Filtering Problem Research Articles

Convergence of nonlinear filterings for stochastic dynamical systems with Lévy noises

We consider a nonlinear filtering problem of multiscale non-Gaussian signal processes and observation processes with jumps. First, we prove that the dimension for the signal system can be reduced by a homogenized approach. Second, convergence of the corresponding nonlinear filtering to the homogenized filtering is shown by a weak convergence technique. Finally, we give an example to explain our result.

Discrete-time estimation of switched stochastic polynomial systems and its application to reconstruction of induction motor variables

This paper presents a solution to the filtering problem for a class of stochastic discrete-time nonlinear polynomial systems with switching in the state equation over linear observations and its application to a mechatronic system. The switching in the state equation is performed between two different nonlinear functions according to a sequence of independent Bernoulli random variables that take the quantities of zero and one. The mean-square filtering solution is obtained for a general nonlinear discrete-time polynomial system and a finite-dimensional system of filtering equations is then obtained for a second degree polynomial system as a particular case. The mean-square estimates of polynomial state terms are expressed as functions of the estimate and covariance matrix. Finally, some numerical simulations are carried out to reconstruct the variable states given a vector output measurement for a linear system, a second degree polynomial system, and an induction motor model to show effectiveness of the proposed algorithm. The proposed method is compared with an extended Kalman filter-based algorithm for discrete-time switched nonlinear systems.

Distributed Mode-Dependent Event-Triggered Passive Filtering for Flexible Manipulator with Semi-Markov Parameters.

In this paper, the passive filtering problem of flexible robotic manipulator is investigated over sensor networks in a distributed manner from the control system perspective. The sensor networks are adopted to estimate true states of flexible robotic manipulator. In particular, the semi-Markov model is utilized for flexible manipulators with varying loads in unstructured environment, which is more flexible for practical implementations. Moreover, the new mode-dependent event-triggering mechanism is developed for distributed filter communications. Based on model transformation, sufficient conditions are first established to guarantee prescribed passive performance under disturbances. Then, desired mode-dependent filters are developed with the aid of convex optimization. In the end, several simulations results of a single-link flexible robotic manipulator are provided to verify the usefulness of the developed filtering algorithm.

Asynchronous Event-Triggered Finite-Time Filtering for Networked Switched T–S Fuzzy Systems

This paper investigates the problem of event-triggered finite-time robust filtering for a class of networked switched T–S fuzzy systems. By adopting the extended dissipative performance index, the $$H_{\infty }$$ and $$L_{2 }-L_{\infty }$$ filtering problems can be solved in a unified framework. We propose an event-triggered scheme to save the network resources. Under the event-triggered scheme, the filter is not synchronized with the corresponding subsystem. By constructing a reasonable Lyapunov–Krasovskii function, we give sufficient conditions for the finite-time extended dissipative of the filtering error system. We employ the T–S fuzzy models to represent the nonlinear subsystems. The filter gains can be obtained by solving some matrix inequalities. Finally, an example is presented to show the efficiency of the method.

Protocol‐based H∞ filtering for piecewise linear systems: A measurement‐dependent equivalent reduction approach

AbstractIn this article, a protocol‐based H∞ filtering problem is investigated for piecewise linear (PWL) systems with mixed delays. Stochastic access protocol (SAP) is utilized to schedule the signal transmission via a constrained communication channel, under which only one measurement value can be transmitted to the filter at each time instant following a Markov process. When SAP is applied to PWL systems, only a part of system modes can be observed due to the incomplete measurement information. Therefore, a measurement‐dependent parameter storage rule with a certain probability distribution is introduced to overcome the difficulties coming from SAP‐induced incomplete information. By resorting to the proposed mode storage rule, a novel measurement‐dependent asynchronous H∞ filter model is constructed and the problem is converted into a new switching process of a larger state space following a reconstructed Markov process. Subsequently, a sufficient condition is established to guarantee the H∞ performance, and the probability‐dependent filter parameters are obtained by applying the stochastic analysis technique. Finally, a numerical example is given to show the effectiveness of the design approach.

A novel full-order and reduced-order fault detection filters design method for continuous-time singular Markov jump systems with complexity transition rates

This work is concerned with the problem of full-order and reduced-order fault detection filters (FDFs) design in a convex optimization frame for continuous-time singular Markov jump systems (CTSMJSs) with complexity transition rates (TRs). A novel Lyapunov function construct approach is utilized to cope with the stochastic admissibility problem for CTSMJSs with complexity TRs. In order to obtain effective full-order and reduced-order FDFs, we decoupled the inequality using the presupposed Lyapunov matrix. Owing to the use of Lyapunov stochastic admissibility theory and a novel decoupling method based on convex polyhedron technique, some sufficient conditions are obtained to guarantee that the resulting full-order and reduced-order FDFs are suitable for CTSMJSs with complexity TRs. In particular, the reduced-order FDF has the advantages of small storage space and fast detection speed compared with the full order FDF. Four illustrative examples are given to explain the effectiveness of the proposed full-order and reduced-order FDFs design method.

Forecasting Nonlinear Systems with LSTM: Analysis and Comparison with EKF.

Certain difficulties in path forecasting and filtering problems are based in the initial hypothesis of estimation and filtering techniques. Common hypotheses include that the system can be modeled as linear, Markovian, Gaussian, or all at one time. Although, in many cases, there are strategies to tackle problems with approaches that show very good results, the associated engineering process can become highly complex, requiring a great deal of time or even becoming unapproachable. To have tools to tackle complex problems without starting from a previous hypothesis but to continue to solve classic challenges and sharpen the implementation of estimation and filtering systems is of high scientific interest. This paper addresses the forecast–filter problem from deep learning paradigms with a neural network architecture inspired by natural language processing techniques and data structure. Unlike Kalman, this proposal performs the process of prediction and filtering in the same phase, while Kalman requires two phases. We propose three different study cases of incremental conceptual difficulty. The experimentation is divided into five parts: the standardization effect in raw data, proposal validation, filtering, loss of measurements (forecasting), and, finally, robustness. The results are compared with a Kalman filter, showing that the proposal is comparable in terms of the error within the linear case, with improved performance when facing non-linear systems.

Passivity-based filtering for networked semi-Markov robotic manipulators with mode-dependent quantization and event-triggered communication

In this article, the networked filtering problem for a class of robotic manipulators with semi-Markov type parameters is investigated under the passivity framework. In particular, the mode-dependent quantization and event-triggered communication scheme are both proposed for increasing the network transmission efficiency. Sufficient stability conditions are first derived by choosing mode-dependent Lyapunov–Krasovskii functionals. Then, the mode-dependent filter gains and the event-triggering parameters are further designed with the help of matrix convex optimization. In the end, a simulation example is provided such that the effectiveness of the proposed filtering method can be well demonstrated.

Resilient H-infinity filtering for networked nonlinear Markovian jump systems with randomly occurring distributed delay and sensor saturation

The H∞ filtering problem for a class of networked nonlinear Markovian jump systems subject to randomly occurring distributed delays, nonlinearities, quantization effects, missing measurements and sensor saturation is investigated in this paper. The measurement missing phenomenon is characterized via a random variable obeying the Bernoulli stochastic distribution. Moreover, due to bandwidth limitations, the measurement output is quantized using a logarithmic quantizer and then transmitted to the filter. Further, the output measurements are affected by sensor saturation since the communication links between the system and the filter are unreliable and is described by sector nonlinearities. The objective of this work is to design a quantized resilient filter that guarantees not only the stochastic stability of the augmented filtering error system but also a prespecified level of H∞ performance. Sufficient conditions for the existence of desired filter are established with the aid of proper Lyapunov–Krasovskii functional and linear matrix inequality approach together with stochastic analysis theory. Finally, a numerical example is presented to validate the developed theoretical results.

Improved Auxiliary Particle Filter for SINS/SAR Navigation

In order to obtain the relatively appropriate importance density function and alleviate the problem of particle degradation, a new improved auxiliary particle filter algorithm is proposed. After calculating the auxiliary variable, the adaptive regulator is employed to obtain the state estimation. So, the latest measurement information is efficiently utilized to establish a better importance density function in the importance sampling process. Then, the process of particle weights’ adaptive adjustment and random-weighted calculation can keep the diversity of particles and improve the filter precision; thus, it can better solve the filter problem of nonlinear system model error and noise interference. The simulation and analysis result show that the proposed algorithm can optimize the filter performance and improve the calculation precision in the positioning of the SINS/SAR integrated navigation system, compared with the other two existing filters.

Nonlinear filtering of stochastic differential equations with correlated Lévy noises

The work concerns nonlinear filtering problems of stochastic differential equations with correlated Lévy noises. First, we establish the Kushner–Stratonovich and Zakai equations through martingale representation theorems and the Kallianpur–Striebel formula. Second, we show the pathwise uniqueness and uniqueness in joint law of weak solutions for the Zakai equation. Finally, we investigate the uniqueness in joint law of weak solutions to the Kushner–Stratonovich equation.

Multi-Agent Estimation and Filtering for Minimizing Team Mean-Squared Error

Motivated by estimation problems arising in autonomous vehicles and decentralized control of unmanned aerial vehicles, we consider multi-agent estimation and filtering problems in which multiple agents generate state estimates based on decentralized information and the objective is to minimize a coupled mean-squared error which we call <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">team mean-square error</i> . We call the resulting estimates as minimum team mean-squared error (MTMSE) estimates. We show that MTMSE estimates are different from minimum mean-squared error (MMSE) estimates. We derive closed-form expressions for MTMSE estimates, which are linear function of the observations where the corresponding gain depends on the weight matrix that couples the estimation error. We then consider a filtering problem where a linear stochastic process is monitored by multiple agents which can share their observations (with delay) over a communication graph. We derive expressions to recursively compute the MTMSE estimates. To illustrate the effectiveness of the proposed scheme we consider an example of estimating the distances between vehicles in a platoon and show that MTMSE estimates significantly outperform MMSE estimates and consensus Kalman filtering estimates.

ТЕКУЩИЕ И УСТАНОВИВШИЕСЯ ОШИБКИ ПСЕВДОГРАДИЕНТНОЙ ФИЛЬТРАЦИИ ЦИЛИНДРИЧЕСКИХ ИЗОБРАЖЕНИЙ

When solving many practical problems, such as the Earth and Space monitoring, medical diagnostics, navigation, robotics, etc., the challenges of image and other multidimensional data processing arise. To solve these problems successfully, their mathematical formulation is required, including a mathematical description that is an image model. Most studies in image processing methods, consider the images as a system of random variables specified on a rectangular grid with dimensions of two and higher. There are much less studies in images defined on curved surfaces. However, many real images are given on cylindrical surfaces, for example, the surface of a pipeline, a tank, a rotation shaft, and etc. Therefore, for a formal description of such images, their corresponding models are required. The 2D models are unsuitable for that it is not possible to represent the correlation properties of a cylindrical image with a rectangular image. The article describes the autoregressive models defined on a spiral-shaped cylindrical grid, that is on a helical line. This model can also be used to represent quasiperiodic stochastic processes. One of the main tasks of image processing is the problem of filtering them against the background of noise considered in this article. In this case the parameters of real images are usually unknown a priori. In addition the images often have significant and random heterogeneity. In this paper the authors use the adaptive pseudogradient algorithms based on cylindrical models to filter homogeneous and inhomogeneous images. These algorithms do not require setting the values of image parameters. The values of the root-mean-square filtering error are obtained based on the parameters of images and noise.

Optimal nonlinear fi ltering of stochastic processes in rescue radar

Subject and Purpose. Smoke, fog, avalanches, debris of collapsed structures and other optically opaque obstacles in both natural and man-made disasters make optical sensors useless for detecting victims. Electromagnetic waves of the decimeter range penetrate well almost all obstacles, reflect from the trapped people and return to the radar receiver. Due to the breathing and heartbeat, the human-reflected sounding signals get the Doppler phase modulation, which is an information signal. These information signals and their properties provide the subject matter for the present research with the aim to create optimal methods and algorithms of random event processing for the prompt location of survivors by rescuers. Method and Methodology. The method of stochastic analysis of the fluctuation Doppler spectra of reflected sounding signals shows that the information signals have properties of conditional Markov processes. Results. The problem of optimal nonlinear filtering of conditional Markov processes entering the radar signal processing unit has been examined closely. An optimal adaptive filter has been proposed to reduce the masking effect of interferences caused by non-stationary noises and sounding signal reflections from stationary objects. The optimality criterion is the minimum mean square error function whose current value is evaluated in real time during the filtering process as the statistics is accumulated. The filter coefficients are calculated by the recurrent, steepest descent algorithm. The real-time work is carried out through the use of fast Fourier transform algorithms. Conclusion. The structure of the optimal adaptive filter to be built into the radar signal processing unit has been developed. Real radar signals have shown that the optimal filtering during the signal processing in systems designed for detecting live people by their breathing and heartbeat facilitates the interpretation of the observed signals. Some spectra of real signals generated by human breathing and heartbeat are presented.

3D Printed, Self-Temperature Compensated Microwave Cavity Notch Filters

Utilizing 3D printing to create custom microwave filters has promising aspects such as light weight and low cost, most importantly including the fact that complicated structures can be printed quickly and inexpensively. Some SLA resins have very high Coefficient of Thermal Expansion (CTE) compared to metal, so SLA 3D printed microwave filters can have frequency responses that are strongly dependent on temperature—a serious problem for narrow band filters. The presented technique overcomes this limitation, and in fact yields an SLA 3D printed filter with better temperature stability than an uncompensated metal 3D printed or a conventionally machined metal filter. Two 3D printed, temperature compensated microwave cavity notch filters have been fabricated using stereolithography (SLA) resins. Both use two different values of CTE for compensation. The 3D printed plastic parts are electroplated with copper. One filter consists of a resonant cavity with the TE011 mode coupled to a TE10 waveguide. The other is a TE101 resonant cavity coupled to TE10 waveguide. As temperature increases, the side walls of the cavities grow, lowering the resonant frequency. At the same time, for the TE011 cavity, an end-wall tuning plunger made of stereolithography resin with a higher CTE than the cavity walls expands at a faster rate. The end wall expansion increases the resonant frequency. In the case of the TE101 cavity, a metallic plunger expands much more slowly than the cavity and effectively withdraws as temperature increases, which increases the resonant frequency.

Алгоритм полиномиальной фильтрации в задачах обработки навигационной информации при квадратичных нелинейностях в уравнениях динамики и измерений. Часть I. Описание и сопоставление с алгоритмами калмановского типа

The paper considers the filtering problems solved in navigation data processing under quadratic nonlinearities both in system and measurement equations. A Kalman type recursive algorithm is proposed, where the predicted estimate and gain at each step are calculated based on the assumption on the Gaussian posterior proba-bility density function of the estimated vector at the previous step and minimization of estimation error covariance matrix using a linear procedure with respect to the current measurement. The similarities between this algorithm and other Kalman type algorithms such as extended and secondorder Kalman filters are discussed. The procedure for estimating the performance and comparing the algorithms is presented.

Linear Kalman-Bucy filter with vector autoregressive signal and noise

The linear Kalman-Bucy filter problem for a system, at that a signal and a noise are vector independent stationary autoregressive processes with orders larger than 1, is investigated. The recurrent equations for filter and its error are delivered. The optimal way of the initial data definition is proposed. Some numerical examples are given. In one of them the algorithm leads to a stationary behavior at infinity. In the other example the Kalman- Bucy filter is impossible because the filter error goes to infinity. A behavior of a signal and its error is illustrated by a simulation of a signal and a noise as vector Gaussian stationary autoregressive processes. The simulation supports theoretical conclusions.

Development of algorithm and programs for two-dimensional filtering problems of incompressible liquids

Development of algorithm and programs for two-dimensional filtering problems of incompressible liquids

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

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

Wavelet Filtering in Shock Stochastic Systems with High Availability

For filtering problems in StSHA under nonGaussian ShD methodological and algorithmically WL support is developed. 3 types of filters are considered: KBF (WLKBF), LPF (WLLPF) and SOLF (WLSOLF). These filters have the following advantages: on-line regime, high accuracy and possibility of algorithmically description of complex ShD. Wavelet filter modifications are based on Galerkin method and Haar wavelet expansions. WLF unlike KBF, LPF and SOLF do not need to integrate system of ordinary differential Eqs. These filters must solve system of linear algebraic Eqs with constant coefficients. KBF (WLKBF) and SOLF (WLSOLF) are recommended for StSHA with additive ShD whereas LPF (WLLPF) are recommended for StSHA with parametric and additive ShD. Basic applications are: on-line identification and calibration of nonstationary processes in StSHA of ShD. Methods are illustrated by example of 3 dimensional differential linear information control system at complex ShD. Basic algorithms and error analysis for KBF (WLKBF) and LPF (WLLPF) are presented and 15 Figure; illustrate filters peculiarities for small and fin damping. These filters allow to estimate the accumulation effects for systematic and random errors. Results may be generalized for filtration, extrapolation with interpolation problems in StSHA and multiple ShD.