Robust Estimation Method Research Articles

A robust direction-of-arrival estimation method for impulsive noise environments

The performance of conventional direction-of-arrival (DOA) estimation methods degrades greatly when there are few snapshots and the noise model is mismatched, especially in impulsive noise environments. To solve this problem, this paper proposes a robust DOA estimation method, which is robust to the probability density function of impulsive noise. First, by exploiting the low-rank decomposition of the residual fitting error matrix and the characteristics of impulsive noise, three conditions of a good cost function in impulsive noise environments are proposed, and a unified cost function framework is established. Based on this, a robust cost function is designed to suppress the contribution of samples with impulsive noise to the cost function. Then, a bi-iterative complex fixed-point algorithm (BI-CFPA) is developed for the nonconvex optimization problem of signal subspace estimation based on the proposed robust cost function. Theoretical analyses indicate that the BI-CFPA has excellent numerical stability and low computational complexity. Finally, with the estimated signal subspace, the multiple signal classification technique is employed to obtain DOA estimates. Simulation results show that the proposed DOA estimator performs better than existing methods in three typical impulsive noise environments, especially under fairly strong impulsive noise.

Robust explicit estimators using the power-weighted repeated medians

This paper consists of two parts. The first part of the paper is to propose an explicit robust estimation method for the regression coefficients in simple linear regression based on the power-weighted repeated medians technique that has a tuning constant for dealing with the trade-offs between efficiency and robustness. We then investigate the lower and upper bounds of the finite-sample breakdown point of the proposed method. The second part of the paper is to show that based on the linearization of the cumulative distribution function, the proposed method can be applied to obtain robust parameter estimators for the Weibull and Birnbaum-Saunders distributions that are commonly used in both reliability and survival analysis. Numerical studies demonstrate that the proposed method performs well in a manner that is approximately comparable with the ordinary least squares method, whereas it is far superior in the presence of data contamination that occurs frequently in practice.

Robust estimation with exponential squared loss for partially linear panel data model with fixed effects

In this article, a robust estimation method is proposed for a partially linear panel data model with fixed effects. We eliminate the fixed effects based on auxiliary linear regression, then approximate the unknown non parametric component with B-spline function, and obtain the robust estimators of the parametric and non parametric components by combining projection matrix with exponential squared loss function. Under some regularity conditions, the asymptotic properties of the resulting estimators are proved. Some simulation studies illustrate that the proposed method is more robust than the semiparametric least squares dummy variable estimator. The proposed procedure is illustrated by a real data application.

Influence of Structure and Texture Feature on Retrieval of Ramie Leaf Area Index

Leaf area index (LAI), as one of the important crop field phenotypes, plays a crucial role in evaluating crop growth and yield. The remote sensing method for crop parameters monitoring makes it possible to obtain crop LAI in a large area, efficiently and non-destructively. Fusion of spectral features, structure features, and texture features obtained by remote sensing images can effectively improve LAI estimation performance, but the impact of crop structure and texture feature differences on LAI remote sensing monitoring remains unclear. In this study, ramie was classified according to the differences of canopy structure, and then the LAI inversion performance of ramie was evaluated under different datasets to determine the contribution of structure features (canopy coverage, plant height) and texture features derived from remote sensing images to LAI estimation. Finally, multi-feature remote sensing indexes were integrated to construct the optimal ramie LAI estimation model. The results showed that structure features and texture features had an effect on ramie LAI inversion performance, and there were significant differences in LAI estimation accuracy among different data sets. A single structure feature or texture feature could not significantly optimize LAI inversion performance, while multi-feature fusion could effectively improve LAI estimation accuracy (R2 = 0.776, RMSE = 0.740). This study provides a robust, practical, and low-cost method for ramie LAI estimation, and provides a reference for crop LAI inversion research based on structural features and texture features.

A study on using robust hedonic regression implementation

This article aims to determine the features affecting the price of a product with the hedonic regression model and to estimate the contribution of each feature to the price by using robust regression estimation methods. For the analysis, the price and feature information of the laptop product group were obtained from the big data source by using the web scraping method. Four alternatives of the hedonic regression model are used to determine the features affecting the price of the laptops. The contribution of each feature to the laptop price is estimated by using the robust (Huber M-estimator) estimation method and the Ordinary Least Squares (OLS) estimation method, and the resulting estimates are compared for both methods. In the framework of the data set used in the study, it is observed that the effective model is the Logarithmic Robust Hedonic Regression Model.

Evaluation of surface reflectance retrieval over diverse surface types using SREM algorithm in varied aerosol conditions for coarse to medium resolution data from multiple spaceborne sensors

ABSTRACT Surface reflectance (SR) is one of the most important components for deriving different biophysical parameters from remotely sensed data. For accurate retrieval of SR, it is essential to accurately estimate the degree of atmospheric alteration to the target signals reaching at-sensor. Simplified and robust SR estimation method (SREM) is one such approximate estimation method that could demonstrate the retrieval of SR from top-of-atmosphere (ToA) signals, without using any precalculated LUTs or aerosol information. The present study attempts to assess the accuracy of the SREM algorithm over varied Indian land surfaces using data from Landsat 8, Sentinel 2, AWiFS and LISS III. The results indicate that while SREM performs quite well for Sentinel 2 over most land surface types, the performance is good for Landsat 8 as well except over water and in coastal aerosol band. SREM retrievals also show high correlation for AWiFS and LISS III but the estimated values are much lower than level 2 SR due to smaller ToA reflectance values. Furthermore, while aerosol load does impact the performance adversely, it is least impactful for Sentinel 2 and LISS III datasets and most over Landsat 8, particularly over water. Additionally, while AWiFS and LISS III SR retrievals are underestimated at all spectral bands, retrieval is slightly underestimated from green to SWIR band in case of Sentinel 2 and SWIR band in case of Landsat 8. Overall, the findings demonstrate that while SREM will need to be modified to adapt to LISS III and AWiFS retrievals, it can, nevertheless, be readily used as a simplified method for quick and approximate estimation of SR over the Indian region using data from Landsat 8 and Sentinel 2.

Simultaneous assessment of ciprofloxacin and dexamethasone in ocular tear fluid by LC-MS/MS: Application to a pharmacokinetic study in rabbits

• Robust and fast method for estimation of CFX and DEX in rabbit tears, aqueous humor, and corneal biofluids using LC-MS/MS were established. • The developed method was successfully validated as per USFDA guidelines. • Simple precipitation technique used for extraction. • The method was applied for the pharmacokinetic study of marketed CFX and DEX eye drop solution in NZ Albino Rabbits. • PK/PD indices and simulation were estimated. A simple and fast LC-MS/MS method was developed and validated for simultaneous quantitation of ciprofloxacin (CIP) and dexamethasone (DEX) in tear fluid and partially validated for aqueous humor and cornea. Samples were cleaned- up by single-step precipitation using methanol as an anti-solvent. Agilent SB C 18 column with a total run time of 4.5 min was used for chromatographic separation utilizing isocratic mode. MS detection was carried out by a triple quadrupole tandem mass spectrometer (TQMS) in the multiple reaction monitoring (MRM) modes utilizing a positive electrospray ionization (+ESI). The developed method showed a wide analytical range (CIP: 0.7812 – 200 ng/mL and DEX: 1.875- 240 ng/mL) with good linearity (r 2 > 0.998) and acceptable accuracy and precision. It also showed excellent recoveries (> 85% for all analytes) and a negligible matrix effect. Finally, this method was successfully applied to the pharmacokinetic (PK) profile of clinically used eye drop solution of CIP and DEX (CiploxD) in preclinical rabbit tears, suggesting its suitability for PK profiling and PK-based dosage regimen design against various pathogens.

Robust DOA Estimation Using VSS-LMS With Low-Rank Matrix Approximation

Direction-of-arrival (DOA) estimation performance of adaptive filtering-based methods, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">e.g.</i> , least mean square (LMS), degrades significantly in adverse conditions ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i.e.,</i> at low signal-to-noise ratio (SNR), small number of antenna array elements and snapshots, and in presence of two closely spaced signal sources). Moreover, these estimation methods require many regulating parameters to efficiently update the step size, which are very difficult to tune manually in practical scenarios. Although the subspace decomposition-based methods, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">e.g</i> ., multiple signal classification (MUSIC), provide somewhat better performance in adverse conditions, they are based on the statistical properties of the signal such as spatial covariance matrix (SCM) and its eigenvalue decomposition (EVD), resulting in high computational complexity. In this paper, a robust DOA estimation method is proposed based on a variable step size LMS algorithm with low rank matrix approximation (LRMA), where the received signal de-noising problem is formulated first as a LRMA problem directly using the received signal observations instead of the SCM, and then the variable step size is calculated from the predicted instantaneous error and the estimated powers of reference and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">de-noised</i> signals. The output spatial spectrum is determined by the reciprocal of the antenna array pattern, and the high peaks in the output spatial spectrum give the received signals estimated directions. The proposed method updates the step size efficiently without choosing any regulating parameter, and achieves improved performance even in adverse conditions due to the de-noising feature of LRMA with low computational complexity. Further, we also conduct the convergence and stability analyses of the proposed iterative estimation method with the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">de-noised</i> signal. Numerical results demonstrate that the proposed method outperforms state-of-the-art methods especially those, which yielded based on adaptive filtering.

Robust Bayesian Estimation of EEG-Based Brain Causality Networks.

The multivariate autoregression (MVAR) model is an effective model to construct brain causality networks. However, the accuracy of MVAR parameter estimation is considerably affected by outliers such as head movements and eye blinks contained in EEG signals, especially in short time windows. We proposed a robust MVAR parameter estimation method based on a Bayesian probabilistic framework and Laplace fitting error known as Lap-SBL. With the Bayesian inference framework, we can accurately estimate the MVAR parameters under short time windows. Additionally, to alleviate the influence of outliers, we model the fitting error using the Laplace distribution instead of the typical Gaussian distribution. We employ convex analysis to model the inference task by approximating the Laplace noise prior with a maximum over Gaussian functions with varying scales. The variational inference approach was used to efficiently estimate the MVAR parameters. The numerical results suggest that the proposed method obtains less parameter estimation bias and more consistent linkages than existing benchmark methods, i.e., LS, LASSO, LAPPS and SBL. The motor imagery experimental data analysis shows that Lap-SBL can better describe the lateralization characteristics of brain network. This lateralization is less apparent in a subject with poor MI classification accuracy. Lap-SBL effectively suppresses the influence of outliers and recovers reliable networks in the presence of outliers and short time windows.

Battery Safety Risk Assessment in Real-World Electric Vehicles Based on Abnormal Internal Resistance Using Proposed Robust Estimation Method and Hybrid Neural Networks

Battery safety issue is developing as one of the main hinders restricting the further application of real-world electric vehicles (EVs). Internal resistance (IR) is one of the important parameters to reflect battery safety, because bigger abnormal IR will cause more heat generation and make the battery easier to cross the critical condition of thermal runway. Safety risk assessment based on abnormal IR can locate this kind unsafe batteries and ensure the safe operation of EVs. Existing studies mostly focus on IR estimation in laboratory, yet is insufficient in real-world abnormal IR detection, which is influenced by random conditions and coupled factors. To cope with this issue, a method is proposed to detect unsafe battery, thereby predicting the thermal runaway. The method can be divided into three parts, i.e., IR estimation, normal IR prediction, and IR evolution law construction and safety risk assessment. First, we analyze the problems of battery IR estimation in real-world scenarios, and propose a robust method to estimate the IR only based on sparse voltage and current. Second, a novel hybrid neural network model is designed and trained to predict normal IRs inputted by temperature, mileage, and state-of-charge. The model combines the advantages of different neural network structures to improve the performance. A double-layer grid searching method is proposed to optimize hyperparameters of the hybrid neural network, aiming to achieve the best accuracy under constructed neural network structure. Finally, the safety boundary indicated by IR is formed by statistic method and the IR evolution law is constructed, then a strategy is proposed to make residual evaluation for safety risk assessment. All the proposed methods are driven by EV historical data to reflect real-world conditions. The results showcase that the method is effective in the cloud for the small IR prediction error with the mean-square-error, mean-relative-error, and max error of 2.45*e-4, 1.78%, and 0.15. In addition, the method can periodically classify the unsafe and normal batteries with 98.6% accuracy for the EVs with the same specification.

Robust estimation for bivariate integer-valued autoregressive models based on minimum density power divergence

This study considers a robust estimation method for bivariate integer-valued autoregressive (BINAR) models using a minimum density power divergence (MDPD) scheme. We first address this problem within a general framework of time series models to verify the strong consistency and asymptotic normality of the MDPD estimator (MDPDE) under regularity conditions. Based on these results, we assert the same asymptotic properties of MDPDE for BINAR models and propose an outlier detection rule based on MDPDE. To assess the performance of the proposed method, we conduct a simulation study. Real data analysis is also carried out for illustration, using the number of monthly earthquakes in the United States.

Association and mediating mechanism between remnant cholesterol and first-ever stroke among the Chinese general population.

Remnant cholesterol (RC) has been suggested to be implicated in atherosclerosis. The objective of the study was to evaluate the association between RC and first-ever stroke in the Chinese general population and to investigate whether the association is mediated via hypertension or diabetes. This study is a retrospective cohort analysis of participants from the China Health and Nutrition Survey. Participants without previous stroke and myocardial infarction in 2009 were enrolled and followed up in 2011 and 2015. Logistic regression analyses were adopted to explore the association of RC with stroke risk. Propensity score methods and doubly robust estimation method were used to ensure the robustness of our findings. Potential mediators were identified by mediation analyses. A total of 7,035 participants were involved, and during 6 years of follow-up, 78 (1.1%) participants experienced a first-ever stroke. Participants with high RC had a significantly higher incidence of stroke (1.4% versus 0.8%; p = 0.007). High RC was associated with 74% higher stroke risk after adjusting for multiple relevant variables (odds ratio [OR], 1.74; 95% CI, 1.06-2.85). The association was consistent in analyses using propensity score methods and doubly robust estimation method. Hypertension showed a significant mediating effect on the association between RC and stroke, while the mediating effect of diabetes was not significant. High RC increased the risk of first-ever stroke in the Chinese general population without previous stroke and myocardial infarction, partially through the pathway of hypertension. RC might be a potential target for the primary prevention of stroke.

Universal robust regression via maximum mean discrepancy

Abstract Many modern datasets are collected automatically and are thus easily contaminated by outliers. This has led to a renewed interest in robust estimation, including new notions of robustness such as robustness to adversarial contamination of the data. However, most robust estimation methods are designed for a specific model. Notably, many methods were proposed recently to obtain robust estimators in linear models, or generalized linear models, and a few were developed for very specific settings, for example beta regression or sample selection models. In this paper we develop a new approach for robust estimation in arbitrary regression models, based on maximum mean discrepancy minimization. We build two estimators that are both proven to be robust to Huber-type contamination. For one of them, we obtain a non-asymptotic error bound and show that it is also robust to adversarial contamination, but this estimator is computationally more expensive to use in practice than the other one. As a by-product of our theoretical analysis of the proposed estimators, we derive new results on kernel conditional mean embedding of distributions that are of independent interest.

Robust Centroid Estimation Method with the Rough and Refined Estimation for Interplanetary Optical Navigation

As the interest in probing deep space increases, it is necessary to enhance the autonomous navigation capabilities of the spacecraft. Since traditional navigation methods rely on ground-based radiometric tracking, the vehicle has a significant communication delay resulting in no ability to handle unexpected situations on time. Image-based optical navigation allows interplanetary spacecraft to determine their orbits autonomously. This paper explores how to accurately extract optical observations from the original images to perform autonomous navigation. First, we introduce a simple and efficient idea to locate valuable contours of the celestial body based on gradient variations. Then, we establish a rough estimation with RANSAC to remove the outliers around the edges. Next, we propose a refined estimation based on the hybrid genetic algorithm to precisely estimate the navigation observations. Lastly, numerous experiments have confirmed that our method achieves outstanding accuracy and robustness.

Imitrob: Imitation Learning Dataset for Training and Evaluating 6D Object Pose Estimators

This paper introduces a dataset for training and evaluating methods for 6D pose estimation of hand-held tools in task demonstrations captured by a standard RGB camera. Despite the significant progress of 6D pose estimation methods, their performance is usually limited for heavily occluded objects, which is a common case in imitation learning, where the object is typically partially occluded by the manipulating hand. Currently, there is a lack of datasets that would enable the development of robust 6D pose estimation methods for these conditions. To overcome this problem, we collect a new dataset (Imitrob) aimed at 6D pose estimation in imitation learning and other applications where a human holds a tool and performs a task. The dataset contains image sequences of nine different tools and twelve manipulation tasks with two camera viewpoints, four human subjects, and left/right hand. Each image is accompanied by an accurate ground truth measurement of the 6D object pose obtained by the HTC Vive motion tracking device. The use of the dataset is demonstrated by training and evaluating a recent 6D object pose estimation method (DOPE) in various setups.

Development and Validation of Robust, Highly Sensitive and Stability-Indicating RP-HPLC Method for Estimation of Deferasirox and its Degradation Products.

A rapid, simple and highly sensitive stability-indicating reverse-phase high-performance liquid chromatographic technique, coupled with a photodiode array detector, was developed and validated for the estimation of Deferasirox (DFS). The chromatographic separation was achieved using a C-18 (250 × 4.6 mm, 5μm) stationary phase and a mobile phase composed of 0.1% orthophosphoric acid and acetonitrile at a flow rate of 1mL/min. The detection was carried out at a wavelength of 245nm with a constant injection volume of 10μL throughout the analysis. With an R2 value of 0.9996, the calibration curve was determined to be linear over an appropriate concentration range of 50-500ng/mL. According to the International Conference on Harmonization (ICH) Q1 (R2) guideline, DFS was evaluated under stress conditions that included hydrolytic (acid, alkali and neutral), oxidative and thermal degradation. The findings demonstrated that significant degradation was observed in acidic degradation conditions, whereas drug substance was found to be stable when exposed to neutral, basic, oxidative and thermal degradation. The developed method was validated as per ICH guidelines. The developed method was employed successfully to estimate the amount of DFS in bulk and pharmaceutical formulation.

Robust nonparametric regression: Review and practical considerations

Nonparametric regression models offer a way to understand and quantify relationships between variables without having to identify an appropriate family of possible regression functions. Although many estimation methods for these models have been proposed in the literature, most of them can be highly sensitive to the presence of a small proportion of atypical observations in the training set. A review of outlier robust estimation methods for nonparametric regression models is provided, paying particular attention to practical considerations. Since outliers can also influence negatively the regression estimator by affecting the selection of bandwidths or smoothing parameters, a discussion of robust alternatives for this task is also included. Using many of the “classical” nonparametric regression estimators (and their robust counterparts) can be very challenging in settings with a moderate or large number of explanatory variables, so recently proposed robust nonparametric regression methods that scale well with a growing number of covariates are also discussed.

An Optimization-Based Robust Dynamic State Estimation for Power Systems with Synchronized Phasor Measurement Units, Involving Disturbance Rejection

State estimation provides the best estimate of the system states using a set of measurements that is divided into two main classes; static and dynamic types. The state estimator should provide an acceptable response in the presence of system changes and/or disturbances. To achieve this aim, considering the high rate of data changes and the high volume of exchanging information, the phasor measurement units could play an outstanding role. Furthermore, due to the inevitable errors of the measurements, and to provide an authentic estimate of the system states using the measured data, a state estimator should be able to eliminate or decrease the undesirable effect of bad data or outliers on the final output of the process. This type of state estimator is called a robust type. In this paper, a dynamic state estimator for a system with the synchronized phasor measurement units is utilized, which is capable of decreasing the effect of disturbances. Simultaneously, the robustness of the state estimation process in the presence of outliers is considered, which enables the state estimation process to reduce the negative effect of outliers on its final output. Therefore, the implemented process is called a robust dynamic state estimation method. By defining different scenarios and utilizing numerical indices, simulation results are thoroughly analyzed based on an explanatory three-bus network and the IEEE standard 14-bus and 57-bus networks using the MATPOWER tool.

Innovative non-asymptotic and robust estimation method using auxiliary modulating dynamical systems

In this paper, we aim to introduce an innovative non-asymptotic and robust estimation method based on the observable canonical form by means of a set of auxiliary modulating dynamical systems. The latter auxiliary systems are given by the controllable canonical form with zero initial condition. The proposed method can be applied to many kinds of linear and nonlinear systems. In this paper, it is applied to estimate the states and the output’s derivatives for linear singular systems with multiple inputs and multiple outputs in noisy environment. First, the considered singular system is transformed into a form similar to the Brunovsky’s observable canonical form with the injection of the inputs’ and outputs’ derivatives. Second, algebraic integral formulas are obtained both for the state variables and the outputs’ derivatives. After giving solutions of the required auxiliary systems, error analysis in discrete noisy case is addressed, where a provided noise error bound can be used to select design parameters. In the end, numerical simulations are given to illustrate the performance of the proposed method.

Robust and Fast Normal Mollification via Consistent Neighborhood Reconstruction for Unorganized Point Clouds.

This paper introduces a robust normal estimation method for point cloud data that can handle both smooth and sharp features. Our method is based on the inclusion of neighborhood recognition into the normal mollification process in the neighborhood of the current point: First, the point cloud surfaces are assigned normals via a normal estimator of robust location (NERL), which guarantees the reliability of the smooth region normals, and then a robust feature point recognition method is proposed to identify points around sharp features accurately. Furthermore, Gaussian maps and clustering are adopted for feature points to seek a rough isotropic neighborhood for the first-stage normal mollification. In order to further deal with non-uniform sampling or various complex scenes efficiently, the second-stage normal mollification based on residual is proposed. The proposed method was experimentally validated on synthetic and real-world datasets and compared to state-of-the-art methods.