Search results for: optimal parameter settings.

Authors: Hai Quang Hong Dam, Hai Ho, Minh Hoang Le Ngo

Abstract:

This paper investigates the problem of blind speech separation from the speech mixture of two speakers. A voice activity detector employing the Steered Response Power - Phase Transform (SRP-PHAT) is presented for detecting the activity information of speech sources and then the desired speech signals are extracted from the speech mixture by using an optimal beamformer. For evaluation, the algorithm effectiveness, a simulation using real speech recordings had been performed in a double-talk situation where two speakers are active all the time. Evaluations show that the proposed blind speech separation algorithm offers a good interference suppression level whilst maintaining a low distortion level of the desired signal.

Keywords: Blind speech separation, voice activity detector, SRP-PHAT, optimal beamformer.

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Authors: Minjeong Kim, Seungchul Lee, Iman Janghorban Esfahani, Jeong Tai Kim, Chang Kyoo Yoo

Abstract:

This study was carried out for an underground subway station at Seoul Metro, Korea. The optimal set-points of the ventilation control system are determined every 3 hours, then, the ventilation controller adjusts the ventilation fan speed according to the optimal set-point changes. Compared to manual ventilation system which is operated irrespective of the OAQ, the IDP-based ventilation control system saves 3.7% of the energy consumption. Compared to the fixed set-point controller which is operated irrespective of the IAQ diurnal variation, the IDP-based controller shows better performance with a 2% decrease in energy consumption, maintaining the comfortable IAQ range inside the station.

Keywords: Indoor air quality, iterative dynamic algorithm, outdoor air information, ventilation control system.

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Authors: Tawiwat V., Phermsak S., Noppasit C.

Abstract:

This paper deals with under actuator dynamic systems such as spring-mass-damper system when the number of control variable is less than the number of state variable. In order to apply optimal control, the controllability must be checked. There are many objective functions to be selected as the goal of the optimal control such as minimum energy, maximum energy and minimum jerk. As the objective function is the first priority, if one like to have the second goal to be applied; however, it could not fit in the objective function format and also avoiding the vector cost for the objective, this paper will illustrate the problem of under actuator dynamic systems with the easiest to deal with comparing between minimum energy and minimum jerk.

Keywords: Under actuator, Dynamic optimal control, Minimumjerk, Minimum energy.

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Authors: M. Wendeker, K. Siadkowska, P. Magryta, Z. Czyz, K. Skiba

Abstract:

In the paper environmental impact analysis the optimal Diesel engine for a light helicopter was performed. The paper consist an answer to the question of what the optimal Diesel engine for a light helicopter is, taking into consideration its expected performance and design capacity. The use of turbocharged engine with self-ignition and an electronic control system can substantially reduce the negative impact on the environment by decreasing toxic substance emission, fuel consumption and therefore carbon dioxide emission. In order to establish the environmental benefits of the diesel engine technologies, mathematical models were created, providing additional insight on the environmental impact and performance of a classic turboshaft and an advanced diesel engine light helicopter, incorporating technology developments.

Keywords: Diesel engine, helicopter, simulation, environmental impact.

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Authors: M. Padmavathi, R. M. Suresh

Abstract:

Every machine plays roles of client and server simultaneously in a peer-to-peer (P2P) network. Though a P2P network has many advantages over traditional client-server models regarding efficiency and fault-tolerance, it also faces additional security threats. Users/IT administrators should be aware of risks from malicious code propagation, downloaded content legality, and P2P software’s vulnerabilities. Security and preventative measures are a must to protect networks from potential sensitive information leakage and security breaches. Bit Torrent is a popular and scalable P2P file distribution mechanism which successfully distributes large files quickly and efficiently without problems for origin server. Bit Torrent achieved excellent upload utilization according to measurement studies, but it also raised many questions as regards utilization in settings, than those measuring, fairness, and Bit Torrent’s mechanisms choice. This work proposed a block selection technique using Fuzzy ACO with optimal rules selected using ACO.

Keywords: Ant Colony Optimization (ACO), Bit Torrent, Download time, Peer-to-Peer (P2P) network, Performance.

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Authors: C. Bruni, F. Delli Priscoli, G. Koch, I. Marchetti

Abstract:

The Connection Admission Control (CAC) problem is formulated in this paper as a discrete time optimal control problem. The control variables account for the acceptance/ rejection of new connections and forced dropping of in-progress connections. These variables are constrained to meet suitable conditions which account for the QoS requirements (Link Availability, Blocking Probability, Dropping Probability). The performance index evaluates the total throughput. At each discrete time, the problem is solved as an integer-valued linear programming one. The proposed procedure was successfully tested against suitably simulated data.

Keywords: Connection Admission Control, Optimal Control, Integer valued Linear Programming, Quality of Service Requirements, Robust Control.

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Authors: H. Kazemi Karegar, S. Jalilzadeh, V. Nabaei, A. Shabani

Abstract:

In this paper, the problem of finding the optimal topological configuration of a deregulated distribution network is considered. The new features of this paper are proposing a multiobjective function and its application on deregulated distribution networks for finding the optimal configuration. The multi-objective function will be defined for minimizing total Energy Supply Costs (ESC) and energy losses subject to load flow constraints. The optimal configuration will be obtained by using Binary Genetic Algorithm (BGA).The proposed method has been tested to analyze a sample and a practical distribution networks.

Keywords: Binary Genetic Algorithm, Deregulated Distribution Network, Minimizing Cost, Reconfiguration.

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Authors: Yuri Boiko, Iluju Kiringa, Tet Yeap

Abstract:

Current drainage attack suggested previously is further studied in regular settings of closed-loop controlled Brushless DC (BLDC) motor with Kalman filter in the feedback loop. Modeling and simulation experiments are conducted in a MATLAB environment, implementing the closed-loop control model of BLDC motor operation in position sensorless mode under Kalman filter drive. The current increase in the motor windings is caused by the controller (p-controller in our case) affected by false data injection of substitution of the angular velocity estimates with distorted values. Operation of multiplication to distortion coefficient, values of which are taken from the distortion function synchronized in its periodicity with the rotor’s position change. A saw function with a triangular tooth shape is studied herewith for the purpose of carrying out the bias injection with current drainage consequences. The specific focus here is on how the asymmetry of the tooth in the saw function affects the flow of current drainage. The purpose is two-fold: (i) to produce and collect the signature of an asymmetric saw in the attack for further pattern recognition process, and (ii) to determine conditions of improving stealthiness of such attack via regulating asymmetry in saw function used. It is found that modification of the symmetry in the saw tooth affects the periodicity of current drainage modulation. Specifically, the modulation frequency of the drained current for a fully asymmetric tooth shape coincides with the saw function modulation frequency itself. Increasing the symmetry parameter for the triangle tooth shape leads to an increase in the modulation frequency for the drained current. Moreover, such frequency reaches the switching frequency of the motor windings for fully symmetric triangular shapes, thus becoming undetectable and improving the stealthiness of the attack. Therefore, the collected signatures of the attack can serve for attack parameter identification via the pattern recognition route.

Keywords: Bias injection attack, Kalman filter, BLDC motor, control system, closed loop, P-controller, PID-controller, current drainage, saw-function, asymmetry.

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Authors: Naveed Ahmed, Gunar Matthies

Abstract:

We deal with the numerical solution of time-dependent convection-diffusion-reaction equations. We combine the local projection stabilization method for the space discretization with two different time discretization schemes: the continuous Galerkin-Petrov (cGP) method and the discontinuous Galerkin (dG) method of polynomial of degree k. We establish the optimal error estimates and present numerical results which shows that the cGP(k) and dG(k)- methods are accurate of order k +1, respectively, in the whole time interval. Moreover, the cGP(k)-method is superconvergent of order 2k and dG(k)-method is of order 2k +1 at the discrete time points. Furthermore, the dependence of the results on the choice of the stabilization parameter are discussed and compared.

Keywords: Convection-diffusion-reaction equations, stabilized finite elements, discontinuous Galerkin, continuous Galerkin-Petrov.

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Authors: C. C. Lv, Y. L. Sun, D. W. Zuo

Abstract:

Cemented carbide balls are usually implemented in industry under the environment of high speed, high temperature, corrosiveness and strong collisions. However, its application is limited due to high fabrication cost, processing efficiency and quality. A novel eccentric lapping method with two rotatable lapping plates was proposed in this paper. A mathematical model was constructed to analyze the influence of each design parameter on this lapping method. To validate this new lapping method, an orthogonal experiment was conducted with cemented carbide balls (YG6). The simulation model was verified and the optimal lapping parameters were derived. The results show that the surface roundness of the balls reaches to 0.65um from 2um in 1 hour using this lapping method. So, using this novel lapping method, it can effectively improve the machining precision and efficiency of cemented carbide balls.

Keywords: Cemented carbide balls, eccentric lapping, high precision, lapping tracks, V-groove.

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Authors: Imen Dhaou

Abstract:

This study examines conditional Value at Risk by applying the GJR-EVT-Copula model, and finds the optimal portfolio for eight Dow Jones Islamic-conventional pairs. Our methodology consists of modeling the data by a bivariate GJR-GARCH model in which we extract the filtered residuals and then apply the Peak over threshold model (POT) to fit the residual tails in order to model marginal distributions. After that, we use pair-copula to find the optimal portfolio risk dependence structure. Finally, with Monte Carlo simulations, we estimate the Value at Risk (VaR) and the conditional Value at Risk (CVaR). The empirical results show the VaR and CVaR values for an equally weighted portfolio of Dow Jones Islamic-conventional pairs. In sum, we found that the optimal investment focuses on Islamic-conventional US Market index pairs because of high investment proportion; however, all other index pairs have low investment proportion. These results deliver some real repercussions for portfolio managers and policymakers concerning to optimal asset allocations, portfolio risk management and the diversification advantages of these markets.

Keywords: CVaR, Dow Jones Islamic index, GJR-GARCH-EVT-pair copula, portfolio optimization.

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Authors: M. A. Masnadi-Shirazi, S. A. Banani

Abstract:

In this paper a comprehensive algorithm is presented to alleviate the undesired simultaneous effects of target maneuvering, observed glint noise distribution, and colored noise spectrum using online colored glint noise parameter estimation. The simulation results illustrate a significant reduction in the root mean square error (RMSE) produced by the proposed algorithm compared to the algorithms that do not compensate all the above effects simultaneously.

Keywords: Glint noise, IMM, Kalman Filter, Kinematics, Target Tracking.

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Authors: Vitoldas Vaitkevičius, Evaldas Šerelis

Abstract:

Silica fume, also known as microsilica (MS) or  condensed silica fume is a by-product of the production of silicon  metal or ferrosilicon alloys. Silica fume is one of the most effective  pozzolanic additives which could be used for ultrahigh performance  and other types of concrete. Despite the fact, however is not entirely  clear, which amount of silica fume is most optimal for UHPC. Main  objective of this experiment was to find optimal amount of silica  fume for UHPC with and without thermal treatment, when different  amount of quartz powder is substituted by silica fume. In this work  were investigated four different composition of UHPC with different  amount of silica fume. Silica fume were added 0, 10, 15 and 20% of  cement (by weight) to UHPC mixture. Optimal amount of silica fume  was determined by slump, viscosity, qualitative and quantitative  XRD analysis and compression strength tests methods.

Keywords: Compressive strength, silica fume, ultrahigh performance concrete, XRD.

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Authors: Yung-Yuan Hsu

Abstract:

The primary objective of this paper was to construct a “kinematic parameter-independent modeling of three-axis machine tools for geometric error measurement" technique. Improving the accuracy of the geometric error for three-axis machine tools is one of the machine tools- core techniques. This paper first applied the traditional method of HTM to deduce the geometric error model for three-axis machine tools. This geometric error model was related to the three-axis kinematic parameters where the overall errors was relative to the machine reference coordinate system. Given that the measurement of the linear axis in this model should be on the ideal motion axis, there were practical difficulties. Through a measurement method consolidating translational errors and rotational errors in the geometric error model, we simplified the three-axis geometric error model to a kinematic parameter-independent model. Finally, based on the new measurement method corresponding to this error model, we established a truly practical and more accurate error measuring technique for three-axis machine tools.

Keywords: Three-axis machine tool, Geometric error, HTM, Error measuring

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Authors: Sangeeta Mandal, Rajib Kar, Durbadal Mandal, Sakti Prasad Ghoshal

Abstract:

In this paper, an optimal design of linear phase digital high pass finite impulse response (FIR) filter using Particle Swarm Optimization with Constriction Factor and Inertia Weight Approach (PSO-CFIWA) has been presented. In the design process, the filter length, pass band and stop band frequencies, feasible pass band and stop band ripple sizes are specified. FIR filter design is a multi-modal optimization problem. The conventional gradient based optimization techniques are not efficient for digital filter design. Given the filter specifications to be realized, the PSO-CFIWA algorithm generates a set of optimal filter coefficients and tries to meet the ideal frequency response characteristic. In this paper, for the given problem, the designs of the optimal FIR high pass filters of different orders have been performed. The simulation results have been compared to those obtained by the well accepted algorithms such as Parks and McClellan algorithm (PM), genetic algorithm (GA). The results justify that the proposed optimal filter design approach using PSOCFIWA outperforms PM and GA, not only in the accuracy of the designed filter but also in the convergence speed and solution quality.

Keywords: FIR Filter; PSO-CFIWA; PSO; Parks and McClellanAlgorithm, Evolutionary Optimization Technique; MagnitudeResponse; Convergence; High Pass Filter

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Authors: Weifeng Wang, Guoqing Huang, Xianwei Zeng

Abstract:

The nearly 21-year-old Jiujiang Bridge, which is suffering from uneven line shape, constant great downwarping of the main beam and cracking of the box girder, needs reinforcement and cable adjustment. It has undergone cable adjustment for twice with incomplete data. Therefore, the initial internal force state of the Jiujiang Bridge is identified as the key for the cable adjustment project. Based on parameter identification by means of static force test data, this paper suggests determining the initial internal force state of the cable-stayed bridge according to the cable force-displacement relationship parameter identification method. That is, upon measuring the displacement and the change in cable forces for twice, one can identify the parameters concerned by means of optimization. This method is applied to the cable adjustment, replacement and reinforcement project for the Jiujiang Bridge as a guidance for the cable adjustment and reinforcement project of the bridge.

Keywords: Cable-stayed bridge, cable force-displacement, parameter identification, internal force state

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Authors: Vu Ngoc Pi

Abstract:

This paper presents a new study on the applications of optimization and regression analysis techniques for optimal calculation of partial ratios of four-step helical gearboxes for getting minimal gearbox length. In the paper, basing on the moment equilibrium condition of a mechanic system including four gear units and their regular resistance condition, models for determination of the partial ratios of the gearboxes are proposed. In particular, explicit models for calculation of the partial ratios are proposed by using regression analysis. Using these models, the determination of the partial ratios is accurate and simple.

Keywords: Gearbox design; optimal design; helical gearbox, transmission ratio.

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Authors: Xiaobai Li, Li Li, Yujin Hu, Weiming Deng, Zhe Ding

Abstract:

A size-dependent Euler–Bernoulli beam model, which accounts for nonlocal stress field, strain gradient field and higher order inertia force field, is derived based on the nonlocal strain gradient theory considering velocity gradient effect. The governing equations and boundary conditions are derived both in dimensional and dimensionless form by employed the Hamilton principle. The analytical solutions based on different continuum theories are compared. The effect of higher order inertia terms is extremely significant in high frequency range. It is found that there exists an asymptotic frequency for the proposed beam model, while for the nonlocal strain gradient theory the solutions diverge. The effect of strain gradient field in thickness direction is significant in low frequencies domain and it cannot be neglected when the material strain length scale parameter is considerable with beam thickness. The influence of each of three size effect parameters on the natural frequencies are investigated. The natural frequencies increase with the increasing material strain gradient length scale parameter or decreasing velocity gradient length scale parameter and nonlocal parameter.

Keywords: Euler-Bernoulli Beams, free vibration, higher order inertia, nonlocal strain gradient theory, velocity gradient.

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Authors: Ladan Maijama’a, Jibril D. Jiya, Ejike C. Anene

Abstract:

This paper presents Differential Evolution Algorithm (DEA) based Variable Structure Position Control (VSPC) of Laboratory DC servomotor (LDCSM). DEA is employed for the optimal tuning of Variable Structure Control (VSC) parameters for position control of a DC servomotor. The VSC combines the techniques of Sliding Mode Control (SMC) that gives the advantages of small overshoot, improved step response characteristics, faster dynamic response and adaptability to plant parameter variations, suppressed influences of disturbances and uncertainties in system behavior. The results of the simulation responses of the VSC parameters adjustment by DEA were performed in Matlab Version 2010a platform and yield better dynamic performance compared with the untuned VSC designed.

Keywords: Differential evolution algorithm, laboratory DC servomotor, sliding mode control, variable structure control.

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Authors: Maria Kalinina, Aron Larsson, Leif Olsson

Abstract:

In the multi objective optimization, in the case when generated set of Pareto optimal solutions is large, occurs the problem to select of the best solution from this set. In this paper, is suggested a method to order of Pareto set. Ordering the Pareto optimal set carried out in conformity with the introduced distance function between each solution and selected reference point, where the reference point may be adjusted to represent the preferences of a decision making agent. Preference information about objective weights from a decision maker may be expressed imprecisely. The developed elicitation procedure provides an opportunity to obtain surrogate numerical weights for the objectives, and thus, to manage impreciseness of preference. The proposed method is a scalable to many objectives and can be used independently or as complementary to the various visualization techniques in the multidimensional case.

Keywords: Imprecise weights, Multiple objectives, Pareto optimality, Visualization.

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Authors: R. Srinivasa Rao

Abstract:

This paper presents a new and efficient approach for capacitor placement in radial distribution systems that determine the optimal locations and size of capacitor with an objective of improving the voltage profile and reduction of power loss. The solution methodology has two parts: in part one the loss sensitivity factors are used to select the candidate locations for the capacitor placement and in part two a new algorithm that employs Plant growth Simulation Algorithm (PGSA) is used to estimate the optimal size of capacitors at the optimal buses determined in part one. The main advantage of the proposed method is that it does not require any external control parameters. The other advantage is that it handles the objective function and the constraints separately, avoiding the trouble to determine the barrier factors. The proposed method is applied to 9 and 34 bus radial distribution systems. The solutions obtained by the proposed method are compared with other methods. The proposed method has outperformed the other methods in terms of the quality of solution.

Keywords: Distribution systems, Capacitor allocation, Loss reduction, Fuzzy, PGSA.

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Authors: Jong Woo Kim, Go Bong Choi, Sang Hwan Son, Dae Shik Kim, Jung Chul Suh, Jong Min Lee

Abstract:

The Markov decision process (MDP) based methodology is implemented in order to establish the optimal schedule which minimizes the cost. Formulation of MDP problem is presented using the information about the current state of pipe, improvement cost, failure cost and pipe deterioration model. The objective function and detailed algorithm of dynamic programming (DP) are modified due to the difficulty of implementing the conventional DP approaches. The optimal schedule derived from suggested model is compared to several policies via Monte Carlo simulation. Validity of the solution and improvement in computational time are proved.

Keywords: Markov decision processes, Dynamic Programming, Monte Carlo simulation, Periodic replacement, Weibull distribution.

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Authors: Leila Jafari, Viliam Makis

Abstract:

In this paper, the joint optimization of the economic manufacturing quantity (EMQ), safety stock level, and condition-based maintenance (CBM) is presented for a partially observable, deteriorating system subject to random failure. The demand is stochastic and it is described by a Poisson process. The stochastic model is developed and the optimization problem is formulated in the semi-Markov decision process framework. A modification of the policy iteration algorithm is developed to find the optimal policy. A numerical example is presented to compare the optimal policy with the policy considering zero safety stock.

Keywords: Condition-based maintenance, economic manufacturing quantity, safety stock, stochastic demand.

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Authors: R. Srinivasa Rao, S. V. L. Narasimham

Abstract:

This paper presents a new and efficient approach for capacitor placement in radial distribution systems that determine the optimal locations and size of capacitor with an objective of improving the voltage profile and reduction of power loss. The solution methodology has two parts: in part one the loss sensitivity factors are used to select the candidate locations for the capacitor placement and in part two a new algorithm that employs Plant growth Simulation Algorithm (PGSA) is used to estimate the optimal size of capacitors at the optimal buses determined in part one. The main advantage of the proposed method is that it does not require any external control parameters. The other advantage is that it handles the objective function and the constraints separately, avoiding the trouble to determine the barrier factors. The proposed method is applied to 9, 34, and 85-bus radial distribution systems. The solutions obtained by the proposed method are compared with other methods. The proposed method has outperformed the other methods in terms of the quality of solution.

Keywords: Distribution systems, Capacitor placement, loss reduction, Loss sensitivity factors, PGSA.

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Authors: V. Amosov, Yu. Kashchuk, A. Krasilnikov, A. Kostin, A. Khovanskiy, A. Leonov, N. Rodionov, R. Rodionov

Abstract:

In present work the problem of the ITER fusion plasma neutron source parameter reconstruction using only the Vertical Neutron Camera data was solved. The possibility of neutron source parameter reconstruction was estimated by the numerical simulations and the analysis of adequateness of mathematic model was performed. The neutron source was specified in a parametric form. The numerical analysis of solution stability with respect to data distortion was done. The influence of the data errors on the reconstructed parameters is shown: • is reconstructed with errors less than 4% at all examined values of δ (until 60%); • is determined with errors less than 10% when δ do not overcome 5%; • is reconstructed with relative error more than 10 %; • integral intensity of the neutron source is determined with error 10% while δ error is less than 15%; where -error of signal measurements, (R0,Z0), the plasma center position,- /parameter of neutron source profile.

Keywords: ITER, neutronsource, neutron source profile reconstruction, Vertical Neutron Camera.

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Authors: M. G. C. A. Cimino, G. Frosini, B. Lazzerini, F. Marcelloni

Abstract:

In the last decades, a number of robust fuzzy clustering algorithms have been proposed to partition data sets affected by noise and outliers. Robust fuzzy C-means (robust-FCM) is certainly one of the most known among these algorithms. In robust-FCM, noise is modeled as a separate cluster and is characterized by a prototype that has a constant distance δ from all data points. Distance δ determines the boundary of the noise cluster and therefore is a critical parameter of the algorithm. Though some approaches have been proposed to automatically determine the most suitable δ for the specific application, up to today an efficient and fully satisfactory solution does not exist. The aim of this paper is to propose a novel method to compute the optimal δ based on the analysis of the distribution of the percentage of objects assigned to the noise cluster in repeated executions of the robust-FCM with decreasing values of δ . The extremely encouraging results obtained on some data sets found in the literature are shown and discussed.

Keywords: noise prototype, robust fuzzy clustering, robustfuzzy C-means

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Authors: Hyoup-Sang Yoon

Abstract:

Video-on-demand (VOD) is designed by using content delivery networks (CDN) to minimize the overall operational cost and to maximize scalability. Estimation of the viewing pattern (i.e., the relationship between the number of viewings and the ranking of VOD contents) plays an important role in minimizing the total operational cost and maximizing the performance of the VOD systems. In this paper, we have analyzed a large body of commercial VOD viewing data and found that the viewing rank distribution fits well with the parabolic fractal distribution. The weighted linear model fitting function is used to estimate the parameters (coefficients) of the parabolic fractal distribution. This paper presents an analytical basis for designing an optimal hierarchical VOD contents distribution system in terms of its cost and performance.

Keywords: VOD, CDN, parabolic fractal distribution, viewing rank, weighted linear model fitting

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Authors: Anatoli Torokhti, Phil Howlett

Abstract:

We present a theory for optimal filtering of infinite sets of random signals. There are several new distinctive features of the proposed approach. First, we provide a single optimal filter for processing any signal from a given infinite signal set. Second, the filter is presented in the special form of a sum with p terms where each term is represented as a combination of three operations. Each operation is a special stage of the filtering aimed at facilitating the associated numerical work. Third, an iterative scheme is implemented into the filter structure to provide an improvement in the filter performance at each step of the scheme. The final step of the concerns signal compression and decompression. This step is based on the solution of a new rank-constrained matrix approximation problem. The solution to the matrix problem is described in this paper. A rigorous error analysis is given for the new filter.

Keywords: stochastic signals, optimization problems in signal processing.

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Authors: Yilun Shang

Abstract:

We study a long-range percolation model in the hierarchical lattice ΩN of order N where probability of connection between two nodes separated by distance k is of the form min{αβ−k, 1}, α ≥ 0 and β > 0. The parameter α is the percolation parameter, while β describes the long-range nature of the model. The ΩN is an example of so called ultrametric space, which has remarkable qualitative difference between Euclidean-type lattices. In this paper, we characterize the sizes of large clusters for this model along the line of some prior work. The proof involves a stationary embedding of ΩN into Z. The phase diagram of this long-range percolation is well understood.

Keywords: percolation, component, hierarchical lattice, phase transition.

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Authors: Anatoli Torokhti, Phil Howlett

Abstract:

A theory for optimal filtering of infinite sets of random signals is presented. There are several new distinctive features of the proposed approach. First, a single optimal filter for processing any signal from a given infinite signal set is provided. Second, the filter is presented in the special form of a sum with p terms where each term is represented as a combination of three operations. Each operation is a special stage of the filtering aimed at facilitating the associated numerical work. Third, an iterative scheme is implemented into the filter structure to provide an improvement in the filter performance at each step of the scheme. The final step of the scheme concerns signal compression and decompression. This step is based on the solution of a new rank-constrained matrix approximation problem. The solution to the matrix problem is described in this paper. A rigorous error analysis is given for the new filter.

Keywords: Optimal filtering, data compression, stochastic signals.

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