Matched Field Processing (MFP) is an inversion technique often employed in source localization applications. Conventional MFP approaches are incapable of producing precise results in the presence of ...extremely impulsive noises, which are typically present in actual applications such as underwater acoustics. This is because the covariance matrix for this category of noises does not converge. Moreover, impulsive noise suppression algorithms fail to provide accurate results. Particularly, fractional lower order moment (FLOM)-based approaches have an unbounded output, and data trimming methods introduce uncertainty into the estimation covariance matrix. In this study, a novel MFP method employing the empirical characteristic function (ECF) is developed. The desirable properties of the characteristic function (CF) result in a robust localization method that is ideally suited for extremely strong tailed noise environments. Using the CF array output, a new covariance-like matrix that can be used in MFP methods has been constructed. To demonstrate the efficiency of the ECF-MFP technique, experiments are conducted in a water tank. Experimental results reveal that this method is very robust in the presence of very heavy tailed noise, a low signal-to-noise ratio, and a tiny sample size. Additionally, it outperforms previous approaches in terms of resolution probability.
This paper introduces a new technique for analytical parameter estimation of skewed α-stable distribution with 1<α≤2. Stable distribution as a four-parameter non-Gaussian distribution is completely ...characterized by its characteristic function (CF). There are some serious limitations in parameter estimation of α-stable distribution due to the lack of closed-form expression for the general α-stable probability density function (PDF). The proposed estimator uses a hierarchical framework based on the skewed α-stable CF, and hence, allows a rapid estimation of parameters with high accuracy in real-time signal processing algorithms. In our scheme, only two values of α-stable CF, which has analytic formula, are utilized to estimate the parameters of α-stable density. In addition, the closed-form expression for estimating the required values of CF is derived. To provide a precise quantitative assessment, our proposed approach is compared with three other state-of-the-art estimators which have analytic formulas through a series of goodness-of-fit tests. Simulation results also demonstrate that the proposed method has a good accuracy both for the symmetric and non-symmetric (skewed) α-stable distributions. Furthermore, the advantage of the proposed CF based method becomes more evident through the experimental results obtained from the high-resolution SAR images.
•A novel approach for parameter estimation of α-stable distribution.•Characteristic exponent, skewness, dispersion and location parameters are estimated analytically•Two points of CF are utilized to establish the hierarchical framework of the estimator•Simple implementation with good accuracy for symmetric and non-symmetric distributions•The superior performance of the estimator for both synthetic and real SAR signals
This study employs the Lamb wave method to detect damage in Fiber–metal laminates (FMLs). The method is based on quasi-isotropic behavior approximation and beamforming techniques. Delay and sum and ...minimum variance distorsionless response beamformers are applied to a uniform linear phased array. The simulation in finite element software is conducted to evaluate the performance of the presented procedure. The two types of damage studied are the following: (1) Delamination between fiber–epoxy and metal layers and (2) crack on the metal layer. The present study has the following important contributions: (1) Health monitoring of multi-damaged FMLs using Lamb waves and beamforming technique, (2) detection of damage type, (3) detection of damage size by 1D phased array, and (4) identification of damages that occurred very close to the laminate edges or close to each other.
By reducing fossil fuel use, renewable energy improves the economy, quality of life, and environment. These impacts make renewable energy forecasting crucial for lowering fossil fuel utilization. ...This paper aims to mathematically improve time series forecasting literature by focusing on solar irradiance applications in Los Angeles, Denver, and Hawaii solar irradiance sites. A three-phased time series forecasting hybrid method is devised for this endeavor. The ARFIMA is used to forecast the original solar irradiance time series in phase I. Next, the dataset’s residuals, are retrieved by subtracting the phase I results from the observed time series to prepare the scenario for the following phase. A novel enhanced fractional Brownian motion is used for residual forecasting in phase II. The parameter estimation in phase II is implemented adaptively to capture the dynamic statistical characteristics of the time series efficiently. Finally, the phases I and II results are numerically conglomerated to form the final forecasting results in phase III. The residual forecasting part, in phase II, reveals a substantial superiority. Also, when comparing the proposed hybrid algorithm results to other existing cutting-edge algorithms applied to the same solar irradiance applications, the output demonstrates that the suggested algorithm has a significantly improved performance.
Image denoising is a crucial task in the field of image processing, and Bayesian estimation has emerged as a prominent approach. To effectively employ Bayesian estimation, it is essential to assume a ...priori distribution corresponding to the transform coefficients of the noise-free image. In this paper, we propose a novel Bayesian image despeckling method that leverages the 2D Complex Generalized Autoregressive Conditional Heteroscedasticity Mixture (CGARCH-M) model within the framework of the 2D Discrete Orthonormal Stockwell Transform (DOST). Prior to introducing this method, we present a novel statistical analysis of the 2D DOST coefficients of log-transformed images. Speckle noise, commonly found in synthetic aperture radar (SAR) images, is modeled as multiplicative noise. To effectively suppress speckle noise, our proposed method utilizes a novel adaptive Bayes risk estimator known as compound maximum a posteriori (CMAP). By employing CMAP, we estimate the noise-free 2D DOST coefficients from the noisy ones, which are modeled using the 2D CGARCH-M. Notably, this paper introduces the 2D CGARCH-M model for 2D complex stochastic processes for the first time, extending the capabilities of the GARCH model and its subsequent extensions that were limited to real-valued processes. The proposed model incorporates location-dependent conditional variances to capture the non-Gaussian statistics of 2D DOST coefficients of log-transformed images and the dependencies between them. Through our statistical analysis, we establish the compatibility between the 2D CGARCH-M model and these coefficients. Our proposed method takes into account both magnitude and phase by utilizing the real and imaginary components of the DOST coefficients concurrently. It provides an optimal and closed-form solution, significantly reducing memory and computational requirements. Moreover, unlike state-of-the-art approaches in this domain, our method exhibits robustness to initial parameter settings. To evaluate the effectiveness of our approach, we conduct comparisons with other denoising methods on artificially speckled aerial images and actual SAR images. The results demonstrate the superior performance of our method.
•2D CGARCH-M models 2D complex stochastic processes and captures statistics and dependencies.•Statistical analysis of 2D DOST coefficients of images, showing their non-Gaussian statistics.•Adaptive CMAP Bayes risk estimator, based on 2D CGARCH-M in 2D DOST domain for image despeckling.•Provides a closed-form solution for despeckling image, reducing memory and computational costs.•Employs absolutely referenced phased information of images.
The low-cost received signal strength indicators (RSSIs) are commonly employed in indoor tracking using various state estimation methods, including particle filters (PFs). In the context of target ...tracking, PFs often employ the constant velocity (CV) and the constant acceleration (CA) models as transition models. This paper proposes an alternative model that replaces the CV with a stacked long short-term memory (LSTM) model. The trained stacked LSTM model is the transition function in the two-step auxiliary sampling importance resampling (TS-ASIR) filter. TS-ASIR filter introduces a two-time step transition model derived from sequential importance sampling (SIS). This filter is characterized by two auxiliary variables representing indices from the previous steps. Besides, the generalized regression neural network (GRNN) is employed for position estimation, utilizing RSSI measurements in an environment with high noise levels. Furthermore, map-aiding (MA) is integrated with the TS-ASIR to reduce localization and tracking errors on a 2-D plane. The MA improves the accuracy by updating particle weights according to a digital map, independently of infrastructure. The MA method updates particle weights twice for the TS-ASIR filter. Notably, when assessing the root mean square error (RMSE), the GRNN+TS-ASIR-LSTM-MA approach demonstrates superior accuracy compared to the filtered estimated GRNN position by the unscented Kalman filter (UKF) that was implemented using the CV model, with improvements of 38.20% and 57.12% in the two considered scenarios.
This paper considers the estimation and detection problems for statistically dependent heavy-tailed signals with no closed-form probability density function (PDF). We propose two parametric PDF ...approximations for symmetric α-stable (SαS) distribution to be utilized in approaches based on the Maximum likelihood (ML) criterion. The nonlinear least square (LS) and curve fitting are used to compute parameters of the new formulations which are functions of the characteristic exponent. Moreover, we study binary signal detection in channels with time-dependent heavy-tailed noise modeled by SαS distribution and first order autoregressive (AR(1)) process. Using the novel PDF approximations in the ML estimator, an algorithm for model parameters estimation of the noise is initially developed. Then, new suboptimal receivers are designed through the use of the new PDF formulations and parameter estimates. Numerical results demonstrate the superiority of the proposed approximations over the existing formulations, and also good accuracy for the estimation algorithm. Additionally, it is shown that the proposed detectors operate near optimal receiver and also outperform the other suboptimal detectors, especially when α is small.
•Two parametric PDF approximations for symmetric α-stable (SαS) distribution are proposed.•For every arbitrary value of α, curve fitting is employed to estimate the model parameters of approximations.•Binary signal detection in the presence of time-dependent heavy-tailed noise described by the SαS AR(1) model is studied.•By usng the proposed PDF approximations in the ML estimator, an algorithm for the noise parameters estimation is developed.•The proposed detectors based on the PDF approximations show the superior and near-optimal performance.
Image denoising and image quality enhancement are major issues in image processing. Additive and multiplicative noise removal is one of the main image enhancement approaches. In this paper, we ...propose a novel 2D Merged Complex Generalized Autoregressive Conditional Heteroscedasticity Mixture (MC-GARCH-M) model for 2D complex stochastic processes. This model effectively captures non-Gaussian statistics and all three types of dependencies within the processes (RRD, IID, and RID) using the proposed linear mapping transformation T. Our statistical analysis shows that the 2D MC-GARCH-M model provides the best fit to the non-Gaussian statistics of the mapped matrix of 2D DOST coefficients compared to Gaussian, Generalized Gaussian, and Stable distributions. We confirm the presence of heteroscedasticity in the mapped matrix using the Engle hypothesis test, verifying ARCH/GARCH effects. The 2D MC-GARCH-M model, with its location-dependent conditional variances, provides a flexible approach for noise removal and modeling complex stochastic processes. Experimental results on artificially speckled aerial and actual SAR images demonstrate that our method outperforms state-of-the-art approaches in terms of speckle removal and preserving the edges and textural information of the image. Key innovations include: a new statistical analysis using linear mapping T showing non-Gaussian heavy-tailed distributions; an adaptive Bayesian estimator, MCMAP, based on the heteroscedastic model for speckle noise removal; and the method's applicability to images with varying mutual information (MI) between real and imaginary parts of 2D DOST coefficients. Our method is adaptive and robust to initial parameter settings, effectively utilizing magnitude and phase information, providing an optimal closed-form solution, reducing memory and computational requirements, and demonstrating robustness to speckle power levels. While requiring more computational resources compared to thresholding methods, our approach is less demanding than other Bayesian algorithms, making it suitable for offline processing.
•MC-GARCH-M model: applicable to all 2D complex stochastic processes.•MC-GARCH-M modeling: Captures non-Gaussian statistics and dependencies between the real and imaginary parts.•Statistical analysis of 2D DOST coefficients: Reveals non-Gaussian properties and dependencies, advancing image processing.•Optimal closed-form solution: Reduces computational costs, increases speed for despeckling image 2D DOST coefficients, removes speckle noise using all three types of dependencies in 2D DOST coefficients.•Employs amplitude and absolutely referenced phased information of images.
