Robust Parameter Estimation Research Articles

Source parameters and moment tensor inversion of April 11, 2020 (mb=4.4), the significant El-Negalah Earthquake, Matrouh, Egypt

ABSTRACT A moderate size felt earthquake with a body wave magnitude (mb = 4.4) shocked the western part of northern Egypt on 11 April 2020. The nature of this seismic source has yet to be fully understood. This paper presents an analysis of the seismic source of this significant earthquake. A robust hypocentral parameters estimation is performed by collecting the data from 29 seismic stations in the Eastern Mediterranean region to reduce the azimuthal gap within the available location. The full-waveform Moment Tensor Inversion (MTI) is applied to derive the faulting mechanism of the quake. The obtained solutions indicate a reverse faulting mechanism. The plausibility of the obtained mechanism is analysed in terms of measuring the Kegan angle and evaluating the stability of the resulting mechanism. The source parameters are estimated using the S-wave amplitude displacement spectra. The obtained source parameters indicate that the seismic moment (Mo) is 8.9 × 1015 Nm, the fault radius L is 1013 m, the stress drop (σ) is 3.8 MPa, and the displacement (d) is 0.053 m. The analysis of this seismic source is of fundamental importance for evaluating seismic hazard in northern Egypt, particularly for critical facilities and safe hydrocarbon exploration.

A Novel DOA Estimation for Low-Elevation Target Method Based on Multiscattering Center Equivalent Model

The multipath in very high-frequency (VHF)radar will reduce the direction-of-arrival (DOA) estimation accuracy for the low-angle target following. Since the target and multipath signals have strong coherence in the spatial domain, it is challenging to distinguish them accurately. Especially in some terrain complex regions, various scattering media cause the multipath echo exhibit the multi-channel and nonuniform energy distribution features. Therefore, the single multipath DOA estimation methods will mismatch the actual signal, resulting in inaccurate DOA estimation. The current letter presents a new DOA estimation approach using a multiple scattering center model in complex terrain to solve the mentioned issue. In the presented method, multiple multipath is analogous to a single one based on the multipath signal’s spatial coherence. The equivalent model represents the DOA estimation problem with a parametric optimization problem, and the accurate estimation results can be attained using the Newton optimization approach. Compared with the conventional sparse reconstruction method, the presented method is not restricted by the Restricted Isometry Property (RIP), and employs a robust parameter estimation method to solve the angle super-resolution problem under the low signal-to-noise ratio (SNR). The experimental results reflect that the presented model and approach can efficiently promote the DOA estimation precision and calculational performance compared to conventional DOA estimation approaches.

A unique cardiac electrocardiographic 3D model. Toward interpretable AI diagnosis.

Mathematical models of cardiac electrical activity are one of the most important tools for elucidating information about heart diagnostics. In this paper, we present an efficient mathematical formulation for this modeling simple enough to be easily parameterized and rich enough to provide realistic signals. It relies on a five dipole representation of the cardiac electric source, each one associated with the well-known waves of the electrocardiogram signal. Beyond the physical basis of the model, the parameters are physiologically interpretable as they characterize the wave shape, similar to what a physician would look for in signals, thus making them very useful in diagnosis. The model accurately reproduces the electrocardiogram signals of any diseased or healthy heart. This new discovery represents a significant advance in electrocardiography research. It is especially useful for diagnosis, patient follow-up or decision-making on new therapies; is also a promising tool for well-performing, transparent and interpretable AI approaches.

Robust estimation in functional comparative calibration models via maximum Lq-likelihood

A fully parametric estimation procedure is proposed for robust estimation of the structural parameter in a functional comparative calibration model, under normality. The proposed estimator is obtained, based on maximum Lq-likelihood approach, first replacing the incidental parameters by estimators depending on the structural parameter. The estimator, called MLqE, depends on a single distortion parameter q, which controls the balance between robustness and efficiency. If q tends to 1, the maximum likelihood estimator (MLE) is obtained. The estimation procedure can be implemented easily by a simple and fast reweighting algorithm. For applying the method to practical and real-data scenarios, a data-based choice of an appropriate value of q is proposed. Consistency and asymptotic normality is established and the covariance matrix is given. The influence function is derived, to show the local robustness properties. Theoretical properties, ease of implementabiliy and empirical results on simulated and real data show the satisfactory behavior of the MLqE and its vantages over the MLE in presence of observations discordant with the assumed model.

Estimating Homogeneous Data-Driven BRDF Parameters From a Reflectance Map Under Known Natural Lighting.

In this article we demonstrate robust estimation of the model parameters of a fully-linear data-driven BRDF model from a reflectance map under known natural lighting. To regularize the estimation of the model parameters, we leverage the reflectance similarities within a material class. We approximate the space of homogeneous BRDFs using a Gaussian mixture model, and assign a material class to each Gaussian in the mixture model. We formulate the estimation of the model parameters as a non-linear maximum a-posteriori optimization, and introduce a linear approximation that estimates a solution per material class from which the best solution is selected. We demonstrate the efficacy and robustness of our method using the MERL BRDF database under a variety of natural lighting conditions, and we provide a proof-of-concept real-world experiment.

Image downsampling expedited adaptive least-squares (IDEAL) fitting improves intravoxel incoherent motion (IVIM) analysis in the human kidney.

To improve the reliability of intravoxel incoherent motion (IVIM) model parameter estimation for the DWI in the kidney using a novel image downsampling expedited adaptive least-squares (IDEAL) approach. The robustness of IDEAL was investigated using simulated DW-MRI data corrupted with different levels of Rician noise. Subsequently, the performance of the proposed method was tested by fitting bi- and triexponential IVIM model to in vivo renal DWI data acquired on a clinical 3 Tesla MRI scanner and compared to conventional approaches (fixed D* and segmented fitting). The numerical simulations demonstrated that the IDEAL algorithm provides robust estimates of the IVIM parameters in the presence of noise (SNR of 20) as indicated by relatively low absolute percentage bias (maximal sMdPB <20%) and normalized RMSE (maximal RMSE <28%). The analysis of the in vivo data showed that the IDEAL-based IVIM parameter maps were less noisy and more visually appealing than those obtained using the fixed D* and segmented methods. Further, coefficients of variation for nearly all IVIM parameters were significantly reduced in cortex and medulla for IDEAL-based biexponential (coefficients of variation: 4%-50%) and triexponential (coefficients of variation: 7.5%-75%) IVIM modelling compared to the segmented (coefficients of variation: 4%-120%) and fixed D* (coefficients of variation: 17%-174%) methods, reflecting greater accuracy of this method. The proposed fitting algorithm yields more robust IVIM parameter estimates and is less susceptible to poor SNR than the conventional fitting approaches. Thus, the IDEAL approach has the potential to improve the reliability of renal DW-MRI analysis for clinical applications.

Robust adaptive parameter estimator design for a multi-sinusoidal signal with fixed-time stability and guaranteed prescribed performance boundary of estimation error

In online parameter estimation, fast and accurate estimation without dependence on the initial conditions with good transient properties is an essential issue. Hence, in this paper, a robust adaptive parameter estimation method is proposed that not only can estimate online the unknown parameters of a multi sinusoidal signal in a finite-time without dependence on the initial conditions but also can guarantee the transient and steady-state performance of the estimated parameters with a predefined boundary. At first, to estimate the frequency, offset, phase and amplitude, the multi-sinusoidal signal is represented in a linear regression form. Then, by defining an auxiliary regressor matrix and vector derived by the original regressor vector and output signal, the estimation error is computed indirectly. By employing this parameter estimation error and utilizing the fixed-time stability property of the terminal sliding mode method and Prescribed-Performance concept, robust adaptation laws are designed in such a way that the convergence time of the estimation error is finite so that its settling time is independent from the initial guess, and this time can be predefined. Moreover the estimation error boundary can be predefined. Furthermore, in this method, only the output measurement is needed and there is no need for any observer or predictor. Using the Lyapunov stability theorem it is proved that the estimation error converges to zero when the measurement is free of noise and for the noisy case the estimation error is uniformly ultimately bounded and converges to a compact set around the origin. Three illustrative examples are provided to demonstrate the advantages and effectiveness of the designed estimation laws compared to some existing methods. Simulation results show that the proposed method can estimate the unknown parameters in fixed-time with a pre-adjustable estimation error boundary, even in the presence of measurement noise and confirms the superiority of the proposed method compared to the two existing methods.

A robust and efficient wall parameter estimation approach for through wall radar

AbstractIn through-wall radar system, the wall parameters, including permittivity, and wall thickness are of crucial importance for locating targets precisely. Recently, to obtain a quick and accurate estimation of wall parameters, an approach based on machine learning was introduced. However, these approaches are less reliable as only simulations results are presented. One of the major concerns with machine learning-based approaches is the generation of training and testing data which require fabrication of wall with different permittivity, thickness, and conductivity. Creating walls with different permittivity, thickness, and conductivity can really be challenging and expensive. Therefore, an effort has been made in this paper to establish a cost-effective and robust machine learning-based wall parameter estimation process with the usage of transmission line method and artificial neural network. The implementation and efficacy of proposed approach have been demonstrated through simulation and experimental results. The proposed approach quickly and accurately predicted the wall relative permittivity and thickness of real building wall. The merit of proposed approach is that it is less complex and computational efficient as it can extract wall parameters from only one measurement and therefore can be used in conjunction with any commercial through-wall radar systems.

Estimation of breeding population size using DNA-based pedigree reconstruction in brown bears.

Robust estimates of demographic parameters are critical for effective wildlife conservation and management but are difficult to obtain for elusive species. We estimated the breeding and adult population sizes, as well as the minimum population size, in a high‐density brown bear population on the Shiretoko Peninsula, in Hokkaido, Japan, using DNA‐based pedigree reconstruction. A total of 1288 individuals, collected in and around the Shiretoko Peninsula between 1998 and 2020, were genotyped at 21 microsatellite loci. Among them, 499 individuals were identified by intensive genetic sampling conducted in two consecutive years (2019 and 2020) mainly by noninvasive methods (e.g., hair and fecal DNA). Among them, both parents were assigned for 330 bears, and either maternity or paternity was assigned to 47 and 76 individuals, respectively. The subsequent pedigree reconstruction indicated a range of breeding and adult (≥4 years old) population sizes: 128–173 for female breeders and 66–91 male breeders, and 155–200 for female adults and 84–109 male adults. The minimum population size was estimated to be 449 (252 females and 197 males) in 2019. Long‐term continuous genetic sampling prior to a short‐term intensive survey would enable parentage to be identified in a population with a high probability, thus enabling reliable estimates of breeding population size for elusive species.

Dynamic Contrast-Enhanced MRI in the Abdomen of Mice with High Temporal and Spatial Resolution Using Stack-of-Stars Sampling and KWIC Reconstruction.

Application of quantitative dynamic contrast-enhanced (DCE) MRI in mouse models of abdominal cancer is challenging due to the effects of RF inhomogeneity, image corruption from rapid respiratory motion and the need for high spatial and temporal resolutions. Here we demonstrate a DCE protocol optimized for such applications. The method consists of three acquisitions: (1) actual flip-angle B1 mapping, (2) variable flip-angle T1 mapping and (3) acquisition of the DCE series using a motion-robust radial strategy with k-space weighted image contrast (KWIC) reconstruction. All three acquisitions employ spoiled radial imaging with stack-of-stars sampling (SoS) and golden-angle increments between the views. This scheme is shown to minimize artifacts due to respiratory motion while simultaneously facilitating view-sharing image reconstruction for the dynamic series. The method is demonstrated in a genetically engineered mouse model of pancreatic ductal adenocarcinoma and yielded mean perfusion parameters of Ktrans = 0.23 ± 0.14 min−1 and ve = 0.31 ± 0.17 (n = 22) over a wide range of tumor sizes. The SoS-sampled DCE method is shown to produce artifact-free images with good SNR leading to robust estimation of DCE parameters.

Parameter estimation in fluid flow models from aliased velocity measurements

Parameter estimation in blood flow models from measured velocity data—as e.g. velocity-encoded MRI—is a key step for patient-specific hemodynamic analysis. However, velocity encoding suffers from competing noise and aliasing artifacts, which negatively impact the parameter estimation results. The aim of this work is to propose a new inverse problem formulation capable of tackling aliased and noisy velocity MRI measurements in parameter estimation in flows. The formulation is based on a modification of the quadratic cost function for velocity measurements. This allows for a correct parameter estimation when they have influence on the whole measurement domain, in spite of aliasing artifacts. The new inverse problem can be solved numerically using any standard solver, and we show how a popular sequential approach can be applied. Numerical results in an aortic flow show robust parameter estimation for velocity encoding ranges until 30% of the maximal velocity of the problem, while the standard inverse problem fails already for any encoding velocity smaller than the true one. Moreover, the parameter estimation results are even improved for reduced velocity encoding ranges when using the new cost function. The presented approach allows therefore for great flexibility in personalization of blood flows models from MRI data commonly encountered in the clinical context.

Slab-driven flow at the base of the mantle beneath the northeastern Pacific Ocean

Flow in the mantle's bottom boundary layer plays an important role in shaping structures and processes in the deep mantle; however, knowledge of lowermost mantle flow patterns remains elusive. In particular, the influence of remnant slabs on lowermost mantle flow is poorly known, although it is likely that slabs play an important role in driving flow and thus in controlling key aspects of lowermost mantle behavior. Measurements of seismic anisotropy can yield relatively direct constraints on slab-induced lowermost mantle flow; however, such observations are challenging to make. We take advantage of the excellent raypath coverage beneath the northeastern Pacific Ocean provided by the USArray deployment in North America to provide detailed sampling of a region that has a long subduction history, with remnant slabs likely impinging on the core-mantle boundary. We present observations of coherent, strong shear wave splitting of SKKS and Sdiff phases across USArray stations and show through global wavefield modeling that the splitting is due to lowermost mantle anisotropy. A stacking approach enables us to make robust estimates of lowermost mantle splitting parameters, which we model by considering realistic mineral physics scenarios. Under the assumption of simple horizontal shear deformation, our observations are consistent with generally north-south flow directions for either a post-perovskite or a bridgmanite mineralogy; ferropericlase cannot explain observations. We speculate that this flow is driven by subducting slab remnants impinging on the core-mantle boundary.

Robust Adaptive Least Mean M-Estimate Algorithm for Censored Regression

An adaptive least mean M-estimate algorithm for censored regression (CR-LMM) is presented for the robust parameter estimation of the censored regression system. To correct the bias produced by censored observation, the estimated error derived from the probit regression model is employed to construct an M-estimate cost function. It can expel the adverse impact of the impulsive noise and is solved by the unconstrained optimization method. Furthermore, the robust variable step-size (VSS) strategy, which is also predicted on the robust cost function, is also utilized to improve the convergence performance of the proposed CR-LMM algorithm, i.e., convergence speed and steady-state mean square deviation. The condition which guarantees the CR-LMM algorithm stability is obtained by analyzing the convergence in the mean and mean-square sense, and the theoretical steady-state result is also derived. Computer simulations in system identification scenarios are carried out to demonstrate that the proposed algorithms are superior to the existing algorithms in the impulsive environment with different background noise and the theoretical results are verified.

Pediatric AIDS-Therapeutic Successes Built on a Foundation of Pediatric Clinical Pharmacology with Pharmacokinetic-Pharmacodynamic Modeling.

Pediatric AIDS-Therapeutic Successes Built on a Foundation of Pediatric Clinical Pharmacology with Pharmacokinetic-Pharmacodynamic Modeling.

Characterizing beam errors for radio interferometric observations of reionization

ABSTRACT A limiting systematic effect in 21-cm interferometric experiments is the chromaticity due to the coupling between the sky and the instrument. This coupling is sourced by the instrument primary beam; therefore it is important to know the beam to extremely high precision. Here, we demonstrate how known beam uncertainties can be characterized using data bases of beam models. In this introductory work, we focus on beam errors arising from physically offset and/or broken antennas within a station. We use the public code oskar to generate an ‘ideal’ SKA beam formed from 256 antennas regularly spaced in a 35-m circle, as well as a large data base of ‘perturbed’ beams sampling distributions of broken/offset antennas. We decompose the beam errors (‘ideal’ minus ‘perturbed’) using principal component analysis (PCA) and Kernel PCA (KPCA). Using 20 components, we find that PCA/KPCA can reduce the residual of the beam in our data sets by $60\!-\!90{{\ \rm per\ cent}}$ compared with the assumption of an ideal beam. Using a simulated observation of the cosmic signal plus foregrounds, we find that assuming the ideal beam can result in $1{{\ \rm per\ cent}}$ error in the epoch of reionization (EoR) window and $10{{\ \rm per\ cent}}$ in the wedge of the 2D power spectrum. When PCA/KPCA is used to characterize the beam uncertainties, the error in the power spectrum shrinks to below $0.01{{\ \rm per\ cent}}$ in the EoR window and $\le 1{{\ \rm per\ cent}}$ in the wedge. Our framework can be used to characterize and then marginalize over uncertainties in the beam for robust next-generation 21-cm parameter estimation.

A Deep Learning Model for Earthquake Parameters Observation in IoT System-Based Earthquake Early Warning

Earthquake early-warning system (EEWS) is inevitable for saving human lives. The fast determination of the Earthquake’s (EQ’s) magnitude and its location is significant in disaster management and EQ risk mitigation. These parameters can be conveyed over the Internet-of-Things (IoT) network to alleviate an EQ disaster. In this article, a deep learning model based on integrating autoencoder (AE) and convolutional neural network (CNN) for a swift pinpointing of EQ magnitude and location after 3 s from the onset of the P-wave is proposed. Thus, we name it 3 s AE and CNN (3S-AE-CNN). The employed data set is observed by three stations from the Japanese Hi-net seismic network. We have trained our model on 12200 events (109.80 thousand 3-s-three-component seismic windows). The model facilitates the extraction of waveforms’ significant features leading to robust estimation of the EQ parameters. The proposed model predicts the magnitude and location of EQ with errors in magnitude, latitude, and longitude that reach 0.000028, 0.0000033, and 0.0001, respectively. The EQ’s parameters calculated by the proposed 3S-AE-CNN model are swiftly sent to a centralized IoT system that in turn directs the involved entity to take suitable action. The obtained results of the 3S-AE-CNN are compared to the conventional manual solution method, which represents the optimum solution mean. The 3S-AE-CNN shows an enhanced performance for the magnitude and location determination as compared with the benchmark method, which proves its effectiveness for EEWS.

Tackling the Unique Challenges of Low-frequency Solar Polarimetry with the Square Kilometre Array Low Precursor: The Algorithm

Coronal magnetic fields are well known to be one of the crucial parameters defining coronal physics and space weather. However, measuring the global coronal magnetic fields remains challenging. The polarization properties of coronal radio emissions are sensitive to coronal magnetic fields. While they can prove to be useful probes of coronal and heliospheric magnetic fields, their usage has been limited by technical and algorithmic challenges. We present a robust algorithm for precise polarization calibration and imaging of low-radio frequency solar observations and demonstrate it on data from the Murchison Widefield Array, a Square Kilometre Array (SKA) precursor. This algorithm is based on the Measurement Equation framework, which forms the basis of all modern radio interferometric calibration and imaging. It delivers high-dynamic-range and high-fidelity full-Stokes solar radio images with instrumental polarization leakages <1%, on par with general astronomical radio imaging, and represents the state of the art. Opening up this rewarding, yet unexplored, phase space will enable multiple novel science investigations and offer considerable discovery potential. Examples include detection of low-level circular polarization from thermal coronal emission to estimate large-scale quiescent coronal fields; polarization of faint gyrosynchrotron emissions from coronal mass ejections for robust estimation of plasma parameters; and detection of the first-ever linear polarization at these frequencies. This method has been developed with the SKA in mind and will enable a new era of high-fidelity spectropolarimetric snapshot solar imaging at low radio frequencies.

The principle of maximum entropy and the probability-weighted moments for estimating the parameters of the Kumaraswamy distribution.

Since Shannon’s formulation of the entropy theory in 1940 and Jaynes’ discovery of the principle of maximum entropy (POME) in 1950, entropy applications have proliferated across a wide range of different research areas including hydrological and environmental sciences. In addition to POME, the method of probability-weighted moments (PWM), was introduced and recommended as an alternative to classical moments. The PWM is thought to be less impacted by sampling variability and be more efficient at obtaining robust parameter estimates. To enhance the PWM, self-determined probability-weighted moments was introduced by (Haktanir 1997). In this article, we estimate the parameters of Kumaraswamy distribution using the previously mentioned methods. These methods are compared to two older methods, the maximum likelihood and the conventional method of moments techniques using Monte Carlo simulations. A numerical example based on real data is presented to illustrate the implementation of the proposed procedures.

Reproducibility of strength performance and strength-endurance profiles: A test-retest study.

The present study was designed to evaluate the test-retest consistency of repetition maximum tests at standardized relative loads and determine the robustness of strength-endurance profiles across test-retest trials. Twenty-four resistance-trained males and females (age, 27.4 ± 4.0 y; body mass, 77.2 ± 12.6 kg; relative bench press one-repetition maximum [1-RM], 1.19 ± 0.23 kg•kg-1) were assessed for their 1-RM in the free-weight bench press. After 48 to 72 hours, they were tested for the maximum number of achievable repetitions at 90%, 80% and 70% of their 1-RM. A retest was completed for all assessments one week later. Gathered data were used to model the relationship between relative load and repetitions to failure with respect to individual trends using Bayesian multilevel modeling and applying four recently proposed model types. The maximum number of repetitions showed slightly better reliability at lower relative loads (ICC at 70% 1-RM = 0.86, 90% highest density interval: [0.71, 0.93]) compared to higher relative loads (ICC at 90% 1-RM = 0.65 [0.39, 0.83]), whereas the absolute agreement was slightly better at higher loads (SEM at 90% 1-RM = 0.7 repetitions [0.5, 0.9]; SEM at 70% 1-RM = 1.1 repetitions [0.8, 1.4]). The linear regression model and the 2-parameters exponential regression model revealed the most robust parameter estimates across test-retest trials. Results testify to good reproducibility of repetition maximum tests at standardized relative loads obtained over short periods of time. A complementary free-to-use web application was developed to help practitioners calculate strength-endurance profiles and build individual repetition maximum tables based on robust statistical models.

Coherent modeling of longitudinal causal effects on binary outcomes.

Analyses of biomedical studies often necessitate modeling longitudinal causal effects. The current focus on personalized medicine and effect heterogeneity makes this task even more challenging. Toward this end, structural nested mean models (SNMMs) are fundamental tools for studying heterogeneous treatment effects in longitudinal studies. However, when outcomes are binary, current methods for estimating multiplicative and additive SNMM parameters suffer from variation dependence between the causal parameters and the noncausal nuisance parameters. This leads to a series of difficulties in interpretation, estimation, and computation. These difficulties have hindered the uptake of SNMMs in biomedical practice, where binary outcomes are very common. We solve the variation dependence problem for the binary multiplicative SNMM via a reparameterization of the noncausal nuisance parameters. Our novel nuisance parameters are variation independent of the causal parameters, and hence allow for coherent modeling of heterogeneous effects from longitudinal studies with binary outcomes. Our parameterization also provides a key building block for flexible doubly robust estimation of the causal parameters. Along the way, we prove that an additive SNMM with binary outcomes does not admit a variation independent parameterization, thereby justifying the restriction to multiplicative SNMMs.