Conventional Linear Filtering Research Articles

Fuzzy EKF-Based Intrusion Detection and Accurate State Estimation of Interconnected DC MGs With CPLs

With the advancement of digital technologies in complex and large-scale power systems, the issue of cyber-attack detection has become of paramount importance to maintain system reliability and performance. In this regard, accurate state estimation plays a key role and leads to proper supervisory decision-making. To detect cyber-attacks in direct current microgrids (DC MGs), a new centralized attack detection system based on the Kalman filter and clustering approach is proposed. On the other hand, appearing nonlinear loads such as constant power loads (CPLs) make the overall system behavior nonlinear and conventional linear Kalman filters ineffective. So, in this paper, an extended Kalman filter (EKF) is utilized. By constructing several output vectors and parallel EKFs, local state estimations are achieved. They are then used to detect attacks based on the residuals and localize them based on the fuzzy clustering approach. The local healthy estimations are aggregated to compute global estimations with low noise. The simulation results on a five-area interconnected DC MG subjected to data integrity and denial-of-service (DoS) attacks show that the proposed approach can detect attacks, evaluate how many attacks occur in the case of multiple attacks, localize the attacks, and obtain accurate state estimations.

Innovation-saturated Koopman Kalman filter for distribution system dynamic state estimation against measurement outliers

Sensor errors, model uncertainty, changes in the surrounding environment, data loss, or malicious network attacks can all result in outliers, which can pollute the measurement process of the distribution system. In this study, to address this problem, a dynamic state estimation method for distribution systems based on innovation-saturated Koopman Kalman filter (IS-KKF) was proposed. The Koopman Kalman filter (KKF) is model-free and data-driven, and estimates nonlinear dynamics through the conventional linear Kalman filter. To make the Koopman Kalman filter robust to measurement outliers, the innovation saturation mechanism applies a saturation function to it. To correct the state estimation, this mechanism is applied to the filtering process. When outliers occur, the distorted innovation is saturated to prevent the state estimation results from being destroyed. Adaptive adjustment of the saturated boundary is a feature of this mechanism. Extensive simulations were carried out on the IEEE 118-bus test system to verify the effectiveness and robustness of the proposed method. The simulation results demonstrate that the proposed method can effectively reject outliers with different amplitudes, types, and continuous times, has significant computational efficiency, and does not require additional measurement redundancy.

Denoising Chaotic Signals Using Ensemble Intrinsic Time-Scale Decomposition

Processing chaotic signals is a complicated task due to their nonlinear and non-periodical properties. Conventional linear filters do not allow to properly denoise signals generated by chaotic systems, distorting the carrier while removing the noise, which is critical for such applications as coherent chaotic communications. In this paper, we propose a novel denoising algorithm, called Ensemble Intrinsic Time-Scale Decomposition (EITD) using specific chaotic noise generators. We may use specific chaotic noise generators in the known Ensemble Empirical Mode Decomposition (EEMD), as we also show. Considering the examples of Rössler and Lorenz systems as chaotic waveforms generators, we compare the developed algorithm modifications with other filtration algorithms using ITD and EMD. We use the root-mean-square error (RMSE) as a metric to estimate the denoising quality. Signal-to-noise ratio (SNR) range -10...20 dB is examined, and white, pink and chaotic noise generators are utilized to disturb signals under study. As a result, we explicitly show that the developed approach provides the error 2-10 times less in the case of white and pink noise, and is capable of denoising chaotic signals in case of all the considered types of noises, in contrast to Conventional and Iterative ITD and EMD algorithms.

Noise reduction in speckle interferometry fringe pattern using adaptive Kalman filter

Fringe pattern denoising is of prime importance in phase demodulation, especially for a single fringe pattern in speckle interferometry. A fringe speckle noise removal algorithm using the Kalman filter is proposed. The conventional linear Kalman filter is implemented with a fixed value of the process and measurement noise covariances; the adaptive Kalman filter is implemented with the process, and measurement noise covariances are estimated in an adaptive manner. The fringe denoising is performed sequentially in a rowwise and columnwise manner. The simulated and experimental results demonstrate the practical applicability of the proposed method, and its performance is appraised using metrics such as the quality index, peak signal-to-noise-ratio, and speckle index.

A Collaborative Spline Adaptive Filter for Nonlinear Echo Cancellation

Acoustic echo causes the quality of communication to degenerate and results in loss of clarity. Though conventional linear adaptive filters have been applied successfully to eliminate linear acoustic echo, they can barely deal with the problem of nonlinear acoustic echo. In this paper, a collaborative spline adaptive filter is presented to eliminate nonlinear acoustic echo. The filter is composed of a linear adaptive filter in the upper branch and a nonlinear spline adaptive filter in the lower branch. The nonlinear one is a Hammerstein system consisting of a spline interpolation function and a subsequent linear adaptive filter. The two branches are collaboratively combined and a mixing parameter is adopted, which can be updated to adjust the proportion of the lower branch output signal. Experimental results show that the presented method can achieve a good performance in nonlinear echo cancelation regardless of whether the nonlinear degree of the echo path varies with time or not.

Near-Optimal Decoding of Incremental Delta-Sigma ADC Output

This paper presents a nonlinear digital decoder (reconstruction filter) for incremental delta-sigma modulators. This decoder utilizes both the magnitude and pattern information of the modulator output to achieve accurate input estimation. Compared to the conventional linear filters with the same oversampling ratio (OSR), it can improve the converter’s signal-to-quantization noise ratio by a few dB to a few 10’s of dB with slight thermal noise performance degradation. Using the proposed decoder, the modulator’s OSR can be a few times less while achieving the same resolution and data rate, thus minimizing the modulator as well as its peripheral circuits’ energy consumption. In this paper, the proposed decoder is optimized for digital implementation, with its function being verified using a modulator prototype. This decoder is mainly designed for dc or near-dc signal conversions and it does not provide frequency notches.

Quadratic approach for single-channel noise reduction

In this paper, we introduce a quadratic approach for single-channel noise reduction. The desired signal magnitude is estimated by applying a linear filter to a modified version of the observations’ vector. The modified version is constructed from a Kronecker product of the observations’ vector with its complex conjugate. The estimated signal magnitude is multiplied by a complex exponential whose phase is obtained using a conventional linear filtering approach. We focus on the linear and quadratic maximum signal-to-noise ratio (SNR) filters and demonstrate that the quadratic filter is superior in terms of subband SNR gains. In addition, in the context of speech enhancement, we show that the quadratic filter is ideally preferable in terms of perceptual evaluation of speech quality (PESQ) and short-time objective intelligibility (STOI) scores. The advantages, compared to the conventional linear filtering approach, are particularly significant for low input SNRs, at the expanse of a higher computational complexity. The results are verified in practical scenarios with nonstationary noise and in comparison to well-known speech enhancement methods. We demonstrate that the quadratic maximum SNR filter may be superior, depending on the nonstationary noise type.

Improvement of Target Detection Based on Signal Dependent Noise Reduction for Hyperspectral Image

In the hyperspectral images (HSI) acquired by the new-generation hyperspectral sensors the signal dependent noise is an important limitation to the detection. Therefore, noise reduction is an important preprocessing step to analyze the information in the hyperspectral image. A signal dependent noise cannot be reduced by conventional linear filtering. Therefore, a new method based on Parallel factor analysis (PARAFAC) decomposition is proposed to estimate the noise of hyperspectral remote sensing image. Then, the estimated noise is used for whitening the colored structural noise. By using this transformation, the data noise from new-generation hyperspectral sensors is diminished, thereby allowing a minimization of negative impacts on hyperspectral detection applications.

Uplink SCMA System With Multiple Antennas

Sparse code multiple access (SCMA) is a codebook-based nonorthogonal multiple access that exploits the coding gain of designed codebooks and the near-optimum performance of belief-propagation (BP) detection. In this paper, we study an uplink SCMA system equipped with multiple receive antennas utilized to get a diversity gain. Assuming that the maximum likelihood detection is applied to the system, we derive the upper bound on the average bit error rate (ABER) and analyze the diversity order which is shown to be the product of the number of receive antennas and the spreading gain. Exploiting the multiple received signals, we also propose a simplified detection method called Gaussian approximation based BP (GA-BP) detection with linear prefiltering . As the first step of the proposed detection, a conventional linear filter is applied to mitigate the multiuser interferences. Then, the GA-BP iteratively removes the residual interferences which may be approximated to a Gaussian random variable for the massive number of user equipments. Numerical results show that for moderate and high signal to noise ratio region the analyzed upper bounds on ABER of SCMA system tightly coincide with the simulation results. Also, for the moderate numbers of antennas, the ABER of GA-BP with matched filter closely approaches to that of the conventional BP detection with much lower computational costs.

Implementation of a nonlinear filter for online nuclear counting

Nuclear counting is a challenging task for nuclear instrumentation because of the stochastic nature of radioactivity. Event counting has to be processed and filtered to determine a stable count rate value and perform variation monitoring of the measured event. An innovative approach for nuclear counting is presented in this study, improving response time and maintaining count rate stability. Some nonlinear filters providing a local maximum likelihood estimation of the signal have been recently developed, which have been tested and compared with conventional linear filters. A nonlinear filter thus developed shows significant performance in terms of response time and measurement precision. The filter also presents the specificity of easy embedment into digital signal processor (DSP) electronics based on field-programmable gate arrays (FPGA) or microcontrollers, compatible with real-time requirements. © 2001 Elsevier Science. All rights reserved.

Bayesian Filtering of Surface EMG for Accurate Simultaneous and Proportional Prosthetic Control

The amplitude of the surface EMG (sEMG) is commonly estimated by rectification or other nonlinear transformations, followed by smoothing (low-pass linear filtering). Although computationally efficient, this approach leads to an estimation accuracy with a limited theoretical signal-to-noise ratio (SNR). Since sEMG amplitude is one of the most relevant features for myoelectric control, its estimate has become one of the limiting factors for the performance of myoelectric control applications, such as powered prostheses. In this study, we present a recursive nonlinear estimator of sEMG amplitude based on Bayesian filtering. Furthermore, we validate the advantage of the proposed Bayesian filter over the conventional linear filters through an online simultaneous and proportional control (SPC) task, performed by eight able-bodied subjects and three below-elbow limb deficient subjects. The results demonstrated that the proposed Bayesian filter provides significantly more accurate SPC, particularly for the patients, when compared with conventional linear filters. This result presents a major step toward accurate prosthetic control for advanced multi-function prostheses.

EXPERIMENTAL TESTS ON LOCAL DAMAGE DETECTION USING OPTICAL FBG SENSORS

In this study, the fiber Bragg grating (FBG)-sensor based local damage detection method is proposed under circumstances with temperature and external loading variations. To compensate the environmental effects, principal component analysis (PCA) is utilized and also the performance of PCA is compared with that of the conventional linear adaptive filter (LF) model. Laboratory tests with a 1/20 scale model of a jacket-type offshore structure with six jacket-legs and a heavy super structure have been carried out for investigating the performance of the proposed damage detection method. From the experimental tests, it is observed that the local damage feature is mostly hidden and difficult to identify due to the environmental effects. By utilizing the conventional LF and PCA models, the effects of the undesirable environmental effects can be efficiently eliminated, and it is also found that the performances of the LF and PCA models are very similar and competitive to each other. However PCA model does not require the information on the temperature and external load variations, hence it can be concluded that the PCA-based local damage detection can be more efficiently applied for FBG-based local damage detection under temperature and external loading variations.

Nonlinear and adaptive undecimated hierarchical multiresolution analysis for real valued discrete time signals via empirical mode decomposition approach

Hierarchical multiresolution analysis is an important tool for the analysis of signals. Since this multiresolution representation provides a pyramid like framework for representing signals, it can extract signal information effectively via levels by levels. On the other hand, a signal can be nonlinearly and adaptively represented as a sum of intrinsic mode functions (IMFs) via the empirical mode decomposition (EMD) algorithm. Nevertheless, as the IMFs are obtained only when the EMD algorithm converges, no further iterative sifting process will be performed directly when the EMD algorithm is applied to an IMF. As a result, the same IMF will be resulted and further level decompositions of the IMFs cannot be obtained directly by the EMD algorithm. In other words, the hierarchical multiresolution analysis cannot be performed via the EMD algorithm directly. This paper is to address this issue by performing a nonlinear and adaptive hierarchical multiresolution analysis based on the EMD algorithm via a frequency domain approach. In the beginning, an IMF is expressed in the frequency domain by applying discrete Fourier transform (DFT) to it. Next, zeros are inserted to the DFT sequence and a conjugate symmetric zero padded DFT sequence is obtained. Then, inverse discrete Fourier transform (IDFT) is applied to the zero padded DFT sequence and a new signal expressed in the time domain is obtained. Actually, the next level IMFs can be obtained by applying the EMD algorithm to this signal. However, the lengths of these next level IMFs are increased. To reduce these lengths, first DFT is applied to each next level IMF. Second, the DFT coefficients of each next level IMF at the positions where the zeros are inserted before are removed. Finally, by applying IDFT to the shorten DFT sequence of each next level IMF, the final set of next level IMFs are obtained. It is shown in this paper that the original IMF can be perfectly reconstructed. Moreover, computer numerical simulation results show that our proposed method can reach a component with less number of levels of decomposition compared to that of the conventional linear and nonadaptive wavelets and filter bank approaches. Also, as no filter is involved in our proposed method, there is no spectral leakage in various levels of decomposition introduced by our proposed method. Whereas there could be some significant leakage components in the various levels of decomposition introduced by the wavelets and filter bank approaches.

Nonlinear filter based decision feedback equalizer for optical communication systems

Nonlinear impairments in optical communication system have become a major concern of optical engineers. In this paper, we demonstrate that utilizing a nonlinear filter based Decision Feedback Equalizer (DFE) with error detection capability can deliver a better performance compared with the conventional linear filter based DFE. The proposed algorithms are tested in simulation using a coherent 100 Gb/sec 16-QAM optical communication system in a legacy optical network setting.

Non-Gaussian Sensor Fusion Analysis with “Gaussian Mixture and Adaptive” Based Cubature Kalman Filtering for Unmanned Aerial Vehicle

In this paper, comparison of adaptive and robust non Gaussian sensor fusion INS/GNSS is proposed to solve specific problem of non linear non Gaussian time variant state space estimation with impulsive measurement noise, different algorithms are proposed based on the most recent approaches in non linear filtering during intentional and non intentional interferences caused by multiple sources, or by the GNSS receivers signal degradation. Non linear filters such as Extended Kalman filter EKF and the last developed Cubature based Kalman Filter are implemented to estimate the navigation flight states for UAV. A specific hypothesis assumes high non Gaussian scenario and low non Gaussian noise level. Especially, alpha stable impulsive noise is simulated and affects GNSS measurement. The modern non linear filter algorithm called Cubature Kalman Filter CKF which provides more accurate estimation with more stability in Tracking data fusion application is compared with conventional non linear filters under non Gaussian constraints as a first step, thus, additional hypothesis is introduced which consists on Gaussian measurement outliers of each non Gaussian densities. In our work, Gaussian sum filtering and adaptive fading algorithms are proposed to solve the problem of IMU/GNSS integration in denied environment. CKF is compared with EKF in ideal conditions and during GNSS impulsive interferences modeled as non Gaussian noises “Sum of Gaussian” supposed to occur during specific interval of time, during the same interval, we assume additional denied environment which consists on the vari\ation of the Gaussian sum noise covariance, then, innovation based adaptive fading approach is selected and used to modify the covariance calculation of the parallel non linear filters performed in this work. Two important results are carried out depending on the variation of the Gaussian mixture density modeled in this work. original results are observed, discussed with real perspectives in navigation data fusion for real time applications under multiple denied environment conditions.

Kernel minimum error entropy algorithm

As an alternative adaptation criterion, the minimum error entropy (MEE) criterion has been receiving increasing attention due to its successful use in, especially, nonlinear and non-Gaussian signal processing. In this paper, we study the application of error entropy minimization to kernel adaptive filtering, a new and promising technique that implements the conventional linear adaptive filters in reproducing kernel Hilbert space (RKHS) and obtains the nonlinear adaptive filters in original input space. The kernel minimum error entropy (KMEE) algorithm is derived, which is essentially a generalized stochastic information gradient (SIG) algorithm in RKHS. The computational complexity of KMEE is just similar to the kernel affine projection algorithm (KAPA). We also utilize the quantization approach to constrain the network size growth, and develop the quantized KMEE (QKMEE) algorithm. Further, we analyze the mean square convergence of KMEE. The energy conservation relation is derived and a sufficient condition that ensures the mean square convergence is obtained. The performance of the new algorithm is demonstrated in nonlinear system identification and short-term chaotic time series prediction.

Noise removal in extended depth of field microscope images through nonlinear signal processing

Extended depth of field (EDF) microscopy, achieved through computational optics, allows for real-time 3D imaging of live cell dynamics. EDF is achieved through a combination of point spread function engineering and digital image processing. A linear Wiener filter has been conventionally used to deconvolve the image, but it suffers from high frequency noise amplification and processing artifacts. A nonlinear processing scheme is proposed which extends the depth of field while minimizing background noise. The nonlinear filter is generated via a training algorithm and an iterative optimizer. Biological microscope images processed with the nonlinear filter show a significant improvement in image quality and signal-to-noise ratio over the conventional linear filter.

Networked Kalman filtering with combined constraints of bandwidth and random delay

Kalman filter is a powerful tool in target tracking and self-localization across wireless sensor networks with many constraints. This paper considers the filters design for networked systems with combined constraints of bandwidth and random delay, and proposes a kind of universal networked Kalman estimator for given linear time invariant (LTI) or determinate parameters (DP) systems, which are also called linear and determinate parameters (LDP) systems jointly. Firstly, two modeling ways to treat bit quantization error vector are given and the corresponding LDP systems taken after bit quantization are established. Secondly, we introduce an equivalent weighted summation form of the conventional linear Kalman filter, which fully uses two essential characteristics, namely offline computation property from the LDP systems and linear weighted summation property from the linear minimum mean square error estimate. Finally, by adopting the replacement and innovation compensation operations, a kind of integrated networked estimator, involving two estimation algorithms with different modeling ways to bit quantization error actually, is presented based on the weighted summation filter for random delay systems. The proposed universal networked estimation algorithms have some outstanding advantages such as extensive application, concise algorithm structure, high estimate accuracy, and good running performance. Several examples are demonstrated to validate the proposed networked estimation algorithms.

Gain-Scheduled Complementary Filter Design for a MEMS Based Attitude and Heading Reference System

This paper describes a robust and simple algorithm for an attitude and heading reference system (AHRS) based on low-cost MEMS inertial and magnetic sensors. The proposed approach relies on a gain-scheduled complementary filter, augmented by an acceleration-based switching architecture to yield robust performance, even when the vehicle is subject to strong accelerations. Experimental results are provided for a road captive test during which the vehicle dynamics are in high-acceleration mode and the performance of the proposed filter is evaluated against the output from a conventional linear complementary filter.

Imprecise expectations for imprecise linear filtering

In most sensor measure based applications, the raw sensor signal has to be processed by an appropriate filter to increase the signal-to-noise ratio or simply to recover the signal to be measured. In both cases, the filter output is obtained by convoluting the sensor signal with a supposedly known appropriate impulse response. However, in many real life situations, this impulse response cannot be precisely specified. The filtered value can thus be considered as biased by this arbitrary choice of one impulse response among all possible impulse responses considered in this specific context. In this paper, we propose a new approach to perform filtering that aims at computing an interval valued signal containing all outputs of filtering processes involving a coherent family of conventional linear filters. This approach is based on a very straightforward extension of the expectation operator involving appropriate concave capacities.