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Search results for: LEAST SQUARES ESTIMATION
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Estimation and Prediction of Vertical Deformations of Random Surfaces, Applying the Total Least Squares Collocation Method
PublicationThis paper proposes a method for determining the vertical deformations treated as random fields. It is assumed that the monitored surfaces are subject not only to deterministic deformations, but also to random fluctuations. Furthermore, the existence of random noise coming from surface’s vibrations is also assumed. Such noise disturbs the deformation’s functional models. Surface monitoring with the use of the geodetic levelling...
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Weighted least squares parameter estimation for model predictive control of integrated wastewater systems at medium time scale.
PublicationW artykule przedstawione zostało sformułowanie i implementacja algorytmu ważonej sumy najmniejszych kwadratów na przesuwnym oknie pomiarowym dla celów estymacji parametrów modelu typu szara skrzynka. Model typu szara skrzynka dynamiki reaktora biologicznego jest wykorzystywany przez moduł sterowania predykcyjnego sterujący zintegrowanym systemem ściekowym w średniej skali czasu. Algorytm estymacji parametrów był walidowany na symulatorze...
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SELECTION OF REFERENCE PLANE BY THE LEAST SQUARES FITTING METHODS
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On noncausal weighted least squares identification of nonstationary stochastic systems
PublicationIn this paper, we consider the problem of noncausal identification of nonstationary, linear stochastic systems, i.e., identification based on prerecorded input/output data. We show how several competing weighted (windowed) least squares parameter smoothers, differing in memory settings, can be combined together to yield a better and more reliable smoothing algorithm. The resulting parallel estimation scheme automatically adjusts...
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Vapor correction of FTIR spectra – A simple automatic least squares approach
PublicationFTIR spectroscopy is one of the best techniques to study intermolecular interactions. However, such an application requires high quality spectra with as little noise as possible, which are often difficult to obtain. One of the main sources of unwanted interference is water vapor. Here a robust method is proposed for automatic, fast and reliable vapor correction of FTIR spectra. The presented least squares approach of vapor subtraction...
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Remarks on the convergence of an iterative method of solution of generalized least squares problem
PublicationW pracy przedstawiona jest metoda iteracyjna znajdowania regularyzowanego (w sensie Tichonowa) rozwiązania układu równań Ax=b z dowolną macierzą A. Dla danej liczby alfa i wektora g daje ona ciąg przybliżeń zbieżny do rozwiązania (w sensie najmniejszych kwadratów) tego układu. Rozwiązanie to minimalizuje odległość zbioru wszystkich rozwiązań średniokwadratowych układu Ax=b od wektora g. Podane zostało również oszacowanie szybkości...
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3D POINT-CLOUD SPATIAL EXPANSION BY TOTAL LEAST-SQUARES LINE FITTING
PublicationPoint-cloud spatial expansion (PCSE) allows the creation of a new pointcloud form that presents an alternative geometry of an entire object in a single spatial view. Spatial expansion facilitates the analysis process and introduces an additional spatial parameter describing the point cloud. An important element of the PCSE method is determining the position of the axis of symmetry of a symmetrical object: the procedure for determining...
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3d point-cloud spatial expansion by total least-squares line fitting
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Power Grid Frequency Estimation Based on Zero Crossing Technique Using Least Squares Method to Approximate Sampled Voltage Signal Around Zero Level
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Use of a Least Squares with Conditional Equations Method in Positioning a Tramway Track in the Gdansk Agglomeration
PublicationSatellite measurement techniques have been used for many years in different types of human activity, including work related to staking out and making use of rail infrastructure. First and foremost, satellite techniques are applied to determine the tramway track course and to analyse the changes of its position during its operation. This paper proposes using the least squares with conditional equations method, known in geodesy (LSce)....
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Use of a Least Squares with Conditional Equations Method in Positioning a Tramway Track in the Gdansk Agglomeration
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Application of the Least Squares Method to the approximation of equally spaced samples in frequency measurement approach
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Application of least squares with conditional equations method for railway track inventory using GNSS observations
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Application of Least Squares with Conditional Equations Method for Railway Track Inventory Using GNSS Observations
PublicationSatellite geodetic networks are commonly used in surveying tasks, but they can also be used in mobile surveys. Mobile satellite surveys can be used for trackage inventory, diagnostics and design. The combination of modern technological solutions with the adaptation of research methods known in other fields of science offers an opportunity to acquire highly accurate solutions for railway track inventory. This article presents the...
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Least Squares Estimators of Peptide Species Concentrations Based on Gaussian Mixture Decompositions of Protein Mass Spectra
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KAMIŃSKI W.: Modelowanie przemieszczeń pionowych mieszaną, ortogonalną metodą najmniejszych kwadratów (Mixed Total Least Squares)
PublicationProblematyka modelowania przemieszczeń pionowych standardową metodą najmniejszych kwadratów i mieszaną ortogonalną metodą najmniejszych kwadratów. Przykłady praktycznych obliczeń na rzeczywistych i symulowanych wynikach obserwacji.
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Prediction of near-bottom water salinity in the Baltic Sea using Ordinary Least Squares and Geographically Weighted Regression models
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Power grid frequency measurement in LabVIEW environment using the least mean squares method to signal phase approximation in the presence of noise
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Interactions between hydration spheres of two different solutes in solution: The least squares fitting with constraints as a tool to determine water properties in ternary systems
PublicationBiological systems are complex and the problem of their description lies in mutual interactions between their components. This paper is focused on model experiment-based studies which can reduce these difficulties. The ternary aqueous N-methylacetamide (NMA)–Na2HPO4 system has been studied by means of the FTIR spectroscopy. A novel difference spectra method aimed to extract the spectral contribution of water affected simultaneously...
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Identification of Unstable Reference Points and Estimation of Displacements Using Squared Msplit Estimation
PublicationThe article presents a new version of the method for estimating parameters in a split functional model, which enables the determination of displacements of geodetic network points with constrained datum. The main aim of the study is to present theoretical foundations of Msplit CD estimation and its basic properties and possible applications. Particular attention was paid to the efficacy of the method in the context of geodetic...
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Parameter and delay estimation of linear continuous-time systems
PublicationIn this paper the problem of on-line identification of non-stationary delay systems is considered. Dynamics of supervised industrial processes is described by ordinary differential equations. Discrete-time mechanization of their continuous-time representations is based on dedicated finite-horizon integrating filters. Least-squares and instrumental variable procedures implemented in recursive forms are applied for simultaneous identification...
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Parameter and delay estimation of linear continuous-time systems
PublicationIn this paper the problem of on-line identification of non-stationary delay systems is considered. Dynamics of supervised industrial processes is usually described by ordinary differential equations. Discrete-time mechanization of their continuous-time representations is based on dedicated finite-horizon integrating filters. Least-squares and instrumental variable procedures implemented in recursive forms are applied for simultaneous...
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A simplified channel estimation procedure for NB-IoT downlink
PublicationThis paper presents a low-complexity channel estimation procedure which is suitable for use in energy-efficient NB-IoT user equipment devices. The procedure is based on the well-established least squares scheme, followed by linear interpolation in the time domain and averaging in the frequency domain. The quality of channel estimation vs. signal-to-noise ratio is evaluated for two channel models and compared with the performance...
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Impact of cross-section centers estimation on the accuracy of the Point cloud spatial expansion using robust M-estimation and Monte Carlo simulation
PublicationThe point cloud spatial expansion (PCSE) method creates an alternative form of representing the shape of symmetrical objects and introduces additional descriptive geometric parameters. An important element of the procedure is determining the course of the axis of symmetry of cylindrical objects based on cross-sections of point clouds. Outliers occurring in laser measurements are of great importance in this case. In this study,...
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On–line Parameter and Delay Estimation of Continuous–Time Dynamic Systems
PublicationThe problem of on-line identification of non-stationary delay systems is considered. The dynamics of supervised industrial processes are usually modeled by ordinary differential equations. Discrete-time mechanizations of continuous-time process models are implemented with the use of dedicated finite-horizon integrating filters. Least-squares and instrumental variable procedures mechanized in recursive forms are applied for simultaneous...
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Smooth least absolute deviation estimators for outlier-proof identification
PublicationThe paper proposes to identify the parameters of linear dynamic models based on the original implementation of least absolute deviation estimators. It is known that the object estimation procedures synthesized in the sense of the least sum of absolute prediction errors are particularly resistant to occasional outliers and gaps in the analyzed system data series, while the classical least squares procedure unfortunately becomes...
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On ''cheap smoothing'' opportunities in identification of time-varying systems
PublicationIn certain applications of nonstationary system identification the model-based decisions can be postponed, i.e. executed with a delay. This allows one to incorporate into the identification process not only the currently available information, but also a number of ''future'' data points. The resulting estimation schemes, which involve smoothing, are not causal. Despite the possible performance improvements, the existing smoothing...
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Iterative‐recursive estimation of parameters of regression models with resistance to outliers on practical examples
PublicationHere, identification of processes and systems in the sense of the least sum of absolute values is taken into consideration. The respective absolute value estimators are recognised as exceptionally insensitive to large measurement faults or other defects in the processed data, whereas the classical least squares procedure appears to be completely impractical for processing the data contaminated with such parasitic distortions. Since...
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Karhunen-Loeve-based approach to tracking of rapidly fading wireless communication channels
PublicationWhen parameters of wireless communication channels vary at a fast rate, simple estimation algorithms, such as weighted least squares (WLS) or least mean squares (LMS) algorithms, cannot estimate them with the accuracy needed to secure the reliable operation of the underlying communication systems. In cases like this, the local basis function (LBF) estimation technique can be used instead, significantly increasing the achievable...
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On joint order and bandwidth selection for identification of nonstationary autoregressive processes
PublicationWhen identifying a nonstationary autoregressive process, e.g. for the purpose of signal prediction or parametric spectrum estimation, two important decisions must be taken. First, one should choose the appropriate order of the autoregressive model, i.e., the number of autoregressive coefficients that will be estimated. Second, if identification is carried out using the local estimation technique, such as the localized version of...
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Identification of nonstationary multivariate autoregressive processes– Comparison of competitive and collaborative strategies for joint selection of estimation bandwidth and model order
PublicationThe problem of identification of multivariate autoregressive processes (systems or signals) with unknown and possibly time-varying model order and time-varying rate of parameter variation is considered and solved using parallel estimation approach. Under this approach, several local estimation algorithms, with different order and bandwidth settings, are run simultaneously and compared based on their predictive performance. First,...
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Optimal and suboptimal algorithms for identification of time-varying systems with randomly drifting parameters
PublicationNoncausal estimation algorithms, which involve smoothing, can be used for off-line identification of nonstationary systems. Since smoothingis based on both past and future data, it offers increased accuracy compared to causal (tracking) estimation schemes, incorporating past data only. It is shown that efficient smoothing variants of the popular exponentially weighted least squares and Kalman filter-based parameter trackers can...
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Marek Zienkiewicz dr inż.
PeopleDoctor engineer Marek Hubert Zienkiewicz is a graduate of the Faculty of Geodesy, Spatial Engineering and Construction at the University of Warmia and Mazury in Olsztyn. During his engineering, master's and doctoral studies he developed his scientific interests under the supervision of representatives of the Olsztyn geodetic compensatory calculus school. In 2011, he obtained the title of Master of Science in Geodesy and Cartography,...
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Identification of models and signals robust to occasional outliers
PublicationIn this paper estimation algorithms derived in the sense of the least sum of absolute errors are considered for the purpose of identification of models and signals. In particular, off-line and approximate on-line estimation schemes discussed in the work are aimed at both assessing the coefficients of discrete-time stationary models and tracking the evolution of time-variant characteristics of monitored signals. What is interesting,...
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Identification of models and signals robust to occasional outliers
PublicationIn this paper estimation algorithms derived in the sense of the least sum of absolute errors are considered for the purpose of identification of models and signals. In particular, off-line and approximate on-line estimation schemes discussed in the work are aimed at both assessing the coefficients of discrete-time stationary models and tracking the evolution of time-variant characteristics of monitored signals. What is interesting,...
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Estimation of DC motor parameters using a simple CMOS camera
PublicationDifferent components of control systems for mobile robots are based on dynamic models. In low-cost solutions such a robot is wheeled and equipped with DC motors, which have to be included in the model of the robot. The model is fairly simple but determination of its parameters needs not to be easy. For instance, DC motor parameters are typically identified indirectly using suitable measurements, concerning engine voltage, current,...
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Estimation of the amplitude of the signal for the active optical gesture sensor with sparse detectors
PublicationIn this paper we deal with the problem of precise gesture recognition for the active optical proximity sensor with sparse 8 photodiodes. We particularly focus on developing the method of estimating the real, usually not observable, maximum signal value representing maximum intensity of light reflected from an obstacle present in the front of the sensor. Different configurations of the fingers were used as an obstacle. The Monte Carlo...
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Identification of Fast Time-varying Communication Channels Using the Preestimation Technique
PublicationAccurate identification of stochastic systems with fast-varying parameters is a challenging task which cannot be accomplished using model-free estimation methods, such as weighted least squares, which assume only that system coefficients can be regarded as locally constant. The current state-of-the-art solutions are based on the assumption that system parameters can be locally approximated by a linear combination of appropriately...
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A Universal Gains Selection Method for Speed Observers of Induction Machine
PublicationProperties of state observers depend on proper gains selection. Each method of state estimation may require the implementation of specific techniques of finding those gains. The aim of this study is to propose a universal method of automatic gains selection and perform its verification on an induction machine speed observer. The method utilizes a genetic algorithm with fitness function which is directly based on the impulse response...
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Modal parameters identification with Particle Swarm Optimization
PublicationThe paper presents method of the modal parameters identification based on the Particle Swarm Optimization (PSO) algorithm [1]. The basic PSO algorithm is modified in order to achieve fast convergence and low estimation error of identified parameters values. The procedure of identification as well as algorithm modifications are presented and some simple examples for the SISO systems are provided. Results are compared with the results...
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Optimally regularized local basis function approach to identification of time-varying systems
PublicationAccurate identification of stochastic systems with fast-varying parameters is a challenging task which cannot be accomplished using model-free estimation methods, such as weighted least squares, which assume only that system coefficients can be regarded as locally constant. The current state of the art solutions are based on the assumption that system parameters can be locally approximated by a linear combination of appropriately...
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On noncausal identification of nonstationary stochastic systems
PublicationIn this paper we consider the problem of noncausal identification of nonstationary,linear stochastic systems, i.e., identification based on prerecorded input/output data. We show how several competing weighted least squares parameter smoothers, differing in memory settings, can be combined together to yield a better and more reliable smoothing algorithm. The resulting parallel estimation scheme automatically adjusts its smoothing...
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Akaike's final prediction error criterion revisited
PublicationWhen local identification of a nonstationary ARX system is carried out, two important decisions must be taken. First, one should decide upon the number of estimated parameters, i.e., on the model order. Second, one should choose the appropriate estimation bandwidth, related to the (effective) number of input-output data samples that will be used for identification/ tracking purposes. Failure to make the right decisions results...
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Assessment of Adjustment of GNSS Railway Measurements with Parameter-Binding Conditions in a Stationary Scenario
PublicationThe study aims to assess the applicability of the ordinary least squares method, robust estimation, and conditions-binded adjustment in processing the six synchronous coordinate pairs of global navigation satellite system (GNSS) receivers. The research is part of the research project InnoSatTrack, focused on the enhancement of the determination of geometrical parameters of railway tracks using GNSS, inertial, and other sensors....
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Determination of API content in a pilot-scale blending by near-infrared spectroscopy as a first step method to process line implementation
PublicationNear infrared (NIR) spectroscopy was used for estimation of powder blend homogeneity and manufacturing control of a medicinal product powder mixture containing active pharmaceutical ingredient (API). Aiming at initiating a Process Analytical Technology (PAT) activity, the first step was a stationary mode atline evaluation. In this, the content of pharmaceutical active compound in the powder mixtures intended to the direct tabletting...
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Resistant to correlated noise and outliers discrete identification of continuous non-linear non-stationary dynamic objects
PublicationIn this article, specific methods of parameter estimation were used to identify the coefficients of continuous models represented by linear and nonlinear differential equations. The necessary discrete-time approximation of the base model is achieved by appropriately tuned FIR linear integral filters. The resulting discrete descriptions, which retain the original continuous parameterization, can then be identified using the classical...
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Resistant to correlated noise and outliers discrete identification of continuous non-linear non-stationary dynamic objects
PublicationIn this study, dedicated methods of parameter estimation were used to identify the coefficients of continuous models represented by linear and nonlinear differential equations. The necessary discrete-time approximation of the base model is achieved by appropriately tuned FIR linear integral filters. The resulting discrete descriptions, which retain the original continuous parameterization, can then be identified using the classical...
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Discrete identification of continuous non-linear and non-stationary dynamical systems that is insensitive to noise correlation and measurement outliers
PublicationThe paper uses specific parameter estimation methods to identify the coefficients of continuous-time models represented by linear and non-linear ordinary differential equations. The necessary approximation of such systems in discrete time in the form of utility models is achieved by the use of properly tuned `integrating filters' of the FIR type. The resulting discrete-time descriptions retain the original continuous parameterization...
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Indirect adaptive controller based on a self-structuring fuzzy system for nonlinear modeling and control
PublicationIn this paper, a unified nonlinear modeling and control scheme is presented. A self-structuring Takagi-Sugeno (T-S) fuzzymodel is used to approximate the unknown nonlinear plant based on I/O data collected on-line. Both the structure and theparameters of the T-S fuzzy model are updated by an on-line clustering method and a recursive least squares estimation(RLSE) algorithm. The rules of the fuzzy model can be added, replaced or...
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Investigation of long-range dependencies in the stochastic part of daily GPS solutions
PublicationThe long-range dependence (LRD) of the stochastic part of GPS-derived topocentric coordinates change (North, East, Up) results with relatively high autocorrelation values with a focus on self-similarity. One of the reasons for such self-similarity in the GPS time series are noises that are commonly recognised to prevail in the form of the flicker noise model. To prove the self-similarity of the stochastic part of GPS time series...