Nonlinear Filtering Research Articles

Nonlinear Filtering and Reinforcement Learning Based Consensus Achievement of Uncertain Multi-Agent Systems

Abstract This paper introduces a novel approach for designing estimators to achieve consensus in uncertain multi-agent systems (MAS), even when various fault conditions are present and communication is assumed to be undirected and connected. The method includes an adaptive fault detection technique to detect faults and a unique adaptation in the unscented Kalman filter (UKF) to adjust noise covariance matrices and reconstruct uncertain states in the multi-agent system is proposed in the framework of Q-learning. Additionally, it involves training neural network internal parameters using previous measurements. A Chebyshev neural network (CNN) is employed to model the uncertain plant, and a hyperbolic tangent-based robust control term is used to mitigate neural network approximation errors. This novel approach is known as reinforced UKF (RUKF). The paper also discusses the asymptotic stability of the proposed method and presents numerical simulations to demonstrate its effectiveness with reduced computational load.

Duality for Nonlinear Filtering II: Optimal Control

This paper is concerned with the development and use of duality theory for a nonlinear filtering model with white noise observations. The main contribution of this paper is to introduce a stochastic optimal control problem as a dual to the nonlinear filtering problem. The mathematical statement of the dual relationship between the two problems is given in the form of a duality principle. The constraint for the optimal control problem is the backward stochastic differential equation (BSDE) introduced in the companion paper. The optimal control solution is obtained from an application of the maximum principle, and subsequently used to derive the equation of the nonlinear filter. The proposed duality is shown to be an exact extension of the classical Kalman-Bucy duality, and different from other types of optimal control and variational formulations given in literature.

Recursive Nonlinear Filtering via Gaussian Approximation With Minimized Kullback–Leibler Divergence

Recursive Nonlinear Filtering via Gaussian Approximation With Minimized Kullback–Leibler Divergence

A High-Precision Map Matching Algorithm Based on Nonlinear Filtering Optimization for IOT Industrial Park

A High-Precision Map Matching Algorithm Based on Nonlinear Filtering Optimization for IOT Industrial Park

Nonlinear Filtering of Classical and Quantum Spin Systems

Nonlinear Filtering of Classical and Quantum Spin Systems

A Novel Nonlinear Filter-Based Robust Adaptive Control Method for a Class of Nonlinear Discrete-Time Systems

This paper introduces an innovative adaptive control approach utilizing a nonlinear filter for a specific subset of nonlinear discrete-time systems, considering the presence of both input and output noise. The system can be transformed into a nonlinear autoregressive moving average with exogenous inputs (NARMAX) model. The concept of discrete Nussbaum gain is introduced to address the theoretical constraint associated with unknown directions of feed-forward or control gains, and the extended adaptive tuning sequence is introduced to facilitate the acceleration of parameter updating. In the case of no noise, asymptotical output tracking and global stability are achieved with the adaptive control. Further, in the presence of input noise and output noise, a novel nonlinear filter is designed to generate a more accurate filtered output, which improves the control system’s ability to adapt and track accurately. Finally, examples are provided to showcase the effectiveness and precision of the method.

Robust Cubature Kalman Filter for Moving-Target Tracking with Missing Measurements.

Handling the challenge of missing measurements in nonlinear systems is a difficult problem in various scientific and engineering fields. Missing measurements, which can arise from technical faults during observation, diffusion channel shrinking, or the loss of specific metrics, can bring many challenges when estimating the state of nonlinear systems. To tackle this issue, this paper proposes a technique that utilizes a robust cubature Kalman filter (RCKF) by integrating Huber's M-estimation theory with the standard conventional cubature Kalman filter (CKF). Although a CKF is often used for solving nonlinear filtering problems, its effectiveness might be limited due to a lack of knowledge regarding the nonlinear model of the state and noise-related statistical information. In contrast, the RCKF demonstrates an ability to mitigate performance degradation and discretization issues related to track curves by leveraging covariance matrix predictions for state estimation and output control amidst dynamic disruption errors-even when noise statistics deviate from prior assumptions. The performance of extended Kalman filters (EKFs), unscented Kalman filters (UKFs), CKFs, and RCKFs was compared and evaluated using two numerical examples involving the Univariate Non-stationary Growth Model (UNGM) and bearing-only tracking (BOT). The numerical experiments demonstrated that the RCKF outperformed the EKF, EnKF, and CKF in effectively handling anomaly errors. Specifically, in the UNGM example, the RCKF achieved a significantly lower ARMSE (4.83) and ANCI (3.27)-similar outcomes were observed in the BOT example.

Nonsingular predefined‐time dynamic surface control of a flexible‐joint space robot with actuator constraints

AbstractTo achieve predefined‐time trajectory tracking control of a flexible‐joint space robot(FJSR) with actuator constraints, a nonsingular predefined‐time dynamic surface control scheme is developed. The input saturation caused by actuator constraints is addressed via the designed predefined‐time anti‐saturation compensator. On this basis, two different control laws are designed for such high‐order nonlinear systems by utilizing the backstepping technique, and a novel nonlinear filter is constructed to filter the virtual control signals, thus avoiding the “differential expansion” phenomenon. Moreover, a singularity‐free auxiliary function is designed to solve the singularity issue generated by the derivative of fractional power terms in the predefined‐time control algorithm framework. The closed‐loop system is proven to be semi‐globally predefined‐timely uniformly ultimately bounded (SGPTUUB) via constructing the suitable Lyapunov function. The difference and effectiveness of the two designed control laws are illustrated by the conducted simulations. Both of them allow the FJSR system to track the desired trajectory in a reasonably predefined time.

Study of the influence of the parametric identifiability degree on the estimation accuracy of navigation system errors

The high-precision correction problem of navigation information for a small unmanned aerial vehicle flying with altitude changes over a wide range is studied. Numerical criteria of parametric identifiability degreefor one class of nonlinear systems represented by the SDC method are considered. Error models for inertial navigation system of various detail levels are studied and the results of mathematical and semi-natural modeling of a nonlinear Kalman filter with different models are presented. Keywords small unmanned aerial vehicle, inertial navigation system, errors, correction, degree of parametric identifiability, nonlinear Kalman filter, SDC method

Prescribed Fixed-Time Control for Constrained Uncertain Nonlinear Cyber-Physical Systems Against Deception Attacks.

In this note, a novel prescribed fixed-time adaptive tracking control scheme is developed to cope with the fixed-time tracking control issue for a category of constrained MIMO nonlinear cyber-physical systems (CPSs) with exogenous perturbations, which suffer from deception attacks started in controller-actuator (C-A) channel. Distinguished from the conservative dynamic surface control (DSC) schemes with a linear filter, a novel nonlinear filter is designed in our strategy, which can tackle the intrinsic issue of explosion of computational complexity and promote the system performance. Besides, a new barrier Lyapunov function (BLF) is designed to ulteriorly enhance the tracking performance on the basis of the prescribed performance function (PPF) approach. Prominently, the proposed control strategy could accommodate the exogenous interferences and deception attacks simultaneously. Furthermore, we have substantiated that the developed approach can not only make certain that all the tracking errors of the resulting closed-loop system, including output tracking errors and virtual tracking errors, enter a prespecified small region near equilibrium point with fixed-time convergence rate, but also guarantee them obey the corresponding constraints throughout the entire control operation, where the regulation time and the tracking accuracy level keep prior known and could be prespecified arbitrarily. Finally, the validity and effectiveness of the proposed control scheme are illustrated through a representative application instance.

Digital Application of Folk Culture Elements in City Branding Visual Identity Shaping

Abstract In this paper, for the visual image shaping of folk culture elements in city branding, the intelligent extraction technology of digital image with image pre-processing, color space conversion, and color extraction as the three core modules is proposed. In terms of image preprocessing, spatial domain filtering is used as a means to explore the two main algorithms of linear filtering and nonlinear filtering, and in the color space conversion module, the RGB color space is converted to the CIE Lab color space with the help of CIE XYZ color. The color map extraction module uses Python language to construct the color collocation relationship network using K-means and color adjacency matrix visualization. Finally, the quantitative experiment on the effect of the city brand visual image that integrates the elements of folk culture is carried out, and 65 city brand visual image samples are quantitatively analyzed, while the AMOS model is applied to test the city brand visual image.

Forecasting hourly WTI oil front monthly price volatility densities

<p>Financial commodity markets have an impact on company values and cash flows, where price movements within frequent time intervals can be both significant and random. Understanding highly frequent price movements is both important and difficult. In this paper, I measured and forecasted volatility for high-frequency (mostly twelve hours per day) WTI Oil front month price movements from 2012 to 2024 (about 40,500 observations). I created a new stochastic volatility model for extracting latent volatility using the non-linear Kalman filter. Stable and strictly ergodic hourly price series, along with the BIC optimal non-linear (generic) general method of moments model coefficients, enabled this process. The latent volatility seemed to separate into two volatility factors. One factor that was very persistent suggested slow mean reversion, and one choppy strongly mean-reverting factor. The data dependence found in the factor volatility series suggested forecasting ability. I applied classical static forecasts and three machine learning regression techniques to predict one-step-ahead volatility. The two volatility factors and one summarizing exponential factor were reported, along with several fit measures, including the root mean square error and Theil's measure of covariance.</p>

Nonlinear Transient Switching Filter for Automatic Buffer Window Adjustment in Short-term Ship Response Prediction

Online ship response prediction is one of the emerging interests in seakeeping due to the extensive range of applications for autonomous control of marine vehicles. In particular, the short-term prediction and online updates of ship response have received special attention. Despite a body of studies on different predictors, the asymptotic properties of estimators given the time series sample size have not been addressed specifically, so the predictors only have been analyzed for a fixed observation window regardless of the intrinsic statistical characteristics in the time series. To this end, the current research has explored the performance of two nonlinear and linear based regressors: support vector regression (SVR) and the adaptive Seasonal Auto-Regressive and Integrated Moving Average (SARIMA) model on the time series data obtained from a simulated semisubmersible platform in different sea states. The experiment demonstrated that the prediction accuracy depends significantly on the observation window length statistical properties with respect to the ship responses in various wave conditions. Therefore, an innovative filter using the weighted average of a proposed function has been introduced to adaptively adjust the buffer window based on the signal statistical characteristics. The encouraging outcomes underscore that the introduced filter not only holds the potential to enhance various predictors employed in autonomous onboard decision-making, guidance, and stabilization systems for both existing and forthcoming intelligent onboard control systems but also offers an avenue to bolster the autonomy of dynamic systems. More precisely, the proposed mechanism could extend its applicability to enhance cognitive systems and enable deterministic decision-making in diverse fields beyond the scope of present contribution.

Multi-Channel Speech Separation Using Spatially Selective Deep Non-Linear Filters

Multi-Channel Speech Separation Using Spatially Selective Deep Non-Linear Filters

An algebraic attack on stream ciphers with application to nonlinear filter generators and WG-PRNG

An algebraic attack on stream ciphers with application to nonlinear filter generators and WG-PRNG

Robust PBFD Nonlinear Filtering Scheme for Active Noise Cancellation With Remote Acoustic Sensing

Robust PBFD Nonlinear Filtering Scheme for Active Noise Cancellation With Remote Acoustic Sensing

Iterated Orthogonal Simplex Cubature Kalman Filter and Its Applications in Target Tracking

In order to increase a nonlinear system’s state estimate precision, an iterated orthogonal simplex cubature Kalman filter (IOSCKF) is presented in this study for target tracking. The Gaussian-weighted integral is decomposed into a spherical integral and a radial integral, which are approximated using the spherical simplex-radial rule and second-order Gauss–Laguerre quadrature rule, respectively, and result in the novel simplex cubature rule. To decrease the high-order error terms, cubature points with appropriate weights are taken from the cubature rule and processed using the provided orthogonal matrix. The structure supporting the nonlinear Kalman filter incorporates the altered points and weights and the calculation steps; from this, the updated time and measurement can be inferred. The Gauss–Newton iteration is employed repeatedly to adjust the measurement update until the termination condition is met and the IOSCKF is attained. The proposed algorithms are applied in target tracking, including CV target tracking and spacecraft orbit tracking, and the simulation results reveal that the IOSCKF can achieve higher accuracy compared to the CKF, SCKF, and OSCKF. In spacecraft orbit tracking simulation, compared with the SCKF, the position tracking accuracy and velocity tracking accuracy of the OSCKF are increased by 2.21% and 1.94%, respectively, which indicates that the orthogonal transformation can improve the tracking accuracy. Furthermore, compared with the OSCKF, the position tracking accuracy and velocity tracking accuracy of the IOSCKF are increased by 2.71% and 2.97%, respectively, which indicates that the tracking accuracy can be effectively improved by introducing iterative calculation into the measurement equation, thus verifying the effectiveness of the method presented in this paper.

Short-Term Load Forecasting Using Nonlinear Dynamic Time Series Autoregressive with Feedback for AZADI Control-Station Erbil-Iraq

The load forecasting is a human or computational technique for accurate preanticipation of electrical load to enhance reliable operation and optimal planning control of system plant for electrical energy flowing without facing any economical and technical limitations, therefore appropriate estimation for present and future consumption cost of electrical loads which are necessary to predict the load demand for generating near to accurate power. During advanced technology at the last few decades, artificial neural networks(ANNs) have been extensively employed in electrical system, they are trained using historical data obtained from plant station. This work is intended to be a study of short-term load forecasting (STLF) basis for a power predicted applied to the actual past load data displayed from Azadi station for Feb.2022 were used in training and validation system of neural grid. The result was evaluated by mean square percentage error of (32.7) for the forecasting dynamic time series method to solve the data over hours, days, and weeks in advance, using a kind of non-linear filtering. Short-term load forecasting tried out with main stages; predicted power load data sets, network training, and forecasting. Neural network used has 3-layers: an input, a hidden, and an output layer. The number of hidden layer neurons can be varied for the different network performance. The active power generation faces economical and technical challenges, therefore appropriate evaluation of loads are much needed. Index Terms— ANN, STLF, MW, Neurons.

1D along-track pre-processing of the GOCE gravity gradients and nonlinear filtering of the radial components Vzz in spatial domain

The paper presents pre-processing and nonlinear filtering of the GOCE gravity gradients (GGs) in spatial domain. At first, a multiple fully automatic 1D along-track pre-processing of the GOCE GGs in the gradiometer reference frame (GRF) is introduced. This tool is based on the nonlinear diffusion filtering in 1D while treating issues like a detection of ‘jumps’ in time series, outliers and unforeseen systematic tendencies. We focus on the 1D along-track pre-processing of the GOCE GGs in GRF for the last period of the GOCE satellite mission (from 2012-12-01 to 2013-10-19) that are later transformed into the local north-oriented frame (LNOF). Afterwards, the radial components Vzz are reduced on a reference surface chosen as a mean value of all altitudes of the GOCE satellite orbits from the processed period. Here they are filtered using the nonlinear diffusion filtering on a closed surface. Finally, a grid of the filtered radial components Vzz in LNOF on the reference surface is obtained.

Improved Square-Root Cubature Kalman Filtering Algorithm for Nonlinear Systems with Dual Unknown Inputs

For nonlinear discrete systems with dual unknown inputs, there are many limitations regarding previous nonlinear filters. This paper proposes two new, improved square-root cubature Kalman filtering (ISRCKF) algorithms to estimate system states and dual unknown inputs. Improved square-root cubature Kalman filtering 1 (ISRCKF1) introduces an innovation that first obtains the unknown input estimates from the measurement equation, then updates the innovation to derive the unknown input estimates from the state equation, then uses the already obtained estimates of the dual unknown inputs to correct the one-step estimate of the state, and finally the minimum variance unbiased estimate of the state is obtained. Improved square-root cubature Kalman filtering 2 (ISRCKF2) builds a unified innovation feedback model, then applies the minimum variance unbiased estimation (MVUE) criterion to obtain the estimates of system states and dual unknown inputs, refining a more concise recursive filter but requiring stronger assumptions. Finally, simulation results demonstrate that the above two algorithms can achieve the optimal estimates of system states and dual unknown inputs simultaneously, and ISRCKF2 further enhances the accuracy of both state and dual unknown inputs estimation, which verifies the validity of the proposed algorithms.