Filtering Problem Research Articles

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.

Event-triggered distributed filtering for discrete-time systems with integral measurements

This paper handles the event-triggered distributed filtering problem for a class of discrete-time systems with integral measurements over sensor networks (SNs). First of all, a plant is monitored by an SN formulated by a digraph. The integral measurement phenomenon is modelled for each node to account for the interval time taken by sample collection. Next, to mitigate the communication burden of network, an event generator function is introduced for each node to regulate the data transmission to its neighbouring nodes. This paper aims to find the suitable filter gains for each node such that the filtering error dynamics satisfies the exponentially ultimately boundedness. Via the Lyapunov stability theory, a sufficient condition is established which ensures the existence of the distributed filter under the desirable performance index. Moreover, the ultimate bound in the performance index is minimized via the robust optimization method. Then, the filter gains are acquired by solving a linear matrix inequality with the YALMIP toolbox. Finally, a numerical simulation example is employed to verify the usefulness of the distributed filtering algorithm developed in this paper.

Terminal filtering of stochastic processes observed on a finite time interval

Annotation. Currently, the problem of evaluating stochastic processes observed under noisy conditions on a finite time interval is solved only for datasets in the form of time series using a limited number of statistical variational or spectral analysis methods, as well as various modifications of regression methods. In this case, parametric criteria are used that depend on individual parameters of the distribution density of the observed process, and not on the density itself, which significantly limits the possibilities of increasing the estimation accuracy. To solve the problem of high-precision estimation of stochastic processes on a finite time interval of their observation, an approach is proposed, firstly, providing optimal estimation according to the criterion depending on the posterior distribution density - the most informative characteristic of the observed process, and secondly, taking into account the dynamic structure of the process and the finiteness of the interval observation. A numerical example is considered to illustrate the effectiveness of the developed approach. Relevance. Currently, the problem of evaluating stochastic processes observed under noisy conditions on a finite time interval (terminal filtering problem) is solved only for datasets in the form of time series using a limited number of statistical variational or spectral analysis methods, as well as various modifications of regression methods. In this case, parametric criteria are used that depend on individual parameters of the distribution density of the observed process, and not on the density itself, which significantly limits the possibilities of increasing the estimation accuracy. Target. In this regard, for stochastic processes of a general form - described by nonlinear stochastic differential equations, it is necessary to develop a method of terminal filtering according to a criterion that takes into account the finiteness of the observation time interval and depends on the posterior distribution density - the most informative characteristic of the observed process (and not on its individual parameters). Results. The proposed solution to the problem of high-precision terminal filtering of stochastic processes - their optimal estimation over a finite observation time interval - is based on the use of a terminal criterion that depends directly on the posterior distribution density and takes into account the finiteness of the observation time interval. When describing the observed stochastic processes, their most general representation was used - nonlinear stochastic differential equations, which significantly expands the field of application of the results obtained in comparison, for example, with time series. The general solution to the problem of optimal terminal filtering is obtained using the Pontryagin maximum principle, the solution to the problem of suboptimal filtering, which significantly reduces computational costs, is based on the method of invariant immersion. Practical significance. A numerical example is considered to illustrate the effectiveness of the developed method. The proposed approach can be widely used in various fields of scientific and technical research: radio engineering, Earth sensing, satellite navigation, astronomy, seismology, geodesy, etc.

IIR Filter Design Using African Buffalo Optimization

In the modern world, the digital signal processing embeds more in real time applications. Several researchers focused on filtering process to identify the limitation in traditional methods. In this article, the meta-heuristic algorithm is deployed for optimizing infinite impulse response (IIR) filter design. The traditional IIR filter results create computational complexity and its performance is worse in the case of a noisy environment. In signal processing, IIR plays several roles in filtering and monitoring the signal amplitude. The African Buffalo Optimization (ABO) is quite easy for implementation and its performance outcomes solved many problems in various domains. Hence, it is selected for solving IIR filter problems for obtaining optimal filter coefficients. Initially, IIR filter is designed for different orders under ABO concept. The ABO based IIR filter’s performance is superior to those obtained by Genetic Algorithm and cuckoo search algorithm. The proposed method’s performance result proves that it has a smaller magnitude error and phase error with fast convergence rate.

Event-triggered distributed filtering for Markov jump systems over sensor networks

This article deals with the distributed filtering problem for a class of discrete-time Markov jump systems over sensor networks. First, in the distributed filtering network, each local filter simultaneously fuses the estimation and measurement from itself and neighboring nodes to achieve the system state estimation. And each sensor intelligent node is embedded with an event-triggered sampling mechanism, which can reduce the computation load or saving limited network bandwidth. Then, we use Bernoulli stochastic variables to describe whether the filtering network can successfully receive the system jump modes. Next, based on the Lyapunov stability theory, we design a distributed filter dependent on partial system modes, which has the exponential stability in mean square and [Formula: see text] performance. Finally, all desired estimator parameters can be obtained by solving a set of linear matrix inequalities. Moreover, two numerical examples are given to illustrate the effectiveness of the distributed [Formula: see text] filtering design approach.

ADAPTIVE GUARANTEED ESTIMATION OF A CONSTANT SIGNAL UNDER UNCERTAINTY OF MEASUREMENT ERRORS

In the guaranteed estimation problems under uncertainty relative to disturbances and meas-urement errors, the admissible sets of their possible values are determined. The solution is chosen due to conditions of guaranteed bounded estimates optimization corresponding to the worst realiza-tion of disturbances and measurement errors. The result of the guaranteed estimation is an unim-provable bounded estimate (information set), which turns to be overly pessimistic (reinsurance) if a prior admissible set of measurement errors is too large compared to their realized values. The admis-sible sets of disturbances and measurement errors can turn to be only rough upper estimates on a short observation interval. The goal of research is the accuracy enhancement problem of guaran-teed estimation when measurement errors are not realized in the worst way, i.e. the environment in which the object operates does not behave as aggressively as it is built in a priori data on the permis-sible set of error values. Research design. The problem of adaptive guaranteed estimation of a con-stant signal from noisy measurements is considered. The adaptive filtering problem is, according to the results of measurement processing, from the whole set of possible realizations of errors, to choose the one that would generate the measurement sequence. Results. An adaptive guaranteed estimation algorithm is presented. The adaptive algorithm construction is based on a multi-alternative method based on the Kalman filter bank. The method uses a set of filters, each of which is tuned to a specific hypoth-esis about the measurement error model. Filter residuals are used to compute estimates of realized measurement errors. The choice of the realization of possible errors is performed using a function that has the meaning of the residual variance over a short time interval. Conclusion. The computa-tional scheme of the adaptive algorithm, the numerical example, and comparative analysis of ob-tained estimates are presented.

Robust fusion steady‐state estimators for networked stochastic uncertain systems with packet dropouts and missing measurements

AbstractIn this article, the robust fusion steady‐state filtering problem is investigated for a class of multisensor networked systems with mixed uncertainties. The uncertainties include state‐dependent and noise‐dependent multiplicative noises, missing measurements, packet dropouts, and uncertain noise variances, the phenomena of missing measurements and packet dropouts occur in a random way, and are described by two Bernoulli distributed random variables with known conditional probabilities. Using a model transformation approach, which consists of augmented approach, de‐randomization approach and fictitious noise approach, the original multisensor system under study is converted into a multi‐model multisensor system with only uncertain noise variances. According to the minimax robust estimation principle, based on the worst‐case subsystems with conservative upper bounds of uncertain noise variances, the robust local steady‐state Kalman estimators (predictor, filter, and smoother) are presented in a unified framework. Applying the optimal fusion algorithm weighted by matrices, the robust distributed weighted state fusion steady‐state Kalman estimators are derived for the considered system. The robustness of the proposed estimators is proved by using a combination method consisting of augmented noise approach, decomposition approach of non‐negative definite matrix, matrix representation approach of quadratic form, and Lyapunov equation approach, such that for all admissible uncertainties, the actual steady‐state estimation error variances of the estimators are guaranteed to have the corresponding minimal upper bounds. The accuracy relations among the robust local and fused steady‐state Kalman estimators are proved. An example with application to autoregressive moving average (ARMA) signal processing is proposed, which shows that the robust local and fusion signal estimation problems can be solved by the state estimation problems. Simulation example verifies the effectiveness and correctness of the proposed results.

Real-Time Point Process Filter for Multidimensional Decoding Problems Using Mixture Models

There is an increasing demand for a computationally efficient and accurate point process filter solution for real-time decoding of population spiking activity in multidimensional spaces. Real-time tools for neural data analysis, specifically real-time neural decoding solutions open doors for developing experiments in a closed-loop setting and more versatile brain-machine interfaces. Over the past decade, the point process filter has been successfully applied in the decoding of behavioral and biological signals using spiking activity of an ensemble of cells; however, the filter solution is computationally expensive in multi-dimensional filtering problems. Here, we propose an approximate filter solution for a general point-process filter problem when the conditional intensity of a cell’s spiking activity is characterized using a Mixture of Gaussians. We propose the filter solution for a broader class of point process observation called marked point-process, which encompasses both clustered – mainly, called sorted – and clusterless – generally called unsorted or raw– spiking activity. We assume that the posterior distribution on each filtering time-step can be approximated using a Gaussian Mixture Model and propose a computationally efficient algorithm to estimate the optimal number of mixture components and their corresponding weights, mean, and covariance estimates. This algorithm provides a real-time solution for multi-dimensional point-process filter problem and attains accuracy comparable to the exact solution. Our solution takes advantage of mixture dropping and merging algorithms, which collectively control the growth of mixture components on each filtering time-step. We apply this methodology in decoding a rat’s position in both 1-D and 2-D spaces using clusterless spiking data of an ensemble of rat hippocampus place cells. The approximate solution in 1-D and 2-D decoding is more than 20 and 4,000 times faster than the exact solution, while their accuracy in decoding a rat position only drops by less than 9% and 4% in RMSE and 95% highest probability coverage area (HPD) performance metrics. Though the marked-point filter solution is better suited for real-time decoding problems, we discuss how the filter solution can be applied to sorted spike data to better reflect the proposed methodology versatility.

Transmission Zeros of Trisection and Quadruplet Bandpass Filters With Mixed Cross Coupling

This article solved the inverse problem for trisection and quadruple bandpass filters (BPFs) with mixed cross coupling. It allows for a given placement of transmission zeros and known main coupling coefficients to determine mixed cross coupling $K = K_{m} + K_{e}$ , containing magnetic and electrical components. Based on the obtained solution, it was established that trisection BPF has ten different options for placing two transmission zeros on the complex plane $S = \sigma + j\Omega $ . It is shown that the considered trisection and quadruplet BPFs can have a second-order transmission zero on the $j\Omega $ axis, which provides a deeper attenuation pole at insertion loss curve. With the help of the obtained inverse problem solution, some restrictions are established on the possible options for the placement of three transmission zeros of quadruplet BPF with mixed cross coupling $K_{14}$ : transmission zeros cannot be placed on the $\sigma $ -axis and two of the three transmission zeros on the $j\Omega $ -axis cannot be equidistantly relative to $S =0$ . It is found that to obtain a flat group delay, the transmission zeros must be located in the S- plane at the corners of an isosceles triangle, the vertex of which lies on the $j\Omega $ axis, and the sides intersect the $\sigma $ -axis. In this case, in addition to the flat group delay, the insertion loss curve has an attenuation pole. Theoretical results are validated with two microstrip quasi-inline trisection BPFs and one stripline quadruplet BPF.

Efficiency of evolutionary search for analog filter synthesis

Design automation presents a trade off between: using expert knowledge to restrict the possible solutions examined; or spending time searching through many, possibly ineffective, solutions. Incorrect assumptions or misapplication of constraints can miss otherwise superior results. Automated search of possible solutions has been shown effective, limited by the available computational resources. This paper presents an evolutionary search method for finding optimized circuit topologies and component values. An example analog filter problem is exhaustively enumerated, to test the efficiency of different stochastic search methods in finding globally optimal solutions. Evolutionary methods are shown to be efficient for this problem. Impacts of varying parameters and techniques of evolutionary search are compared for a more complex asymmetric bandpass filter problem. Genetic Algorithm and Evolutionary Strategy methods are found to have similar performance. Hybrid evolutionary methods using Differential Evolution for component value optimization are found to be more efficient with limited: component count; or computational resources. The hybrid method used is shown to scale to more complex problems without changing parameters. Proposed comparison metrics, normalized for experimental variables, show the efficiency of this work improves upon published benchmarks. This is achieved without restricting the synthesized topologies to known structures, producing novel results more effective than prior works.

Application of Conditional-Optimal Filter for Synthesis of Suboptimal Control in the Problem of Optimizing the Output of a Nonlinear Differential Stochastic System

We propose a suboptimal solution for the control problem for the Ito diffusion process and linear controlled output with a quadratic quality criterion for the case of indirect observations of the state. We use the previously obtained solution of the problem with complete information, the concept of separation between control and filtering problems, and the method of conditionally optimal filtering developed by V.S. Pugachev. We propose an alternative to the traditional practical approach for the synthesis of suboptimal control in a problem with incomplete information, which consists in a formal substitution in the solution of a state with its estimate. Instead of the problem of optimizing the output generated by the original model of the differential equation, we use as the state an estimate of a conditionally optimal filter. We develop one version of the numerical implementation of the proposed algorithm based on the Monte Carlo method and computer simulation.

Finite-horizon H ∞ state estimation for time-varying complex networks based on the outputs of partial nodes

In this paper, the partial-nodes-based resilient filtering problem for a class of discrete time-varying complex networks is investigated. In order to reduce the effect of imprecision of filter parameters on estimation performance, a set of resilient filters is proposed. The measurement output from all network nodes may not be available in the actual system, but only from a fraction of nodes. The state estimators are designed for the time-varying complex network based on partial nodes to make the estimation error achieve the performance constraint over a finite horizon. By employing the completing-the-square technique and the backward recursive Riccati difference equations, the sufficient conditions for the existence of the estimator are derived. Then the gain of the estimator is calculated. Finally, a numerical example is provided to illustrate the effectiveness of the proposed method.

Generalised KYP lemma with its application in finite frequency H ∞ distributed filter design for nonideally interconnected networked control systems

This paper addresses the generalised Kalman-Yakubovich-Popov (GKYP) lemma and its application in finite frequency (FF) distributed filter design for networked control systems (NCSs). The network communication channels between subsystems are considered to be affected by uncertainties. Firstly, based on the proposed linear matrix inequality characterisation for an FF region and S-procedure, a GKYP lemma is presented for NCSs. After that, the FF bounded realness and FF positive realness in terms of individual subsystems are studied as special cases of the proposed GKYP lemma. Moreover, as an application of the developed GKYP lemma, the FF distributed filtering problem for nonideally interconnected NCS is studied. Finally, illustrative examples are given to show that the developed EF methods have less conservation than the common method over the entire frequency region.

Profiling functions application for layered dielectric filter synthesys problem statement

A novel mathematical apparatus allowing formulation and justification of a new approach towards the setting of the mathematical problem of band-pass layered dielectric filters (LDF) synthesis is developed. Аrbitrary layered dielectric systems with piecewise continuous physical media parameters given by the functions of dielectric permittivity and of magnetic permeability, both depending on the coordinate along the normal to the layer pile, with fixed discontinuity points of at least one of the mentioned functions are examined. For such systems, an important conservation law for the difference of the squares of absolute amplitude values of plane waves propagating left and right in given layered medium is stated, which further leads to the traditional energy conservation law in lossless layered media. This new identity law allows turning from synthesis problems in terms of fractional rational energy reflectivity and transmittance of layered systems to equivalent tasks for profiling functions introduced in the work, representing only the numerator or only the denominator of the expressions usually considered in the synthesis. A new concept of the feasible ideal is introduced for the energy coefficients of reflection and transmission of layered systems. It is shown that the feasibility of the energy coefficients of reflection and transmission of layered systems is equivalent to the feasibility of the profiling functions of such systems, which together with the main identity allows a significant change of the existing LDF synthesis approach. The rule for converting the ideal of the reflection or transmission coefficient into the ideal of the profiling function is given. The proposed synthesis problem statement leads to considerably less intensive computational procedures.

Costly Consideration and Dynamic Choice Set Formation

Dynamic choices of cognitively constrained individuals have been ascribed, by the rational inattention theory, as being a filtering problem, in which the attentional intensity is consciously elected. Human attention, however, is not merely of voluntary intensity; it is rather of volitional placement nature. In this article, I study the implications of a dynamic theory of volitional attention describing individuals who choose among the alternatives that are induced by their attentional choices. Firstly, a consumer search application using US scanner data indicates that attentional choices are characterized by complementarities. Costs do not exclusively depend on the cardinality of consideration sets, but also on experience and similarities between considered items. Neglecting, thereby, attentional placement aspects potentially leads to misidentification of preference characteristics. Secondly, participation inertia in financial markets is revisited under the scope of volitional attention and a cultural-based argument of why it can be optimal not to participate is provided.

Fault Detection Finite-Time Filter Design for T–S Fuzzy Markovian Jump System with Missing Measurements

The primary purpose of this work was to address the problem of finite-time fault detection filtering for a class of discrete-time Takagi–Sugeno (T–S) fuzzy Markovian jump systems subject to randomly occurring uncertainties, time-varying delay, missing measurements and partly unknown transition probability matrices. Precisely the missing measurement phenomenon in the network environment satisfies the Bernoulli distributed white noise sequences. Firstly a fuzzy rule-dependent filter is constructed for estimating the unmeasured states of the system and the corresponding fault detection problem. Further, based on the filtering problem, the error between residual and fault is minimized with the prescribed strict $$(\mathsf {Q},\mathsf {S},\mathsf {R})$$ - $$\gamma $$ dissipativity performance. Secondly, the sufficient criteria are derived to ensure the filtering error system to be finite-time stochastic bounded. Finally, the applicability and usefulness of the proposed filter design through two numerical examples are verified.

Coprime factorization of polytopic LPV systems based on a homogeneous polynomial approach

AbstractThis paper presents novel linear matrix inequalities (LMI)‐based conditions to address the coprime factorization problem for polytopic linear parameter‐varying (LPV) systems in both the continuous‐ and discrete‐time cases. The proposed conditions rely on the use of homogeneous polynomial parameter‐dependent (HPPD) matrix solutions of arbitrary degree g, which are used to obtain coprime factorization descriptions subject to time‐varying parameters defined inside a polytopic structure with known vertices. For a given degree g, synthesis of right and left coprime factorizations in terms of two special state‐feedback and filtering problems under quadratic performance are provided. Existence conditions are given from linear matrix inequalities relaxations based on an extension of Pólya's theorem and the HPPD approach. The effectiveness of the proposed conditions is evaluated by means of numerical examples.

A short review of alternative ingredients and technologies of inorganic UV filters.

The growing need to use sunscreens is a concrete reality, and it is associated with the increase in the population's awareness of the ultraviolet (UV) radiation damage. Inorganic UV filters promote the formation of particles/pigments film over the skin surface, reflecting, dispersing, and absorbing the radiation. Investigations of this class of filters demonstrate the emergence of alternative ingredients and new technologies. In this review, we presented potential candidates for alternative UV inorganic filters, such as hydroxyapatite, cerium dioxide, and hydrotalcite. Specialized literature identified hydroxyapatite and cerium dioxide as actives with good performances, with a broad spectrum of absorption against UV radiation. Both of them were considered safe against degradation and skin erythema formation. Inorganic compounds as an alternative to circumvent degradation problems of organic UV filters containing PABA were also analyzed, with hydrotalcite having a good performance in improving the performance of classic ingredients, bypassing photoinstability, and improving safety, in addition to preventing skin irritability. Further investigations of these ingredients and interactions with sunscreen formulations are necessary to overall explore their safety and efficacy, encouraging future researches for more inorganic UV filters.

Robust fault detection filter design for a class of discrete‐time conic‐type non‐linear Markov jump systems with jump fault signals

This study investigates the robust fault detection filter design problem for a class of discrete-time conic-type non-linear Markov jump systems with jump fault signals. The conic-type non-linearities satisfy a restrictive condition that lies in an n -dimensional hyper-sphere with an uncertain centre. A crucial idea is to formulate the robust fault detection filter design problem of non-linear Markov jump systems as filtering problem. The authors aim to design a fault detection filter such that the augmented Markov jump systems with conic-type non-linearities are stochastically stable and satisfy the given performance against the external disturbances. By means of the appropriate mode-dependent Lyapunov functional method, sufficient conditions for the existence of the designed fault detection filter are presented in terms of linear matrix inequalities. Finally, a practical circuit model example is employed to demonstrate the availability of the main results.

Maximum likelihood-based robust state estimation over a horizon length during measurement outliers

In this paper, a novel approach towards horizon-based maximum likelihood (ML) state estimator is proposed that makes the state estimation process more robust against unmodeled and unstructured noise and disturbances in the state-space models. State space models provide a powerful way to perform state and parameter estimation for dynamical systems. However, if the measurements are contaminated by outliers and disturbances with no known models, the estimation process is highly biased. A ML-based approach is used to find a batch solution for the filtering problem. Based on ML solution, a robust algorithm is proposed that seamlessly estimates dynamic state in the presence of zero or non-zero mean measurement outliers. The proposed algorithm that dictates this switching uses an explicit outlier detection mechanism that enables its seamless working. Simulations have been carried out for a moving target tracking application as an example to demonstrate the resilience of the proposed method against zero-mean and non-zero mean measurement outliers in comparison to state-of-the-art methods.