Extended Complex Kalman Filter Research Articles

Frequency estimation of distorted non-stationary signals using complex H∞ filter

Mechanical vibration signals are always composed of harmonics of different order. A novel estimator is proposed for estimating the frequency of sinusoidal signals from measurements corrupted by White Gaussian noise with zero mean. Also low frequency sinusoidal signal is considered along with third and fifth order harmonics in presence of noise for estimating amplitudes and phases of different harmonics. The proposed estimator known as complex H∞ filter is applied to a noisy sinusoidal signal model. State space modeling with two and three state variables is used for estimation of frequency in presence of white noise. Various comparisons in terms of simulation results for time varying frequency reveal that the proposed adaptive filter has significant improvement in noise rejection and estimation accuracy. Comparison in performance between two and three states modeling is presented in terms of mean square error (MSE) under different SNR conditions .The computer simulations clearly indicate that two states modeling based on Hilbert transform performs better than three states modeling under high noisy condition. Frequency estimation performance of the proposed filter is also being compared with extended complex Kalman filter (ECKF) under same noisy conditions through simulations.

Phase and amplitude imaging from noisy images by Kalman filtering

We propose and demonstrate a computational method for complex-field imaging from many noisy intensity images with varying defocus, using an extended complex Kalman filter. The technique offers dynamic smoothing of noisy measurements and is recursive rather than iterative, so is suitable for adaptive measurements. The Kalman filter provides near-optimal results in very low-light situations and may be adapted to propagation through turbulent, scattering, or nonlinear media.

Tracking of non-stationary distorted power signals using complex H<SUB align=right>∞ filter

The present study proposes a novel method of tracking the time-varying frequency and amplitude of a distorted power signal using a complex H∞ filter. A new model structure is proposed for estimation of different power quality disturbances of a distorted power signal. The amplitude and phase of different harmonics are also estimated which shows the robustness of the filter. The performance of complex H∞ filter has been compared with those of extended complex Kalman filter (ECKF) considering signals, which can represent worst case measurement and network conditions in a typical power system. State space representation with three states is used for estimation of amplitude and frequency in presence of white noise. Results of simulation demonstrate that under identical conditions, the performance of complex H∞ filter is better compared to ECKF.

Implementation of a robust complex extended Kalman filter with LabVIEW for detection in a distorted signal

This article proposes the PC-based LabVIEW as the software to develop the algorithm of the robust complex extended Kalman filter (RCEKF) to detect the parameters of the voltage signal in power syst...

LabVIEW implement for distorted signal detection with robust complex extended Kalman filter

This paper presents the personal computer (PC)-based LabVIEW as software to develop the algorithm of the robust complex extended Kalman filter (RCEKF) for detection of the parameters of voltage signal in power systems. The hardware of this paper is to take sample-and-hold card and DAQ (data acquisition) card for extracting the datum from the outside system to the PC, the program computes the amplitude, frequency and phase of the voltage signal with RCEKF. For validating the performance of RCEKF in this paper, the voltage signal from function generator and laboratory are applied to check the feasibility of algorithm firstly and then this application was also used in the TPC (Taiwan Power Company) secondary substation in Sijhou, Taiwan. Key words: Complex Kalman filter, robust algorithm, voltage distorted signal, LabVIEW.

Bad data analysis in power system measurement estimation using complex artificial neural network based on the extended complex Kalman filter

AbstractThis paper proposes a method for bad data analysis in power system measurement estimation using complex artificial neural network (CANN) based on the extended complex Kalman filter (ECKF). The proposed algorithm is better in noise immunity since the link weighting in the CANN can be automatically adjusted with trained data through the ECKF. Moreover, the CANN is quite suitable for complex training data such as complex power in a power system since its input and output performs a nonlinear mapping. Four systems including a 6‐bus system, the IEEE 30‐bus system, IEEE 118‐bus system, and a practical system are used as examples to verify the feasibility of the ECKF‐CANN approach. Results show the proposed algorithm has increased sensitivity in identifying gross measurement errors with respect to the standard ANN. Copyright © 2009 John Wiley & Sons, Ltd.

A Robust Technique for Frequency Estimation of Distorted Signals in Power Systems

This paper presents a technique comprising a robust extended complex Kalman filter and a sliding-surface-enhanced fuzzy adaptive controller (RECKF-FAC) for frequency and amplitude estimations of distorted signals in a power system. With the aid of fuzzy theory, the proposed approach is more effective for solving the uncertainty of frequency estimation. The robust extended complex Kalman filter (RECKF) is employed to suppress the abnormalities from abnormal data of measurements for promoting the efficiency in frequency estimation, whereas the sliding-surface-enhanced fuzzy adaptive controller (FAC) is used to adjust the Kalman gain and covariance for solving heuristic choices of a hysteresis type of decision. Three cases, including a single sinusoid, harmonic signals, and an actual signal from a stainless-steel factory, are examined to verify the feasibility of the proposed approach. As a result, the proposed approach cannot only perform the extended complex Kalman filter (ECKF) without changing any form but can also enhance the estimation accuracy and reduce the computation time. Results of comparative studies of the technique proposed with the ECKF and RECKF are presented in this paper.

複素拡張カルマンフィルタを用いたウェイポイントナビゲーションの実装

複素拡張カルマンフィルタを用いたウェイポイントナビゲーションの実装

Frequency Estimation of Distorted Power System Signals Using a Robust Algorithm

This paper proposes a robust algorithm based on an extended complex Kalman filter (ECKF) for improving frequency estimation of distorted power system signals. In general, abnormal data obtained from measurements may cause noises and disturbances of power systems as well as affect the accuracy of frequency estimation. For this reason, the proposed algorithm is employed to suppress the abnormalities from abnormal data of measurements for promoting the efficiency in frequency estimation. Moreover, not only can it perform the ECKF without changing any form of it, but it can also save the execution time. Results of frequency estimation for distorted signals using the proposed method are compared with the ECKF.

Sensorless direct vector control of an induction motor

In high-performance variable speed AC drive systems it is often important to accurately determine machine parameters and rotor speed values. An extended complex Kalman filter (ECKF) is used to estimate rotor resistance and mutual inductance without the use of a speed sensor. Such estimates are important in air gap flux orientation control. The ECKF is chosen over the more common extended Kalman filter based on the real-valued model as it is not as computationally intensive. The model of an induction machine obtained by the spiral vector theory and the ECKF are used to develop a new adaptive direct air gap flux orientation control with two sensors: one for the stator voltage and one for the stator current without Park transformation. The simulation tests show the effectiveness of the proposed adaptive direct air gap flux orientation control method.

Nonlinear Estimation of Harmonic Signals

A nonlinear harmonic estimator (NHE) is proposed for extracting a harmonic signal and its fundamental frequency in the presence of white noise. This estimator is derived by applying an extended complex Kalman filter (ECKF) to a multiple sinusoidal model with state-representation and then efficiently specializing it for the case of harmonic estimation. The effectiveness of the NHE is verified using computer simulations.

Fast and Accurate Estimation of Power System Frequency for Power Quality Studies

This article presents a new approach for the estimation of power system frequency for power quality studies using bus voltage signals corrupted with noise and harmonics. The method involves application of a nonlinear filtering technique like a Kalman filter in the complex domain known as extended complex Kalman filter (ECKF). This article systematically outlines the development of the complex Kalman filter model using one phase measurement in the state space form and relevant equations to compute the Kalman gain. The nonlinear filter is then applied to several static and dynamic conditions of the power system and the frequency is estimated. Presence of harmonics and noise in bus voltage signal is taken into consideration in evaluating the performance of this new filter in terms of rejecting noise and harmonics. In the presence of decaying dc components in the signal, the new filter is found to be very effective as validated from the digital simulation tests. Further the ECKF is applied for the frequency estimation of an ac-dc system during load and line reactance changes and the estimation results reveal high accuracy and convergence. In general, it is observed that the proposed filter outperforms in terms of accuracy and speed of convergence the reported real extended Kalman filter during sudden transient changes.

An extended complex Kalman filter for frequency measurement of distorted signals

The design of an extended complex Kalman filter for the measurement of power system frequency has been presented in this paper. The design principles and the validity of the model have been outlined. A complex model has been developed to track a distorted signal that belongs to a power system. The model inherently takes care of the frequency measurement along with the amplitude and phase of the signals. The theory has been applied to standard test signals representing the worst-case measurement and network conditions in a typical power system. The proposed algorithm is suitable for real-time applications where the measurement noise and other disturbances are high. The complex quantities can be conveniently handled using a floating point processor. Comparison of the results of the proposed method with those obtained from a real extended Kalman filter reveals the superior performance of the former method.

Frequency estimation of distorted power system signals using extended complex Kalman filter

The paper proposes an extended complex Kalman filter and employs it for the estimation of power system frequency in the presence of random noise and distortions. From the discrete values of the 3-phase voltage signals of a power system, a complex voltage vector is formed using the well known /spl alpha//spl beta/-transform. A nonlinear state space formulation is then obtained for this complex signal and an extended Kalman filtering approach is used to compute the true state of the model iteratively with significant noise and harmonic distortions. As the frequency is modeled as a state, the estimation of the state vector yields the unknown power system frequency. Several computer simulations test results are presented in the paper to highlight the usefulness of this approach in estimating near nominal and off-nominal power system frequencies.

A nonlinear filter for estimating a sinusoidal signal and its parameters in white noise: on the case of a single sinusoid

A nonlinear filter is proposed for estimating a complex sinusoidal signal and its parameters (frequency, amplitude, and phase) from measurements corrupted by white noise. This filter is derived by applying an extended complex Kalman filter (ECKF) to a nonlinear stochastic system whose state variables are a function of its frequency and a sample of an original signal, and then, proof of the stability is given in the case of a single complex sinusoid. Simulations demonstrate that the proposed nonlinear filter is effective as a method for estimating a single complex sinusoid and its frequency under a low signal-to-noise ratio (SNR). In addition, the effect of the initial condition in the filter on frequency estimation is also discussed.