Mean Square Estimation Error Research Articles

RSS Localization Using an Optimized Fusion of Two Deep Neural Networks

The problem of received signal strength (RSS) source localization in wireless sensor networks has raised attention in recent years due to its low complexity. However, the performance of the RSS localization algorithms is degraded due to malicious phenomena such as multipath and fading. Hence, machine learning and especially deep neural networks (DNNs) are applied to solve this problem. So far, convolutional the neural network (CNN), the recurrent neural network (RNN), and multilayer perceptron (MLP) are used to this end. In this letter, neural networks such as MLP, CNN, and RNN are suggested to be combined pairwise. In this regard, we propose to use a fusion of two general neural network localization estimators. To design the combination coefficients, a heuristic approach based on the errors of the training step of two neural networks are suggested. Moreover, two optimized approaches for selecting the combination coefficients are provided based on mean and variances and also based on the mean square error of the combined estimator. The simulation results show improvement of the localization accuracy by fusion of two neural networks.

A Novel Electro-Thermal Model of Lithium-Ion Batteries Using Power as the Input

Considering that use of measured current as input of a battery model may cause distortion of the model due to low accuracy of the on-board current sensor and that power can be used to indicate energy transmission in an electric vehicle model, the power input internal resistance model is widely used in simulation of whole electric vehicles. However, since no consideration is given to battery polarization and electro-thermal coupling characteristics, the foregoing model cannot be used to describe the internal temperature change of batteries under working conditions. Three contributions are made in the present study: (1) ternary lithium-ion batteries were taken as the research objects and a second-order RC equivalent circuit model with power as the input was established in the present study; (2) A dynamic heat generation rate model suitable for RC equivalent circuits was built based on coupled electrical and thermal characteristics of lithium-ion batteries; (3) An electric model and a two-state equivalent thermal network model were further built and combined by using the heat generation rate model to form a power input electro-thermal model. Parameters of the model so formed were identified offline, and the battery model was verified with respect to accuracy under seven working conditions. The results show that the maximum root mean square error in voltage estimation, current estimation, and surface temperature estimation is 19.38 mV, 9.51 mA, and 0.19 °C respectively, which indicates that the power input electro-thermal model can describe the electrical and thermal dynamic behavior of batteries more accurately and comprehensively than the traditional power input internal resistance model.

Geo-CropSim: A Geo-spatial crop simulation modeling framework for regional scale crop yield and water use assessment

Remote sensing derived datasets (e.g. Leaf Area Index (LAI)) are increasingly being used in process based cropping system models to improve the prediction skill of the simulations when implementing operationally at regional scale. However, challenges such as inadequate quality of the available remote sensing data products and high reliance of models on climate variables and their uncertainties still exist. To address these challenges, we developed Geo-CropSim, a spatial modeling framework to use high quality remote sensing products in the Environmental Policy Integrated Climate (EPIC) agroecosystem model to regulate simulated processes and improve predictions of crop yield and evapotranspiration. Geo-CropSim comprises three main features 1) pixel level model initialization using crop emergence dates; 2) ability of the EPIC model to read in the PROSAIL (i.e. combined PROSPECT leaf optical properties model and SAIL canopy bidirectional reflectance model) inversion-based crop type LAI; and 3) a stress adjustment function to regulate simulated stress using LAI anomalies. To understand its performance, we implemented it over the State of Nebraska to estimate corn (Zea mays L.) and soybean (Glycine max [Merr.]) yields and evapotranspiration (ET) for 2012 (drought year) and 2015 (normal year) at 500-m resolution. Results showed that emergence dates and seasonal LAI captured spatial and temporal differences in crop progression (e.g. delayed planting in 2015) and growth (e.g. declined LAI in 2012) driven by regional differences in crop management and weather conditions very well. These differences were reflected in Geo-CropSim yield estimates, and showed improved spatial and temporal details compared over those from EPIC simulations obtained without using remote sensing derived emergence and LAI. Results revealed that Mean Absolute Percentage Error (MAPE) and Root Mean Square Error (RMSE) of Geo-CropSim yield estimates, computed based on USDA-NASS reported yields, were 18.85% and 1.22 Mg ha−1 for corn, and 17.90% and 0.46 Mg ha−1 for soybeans, respectively, which are substantially lower than those of original EPIC estimates (MAPE = 33.74% and RMSE = 2.18 Mg ha−1 for corn; and MAPE = 40.71% and RMSE = 0.98 Mg ha−1 for soybeans). Further, Geo-CropSim was able to capture ET and transpiration dynamics reasonably well (e.g. 10–12 % lower values for soybeans compared to corn values), and showed good agreement with flux measurements (i.e. R2 values of 0.63 and 0.72, RMSE values of 29.88 and 33.41 mm, and MAPE values of 5.0% and 6.8% for corn and soybean, respectively). Overall, this study demonstrated that Geo-CropSim has considerable potential to serve as a reliable operational tool to assess crop yields and water use under various cropping systems and to help in regional yield monitoring and water resource management.

Channel Estimation for Intelligent Reflecting Surface Assisted Backscatter Communication

Intelligent reflecting surface (IRS) is a promising technology to improve the performance of backscatter communication systems by smartly reconfiguring the multi-reflection channel. To fully exploit the passive beamforming gain of IRS in backscatter communication, channel state information (CSI) is indispensable but more practically challenging to acquire than conventional IRS-assisted systems, since IRS passively reflects signals over both the forward and backward (backscattering) links between the reader and tag. To address this issue, we propose in this letter a new and efficient channel estimation scheme for the IRS-assisted backscatter communication system. To minimize the mean-square error (MSE) of channel estimation, we formulate and solve an optimization problem by designing the IRS training reflection matrix for channel estimation under the constraints of unit-modulus elements and full rank. Simulation results verify the effectiveness of the proposed channel estimation scheme as compared to other baseline schemes.

Exposure assessment of PM2.5 using smart spatial interpolation on regulatory air quality stations with clustering of densely-deployed microsensors

Accurate mapping of air pollutants is essential for epidemiological studies and environmental risk assessments. Concentrations measured by air quality monitoring stations (AQMS) have primarily been used to assess the exposure of PM2.5. However, the low coverage and amount of monitoring stations affect the errors of spatial interpolation or geostatistical estimates. In contrast to other integrated approaches developed for improved air pollution estimates, this study utilizes data from low-cost microsensors densely deployed in Taiwan to improve the popular spatial interpolation approach called inverse distance weighting (IDW). A large dataset from thousands of low-cost sensors could improve spatial interpolation by describing the distribution of PM2.5 in detail. Therefore, this study presents a clustering-based method to assess the distribution of PM2.5. Then, a smarter IDW is performed based on correlated observations from the selected air quality stations. The publicly available data chosen for this investigation pertained to Taiwan, which has deployed 74 monitoring stations and more than 11,000 low-cost sensors since December 2020. The results of leave-one-out cross-validation indicate that there are fewer PM2.5 estimation errors in the developed approach than in estimations that use kriging across almost all of the months and sampled dates of 2019 and 2020, particularly those with higher PM2.5 spatial heterogeneities. Spatial heterogeneities could result in more significant estimation errors in mainstream approaches. The root mean square error of the monthly average estimate for PM2.5 ranged from 1.17 to 3.86 μg/m3. We also found that the clustering of one month characterizing the pattern of PM2.5 distribution could perform well in spatial interpolations based on historical data from monitoring stations. According to the information on the openaq platform, low-cost sensors are in demand in cities and areas. This trend might pave the way for the application of the proposed approach in other areas for superior exposure assessments.

Poisson Regression-Based Mean Estimator

The most frequent method for modeling count responses in numerous investigations is the Poisson regression model. Under simple random sampling, this paper offers utilizing Poisson regression-based mean estimator and discovers its associated formula of the mean square error (MSE). The MSE of the proposed estimator is compared to the MSE of traditional ratio estimators in theory. As a result of these evaluations, the proposed estimator has been proven to be more efficient than traditional estimators. Furthermore, the practical results corroborated the theoretical findings.

Feasibility Study of an Automated Carbohydrate Estimation System Using Thai Food Images in Comparison With Estimation by Dietitians.

Carbohydrate counting is essential for well-controlled blood glucose in people with type 1 diabetes, but to perform it precisely is challenging, especially for Thai foods. Consequently, we developed a deep learning-based system for automatic carbohydrate counting using Thai food images taken from smartphones. The newly constructed Thai food image dataset contained 256,178 ingredient objects with measured weight for 175 food categories among 75,232 images. These were used to train object detector and weight estimator algorithms. After training, the system had a Top-1 accuracy of 80.9% and a root mean square error (RMSE) for carbohydrate estimation of <10 g in the test dataset. Another set of 20 images, which contained 48 food items in total, was used to compare the accuracy of carbohydrate estimations between measured weight, system estimation, and eight experienced registered dietitians (RDs). System estimation error was 4%, while estimation errors from nearest, lowest, and highest carbohydrate among RDs were 0.7, 25.5, and 7.6%, respectively. The RMSE for carbohydrate estimations of the system and the lowest RD were 9.4 and 10.2, respectively. The system could perform with an estimation error of <10 g for 13/20 images, which placed it third behind only two of the best performing RDs: RD1 (15/20 images) and RD5 (14/20 images). Hence, the system was satisfactory in terms of accurately estimating carbohydrate content, with results being comparable with those of experienced dietitians.

MSE analysis for the finite order joint frequency tracking and channel estimation in OFDM systems

ABSTRACT The technique of orthogonal frequency division multiplexing is very sensitive to the carrier frequency offset (CFO). The requirement for high estimation accuracy when we acquire the CFO value is demanding. An efficient high-order approximation algorithm for jointly estimating the CFO and the channel impulse response (CIR) has been presented in the literature. From their simulation results, it is found that the estimator mean-square error (MSE) values are very close to the Cramer-Rao bound values, indicating that the highest estimation accuracy is achieved. However, no theoretical analysis is provided to confirm this assertion. In this article, we derive the theoretical formulas for the CFO MSE and the average CIR MSE for the estimators. It is found that the theoretical MSE for a joint CFO and CIR estimation problem approximates the Cramer-Rao bound when the signal-to-noise ratio (SNR) is high and the generalized CAZA sequence is used as the preamble. From our simulations, the theoretical results still hold true even for an SNR as low as 5 dB. Consequently, the range of SNR for which the theoretical analysis is valid is quite large.

A modified pseudo-copula regression model for risk groups with various dependency levels

In this study, the modified pseudo-Gaussian copula function is considered together with marginal gamma and Poisson generalized linear models and a modified pseudo-copula regression model is proposed to model dependency between claim severity and frequency. With the pseudo-copula, close estimates to the real values were found, and flexible dependency modelling is presented with the modified correlation coefficients according to the dependence between the claim severity and frequency of different risk groups. The pseudo-maximization by parts method was used for parameter estimation by developing the maximization by parts algorithm. The proposed model was analyzed with both simulation and real data analysis. Under the assumption of independence and when dependency is taken into account, the mean square errors of the parameter estimates according to different modifications were calculated and compared. The parameters estimated by the modified pseudo-copula regression model have lower errors than the estimates found using the model with fixed correlation coefficient and the model under the independence assumption. Finally, the models were compared and it was observed that the proposed model gives better results.

Marshall-Olkin Lindley-Log-logistic distribution: Model, properties and applications

Abstract The authors introduce a new generalized distribution called the Marshall-Olkin Lindley-Log-logistic (MOLLLoG) distribution and discuss its distributional properties. The properties include hazard function, quantile function, moments, conditional moments, mean and median deviations, Bonferroni and Lorenz curves, distribution of the order statistics and Rényi entropy. A Monte Carlo simulation study was used to examine the bias, relative bias and mean square error of the maximum likelihood estimators. The betterness of the new distribution compared to other distributions is illustrated by means of two real life datasets.

Deep Learning-Based Phase Noise Compensation in Multicarrier Systems

This letter presents a deep learning (DL) algorithm for compensating the impacts of phase noise in channel estimation and data detection for multicarrier systems. The proposed DL algorithm replaces conventional estimators’ iterative process and therefore reduces complexity. The input to this algorithm is the first iteration of the conventional least squares (LS) estimator, which requires no knowledge of channel and phase-noise statistics. The proposed algorithm is trained offline using simulation data and then exploited for online phase noise compensation. The simulation results show that the proposed DL algorithm outperforms the conventional estimators and achieves a 6 dB reduction in the mean-squared error (MSE) of channel estimation and a 45% improvement in the bit-error rate (BER).

State of charge estimation of Lithium-ion batteries based on the probabilistic fusion of two kinds of cubature Kalman filters

The accurate simulation of batteries’ dynamic characteristics is important for improving the State of Charge (SoC) estimation performance. However, an equivalent circuit model of batteries tends to have changing simulation accuracy of the battery’s dynamic characteristics during SoC estimation. Although the adaptive high-degree cubature Kalman filter (AHCKF) has a more accurate estimation of the dynamic characteristics simulated by the battery model than the adaptive cubature Kalman filter (ACKF) does, AHCKF may have lower estimation accuracy of the battery’s real dynamic characteristics. Therefore, AHCKF does not always outperform ACKF at each time step during SoC estimation.To improve SoC estimation accuracy, this paper proposes an estimation method based on the probabilistic fusion of ACKF and AHCKF. Furthermore, the impact of the filters’ initial weights on the accuracy of the fusion method is analyzed. Under the dynamic stress test, when ACKF’s initial weight is 0.5, the mean absolute error and the root mean square error of SoC estimation based on the proposed method decrease by 22.35% and 6.36% compared with ACKF, respectively, as well as 7.04% and 4.63% compared with AHCKF, respectively. The result shows that the proposed method can improve the accuracy of SoC estimation when the filters’ initial weights are appropriately set.

Recent advances in shrinkage-based high-dimensional inference

Recently, the shrinkage approach has increased its popularity in theoretical and applied statistics, especially, when point estimators for high-dimensional quantities have to be constructed. A shrinkage estimator is usually obtained by shrinking the sample estimator towards a deterministic target. This allows to reduce the high volatility that is commonly present in the sample estimator by introducing a bias such that the mean-square error of the shrinkage estimator becomes smaller than the one of the corresponding sample estimator. The procedure has shown great advantages especially in the high-dimensional problems where, in general case, the sample estimators are not consistent without imposing structural assumptions on model parameters.In this paper, we review the mostly used shrinkage estimators for the mean vector, covariance and precision matrices. The application in portfolio theory is provided where the weights of optimal portfolios are usually determined as functions of the mean vector and covariance matrix. Furthermore, a test theory on the mean–variance optimality of a given portfolio based on the shrinkage approach is presented as well.

Bayesian Learning-Based Linear Decentralized Sparse Parameter Estimation in MIMO Wireless Sensor Networks Relying on Imperfect CSI

Optimal linear minimum mean square error (MMSE) transceiver design techniques are proposed for Bayesian learning (BL)-based sparse parameter vector estimation in a multiple-input multiple-output (MIMO) wireless sensor network (WSN). Our proposed transceiver designs rely on majorization theory and hyperparameter estimates obtained from the BL module for minimizing the mean square error (MSE) of parameter estimation at the fusion center (FC). The linear transceiver design framework is initially proposed for the general scenario with arbitrary SNR sensor observations, followed by a special case with high-SNR sensor observations scenario. Our analysis also incorporates the channel correlation. The MMSE channel estimates are determined for the sensors (SNs), followed by a robust transceiver design procedure that is resilient to the channel state information (CSI) uncertainty arising due to the channel estimation error, an aberration that is unavoidable in practical implementations. Our simulation results demonstrate the improved performance of the proposed BL framework and optimal MMSE transceiver design in sparse parameter estimation relying on realistic imperfect channel estimates over the benchmarks.

Reanalysis Surface Mass Balance of the Greenland Ice Sheet Along K‐Transect (2000–2014)

AbstractAccurate estimates of surface mass balance over the Greenland ice sheet (GrIS) would contribute to understanding the cause of recent changes and would help to better estimate the future contribution of the GrIS to sea‐level rise. Given the limitations of in‐situ measurements, modeling, and remote sensing, it is critical to explore the opportunity to merge the available data to better characterize the spatial and temporal variation of the GrIS surface mass balance (SMB). This work utilizes a particle batch smoother data assimilation technique that yields SMB estimates that benefit from the snow model Crocus and a 16‐day albedo product derived from satellite remote sensing data. Comparison of the results against in‐situ SMB measurements shows that the assimilation of the albedo product reduces the root mean square error of the posterior estimates of SMB by 51% and reduces bias by 95%.

Almost sure convergence of randomised‐difference descent algorithm for stochastic convex optimisation

Stochastic gradient descent algorithm is a classical and useful method for stochastic optimisation. While stochastic gradient descent has been theoretically investigated for decades and successfully applied in machine learning such as training of deep neural networks, it essentially relies on obtaining the unbiased estimates of gradients/subgradients of the objective functions. In this paper, by constructing the randomised differences of the objective function, a gradient-free algorithm, named the stochastic randomised-difference descent algorithm, is proposed for stochastic convex optimisation. Under the strongly convex assumption of the objective function, it is proved that the estimates generated from stochastic randomised-difference descent converge to the optimal value with probability one, and the convergence rates of both the mean square error of estimates and the regret functions are established. Finally, some numerical examples are prsented.

An Enhanced Method for Tail Index Estimation under Missingness

Extreme events in earthquakes, wind speed, among others are rare but may lead to catastrophic effects on humans and the environment. The primary parameter in the estimation of such rare events is the tail index which measures the tail heaviness of an underlying distribution. Since extreme events are rare, the presence of missing observations may further lead to flawed. In view of this, there is a growing effort by researchers to address this problem. However, the existing methods of estimating the tail index use only the available nonmissing data. Thus, if the missing observations are influential values, ignoring them could introduce more bias and higher mean square error (MSE) in the tail index estimation and subsequently other extreme event--estimators such as high quantiles and small exceedance probabilities. In this study, we propose imputation of the missing observations before applying some standard estimators (Hill and geometric-type) to estimate the tail index. Through a simulation study, we assess the performance of the standard estimators under the proposed data enhancement method and the existing modified estimators of the tail index. The results show that the enhanced estimators have relatively lower bias and MSE. The estimation method was illustrated with a practical dataset on wind speed with missing values. Therefore, we recommend imputation mechanism as viable for enhancing the performance of tail index estimators in the case where there is missingness.

The Extrapolation Performance of Survival Models for Data With a Cure Fraction: A Simulation Study

ObjectivesCurative treatments can result in complex hazard functions. The use of standard survival models may result in poor extrapolations. Several models for data which may have a cure fraction are available, but comparisons of their extrapolation performance are lacking. A simulation study was performed to assess the performance of models with and without a cure fraction when fit to data with a cure fraction. MethodsData were simulated from a Weibull cure model, with 9 scenarios corresponding to different lengths of follow-up and sample sizes. Cure and noncure versions of standard parametric, Royston-Parmar, and dynamic survival models were considered along with noncure fractional polynomial and generalized additive models. The mean-squared error and bias in estimates of the hazard function were estimated. ResultsWith the shortest follow-up, none of the cure models provided good extrapolations. Performance improved with increasing follow-up, except for the misspecified standard parametric cure model (lognormal). The performance of the flexible cure models was similar to that of the correctly specified cure model. Accurate estimates of the cured fraction were not necessary for accurate hazard estimates. Models without a cure fraction provided markedly worse extrapolations. ConclusionsFor curative treatments, failure to model the cured fraction can lead to very poor extrapolations. Cure models provide improved extrapolations, but with immature data there may be insufficient evidence to choose between cure and noncure models, emphasizing the importance of clinical knowledge for model choice. Dynamic cure fraction models were robust to model misspecification, but standard parametric cure models were not.

On the ridge estimation of the Conway‐Maxwell Poisson regression model with multicollinearity: Methods and applications

AbstractIn data analysis, count data modeling contributing a significant role. The Conway‐Maxwell Poisson (COMP) is one of the flexible count data models to deal over and under dispersion. In the COMP regression model, when the explanatory variables are correlated, then the maximum likelihood estimator does not give efficient results due to the large standard error (SE) of the estimates. To overcome the effect of multicollinearity, we have proposed some ridge regression estimators in the COMP regression model by introducing dispersion parameter in the context of overdispersion, equidispersion, and underdispersion. The Iterative reweighted least method is used for the estimation of ridge regression coefficients in the COMP regression model. To evaluate the performance of the proposed estimators, we use mean squared error (MSE) as the performance evaluation criteria. Theoretical comparison of the proposed estimators with the competitor estimators is made and conditions of efficiency have been derived. The proposed estimator is evaluated with the help of a simulation study and two real applications. The results of the simulation study and real applications show the superiority of the proposed estimator because the proposed estimator produces smaller MSE and SEs of the COMP regression estimates with multicollinearity.

Bootstrap selection of ridge regularization parameter: a comparative study via a simulation study

In multiple linear regressions, it is known that least-squares estimates of the parameters are likely to be too large in absolute value and possibly of wrong sign, if explanatory variables are correlated. To reduce the undesirable effects of collinearity, the ridge estimator has been proposed as an alternative method to the least squares estimator. The biggest debate with the ridge estimator is the selection of the regularization parameter. Several methods for the selection of the regularization parameter have been discussed. Although most of these methods are based on minimizing the mean square error of the ridge estimator, bootstrap resampling method is also proposed to provide an optimal regularization parameter which gives an estimate of mean square error of prediction. The purpose of this paper is to provide a comprehensive study of regularization parameter selection methods which consider bootstrap approach as well as estimation and prediction approaches. The paper concludes with application of these procedures to simulation studies and real data.