Unknown Filter Research Articles

Noise Impact on Optimum Parameters for Signal Deconvolution

In many areas, such as speech processing, communication, and measurement systems, where the actual signal is not directly available, Wiener deconvolution is a widely used signal restoration technique. The accuracy of the estimated signal in Wiener deconvolution is determined by the unknown filter parameter. To compute this unknown parameter, complex and time-consuming numerical as well as iterative computation approaches were proposed in the literature, which also often compute an unoptimized unknown filter parameter. To address the computational problem and estimate a more accurate unknown filter parameter, the authors reported an analytical solution in a prior work for a given signal to noise ratio. However, it was revealed that the actual optimum parameter value also varies with noise also. In this paper, the authors propose a new analytical solution for optimum parameter estimation that includes noise as well. The authors compared the modified analytical solution to existing numerical computation methods for different values of Signal to Noise Ratio and demonstrated that the proposed methods’ optimum parameter estimation is always close to the actual optimum value, which resulted in more accurate signal deconvolution. Proposed mathematical solutions are also verified with experimental signals, acquired in a laboratory.

Remaining useful life prediction of proton exchange membrane fuel cell based on Wiener process and Bayesian GRU network considering multi-source uncertainties

ABSTRACT Proton exchange membrane fuel cell (PEMFC) is considered as one of the most promising green energy devices. Although fruitful results can be available for the remaining useful life (RUL) prediction of PEMFC, stochastic uncertainties have never been considered. To tackle this problem, a hybrid method is proposed in this paper. Wiener process with temporal uncertainty and individual uncertainty is adopted to model the degradation of the state of health (SOH), which is then estimated from monitoring voltage with measurement noise using the unscented Kalman filter (UKF), where unknown filtering and model parameters are jointly identified by expectation-maximization (EM) algorithm and Rauch-Tung-Striebel (RTS) smoother. Finally, gated recurrent unit (GRU) network is employed to realize the RUL prediction with the prediction uncertainty quantified by the Bayesian variational inference technology. The proposed method is verified on the experimental data. Results indicate that smaller mean absolute percentage error (MAPE), root mean square error (RMSE), and mean absolute error (MAE) values can be obtained compared with other methods. When 60% data are used for prediction, the proposed method can achieve a RUL prediction accuracy with 1.63% and 2.17% relative errors under static and dynamic conditions, respectively, which illustrates the feasibility and superiority of the proposed method.

Parametric identification of ARMAX models with unknown forming filters

Abstract In this paper, we present the parameter estimation algorithm for the class of an extended ARMAX model containing a ‘coloured’ noise sequence, formed by an unknown finite-dimensional linear filter. This algorithm represents the extended versions of residual whitening method and least squares method, working in parallel, to identify the extended parameters obtained after the suggested linear model transformation. The strong consistency of the suggested method (convergence with probability one of the obtained extended parameters to their exact values) is proven. A good performance of the proposed method is illustrated by a numerical example with all polynomials containing unknown parameters.

The least‐square design of minimum‐order allpass‐based infinite impulse response multi‐notch filters

SummaryThe paper investigates the least‐square design of minimum‐order infinite impulse response multi‐notch filters. Monotonically decreasing nature of the stable allpass filter's phase response, characterizing the allpass‐based multi‐notch filter, along with the simple relation between coefficients and the phase response of the allpass filter, allows the formulation of the multi‐notch filter's magnitude response specifications as the linear equality constraints regarding the positions of notch, left‐ and right‐hand cutoff frequencies. Since the number of such constraints equals triple the number of notch frequencies, while the number of unknown filter coefficients equals double the number of notch frequencies, variable elimination is first performed to ensure that specifications regarding the notch frequencies positions are strictly satisfied. The remaining overdetermined system of linear equations is then solved in the least‐square sense, leading to the approximate satisfaction of left‐ and right‐hand cutoff frequencies positions. Proposed design method is also compared with some of the existing infinite impulse response multi‐notch filter design methods.

Manifold Gradient Descent Solves Multi-Channel Sparse Blind Deconvolution Provably and Efficiently

Multi-channel sparse blind deconvolution, or convolutional sparse coding, refers to the problem of learning an unknown filter by observing its circulant convolutions with multiple input signals that are sparse. This problem finds numerous applications in signal processing, computer vision, and inverse problems. However, it is challenging to learn the filter efficiently due to the bilinear structure of the observations with respect to the unknown filter and inputs, as well as the sparsity constraint. In this paper, we propose a novel approach based on nonconvex optimization over the sphere manifold by minimizing a smooth surrogate of the sparsity-promoting loss function. It is demonstrated that manifold gradient descent with random initializations will probably recover the filter, up to scaling and shift ambiguity, as soon as the number of observations is sufficiently large under an appropriate random data model. Numerical experiments are provided to illustrate the performance of the proposed method with comparisons to existing ones.

On Improved Training of CNN for Acoustic Source Localisation

Convolutional Neural Networks (CNNs) are a popular choice for estimating Direction of Arrival (DoA) without explicitly estimating delays between multiple microphones. The CNN method first optimises unknown filter weights (of a CNN) by using observations and ground-truth directional information. This trained CNN is then used to predict incident directions given test observations. Most existing methods train using spectrally-flat random signals and test using speech. In this paper, which focuses on single source DoA estimation, we find that training with speech or music signals produces a relative improvement in DoA accuracy for a variety of audio classes across 16 acoustic conditions and 9 DoAs, amounting to an average improvement of around 17% and 19% respectively when compared to training with spectrally flat random signals. This improvement is also observed in scenarios in which the speech and music signals are synthesised using, for example, a Generative Adversarial Network (GAN). When the acoustic environments during test and training are similar and reverberant, training a CNN with speech outperforms Generalized Cross Correlation (GCC) methods by about 125%. When the test conditions are different, a CNN performs comparably. This paper takes a step towards answering open questions in the literature regarding the nature of the signals used during training, as well as the amount of data required for estimating DoA using CNNs.

Identification of Unknown Filter in a Half-Strip

We consider the analogue of the classic Wiener filtering theory to a half-strip of complex domain. In this paper all test signal obtained that solving the filter identification problem for the Hardy spaces in a half-strip. This result can be used for the investigations of electrical, optical, acoustical signals.

Robust generalized filtering of uncertain Lipschitz nonlinear systems under measurement delays

In the present study, a generalized structure for the robust filtering, which adequately addresses both the dynamic and the static-gain filter structures, is accounted for the uncertain Lipschitz nonlinear systems with the measurement delays, parametric uncertainties, and disturbances. The proposed robust filtering approach uses a Lyapunov–Krasovskii functional with a specialized stipulation for dealing with the measurement lags, employs a delay-range-dependent stability method for tackling the delayed dynamics, applies the upper bounds on norms of the uncertainties to deal with parametric variations, and explores the $$L_2 $$ stability condition to handle the exogenous perturbations. The nonlinear dynamics is tempered by the direct infusion of the Lipschitz continuity, and uncertainties are modeled using bounds on the uncertain matrices norms to render a linear matrix inequality (LMI)-based design. The proposed filtering approaches establish the $$L_2 $$ stability for the filtering error and efficaciously reckon the solution of unknown filter matrices using the LMI-oriented computational algorithms. Numerical simulation example is appended to manifest the effectuality of the proposed results.

Analytical Insights Into Parameter Estimation for Wiener Deconvolution

All real-time signals observed from various measurement systems require signal-processing techniques like the deconvolution, to compensate for the effect of transfer function of the systems. Wiener deconvolution is a widely used signal-processing technique for signal restoration. Often, if the power spectral density of signal and noise is unknown, the accuracy of the restored signal depends on an unknown filter parameter. In the literature, time-consuming, iterative, computational methods were reported to estimate the parameter. However, many of these methods give a range of optimum values instead of an unique value and often lead to either over-smoothing or under-smoothing. In this paper, novel analytical expressions are presented through which the unknown parameter can be estimated explicitly. The analytical results of this study are compared with the numerical methods, and they are found to be accurate and robust against numerical evaluation. Further, the results are demonstrated for signals obtained experimentally from the pulsed electroacoustic system and a network, in authors’ laboratory.

Play of the unconscious in pre-service teachers’ self-reflection around race and racism

Reading psychoanalytic theory of the unconscious desire for wholeness in the light of the notion of white racial supremacy, this study explores a constituted difficulty that self-reflection around the issues of race and racism confronts by exploring three white male pre-service teachers’ emotional experiences inscribed in their responses to the process of engaging in self-reflection. The pervasiveness of strong emotional reactions to the process of engaging in self-reflection spoke volumes not only about how uncomfortable the participants felt in the face of ambivalence, incommensurability and vulnerability but also about their active resistance against their emotional states to defend their unconscious desire for wholeness that is intensified by the forces of white racial supremacy. This study also seeks to elaborate problems inherent in teachers’ self-reflection and why and how unknown and unconscious emotional world filters and at times hinders the participants’ willingness to inquire into their own relationship to race and racism. In the final section, the author discusses how the findings may be used to imagine how teachers’ unknown and unconscious emotional world can become subjective curriculum which in turn becomes a foundation for students’ learning or lack thereof and also informs the field of teacher education engaging in critical self-reflection.

基于特征向量的线性相位FIR滤波器设计

本文将线性相位FIR滤波器的设计表示成一个实对称正定矩阵的特征问题。根据求解该矩阵的最小特征值所对应的特征向量来确定滤波器的系数。通过在通带取平均的方法，避免了参考频率的设定问题。仿真结果表明，该方法提高了特征滤波器法的设计性能。 In this paper, the design of a linear phase finite impulse response filter is formulated as an eigen problem of a real, symmetric, positive-definite matrix. The unknown filter coefficients can be obtained by calculating the eigenvector corresponding to the minimum eigenvalue of the matrix. The modified method does not need a reference frequency point for normalization as done in traditional eigenfilters. Instead, average over the passband is carried out. Simulations show that the modified method leads to improved design performance.

IIR model identification using a modified inclined planes system optimization algorithm

Inclined planes system optimization (IPO) is a new optimization algorithm inspired by the sliding motion dynamic along a frictionless inclined surface. In this paper, with the aim of create a powerful trade-off between the concepts of exploitation and exploration, and rectify the complexity of their structural parameters in the standard IPO, a modified version of IPO (called MIPO) is introduced as an efficient optimization algorithm for digital infinite-impulse-response (IIR) filters model identification. The IIR model identification is a complex and practical challenging problem due to multimodal error surface entanglement that many researches have been reported for it. In this work, MIPO utilizes an appropriate mechanism based on the executive steps of algorithm with the constant damp factors. To do this, unknown filter parameters are considered as a vector to be optimized. In implementation, at first, to demonstrate the effectiveness of the proposed method, 10 well-known benchmark functions have been considered for evaluating and testing. In addition, statistical analysis on the powerfulness, efficiency and applicability of the MIPO algorithm are presented. Obtained results in compared to some other popular methods, confirm the efficiency of the MIPO algorithm that makes the best optimal solutions and has a better performance and acceptable solutions.

Full Order H∞ Filter Design for Delayed Singular Systems with Unknown Input and Bounded Disturbance: Time and Frequency Domain Approaches

This paper investigates the problem of the full order H∞ unknown input filter designs in time and frequency domain. The considered systems are linear singular ones with delayed states, delayed input, unknown input and bounded disturbance. Firstly, an Unknown Input Observer (UIO) and a H∞ Unknown Input Filter (H∞ UIF) for such systems are proposed respectively in the time domain. This approach is based on Lyapunov-Krasovskii stability theory, where the gain implemented in the design is an optimal solution of linear matrix inequalities (LMIs). Secondly, a frequency-domain approach is derived from time-domain results by using the factorization approach. The proposed methods show their effectiveness on an illustrative example.

Temporal Filtering of InSAR Data Using Statistical Parameters From NWP Models

Finding solutions for the mitigation of atmospheric phase delay patterns from differential synthetic aperture radar interferometry (d-InSAR) observations is currently one of the most active research topics in radar remote sensing. Recently, many studies have analyzed the performance of regional numerical weather prediction (NWP) models for this task; however, despite the significant efforts made to optimize model parameterizations, most of these studies have concluded that current regional NWPs are not able to robustly reproduce the atmospheric phase delay structures that affect SAR interferograms. Despite these previous findings, we have revisited the application of NWPs for atmospheric correction using a different analysis strategy. In contrast to earlier studies, which assessed the quality of NWP-derived phase screen data, we have studied NWPs from a statistical angle by analyzing whether they are able to provide realistic information about the statistical properties of atmospheric phase signals in d-InSAR data. We have determined that NWP forecasts can provide relevant statistical information about the atmospheric phase screen captured in d-InSAR data. Based on this, this study presents a new atmospheric phase filtering approach that is using statistical atmospheric information as a prior in order to optimize the choice of unknown filter parameters. The mathematical concept of the prior-driven filtering approach is outlined, and its implementation is explained. We have determined the performance of this new filter concept and have shown that it comes very close to a filter optimum.

Relative Localization Approach for Combined Aerial and Ground Robotic System

The objective of this paper is to develop a relative localization method for coordinated control of multi-robotic systems equipped with both aerial and ground vehicles. To overcome the issues of filter initialization and state bias at hard linearization in the general EKF approach, this paper proposes a pseudo-linear measurement-based technique for relative localization where true nonlinear measurements are algebraically transformed into pseudo-linear measurements. These pseudo-linear measurements are then employed for sensor fusion. A nonlinear observability analysis is performed to identify the sufficient conditions under which the proposed pseudo-linear measurement-based relative localization scheme is locally weakly observable. The estimation consistency is analyzed in order to verify that the proposed estimator is consistent and that none of the covariance matrixes lead to ill conditions during the estimation process. The performance of the proposed relative localization scheme is compared with traditional EKF-based methods for unknown filter initialization. The results demonstrate that the proposed method is capable of achieving both the acceptable positional and orientational accuracy within 12 iterations, whereas traditional methods require more than 250 iterations to achieve the same accuracy. This observation verified that the proposed relative localization approach has fast convergence property for unknown filter initialization compared to traditional EKF-based methods.

Parametric meta-filter modeling from a single example pair

We present a method for learning a meta-filter from an example pair comprising an original image $$A$$ A and its filtered version $$A^\prime $$ A ? using an unknown image filter. A meta-filter is a parametric model, consisting of a spatially varying linear combination of simple basis filters. We introduce a technique for learning the parameters of the meta-filter $$f$$ f such that it approximates the effects of the unknown filter, i.e., $$f(A)$$ f ( A ) approximates $$A^\prime $$ A ? . The meta-filter can be transferred to novel input images, and its parametric representation enables intuitive tuning of its parameters to achieve controlled variations. We show that our technique successfully learns and models meta-filters that approximate a large variety of common image filters with high accuracy both visually and quantitatively.

Teaching–learning-based Optimization Algorithm for Parameter Identification in the Design of IIR Filters

This paper presents a teaching–learning-based optimization (TLBO) algorithm to solve parameter identification problems in the designing of digital infinite impulse response (IIR) filter. TLBO based filter modelling is applied to calculate the parameters of unknown plant in simulations. Unlike other heuristic search algorithms, TLBO algorithm is an algorithm-specific parameter-less algorithm. In this paper big bang–big crunch (BB–BC) optimization and PSO algorithms are also applied to filter design for comparison. Unknown filter parameters are considered as a vector to be optimized by these algorithms. MATLAB programming is used for implementation of proposed algorithms. Experimental results show that the TLBO is more accurate to estimate the filter parameters than the BB–BC optimization algorithm and has faster convergence rate when compared to PSO algorithm. TLBO is used where accuracy is more essential than the convergence speed.

A Blind Source Separation Method for Convolved Mixtures by Non-Stationary Vibration Signals

Abstract A simple and feasible of BSS method to separate the convolution mixture of non-stationary vibration signals is present in this paper. The method is carried out by means of two iterative procedures: The first procedure is to estimate the coefficients of the filters. The independence criterion is used and the unknown filters are obtained by a back propagation procedure by means of simplifying the coefficients of filters. The next procedure is to estimate the source vibration signals. The coupled vibration signals are obtained by means of the filters gotten from the former procedure and the estimation sources are obtained through decoupled procedure. Simulation and experiment results show that the method is effective. This improved method can be used to separate convolutive mixtures with non-stationary mechanical vibrations.

Ocean‐generated magnetic field study based on satellite geomagnetic measurements: 2. Signal inference

The work presented here is the second part of an ocean‐generated magnetic field study and provides a procedure for inferring the ocean‐generated magnetic field from satellite geomagnetic measurements. The procedure was first tested on synthetic data. The simulation employed a hypothetical satellite measuring the magnetic field at an altitude of 400 km. The “measurements” (generated by the CM4 and CHAOS models) included the core field, the lithospheric field, the ionospheric and magnetospheric fields, the secular variation, and the ocean‐generated magnetic field. The search algorithm, as proposed in part 1, converts irregular measurements into fields on a regular grid. The filtration procedure is based on the Savitzky‐Golay algorithm. The procedure includes four steps providing seven unknown filter parameters. Parameter values were obtained by solving the problem of minimizing the spatially averaged squared residuals between the inferred field and the model field. Then, the parameters were used in the filter to infer the ocean‐generated magnetic field that was initially added to the “measurements.” The inferred signal, although spatially corrupted and having a smaller magnitude (60% of the magnitude of the initial signal), indicated the presence of magnetic anomalies within the Southern Ocean. The technique was then applied to CHAMP geomagnetic measurements. The result of filtering was clear magnetic anomalies within the Southern Ocean with a spatial character that were close to what models of the ocean‐generated magnetic field provided. The magnitude of the inferring signal was 5 nT, the corrected values were 7–8 nT, 1–2 nT larger than the modeled field magnitude. To compare the temporal variability of the inferred field with the variability of sea surface height, ten 10° by 10° areas were selected within the Southern Ocean and the root‐mean‐square of both SSH and the magnetic field were computed for each area. A comparison of the results indicated a close similarity between SSH and the magnetic field temporal variability, which allowed the identification of the inferred field as the ocean‐generated magnetic field.

Utilising variable vector step-size in normalised LMS algorithm

A new variable step-size normalised least mean square (NLMS) algorithm is proposed in this paper, which is designed for the applications where the unknown filter has an exponential decay impulse response. In the proposed algorithm, a variable vector step-size is used on the basis of maximising the decrease of the mean square deviation (MSD). Theoretical analysis is given to show the validity. Compared with other variable step-size NLMS algorithms, the proposed method has a faster convergence rate and smaller steady state mean square error (MSE). Simulation results show the improved performance of the proposed algorithm. The same idea of utilising variable vector step-size can be expanded to other variable step-size NLMS algorithms.