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    Wyświetlanie 1-13 z 13
    Tytuł:
    Regular design equations for the continuous reduced-order Kalman filter
    Autorzy:
    Hippe, P.
    Powiązania:
    https://bibliotekanauki.pl/articles/229993.pdf
    Data publikacji:
    2011
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    optimal estimation
    polynomials
    multivariable systems
    continuous-time systems
    Opis:
    Reduced-order Kalman filters yield an optimal state estimate for linear dynamical systems, where parts of the output are not corrupted by noise. The design of such filters can either be carried out in the time domain or in the frequency domain. Different from the full-order case where all measurements are noisy, the design equations of the reduced-order filter are not regular. This is due to the rank deficient measurement covariance matrix and it can cause problems when using standard software for the solution of the Riccati equations in the time domain. In the frequency domain the spectral factorization of the non-regular polynomial matrix equation does not cause problems. However, the known proof of optimality of the factorization result also requires a regular measurement covariance matrix. This paper presents regular (reduced-order) design equations for reduced-order Kalman filters in the time and in the frequency domains for linear continuous-time systems. They allow to use standard software for the design of the filter, to formulate the conditions for the stability of the filter and they also prove that the existing frequency domain solutions obtained by spectral factorization of a non-regular polynomial matrix equation are indeed optimal.
    Źródło:
    Archives of Control Sciences; 2011, 21, 4; 349-361
    1230-2384
    Pojawia się w:
    Archives of Control Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Regular design equations for the discrete reduced-order Kalman filter
    Autorzy:
    Hippe, P.
    Powiązania:
    https://bibliotekanauki.pl/articles/229814.pdf
    Data publikacji:
    2012
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    optimal estimation
    polynomials
    multivariable systems
    discrete-time systems
    Opis:
    In the presence of white Gaussian noises at the input and the output of a system Kalman filters provide a minimum-variance state estimate. When part of the measurements can be regarded as noise-free, the order of the filter is reduced. The filter design can be carried out both in the time domain and in the frequency domain. In the case of full-order filters all measurements are corrupted by noise and therefore the design equations are regular. In the presence of noise-free measurements, however, they are not regular so that standard software cannot readily be applied in a time-domain design. In the frequency domain the spectral factorization of the non-regular polynomial matrix equation causes no problems. However, the known proof of optimality of the factorization result requires a regular measurement covariance matrix. This paper presents regular (reduced-order) design equations for the reduced-order discrete-time Kalman filter in the time and in the frequency domains so that standard software is applicable. They also allow to formulate the conditions for the stability of the filter and to prove the optimality of the existing solutions.
    Źródło:
    Archives of Control Sciences; 2012, 22, 2; 161-174
    1230-2384
    Pojawia się w:
    Archives of Control Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Optimal state observation using quadratic boundedness: Application to UAV disturbance estimation
    Autorzy:
    Cayero, Julián
    Rotondo, Damiano
    Morcego, Bernardo
    Puig, Vicenç
    Powiązania:
    https://bibliotekanauki.pl/articles/330391.pdf
    Data publikacji:
    2019
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    disturbance estimation
    unmanned aerial vehicle
    optimal estimation
    optimal filtering
    system modelling
    statek powietrzny bezzałogowy
    oszacowanie optymalne
    modelowanie systemowe
    Opis:
    This paper presents the design of a state observer which guarantees quadratic boundedness of the estimation error. By using quadratic Lyapunov stability analysis, the convergence rate and the ultimate (steady-state) error bounding ellipsoid are identified as the parameters that define the behaviour of the estimation. Then, it is shown that these objectives can be merged in a scalarised objective function with one design parameter, making the design problem convex. In the second part of the article, a UAV model is presented which can be made linear by considering a particular state and frame of reference. The UAV model is extended to incorporate a disturbance model of variable size. The joint model matches the structure required to derive an observer, following the lines of the proposed design approach. An observer for disturbances acting on the UAV is derived and the analysis of the performances with respect to the design parameters is presented. The effectiveness and main characteristics of the proposed approach are shown using simulation results.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2019, 29, 1; 99-109
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Influence of Drift on Efficiency of Optimal Analog Adaptive Communication Systems with Feedback and Its Compensation
    Autorzy:
    Jędrzejewski, K.
    Powiązania:
    https://bibliotekanauki.pl/articles/227312.pdf
    Data publikacji:
    2013
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    communication systems
    feedback
    drift compensation
    optimal adaptive estimation
    Opis:
    Results of analysis of drift influence on operation and efficiency of optimal analog adaptive communication systems with feedback and a new approach to drift compensation in these systems are presented in the paper. The proposed approach is based on application of the extended multidimensional adaptive algorithm that estimates simultaneously the value of a transmitted sample and the value of an unknown drift rate. The knowledge of the drift rate enables drift compensation and improves transmission efficiency of systems suffering problems related to drifts.
    Źródło:
    International Journal of Electronics and Telecommunications; 2013, 59, 1; 51-58
    2300-1933
    Pojawia się w:
    International Journal of Electronics and Telecommunications
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Fixed precision estimation of the maximal value of a bounded random variable
    Autorzy:
    Sierociński, Andrzej
    Powiązania:
    https://bibliotekanauki.pl/articles/748352.pdf
    Data publikacji:
    1986
    Wydawca:
    Polskie Towarzystwo Matematyczne
    Tematy:
    Sequential estimation
    Optimal stopping
    Opis:
    .
    The object of this paper is to survey the methods of fixed precision estimation of the maximal value of a bounded random variable. In particular the paper gives solutions to this problem for a class of distributions with unknown scale parameter (section 2) and for a class of distributions with certain features of symmetry (section 3). The sequential procedures solving both subproblems are not only asymptotically consistent and asympto-tically efficient in the sense of Chow and Robbins (like that presented in section 4), but they assure the exact consistency. Moreover, in section 5, the case of the uniform distribution and the problem of finding the optimal stopping rule in this case are discussed in detail.
    Źródło:
    Mathematica Applicanda; 1986, 14, 27
    1730-2668
    2299-4009
    Pojawia się w:
    Mathematica Applicanda
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Comparison at optimal levels of classical tail index estimators: a challenge for reduced-bias estimation?
    Autorzy:
    Gomes, M.
    Henriques-Rodrigues, Lígia
    Powiązania:
    https://bibliotekanauki.pl/articles/729988.pdf
    Data publikacji:
    2010
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    statistics of extremes
    semi-parametric estimation
    bias estimation
    heavy tails
    optimal levels
    Opis:
    In this article, we begin with an asymptotic comparison at optimal levels of the so-called "maximum likelihood" (ML) extreme value index estimator, based on the excesses over a high random threshold, denoted PORT-ML, with PORT standing for peaks over random thresholds, with a similar ML estimator, denoted PORT-MP, with MP standing for modified-Pareto. The PORT-MP estimator is based on the same excesses, but with a trial of accommodation of bias on the Generalized Pareto model underlying those excesses. We next compare the behaviour of these ML implicit estimators with the equivalent behaviour of a few explicit tail index estimators, the Hill, the moment, the generalized Hill and the mixed moment. As expected, none of the estimators can always dominate the alternatives, even when we include second-order MVRB tail index estimators, with MVRB standing for minimum-variance reduced-bias. However, the asymptotic performance of the MVRB estimators is quite interesting and provides a challenge for a further study of these MVRB estimators at optimal levels.
    Źródło:
    Discussiones Mathematicae Probability and Statistics; 2010, 30, 1; 35-51
    1509-9423
    Pojawia się w:
    Discussiones Mathematicae Probability and Statistics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    State estimation of linear dynamic system with unknown input and uncertain observation using dynamic programming
    Autorzy:
    Janczak, D.
    Grishin, Y.
    Powiązania:
    https://bibliotekanauki.pl/articles/970019.pdf
    Data publikacji:
    2006
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    sterowanie optymalne
    state estimation
    optimal control
    Bellman principle
    Opis:
    The paper is devoted to deriving a novel estimation algorithm for linear dynamic system with unknown inputs when observations contain outliers. The algorithm is derived for arbitrary input signals and does not require a priori statistical information concerning input signals. The filtering problem is considered as a control problem in which the unknown input is regarded as a controlling signal for system dynamics, which is described by Kalman equations. In this case, optimal control using Bellman dynamic programming can be calculated. The problem is complicated by the presence of outliers in the observations. To cope with this problem the Lainiotis' partitioning theorem has been used. The nonlinear algorithm of state estimation is obtained. Presented approach can be used both in control systems and decision procedures in tracking systems.
    Źródło:
    Control and Cybernetics; 2006, 35, 4; 851-862
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Confidence interval with specified precision for the mean value in a sequence of Gaussian variables
    Autorzy:
    Gołdys, Beniamin
    Powiązania:
    https://bibliotekanauki.pl/articles/747956.pdf
    Data publikacji:
    1982
    Wydawca:
    Polskie Towarzystwo Matematyczne
    Tematy:
    Optimal stopping,Tolerance and confidence regions,Non-Markovian processes: estimation
    Opis:
    .
    Consider the class C of real-valued stochastic processes of the form Xt=m+mt+ξt, with discrete t=1,2,⋯, such that mt→0 and the ξt are random variables with normal distributions N(0,σt), where σt→0. Required is a sequence of estimators m^t for the parameter m, determined by X1,⋯,Xt and a stopping rule τ, such that for every ε>0 and 0
    Źródło:
    Mathematica Applicanda; 1982, 10, 18
    1730-2668
    2299-4009
    Pojawia się w:
    Mathematica Applicanda
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Query-condition-aware V-optimal histogram in range query selectivity estimation
    Autorzy:
    Augustyn, D. R.
    Powiązania:
    https://bibliotekanauki.pl/articles/200079.pdf
    Data publikacji:
    2014
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    query selectivity estimation
    attribute values distribution
    Query-Condition-Aware V-optimal histogram
    Opis:
    Obtaining the optimal query execution plan requires a selectivity estimation. The selectivity value allows to predict the size of a query result. This lets choose the best method of query execution. There are many selectivity obtaining methods that are based on different types of estimators of attribute values distribution (commonly they are based on histograms). The adaptive method, proposed in this paper, uses either attribute values distribution or range query condition boundaries one. The new type of histogram - the Query-Conditional-Aware V-optimal one (QCA-V-optimal) - is proposed as a non-parametric estimator of a probability density function of attribute values distribution. This histogram also takes into account information about already processed queries. This information is represented by the 1-dimensional Query Condition Distribution histogram (HQCD) which is an estimator of the include function PI which is also introduced in this paper. PI describes so-called regions of user interest, i.e. it shows how often regions of attribute values domain were used by processed queries. Advantages of the proposed method based on QCA-V-optimal are presented. Conducted experiments reveal small values of a mean relative selectivity estimation error comparing to the error values obtained by methods based on the relevant classical V-optimal histogram and Equi-height one.
    Źródło:
    Bulletin of the Polish Academy of Sciences. Technical Sciences; 2014, 62, 2; 287-303
    0239-7528
    Pojawia się w:
    Bulletin of the Polish Academy of Sciences. Technical Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Sensor network design for the estimation of spatially distributed processes
    Autorzy:
    Uciński, D.
    Patan, M.
    Powiązania:
    https://bibliotekanauki.pl/articles/929585.pdf
    Data publikacji:
    2010
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    projekt optymalny
    estymacja parametrów
    sieć sensorowa
    identyfikacja źródłowa
    optimal experiment design
    parameter estimation
    sensor network
    source identification
    Opis:
    In a typical moving contaminating source identification problem, after some type of biological or chemical contamination has occurred, there is a developing cloud of dangerous or toxic material. In order to detect and localize the contamination source, a sensor network can be used. Up to now, however, approaches aiming at guaranteeing a dense region coverage or satisfactory network connectivity have dominated this line of research and abstracted away from the mathematical description of the physical processes underlying the observed phenomena. The present work aims at bridging this gap and meeting the needs created in the context of the source identification problem. We assume that the paths of the moving sources are unknown, but they are sufficiently smooth to be approximated by combinations of given basis functions. This parametrization makes it possible to reduce the source detection and estimation problem to that of parameter identification. In order to estimate the source and medium parameters, the maximum--ikelihood estimator is used. Based on a scalar measure of performance defined on the Fisher information matrix related to the unknown parameters, which is commonly used in optimum experimental design theory, the problem is formulated as an optimal control one. From a practical point of view, it is desirable to have the computations dynamic data driven, i.e., the current measurements from the mobile sensors must serve as a basis for the update of parameter estimates and these, in turn, can be used to correct the sensor movements. In the proposed research, an attempt will also be made at applying a nonlinear model-predictive-control-like approach to attack this issue.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2010, 20, 3; 459-481
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Optimal allocation for equal probability two-stage design
    Autorzy:
    Molefe, Wilford
    Powiązania:
    https://bibliotekanauki.pl/articles/2156993.pdf
    Data publikacji:
    2022-12-15
    Wydawca:
    Główny Urząd Statystyczny
    Tematy:
    sample designs
    optimal allocation
    composite estimation
    mean squared error
    two-stage sampling
    simple random sampling without replacement
    Opis:
    This paper develops optimal designs when it is not feasible for every cluster to be represented in a sample as in stratified design, by assuming equal probability two-stage sampling where clusters are small areas. The paper develops allocation methods for two-stage sample surveys where small-area estimates are a priority. We seek efficient allocations where the aim is to minimize the linear combination of the mean squared errors of composite small area estimators and of an estimator of the overall mean. We suggest some alternative allocations with a view to minimizing the same objective. Several alternatives, including the area-only stratified design, are found to perform nearly as well as the optimal allocation but with better practical properties. Designs are evaluated numerically using Switzerland canton data as well as Botswana administrative districts data.
    Źródło:
    Statistics in Transition new series; 2022, 23, 4; 129-148
    1234-7655
    Pojawia się w:
    Statistics in Transition new series
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    An integrodifferential approach to modeling, control, state estimation and optimization for heat transfer systems
    Autorzy:
    Rauh, A.
    Senkel, L.
    Aschemann, H.
    Saurin, V. V.
    Kostin, G. V.
    Powiązania:
    https://bibliotekanauki.pl/articles/331160.pdf
    Data publikacji:
    2016
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    heat transfer
    predictive control
    optimal control
    state estimation
    disturbance estimation
    distributed parameter systems
    sensitivity analysis
    wymiana ciepła
    regulacja predykcyjna
    układ o parametrach rozłożonych
    analiza wrażliwości
    Opis:
    In this paper, control-oriented modeling approaches are presented for distributed parameter systems. These systems, which are in the focus of this contribution, are assumed to be described by suitable partial differential equations. They arise naturally during the modeling of dynamic heat transfer processes. The presented approaches aim at developing finite-dimensional system descriptions for the design of various open-loop, closed-loop, and optimal control strategies as well as state, disturbance, and parameter estimation techniques. Here, the modeling is based on the method of integrodifferential relations, which can be employed to determine accurate, finite-dimensional sets of state equations by using projection techniques. These lead to a finite element representation of the distributed parameter system. Where applicable, these finite element models are combined with finite volume representations to describe storage variables that are—with good accuracy—homogeneous over sufficiently large space domains. The advantage of this combination is keeping the computational complexity as low as possible. Under these prerequisites, real-time applicable control algorithms are derived and validated via simulation and experiment for a laboratory-scale heat transfer system at the Chair of Mechatronics at the University of Rostock. This benchmark system consists of a metallic rod that is equipped with a finite number of Peltier elements which are used either as distributed control inputs, allowing active cooling and heating, or as spatially distributed disturbance inputs.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2016, 26, 1; 15-30
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On the smoothed parametric estimation of mixing proportion under fixed design regression model
    Autorzy:
    Ramakrishnaiah, Y. S.
    Trivedi, Manish
    Satish, Konda
    Powiązania:
    https://bibliotekanauki.pl/articles/1359251.pdf
    Data publikacji:
    2019-04-25
    Wydawca:
    Główny Urząd Statystyczny
    Tematy:
    mixture of distributions
    mixing proportion
    smoothed parametric estimation
    fixed design regression model
    mean square error
    optimal band width
    strong consistency
    asymptotic normality
    Opis:
    The present paper revisits an estimator proposed by Boes (1966) - James (1978), herein called BJ estimator, which was constructed for estimating mixing proportion in a mixed model based on independent and identically distributed (i.i.d.) random samples, and also proposes a completely new (smoothed) estimator for mixing proportion based on independent and not identically distributed (non-i.i.d.) random samples. The proposed estimator is nonparametric in true sense based on known “kernel function” as described in the introduction. We investigated the following results of the smoothed estimator under the non-i.i.d. set-up such as (a) its small sample behaviour is compared with the unsmoothed version (BJ estimator) based on their mean square errors by using Monte-Carlo simulation, and established the percentage gain in precision of smoothed estimator over its unsmoothed version measured in terms of their mean square error, (b) its large sample properties such as almost surely (a.s.) convergence and asymptotic normality of these estimators are established in the present work. These results are completely new in the literature not only under the case of i.i.d., but also generalises to non-i.i.d. set-up.
    Źródło:
    Statistics in Transition new series; 2019, 20, 1; 87-102
    1234-7655
    Pojawia się w:
    Statistics in Transition new series
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-13 z 13

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