics and input quantization under predefined accuracy. Radial basis function neural networks (RBFNNs) are employed to estimate unknown nonlinear items. A dynamic signal is established to handle the trouble introduced by the unmodeled dynamics. Moreover, the predefined precision control is realized with the aid of two key functions. Unlike the existing works on nonlinear MASs with unmodeled dynamics, to avoid the issue of "explosion of complexity," the dynamic surface control (DSC) method is applied with the nonlinear filter. By using the designed controller, the consensus errors can gather to a precision assigned a priori. Finally, the simulation results are given to demonstrate the effectiveness of the proposed strategy.

A Nonlinear Filter based on GSK for Relative Navigation Using Relative Orbital Elements

Due to the sensitivity of the relative orbital elements model to the measurement noise, the non-stationary heavy-tailed noise(NSHT) induced by the time-varying environment during the relative navigation usually leads to filter divergence. To address this problem, a new nonlinear filter based on Gaussian-Student's-Multivariate K(GSK) mixture distribution is proposed in this paper. A Dirichlet stochastic mixture vector fusing Gaussian, Student's t, and Multivariate K distributions is introduced, thus proposing a GSK mixture distribution modeling measurement likelihood; then the Kullback-Leibler Divergence (KLD) of the true posteriori probability density function(PDF) and the approximate posteriori PDF are minimized by a variational Bayesian(VB) technique to solve for the state and parameter approximate a posteriori estimations, and finally a new nonlinear filter based on the GSK mixture distribution is derived for angles-only relative navigation in time-varying environments. Simulation outcomes indicate that the filter can realize state estimation in non-stationary states effectively with 45.16% higher estimation accuracy than the existing advanced filters.

A novel constrained skew-Gaussian filter and its application to maneuverable reentry vehicle tracking

The state of the system generally satisfies specific constraints imposed by material properties or physical laws, so the application of these constraints can improve the accuracy of state estimation. In this paper, a novel recursive filter referred as constrained high-degree cubature skew-Gaussian filter (CHCSGF) is proposed, which achieves soft-constrained state estimation by compressing the probability density of unconstrained states with constraint information. First, the probability density of the state under inequality soft constraints is modeled as a skew-Gaussian (SG) distribution, rather than truncated or single Gaussian distributions. Then, a recursive constrained SG filter is developed to handle inequality soft constraints in linear systems. Addressing nonlinear challenges, a 5th-degree spherical-radial cubature approximation method is presented to numerically calculate SG-weighted integrals for the nonlinear transformation of SG distribution. Finally, the CHCSGF algorithm is proposed using this method to tackle nonlinear filtering problems. The CHCSGF is applied to reentry trajectory tracking to improve estimation accuracy by dealing with heat flow, dynamic pressure and overload constraints during reentry flight. Simulation results demonstrate that the CHCSGF achieves higher estimation accuracy than unconstrained methods under nonlinear inequality soft constraints, and is robust to the constraints with a prior error. Compared to particle filter and moving horizon estimation, the computational complexity of CHCSGF is significantly reduced.

Fully distributed dynamic event-triggered reliable COR of nonlinear MASs with communication link faults and actuator faults for directed graphs

The issue of fault-tolerant cooperative output regulation (COR) for nonlinear uncertain multiagent systems (MASs) under communication link faults (LFs) and actuator faults is investigated in this paper. This is the first attempt to study the fault-tolerant COR problem for the aforementioned MASs under directed graphs. To handle unknown LFs and avoid using global information, adaptive event-triggered (ET) observers are designed to estimate the exosystem state. That is, resilience against communication LFs is translated to distributed observer design. To overcome the “explosion of complexity” and obtain asymptotically stable results, dynamic surface control (DSC) techniques are introduced. Unlike existing linear DSC techniques that generate boundary layer errors, this paper introduces nonlinear filters with compensation terms into dynamic surfaces to eliminate boundary layer errors. Adaptive control laws that can achieve asymptotically regulated output are then developed based on the improved DSC techniques. It is shown that the developed control strategy can achieve fault-tolerant COR for the considered MASs. Additionally, the implemented dynamic event-triggered mechanism (ETM) ensures strictly positive minimum event-triggered intervals (ETIs) and avoids Zeno behavior. Finally, a practical simulation example reveals the effectiveness of the suggested scheme.

Estimating the Purse Seine Net Geometry during a Hauling Operation Using a Data Assimilation Method

The dynamics of fishing nets can be estimated by modeling and numerically computing the forces acting on them. However, the dynamic models of fishing nets are highly nonlinear owing to the significant influence of hydrodynamic forces acting on the net. Therefore, if there are unknown parameters that define the state of motion in the model, it is often difficult to achieve high accuracy in the numerical simulations of fishing gear and evaluate its dynamics. To address this issue, a method is proposed for estimating these unknown parameters by integrating a nonlinear Kalman filter into a fishing net dynamics model. This study aimed to estimate the hauling velocity of large- and medium-sized purse seine fishing nets, which can be a challenging parameter to measure. The calculations are based on the data obtained from a research operation conducted by the Marine Fisheries Research and Development Center in 2019 using the purse seine fishing vessel “Taikei Maru No. 1”. The time series of the hauling-net velocity was estimated based on the results of the estimation experiment. These results allowed the estimation of the hauling velocity and calculation of the net dynamics during the hauling process. This shows that net dynamics simulation is possible even with unknown parameters.

Analysis of methods and algorithms for image filtering and quality enhancement

This paper addresses the prevalent issue of image noise and presents methods for its mitigation. The paper describes, analyses and tests a variety of image filtering techniques, with specific reference to their use in different contexts. The filtering methods can be classified into two principal categories: linear filters, which include the Gaussian and mean filters, and non-linear filters, which comprise the median filter, the Fast Fourier Transform (FFT), the Non-Local Means (NLM) filter, and the anisotropic diffusion filter. The efficacy of each filter is mathematically described and evaluated on RGB images using the Python programming language. The study delineates the evaluation metrics and their respective advantages and disadvantages. The Root Mean Square Error (RMSE) and Peak Signal-to-Noise Ratio (PSNR) are employed as criteria for the analysis of algorithm efficiency. Furthermore, the mean execution time for each algorithm is also monitored. The experimental data suggests that linear filters are relatively fast but produce inferior results and are best employed as preparatory measures. Non-linear filters have been demonstrated to be more robust and applicable to a variety of noise types, although it has been established that they require parameter fine-tuning. The study demonstrates that anisotropic diffusion is suitable for both manual image processing and real-time applications, offering an optimal balance between processing speed and denoised image quality. NLM is optimal for high-quality single image processing due to its superior results, despite a slower processing speed. FFT is noted for its efficiency in eliminating periodic noise. Further research will be conducted on advancing filtering techniques for different real-world scenarios and autonomous systems.

Multilayer neuroadaptive constraint-handling control architecture for a family of nonlinear systems with uncertainty compensation

In practical applications, there are some requirements for time-varying constraints on full system states. Currently, Barrier Lyapunov Function is a popular tool for constraint control. However, how to handle various uncertainties while satisfying constraint requirements is worth further research. Accordingly, a high-performance multilayer neuroadaptive constraint-handling controller for a class of nonlinear systems with uncertainty compensation will be developed. Significantly, asymmetric time-varying constraints for full system states can be implemented. Furthermore, a set of novel multilayer neuroadaptive disturbance observers will be proposed to address modeling uncertainties. Moreover, by introducing a set of nonlinear command filters, the intelligent control algorithm will be designed via the command filtered backstepping method. The stability of the whole closed-loop system is strictly proved. Additionally, the proposed algorithm is applied to different nonlinear systems including a hydraulic robotic manipulator system to verify its feasibility.

Local Mean Suppression Filter for Effective Background Identification in Fluorescence Images.

We present an easy-to-use, nonlinear filter for effective background identification in fluorescence microscopy images with dense and low-contrast foreground. The pixel-wise filtering is based on comparison of the pixel intensity with the mean intensity of pixels in its local neighborhood. The pixel is given a background or foreground label depending on whether its intensity is less than or greater than the mean respectively. Multiple labels are generated for the same pixel by computing mean expression values by varying neighborhood size. These labels are accumulated to decide the final pixel label. We demonstrate that the performance of our filter favorably compares with state-of-the-art image processing, machine learning, and deep learning methods. We present three use cases that demonstrate its effectiveness, and also show how it can be used in multiplexed fluorescence imaging contexts and as a denoising step in image segmentation. A fast implementation of the filter is available in Python 3 on GitHub.

Optimization based data enrichment using stochastic dynamical system models

We develop a general framework for state estimation in systems modeled with noise-polluted continuous time dynamics and discrete time noisy measurements. Our approach is based on maximum likelihood estimation and employs the calculus of variations to derive optimality conditions for continuous time functions. We make no prior assumptions on the form of the mapping from measurements to state-estimate or on the distributions of the noise terms, making the framework more general than Kalman filtering/smoothing where this mapping is assumed to be linear and the noises Gaussian. The optimal solution that arises is interpreted as a continuous time spline, the structure and temporal dependency of which is determined by the system dynamics and the distributions of the process and measurement noise. Similar to Kalman smoothing, the optimal spline yields increased data accuracy at instants when measurements are taken, in addition to providing continuous time estimates outside the measurement instances. We demonstrate the utility and generality of our approach via illustrative examples that render both linear and nonlinear data filters depending on the particular system. Application of the proposed approach to a Monte Carlo simulation exhibits significant performance improvement in comparison to a common existing method.

A class of robust nonlinear quaternion volterra adaptive filter based on recursive Tukey’s Biweight M-estimate and its performance analysis

A class of robust nonlinear quaternion volterra adaptive filter based on recursive Tukey’s Biweight M-estimate and its performance analysis

Developed square-root cubature Kalman filter-based solution for improving power system state estimation with unknown inputs and non-Gaussian noise

Understanding the ever-changing dynamics of power systems is crucial, and dynamic state estimation (DSE) plays a vital role in achieving this. However, traditional nonlinear Kalman filters (NKFs) face limitations: lack of access to control inputs and presence of non-Gaussian noise in measurements, impacting their accuracy and robustness. This research introduces a novel robust DSE method that tackles these challenges head-on. For the first time in DSE, it leverages the predictive power of Holt-Winters Triple Exponential Smoothing to model the time-varying behavior of control inputs. This innovative approach allows for the simultaneous estimation of dynamic state variables such as the rotor angle and rotor speed changes, as well as transient voltages and control inputs like mechanical input torque and excitation voltage, even in the presence of non-Gaussian noise. Furthermore, the method employs modified projection statistics and a Cauchy function. This unique combination effectively bounds the influence of observation outliers while maintaining high statistical estimation efficiency. This innovative approach utilizes a square cubature Kalman filter (SCKF) for enhanced numerical stability. Extensive simulations under various anomalous conditions demonstrate the method's superior accuracy and efficiency in estimating the state vector. These results highlight its potential to significantly improve power system estimation and pave the way for real-time applications.