Optimal Filtering Problem Research Articles

Passive Power Filter Optimization Problem Based on Adaptive Multipopulation NSGA-II and CRITIC-TOPSIS

The best configuration of passive filters in extra-high voltage systems is investigated in this study using a two-stage multiobjective decision-making (MODM) framework. A collection of Pareto solutions is found using an adaptive multipopulation-modified nondominated ranking genetic algorithm (AMP NSGA-II) in the first stage. The goals taken into account include the least fundamental reactive power compensation losses, overall cost and maintenance cost, and simultaneous minimum harmonic current distortion rate. The objective weights are determined and the optimum solution is chosen in the second stage using the criteria importance interrelationship (CRITIC) and similarity ranking preference technique (TOPSIS). A number of examples show how the suggested method performs more effectively than the conventional and well-known algorithm and can identify the relationship between the objective functions, indicating that the suggested scheme has better superiority in filters and has a promising future in the solution of multiobjective problems.

Integrated Renewable Smart Grid System Using Fuzzy Based Intelligent Controller

In high power medium voltage applications, the utilization of 5-H Bridge Multi-Level Inverter (MLI) has grown vastly in recent years. The 5-H Bridge MLI can effectively control link voltage as well as power factor. However, the inverter imparts harmonics owing to the high switching frequency. Hence Inductance Capacitance Inductance (LCL) filter is implemented at its output to mitigate harmonics in presence of non-linear load. It’s of highly important to choose LCL parameters wisely in order to attain good filtering effect. This work investigates the application of 5-H Bridge MLI with LCL filter at the output for efficient integration of renewable energy sources on to the grid. A modified fuzzy heuristic approach is used to solve LCL power filter optimization problem at output of 5-H Bridge Multi-Level Inverter. Subject to the constraint’s harmonic distortion and losses of the inverter, multi objective optimization problem is solved to obtain LCL filter optimal values. The optimized LCL filter design was applied to a grid connected cascaded H-bridge MLI of rating 4.5 MW, 11 kV. MATLAB-Simulink is utilized for modelling and simulating the system. The results showed that the system is more efficient and generic. dSPACE Hardware in Loop (HIL) test system was used to verify the efficacy of the prototype system.

Maximum cross section method in the filtering problem for continuous systems with Markovian switching

Abstract New solution algorithms of optimal filtering problem are proposed for systems with random structure and continuous time. This problem consists in estimating the current state of system based on the results of measurements. The mathematical model of the system includes nonlinear stochastic differential equations whose right-hand side determines the structure of the dynamic system or mode of operation. The right-hand side may vary at random time moments. The number of structures of the system is assumed to be finite and the process of changing the structure to be Markov or conditionally Markov. The state vector of such system consists of two components, namely, a vector with real coordinates and an integer structure number. The law of change of the structure number is determined by the distribution of the random time interval between switchings with a given intensity dependent on the state of system.

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.

Filter Design and Optimization of Electromechanical Actuation Systems Using Search and Surrogate Algorithms for More-Electric Aircraft Applications

In this article, the dc filter design and optimization problem is studied for dc electrical power distribution systems onboard more-electric aircraft. Component sizing models are built to serve as the basis of the optimization whose objectives are mass and power loss of this filter. A categorization strategy of search and surrogate algorithms is proposed and used for the target multiobjective optimization problem (MOOP). A genetic algorithm is utilized as a search algorithm to identify potential best solutions based on a set of filter sizing functions (subject to constraints). In addition, two machine learning (ML) algorithms are considered as surrogate algorithms to address the same optimization problem. In the ML training process, a constraint violation model is applied since there are various constraints in optimization, and this kind of classification model is relatively difficult to train. A support vector machine is applied for the constraint violation model; after that, two artificial neural networks are trained as the final surrogate model for mapping design variables to filter performance. To address these issues, a novel category of search and surrogate algorithms is proposed. Both algorithms are explored to solve the filter MOOP, and their optimization results are compared at the end.

Forward backward doubly stochastic differential equations and the optimal filtering of diffusion processes

The connection between forward backward doubly stochastic differential equations and the optimal filtering problem is established without using the Zakai's equation. The solutions of forward backward doubly stochastic differential equations are expressed in terms of conditional law of a partially observed Markov diffusion process. It then follows that the adjoint time-inverse forward backward doubly stochastic differential equations governs the evolution of the unnormalized filtering density in the optimal filtering problem.

Статистические алгоритмы фильтрации для систем со случайно изменяющейся структурой

New algorithms for solving the optimal filtering problem for continuous-timesystems with a random structure are proposed. This problem is to estimate the currentsystem state vector from observations. The mathematical model of the dynamic systemincludes nonlinear stochastic differential equations, the right side of which defines the systemstructure (regime mode). The right side of these stochastic differential equations may bechanged at random time moments. The structure switching process is the Markov or conditionalMarkov random process with a finite set of states (structure numbers). The state vectorof such system consists of two components: the real vector (continuous part) and the integerstructure number (discrete part). The switch condition for the structure number may bedifferent: the achievement of a given surface by the continuous part of the state vector orthe distribution of a random time period between structure switchings. Each ordered pairof structure numbers can correspond to its own switch law. Algorithms for the estimation of the current state vector for systems with a randomstructure are particle filters, they are based on the statistical modeling method (MonteCarlo method). This work continues the authors’ research in the field of statistical methodsand algorithms for the continuous-time stochastic systems analysis and filtering.

Variance-constrained filtering for nonlinear systems with randomly occurring quantized measurements: recursive scheme and boundedness analysis

In this paper, the robust optimal filtering problem is discussed for time-varying networked systems with randomly occurring quantized measurements via the variance-constrained method. The stochastic nonlinearity is considered by statistical form. The randomly occurring quantized measurements are expressed by a set of Bernoulli distributed random variables, where the quantized measurements are described by the logarithmic quantizer. The objective of this paper is to design a recursive optimal filter such that, for all randomly occurring uncertainties, randomly occurring quantized measurements and stochastic nonlinearity, an optimized upper bound of the estimation error covariance is given and the desired filter gain is proposed. In addition, the boundedness analysis problem is studied, where a sufficient condition is given to ensure the exponential boundedness of the filtering error in the mean-square sense. Finally, simulations with comparisons are proposed to demonstrate the validity of the presented robust variance-constrained filtering strategy.

Matrices whose inverses are tridiagonal, band or block-tridiagonal and their relationship with the covariance matrices of a random Markov process

The article discusses the matrices of the form A1n, Amn, AmN, whose inverses are: tridiagonal matrix A-1n (n - dimension of the A-mn matrix), banded matrix A-mn (m is the half-width band of the matrix) or block-tridiagonal matrix A-m N (N = n x m - full dimension of the block matrix; m - the dimension of the blocks) and their relationships with the covariance matrices of measurements with ordinary (simple) Markov Random Processes (MRP), multiconnected MRP and vector MRP, respectively. Such covariance matrices frequently occur in the problems of optimal filtering, extrapolation and interpolation of MRP and Markov Random Fields (MRF). It is shown, that the structures of the matrices A1n, Amn, AmN have the same form, but the matrix elements in the first case are scalar quantities; in the second case matrix elements represent a product of vectors of dimension m; and in the third case, the off-diagonal elements are the product of matrices and vectors of dimension m. The properties of such matrices were investigated and a simple formulas of their inverses were found. Also computational efficiency in the storage and the inverse of such matrices have been considered. To illustrate the acquired results, an example on the covariance matrix inversions of two-dimensional MRP is given.

Joint window and filter optimization for new waveforms in multicarrier systems

One of the demands of the next-generation wireless communication systems is being supportive to asynchronous traffic types. In order to meet this demand, many waveform candidates for next-generation wireless communication systems have low out-of-subband emissions (OOSBE) of the transmitted signal, and the popular ones deploy either filtering or windowing at the transmitter. In this paper, a joint windowing and filtering multi-carrier waveform based on a generalized orthogonal frequency division multiplexing (OFDM) system is proposed. A joint window and filter optimization problem to minimize OOSBE is also formulated. The optimization problem is first divided into two solvable subproblems using interior-point methods, and then an iterative algorithm is proposed to obtain the optimal window and filter pair. Simulation results suggest that the proposed joint windowing and filtering waveform has an advantage in suppressing OOSBE or enhancing spectral efficiency, and is more robust to frequency asynchronism compared to waveforms deploying only either filtering or windowing.

Optimal filtering for a class of linear Itô stochastic systems: The dichotomic case

This paper focuses on the problem of optimal H2 filtering for a class of continuous-time stochastic systems without assuming their exponential stability in the mean square sense. Indeed, the stability assumption is relaxed and we assume instead that the Lyapunov operator associated to the dynamical stochastic system is exponentially dichotomic. The optimal solution of the considered optimization problem is expressed in terms of the unique solution of a suitable algebraic Lyapunov equation and the stabilizing solution of a certain algebraic Riccati equation.

Optimal filter for MJL system with delayed modes and observations

This study investigates the optimal filter for Markov jump linear (MJL) system with multiple delayed modes and observations, in which the data losses are introduced naturally and the Markov chains are assumed to be known up to the present time. To deal with the mode and observation delays, a reorganised observation sequence is defined. Moreover, the optimal filter problem is transformed into one of the delay-free system which is just with jumping parameters and multiplicative noises. An optimal MJL filter is presented based on the mean squared method, where the filter gains are determined by solving a set of generalised coupled Riccati difference equations based on a set of coupled Lyapunov equations. Alternatively, an optimal stationary MJL filter is developed, where the filter gains are derived by solving a set of generalised coupled algebraic Riccati equations based on coupled algebraic Lyapunov equations. It can be shown that the difference Riccati equations developed in the former filter converge to the stationary ones under appropriate conditions.

Minimax l-optimal at Time-Domain Linear Filtering

The article is devoted to one approach to optimal filtration. We consider a Wiener filter scheme. The proposed statement has two differences from the classical one. The first difference is that the input influences (useful signal and interference) are limited to the maximum absolute values, and not variances. The second difference is that the quality criterion is also the maximum absolute value, and not the variance of the error. Thus, the quadratic criterion in Wiener’s formulation is replaced by a criterion in the form of the l∞-norm (Chebyshev-norm). Therefore, the proposed problem is called the l∞optimal filtering problem. An original way of selecting input filters for signals for this task is proposed. The method allows creating sets of signals with complex limitations of the absolute values of the signals and their derivatives. The calculation of the quality criterion reduces to Bulgakov's problem of the accumulation of perturbations. For a system with discrete time, the quality criterion is written in the form of a sum of an infinite series. Convergence conditions of the series are obtained. If the conditions of convergence are satisfied, an infinite series with any desired accuracy can be replaced by its partial sum. In this case, a quality criterion is obtained in the form of the l1-norm of the impulse response of the filter. It is proposed to numerically search for the impulse response of an optimal filter by the method of subgradient descent. An example of searching for a l∞-optimal filter is considered. The result is compared with classic bandpass filters. The possibility of reducing the phase delay of the filter in the passband is shown.

Robust optimal filtering for linear time‐varying systems with stochastic uncertainties

In this study, the robust optimal filtering problem is investigated for a class of linear time-varying systems with stochastic uncertainties. A new model is presented that accounts for both stochastic parameter uncertainties and noise. On the basis of the new model, a robust optimal filter is proposed. It takes stochastic uncertainties into full consideration, but does not depend on any specific structure of uncertainties. By resorting to linear system theory and utilising stochastic analysis methods, the filter gain is designed such that the estimation error covariance is minimised at each time step. The authors' developed filtering algorithm is recursive, and therefore suitable for real-time online applications. In the end, two simulation studies are performed to illustrate the effectiveness and applicability of their proposed strategy.

Information filtering for time-delay systems

This paper presents the information filter, which is developed in filtered forms, for time-delay systems which include continuous-time case and discrete-time case. By introducing delay-free observation, the optimal filtering problems for time-delay systems can be converted into multiple steps prediction problems for delay-free systems. Then, the recursive forms for optimal filter are given via innovation approach in Hilbert space. Furthermore, the information filter in Riccati recursions can be derived by using the matrix inversion Lemma to optimal filtering formulas. Finally, the distributed Kalman filter for time-delay systems is designed based on information filter developed.

Filter Design for Generalized Frequency-Division Multiplexing

In this paper, optimal filter design for generalized frequency-division multiplexing (GFDM) is considered under two design criteria: rate maximization and out-of-band (OOB) emission minimization. First, the problem of GFDM filter optimization for rate maximization is formulated by expressing the transmission rate of GFDM as a function of GFDM filter coefficients. It is shown that Dirichlet filters are rate-optimal in additive white Gaussian noise (AWGN) channels with no carrier frequency offset (CFO) under linear zero-forcing (ZF) or minimum mean-square error (MMSE) receivers, but in general channels perturbed by CFO a properly designed nontrivial GFDM filter can yield better performance than Dirichlet filters by adjusting the subcarrier waveform to cope with the channel-induced CFO. Next, the problem of GFDM filter design for OOB emission minimization is formulated by expressing the power spectral density (PSD) of the GFDM transmit signal as a function of GFDM filter coefficients, and it is shown that the OOB emission can be reduced significantly by designing the GFDM filter properly. Finally, joint design of GFDM filter and window for the two design criteria is considered.

Marginalized Continuous Time Bayesian Networks for Network Reconstruction from Incomplete Observations

Continuous Time Bayesian Networks (CTBNs) provide a powerful means to model complex network dynamics. How- ever, their inference is computationally demanding — especially if one considers incomplete and noisy time-series data. The latter gives rise to a joint state- and parameter estimation problem, which can only be solved numerically. Yet, finding the exact parameterization of the CTBN has often only secondary importance in practical scenarios. We therefore focus on the structure learning problem and present a way to analytically marginalize the Markov chain underlying the CTBN model with respect its parameters. Since the resulting stochastic process is parameter-free, its inference reduces to an optimal filtering problem. We solve the latter using an efficient parallel implementation of a sequential Monte Carlo scheme. Our framework enables CTBN inference to be applied to incomplete noisy time-series data frequently found in molecular biology and other disciplines.

Single-channel noise reduction via semi-orthogonal transformations and reduced-rank filtering

This paper investigates the problem of single-channel noise reduction in the time domain. The objective is to find a lower dimensional filter that can yield a noise reduction performance as close as possible to or even better than that obtained by the full-rank solution. This is achieved in three steps. First, we transform the observation signal vector sequence, through a semi-orthogonal matrix, into a sequence of transformed signal vectors with a reduced dimension. Second, a reduced-rank filter is applied to get an estimate of the clean speech in the transformed domain. Third, the estimate of the clean speech in the time domain is obtained by an inverse semi-orthogonal transformation. The focus of this paper is on the derivation of semi-orthogonal transformations under certain estimation criteria in the first step and the design of the reduced-rank optimal filters that can be used in the second step. We show how noise reduction using the principle of rank reduction can be cast as an optimal filtering problem, and how different semi-orthogonal transformations affect the noise reduction performance. Simulations are performed under various conditions to validate the deduced filters for noise reduction.

Application of optimal filtering methods for on-line of queueing network states

We show the solution to the optimal filtering problem for states of Markov jump processes by observations of multivariant point processes. A characteristic feature of observations is that their compensators are random linear functions of the system state, and the composite "state---observations" process does not possess the Markov property. The provided optimal filtering estimate is expressed via the solution of some recurrent system of linear differential equations and algebraic relations. We present examples of using theoretical results to construct typical models of real queueing networks. We establish the connections between our new optimal filtering algorithm and classical results of Kalman---Bucy and Wonham. We propose a solution for the problem of estimating the current state of a UDP connection given the observations of video stream.

Waveform Design for Radar STAP in Signal Dependent Interference

Waveform design is a pivotal component of the fully adaptive radar construct. In this paper we consider waveform design for radar space time adaptive processing (STAP), accounting for the waveform dependence of the clutter correlation matrix. Due to this dependence, in general, the joint problem of receiver filter optimization and radar waveform design becomes an intractable, non-convex optimization problem, Nevertheless, it is however shown to be individually convex either in the filter or in the waveform variables. We derive constrained versions of: a) the alternating minimization algorithm, b) proximal alternating minimization, and c) the constant modulus alternating minimization, which, at each step, iteratively optimizes either the STAP filter or the waveform independently. A fast and slow time model permits waveform design in radar STAP but the primary bottleneck is the computational complexity of the algorithms.