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Abstract: The Kalman filter has been used in a wide variety of engineering applications. There are two typical forms in implementing the nonlinear Kalman filter in conjunction with linearisation trajectory for which calculation of Jacobian matrices is involved: the linearised Kalman filter (LKF) and the extended Kalman filter (EKF). This paper aims to serve as a tutorial to the readers for providing better understanding and correctly implementing the two forms of nonlinear filters. Some critical remarks useful in designing a nonlinear Kalman filter are pointed out. Linearisation of the trajectory for the LKF and EKF is discussed. Performance degradation due to linearisation error is illustrated. Divergence problem for the LKF is presented. Implementation practice for the LKF and the EKF via total state estimate in conjunction with the error state estimate (in which the state variables are incremental quantities) are provided. Discussion on increase of dynamic process noise to the estimation precision in LKF and EKF is involved. Clear description of the implementation algorithms is provided. The step-by-step procedure for performing the filters is provided accompanied with two geodetic navigation examples. The materials prepared in this paper can be modified for further development in various applications. [ABSTRACT FROM AUTHOR]

Abstract: Electrical capacitance tomography (ECT) attempts to image the permittivity distribution of an object by measuring the electrical capacitances between sets of electrodes placed around its periphery. Successful applications of ECT depend on the speed and precision of the image reconstruction algorithms. Image reconstruction for ECT is a typical ill-posed problem, methods that ensure the stability of a solution while enhancing the quality of the reconstructed images should be used to obtain a meaningful reconstruction result. In this paper, an image reconstruction algorithm for ECT is presented. The standard Tikhonov regularization method is extended using a combination estimation method and an extended stabilizing item according to the ill-posed characteristics of ECT. The image reconstruction problem is transformed into an optimization problem and the Newton algorithm is employed to solve the objective function. The proposed algorithm is tested by the noise-free capacitance data and the noise-contaminated capacitance data. Numerical simulations indicate that the proposed algorithm is efficient and can overcome the numerical instability of ECT image reconstruction. In the cases of the reconstructed objects considered in this paper, the reconstruction results show much improvement in the accuracy. The spatial resolution of the reconstructed images by the proposed algorithm is enhanced and the artifacts in the reconstructed images can be eliminated effectively. In addition, the reconstruction results from the noise-contaminated capacitance data also show a good robustness to noise. As a result, an efficient method for ECT image reconstruction is introduced. [Copyright &y& Elsevier]

The research reported in this paper is related to the ultra-wide-band radar technology that may be employed in care services for elderly and disabled persons. Three algorithms for preprocessing of measurement data from an impulse radar sensor, when applied for such people monitoring, are compared with respect to the uncertainty of estimation of echo parameters. These are: an algorithm based on the maximum-envelope of the measured radar data, an algorithm based on curve-fitting in the spectrum domain of those data, and a modified CLEAN algorithm. Results of the numerical experiments performed on both semi-synthetic data and real-world data, obtained by means of an impulse-radar sensor, are demonstrated. [ABSTRACT FROM AUTHOR]

Abstract: The energy-based method (EBM) can be used to estimate the amplitude of a sine-wave either directly from Discrete Fourier Transform (DFT) samples or indirectly. In this paper the accuracies achieved with both these approaches are compared when some of the most commonly used cosine class windows are adopted. The effect on the estimation accuracy of the algorithm error, the spectral interference from the image component, and wideband noise superimposed to the sine-wave signal are separately evaluated and compared. The statistical efficiencies of both procedures with respect to the unbiased single-tone Cramér-Rao lower bound are determined and compared. Moreover, the overall root mean square of the amplitude estimation error achieved when taking into account all the three contributions above is derived for both direct and indirect estimation procedures. The accuracy of the obtained expressions is verified by means of computer simulations. Besides, experimental data validate the theoretical results. [Copyright &y& Elsevier]

Abstract: In this paper a new recursive adaptive filter based on a fast Gauss–Newton method has been proposed for the estimation of power quality (PQ) indices for time-varying voltage and current signals in an electric power system. The presented algorithm is based on the minimization of a weighted forgetting factor based error cost function by the use of Recursive Gauss–Newton method. Further a Hessian matrix approximation is used to produce a fast recursive algorithm, which is immune to random noise, waveform distortion and increases the speed of convergence and accuracy. The algorithm models the typical time-varying signal and the accompanied distortions due to harmonics and random noise in a manner that will be suitable for real-time PQ indices estimation. Further, the forgetting factor is tuned in accordance with signal error covariance to provide improved performance. Also power system frequency variations are estimated and correction factors are derived. The effects of sub harmonics, and interharmonics in the signal have been considered while estimating the various PQ indices. [Copyright &y& Elsevier]

Abstract: In the visual object tracking, the Kalman filter presents commonly the state model and observation model uncertainty in the actual performance of Gaussian noise, so it makes the estimation of certain parameters produce errors in the model, and results in decreasing estimation precision. In order to enhance the stability of the Kalman filter, an algorithm based on centroid weighted Kalman filter (CWKF) for object tracking is proposed in this paper. The algorithm firstly uses background subtraction method to detect moving target region, and then uses the Kalman filter to predict target position, combining centroid weighted method to optimize the predictive state value, finally updates observation data according to the corrected state value. Tracking experiments show that the algorithm can detect effectively moving objects and at the same time it can quickly and accurately track moving objects with good robustness. [Copyright &y& Elsevier]

Abstract: This paper deals with the detection of power quality anomalies which preserve the frequency of the power line, in particular sags and swells. Three statistical estimators have been used (variance, skewness and kurtosis) to enhance characterization of these anomalies. The proposed measurement strategy is funded in the tuning of the signal under test via a sliding window over which computation is performed. Then, the calculation of the statistical features reveals the inherent properties of the signal: amplitude, frequency and symmetry. The work primarily examines a number of synthetics in order to extract the theoretical statistical features. Then the algorithm is corroborated using real-life signals, obtaining an accuracy of 83%. This experience is part of the design of an instrument for the measurement of the power quality. [Copyright &y& Elsevier]

Abstract: This paper presents a modified adaptive linear neuron (ADALINE) structure, called self-synchronized adaptive linear neuron (S-ADALINE) network for fast and accurate estimation of power system harmonics. The proposed network relies on the Levenberg gradient descent (LGD) method based parameter updating rule and is capable of dealing with both nominal and off-nominal frequency conditions, rather than the existing modified Widrow–Hoff delta rule based ADALINE network which provides good accuracy only at nominal frequency. Moreover, the S-ADALINE provides faster response and better noise immunity than the conventional approach. The only flaw of the proposed network is its high computational load. Based on simulation studies, performances of the proposed harmonic estimator at different operating conditions have been presented and its accuracy and response time have been compared with the conventional ADALINE structure. [Copyright &y& Elsevier]

Abstract: As the demand of electrical energy increases, it is vital to replace inefficient motors with new energy efficient ones. The first step towards achieving this goal is to estimate the existing motors efficiencies accurately to determine how much energy saving will be achieved by using energy efficient motors. This paper proposes an economical and accurate approach for motor field efficiency estimation using bacterial foraging algorithm. The approach relies on the measurement of the stator current, stator voltage, input power, stator resistance and rotor speed of the motor without conducting no-load and locked-rotor tests. The BF algorithm is used to determine the equivalent circuit parameters of the motor. The efficiency is then estimated using these parameters. The advantages of the proposed method over the existing methods are simple procedure, efficiency can be estimated accurately without conducting any invasive tests and inexpensive. The approach has been tested on a 5 HP motor and the results are compared with particle swarm optimization method, immune algorithm method, torque gauge method, equivalent circuit method, slip method, current method and segregated loss method. The results demonstrate that the proposed approach can accurately estimate the field efficiency of motor. Accordingly, it is suitable for conducting energy audits and management of the motor. [Copyright &y& Elsevier]

Abstract: In this paper, an envelope estimation algorithm based on the resonance modes of the mechanical system is proposed and the exponential decay frequency of the envelope signal could be further estimated to be a quantified index for the bearing defect diagnosis. According to the vibration spectrum of the bearing system, the resonance frequencies in the range of its corresponding resonance modes could be initially designated and further revised. Under the assumption of stepwise functions for the envelope signals, the vibration signal could be decomposed into the sinusoidal function bases with fundamental frequencies at the corresponding resonance frequencies. Thus, the envelope signals could be retrieved by estimating the stepwise functions. In addition, the reconstructed signal with noise rejection could be derived from the envelope signals. According to the envelope signals, the exponential decay frequency is estimated to be the diagnosis index of the bearing running condition. In the simulated and experimental studies, it is found that the envelope estimation algorithm could be effectively applied in the signal processing for the bearing vibrations. In addition, the envelope spectra also show good consistency between the proposed method and the high-frequency resonance technique. Finally, it is shown that the exponential decay frequency could successfully be the quantified index for the bearing defect diagnosis. [Copyright &y& Elsevier]

Abstract: Power harmonic estimation is essential for evolving suitable protection and control strategies of power networks. Parametric approaches exhibit super-resolution and have been gradually applied in practice. However, they are susceptible to the presence of noise in the signals. The analysis accuracy will be abruptly reduced and even ineffective under non-Gaussian or impulsive noise environment. In this paper, a novel approach based on M-Estimators for harmonic estimation is proposed to overcome the above shortcomings. The derivation of Gauss–Newton iteration equations of harmonic frequency, amplitude and phase is presented. Further, the ESPRIT algorithm is also employed to acquire the initial values of harmonic frequencies, which avoids the objective function of M-Estimator to be stuck in local minima and improves the convergence rate of optimization. The numerical simulations and experimental results verify the feasibility and effectiveness of the proposed method. [Copyright &y& Elsevier]

Abstract: In this paper, the comparison between several frequency estimation algorithms for power quality frequency assessment is shown. These include spectral, adaptive filtering, mixed time and frequency domain, least-squares and eigenvector decomposition algorithms. The different algorithms’ results are compared for three typical power measurement situations that include harmonics and noise. The main objective is to select the most promising algorithms for implementation in a digital signal processor, in the context of typical power quality frequency disturbance measurements. [Copyright &y& Elsevier]

Abstract: This paper presents an integrated design framework to utilize multi-sensor data fusion (MSDF) techniques for process monitoring enhancement to detect and diagnose sensor and process faults. Two different distributed and centralized architectures are presented to integrate the multi-sensor data based on extended Kalman filter (EKF) data fusion algorithm. The distributed integration architecture uses the state-vector fusion method, while the centralized integration architecture is based on the output augmented fusion (OAF) method. The usual approach in the classical EKF implementation is based on the assumption of constant diagonal matrices for both the process and measurement covariances. This inflexible constant covariance set-up may cause degradation in the EKF performance. A new adaptive modified EKF (AMEKF) algorithm has been developed to prevent the filter divergence and hence leading to an improved EKF estimation. A set of simulation studies have been conducted to demonstrate the performances of the proposed adaptive and non-adaptive process monitoring approaches on a continuous stirred tank reactor (CSTR) benchmark problem. The sensor fault studies include the sensor faults due to drift in calibration and drift in sensor degradation anomalies. Whereas, the process faults consist of four probable CSTR faults in cascaded single, double, triple and quadruple set-up. [Copyright &y& Elsevier]

Abstract: If the RMS value is obtained by digital processing of a sequence of signal samples, both the uncertainty and the bias of the measured value depend on the algorithm used. Since in practice signal sampling is usually non-coherent, leakage occurs in the signal DFT spectrum and the definition of the RMS of periodic signals in the time domain is violated. This paper presents an overview of estimation of RMS values by comparing five different DSP algorithms of RMS measurements by non-coherent sampling from the point of view of measurement bias and uncertainty for various leakage levels and the data window used. The results of simulations and examples of measurements are evaluated for both monofrequency and multifrequency signals. For non-coherent signal sampling, we compare time domain signal processing based on signal windowing with classical RMS estimation. This is shown to be an effective approach to RMS value measurement. A new method for finding the exact signal frequency by non-coherent sampling is introduced, and a method for effective RMS value bias correction in the frequency domain is presented. Methods for estimating RMS values in the time and frequency domains are compared. [Copyright &y& Elsevier]

Abstract: An algorithm to improve the estimation of the active power of electrical systems in the non-coherent sampling is proposed in this paper. It is based on smoothing the sampled data by windowing, and then averaging of the discrete Fourier transform (DFT) coefficients in the frequency domain to reduce the leakage effects. The simulation and experimental results are presented showing that averaging of the DFT coefficients provides better estimation of the active power then only by windowing. The use of a suitable algorithm depends on the positions of the frequency components, on a number of observed periods, and on the signal to noise ratio. [Copyright &y& Elsevier]

Abstract: In this paper, an inverse square-root adaptive filtering algorithm for recursive least squares estimation (QR-RLS) was used to carry out the optimal estimation of the relevant information coming from a rollover sensor placed in car under performance tests. In this case, the noise that corrupts the relevant signal coming from the sensor is so dangerous that its negative influence on the electrical systems of the car can prevent both drivers and intelligent systems embedded in today’s cars from making intelligent driving decisions that can save millions of lives every year. For this reason, the solution to this problem safety related problem deserves our full attention. Here, in order to solve this problem, a QR-RLS adaptive filter was used. The results of the experiment were satisfactory, an optimal rollover sensor with very low uncertainty of measurement, very good repeatability, very low non-linearity and a satisfactory sensitivity was designed. Furthermore, a significant improvement of 45dB in the signal-to-noise ratio (SNR) at the system output was achieved. [Copyright &y& Elsevier]