Kalman Filtering Techniques

A hybrid algorithm for phasor estimation is proposed that is immune to DC offset and current transformer (CT) saturation problems. The algorithm utilizes partial sum (PS)-based and multistage least-squares (MLS)-based methods before and after CT saturation is detected, respectively. The MLS-based method is initiated when the third difference of the secondary current detects the start point of the first saturation period. The determination of each saturation period is based on the sum of the secondary current from the start point of the first saturation period. A least-squares (LS) technique estimates the DC offset parameters from the single-cycle difference of the secondary current in the unsaturated periods. Removal of DC offset from the secondary current yields the sinusoidal waveform portion. Finally, the LS technique is used once again to estimate the phasor from the sinusoidal waveform portion. The performance of the algorithm was evaluated for a-g faults on a 345-kV 100-km overhead transmission line. The electromagnetic transient program was used to generate fault current signals for different fault angles and remanent fluxes. The performance evaluation shows that the proposed algorithm accurately estimates the phasor of a current signal regardless of DC offset and CT saturation. The paper concludes by describing the hardware implementation of the algorithm on a prototype unit based on a digital signal processor.

It is well-known that the noise associated with the collection of an astronomical image by a CCD camera is largely Poissonian. One would expect, therefore, that computational approaches that incorporate this a priori information will be more effective than those that do not. The Richardson-Lucy (RL) algorithm, for example, can be viewed as a maximum-likelihood (ML) method for image deblurring when the data noise is assumed to be Poissonian. Least-squares (LS) approaches, on the other hand, are based on the assumption that the noise is Gaussian with fixed variance across pixels, which is rarely accurate. Given this, it is surprising that in many cases results obtained using LS techniques are relatively insensitive to whether the noise is Poissonian or Gaussian. Furthermore, in the presence of Poisson noise, results obtained using LS techniques are often comparable with those obtained by the RL algorithm. We seek an explanation of these phenomena via an examination of the regularization properties of particular LS algorithms. In addition, a careful analysis of the RL algorithm yields an explanation as to why it is more effective than LS approaches for star-like objects, and why it provides similar reconstructions for extended objects. Finally a comparative convergence analysis of the two algorithms is carried out, with a section devoted to the convergence properties of the RL algorithm. Numerical results are presented throughout the paper. The subject treated in this paper is not purely academic. In comparison with many ML algorithms, the LS algorithms are much easier to use and to implement, are computationally more efficient, and are more flexible regarding the incorporation of constraints on the solution. Consequently, if little to no improvement is gained in the use of an ML approach over an LS algorithm, the latter will often be the preferred approach.

The paper describes the development of discrete-time six pulse HVDC converter models for small signal stability analysis and controller design. Assuming that the converter firing and the end of commutation period as two discrete time instants, a suitable linearized converter model is then interfaced with a current controller and an R-L load to determine the overall system model. Two separate, but similar, methods are used to find the system model. They are state space model with cyclic rate sampling and transfer function model derived using the modified-z transform. The models are then studied through their the stability boundaries and root loci and are verified through digital computer simulation.

In this paper, we consider a continuous-time linear system with finite jumps at discrete instants of time. An iterative method to compute the L <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> -induced norm of a linear system with jumps is presented. Each iteration requires solving an algebraic Riccati equation. We also show that a linear feedback interconnection of a continuous-time finite dimensional linear time- invariant (FDLTI) plant and a discrete-time finite dimensional linear Shift-invariant (FDLSI) controller can be represented as a linear system with jumps. This leads to an iterative method to compute the L <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> -induced norm of a sampled-data system.

In this paper, a Least Squares (LS) based harmonic and frequency estimation method is proposed to analyze power signals with rapidly changing characteristics in time such as Electric Arc Furnaces (EAFs) as an alternative to the classical Discrete Fourier Transform (DFT)-based methods. Although DFT based harmonic analysis methods provide fast and accurate solutions for stationary signals, solutions become less accurate under frequency deviations especially when the signal is sampled at low rates. This paper presents an approach which can accurately calculate the harmonic components of the signals, when the fundamental periods cannot be expressed as integer numbers due to the low sampling rate. One of the outstanding parts of the proposed approach is that, it is possible to increase the performance of harmonic and interharmonic estimation by increasing the performance of frequency estimation with LS technique in cases of rapidly time varying signals such as EAF currents and voltages. The reliability of the proposed approach is proven with synthetically and realistically generated EAF current signals and the results are also evaluated by running the method on field measurements collected at transformer substations supplying EAF plants both for harmonics and interharmonics estimation. Compatibility of the proposed method with parallel processing is also investigated to prove its usability in real-time applications.

We examine the applicability of different channel estimation techniques for EGPRS (enhanced global packet radio system) modems. Correlation and least squares (LS) techniques are analyzed and compared. The LS technique is presented as the candidate for EGPRS. Finally, possible modifications of the LS algorithm are discussed.

&lt;p&gt;Multiple-input multiple-output (MIMO) systems play a vital role in fourth generation wireless systems to provide advanced data rate. In this paper, a better performance and reduced complexity channel estimation method is proposed for MIMO systems based on matrix factorization. This technique is applied on training based least squares (LS) channel estimation using STBC for performance improvement. Simulation results indicate that the proposed method not only alleviates the performance of MIMO channel estimation but also significantly reduces the complexity caused by matrix inversion. The performance evaluations are validated through computer simulations using MATLAB in terms of bit error rate (BER) for modified LS with LS and MMSE channel estimation techniques. Simulation results show that the BER performance and complexity of the proposed method clearly outperforms the conventional LS channel estimation method.&lt;/p&gt;&lt;p&gt;&lt;em&gt;Journal of Advanced College of Engineering and Management, Vol. 1, 2015&lt;/em&gt;, pp. 11-24&lt;/p&gt;

In this paper, we consider the coordination problem of double integrator dynamics under the assumption of intermittent communication between agents in the presence of time-varying communication delays. More precisely, we consider the containment control problem with multiple dynamic leaders under a directed interconnection graph topology. We present distributed control algorithms, in the full and partial state feedback cases, where the communication between agents is performed only at some discrete instants of time in the presence of irregular communication delays and packet dropouts. It is shown that the proposed approach leads to our control objectives under sufficient conditions that relate the characteristics of the communication process and the control gains. The effectiveness of the proposed control schemes is illustrated through numerical examples.

We consider a continuous-time stochastic volatility model. The model contains a stationary volatility process, the density of which, at a fixed instant in time, we aim to estimate. We assume that we observe the process at discrete instants in time. The sampling times will be equidistant with vanishing distance. A Fourier-type deconvolution kernel density estimator based on the logarithm of the squared processes is proposed to estimate the volatility density. An expansion of the bias and a bound on the variance are derived.

DIRECT PROBABILITY 17501805. Some Results and Tools in Probability Theory (By Bernoulli, de Moivre, and Laplace). The Distribution of the Arithmetic Mean, 17561781. Chance or Design: Tests of Significance. Theory of Errors and Methods of Estimation. Fitting of Equations to Data, 17501805. INVERSE PROBABILITY BY BAYES AND LAPLACE, WITH COMMENTS ON LATER DEVELOPMENTS. Induction and Probability: The Philosophical Background. Bayes, Price, and the Essay, 17641765. Equiprobability, Equipossibility, and Inverse Probability. Laplace's Applications of the Principle of Inverse Probability in 1774. Laplace's General Theory of Inverse Probability. The Equiprobability Model and the Inverse Probability Model for Games of Chance. Laplace's Methods of Asymptotic Expansion, 1781 and 1785. Laplace's Analysis of Binomially Distributed Observations. Laplace's Theory of Statistical Prediction. Laplace's Sample Survey of the Population of France and the Distribution of the Ratio Estimator. THE NORMAL DISTRIBUTION, THE METHOD OF LEAST SQUARES, AND THE CENTRAL LIMIT THEOREM. GAUSS AND LAPLACE, 18091828. The Early History of the Central Limit Theorem, 18101853. Derivations of the Normal Distribution as a Law of Error. Gauss's Linear Normal Model and the Method of Least Squares, 1809 and 1811. Laplace's Large-Sample Theory of Linear Estimation, 18111827. Gauss's Theory of Linear Unbiased Minimum Variance Estimation, 18231828. SELECTED TOPICS IN ESTIMATION THEORY 18301930. On Error and Estimation Theory, 18301890. Bienaym?'s Proof of the Multivariate Central Limit Theorem and His Defense of Laplace's Theory of Linear Estimation, 1852 and 1853. Cauchy's Method for Determining the Number of Terms to be Included in the Linear Model and for Estimating the Parameters, 18351853. Orthogonalization and Polynomial Regression. Statistical Laws in the Social and Biological Sciences, Poisson, Quetelet, and Galton, 18301890. Sampling Distributions under Normality. Fisher's Theory of Estimation, 19121935, and His Immediate Precursors. References. Index.

Sensitivity analysis of material balance calculations — an application to a cement clinker grinding process

Based on the design equation of mechanism and the least-squares techniques, a rapidly convergent iteration method and simple direct methods for the synthesis of mechanisms are presented. It is proved that the so-called linear superposition method is a special case of the direct methods whose effectiveness depends upon the singular nature of the normal equations of the least-squares method as well as the smallness of the Lagrange multipliers of the compatibility equations for the mechanism. While the significance of the latter has been recognized in the literature, that of the former has not been documented in the literature. By examining the correlation matrix and the condition number for the normal equations, we show that these are near-singular. This property provides a fundamental basis for the direct methods presented in this paper. The sensitivity of solutions to the design specifications and to the precision of floating point computations also is discussed. The theory and associated algorithms can be applied to the synthesis of any planar or spatial mechanism where the use of the least-squares technique is contemplated.

Channel characterization is essential to develop a reliable communication system. In this article, a time-domain cyclic correlation-based channel impulse response (CIR) estimation technique is proposed for frequency-domain pilot aided orthogonal frequency division multiplexing (OFDM) sounding systems. The proposed system provides an improved mean squared error (MSE) as compared to least square (LS) and minimum least square (MMSE) techniques. In this paper, periodic comb-type pilots are considered. The time-domain cyclic correlation results of the up-sampled frequency-domain pilot sequence contain multiple copies of CIR with a length equal to the sequence length. The aggregated response from various copies of CIR in one symbol results in a better CIR estimation. The proposed system provides better performance with very less computational complexity. The performance of the system is evaluated in the Rayleigh channel. The results show that the proposed method can be a better alternative to LS and MMSE technique for OFDM sounding systems.

This paper presents a generalized approach to identify the structure of governing nonlinear equations of motion from the time history of state variables and control functions. An integral form involving a low-pass filter in conjunction with sparse approximation tools is used to find a parsimonious model for underlying true dynamics from noisy measurement data. Two chaotic oscillatory systems as well as the well-known problem of identifying the central force field from position-only observation data are considered to validate the developed approach. The simulation results considered in the paper demonstrate the performance of the developed approach in learning unknown nonlinear system dynamics accurately with fewer basis functions as compared with classical least-squares regression techniques and emerging deep learning approaches. A comparison of the sparse identification techniques with classical least-squares regression techniques and emerging deep learning approaches reveals the utility of the methodology developed in the paper.

New distribution theory for the estimation of structural break point in mean