Discussions on phase-reconstructing algorithms for 3D digitizing structure-light profilometry

Decoupled State-Estimation in Energy Control Centres

Sampling experiments were conducted to compare least squares (LS) and weighted least squares (WLS) estimators in heteroscedastic linear regression. Variance estimates obtained both from replicates, si2, and from a modification of Rao's [1970] MINQUE estimator, j2, were used as weighting factors in WLS estimation. Efficiency comparisons of the LS, WLS(s 2), and WLS(g 2) estimators were based on the generalized variance, the Euclidean norm, the variance of the slope estimator, and the variance of the estimator of E(y I x). It was found thatLS estimators are remarkably robust, and only for marked variance heterogeneity or many replicates at each point are weighted estimators uniformly better. In general, unless the number of replicates at each point is large (> 10), WLS (9 2) estimators are more efficient than WLS(s,2).

The overlay modeling errors are commonly modeled as the sum of inter-field and intra-field errors in lithography process of wafer stepper. The inter-field errors characterize the global effect while the intra-field errors represent the local effect. To have a better resolution and alignment accuracy, it is important to model the overlay errors and compensate them into tolerances. This paper proposes a weighted least squares (WLS) estimator for two general overlay error models such that more accurate linear term parameters of the overlay error can be obtained. First, the least squares (LS) estimator is applied to obtain the parameters of linear and nonlinear terms. We intend to estimate the parameters of linear term while taking the nonlinear term as our modeling residual errors. Next, we use the WLS estimator to obtain more accurate parameters of linear term and thus reduced the modeling errors by choosing appropriate stepper control parameters. The WLS estimator is applied to a real data set collecting 537 wafers from a wafer fabrication facility. The test results demonstrate that the estimated linear term parameters of the WLS estimator are much more close to the assumed ones than the LS estimator.

The weighted least squares (WLS) algorithm is widely employed for designing quadrature mirror filters (QMF) in the frequency domain. The equiripple nature of the WLS design and its performance near the filter band edge have been reported to be better than that of the least squares (LS) design. It is known that these design techniques suffer from pass-band anomaly under different stop band frequencies. We have proposed an algorithm to eliminate pass-band anomaly of LS design. In this paper, we show that WLS can be modified in way similar to that proposed for the LS design. The characteristics of the resulting filters satisfy the stop band requirements and do not show anomaly in the pass band region.

We revisit the problem of blind calibration of uniform linear sensors arrays for narrowband signals and set the premises for the derivation of the optimal blind calibration scheme. In particular, instead of taking the direct (rather involved) Maximum Likelihood (ML) approach for joint estimation of all the unknown model parameters, we follow Paulraj and Kailath’s classical approach in exploiting the special (Toeplitz) structure of the observed covariance. However, we offer a substantial improvement over Paulraj and Kailath’s Least Squares (LS) estimate by using asymptotic approximations in order to obtain simple, (quasi-)linear Weighted LS (WLS) estimates of the sensors’ gains and phases offsets with asymptotically optimal weighting. As we show in simulation experiments, our WLS estimates exhibit near-optimal performance, with a considerable improvement (reaching an order of magnitude and more) in the resulting mean squared errors, w.r.t. the corresponding ordinary LS estimates. We also briefly explain how the methodology derived in this work may be utilized in order to obtain (by certain modifications) the asymptotically optimal ML estimates w.r.t. the raw data via a (quasi)-linear WLS estimate.

Weibull distribution is widely used in various areas such as life tables, failure rates, and definition of wind speed distribution. Therefore, parameter estimation for the Weibull distribution is an important problem in many real data applications. The least square (LS), the weighted least square (WLS) and the maximum likelihood (ML) are the most popular methods for the parameter estimation in the Weibull distribution. In this study, based on the LS, WLS and ML estimation methods, a multi-objective programming approach is proposed for the parameter estimation of two-parameter Weibull distribution. This new approach evaluates together LS, WLS and ML methods in the estimation process. NSGA-II method, which is a multi-objective heuristic optimization method, is used to solve the proposed multi-objective estimation model. To evaluate the applicability and performance of the proposed approach, a detailed Monte Carlo simulation study based on deficiency criteria and a real data application are designed. The results illustrated that the proposed multi-objective programming approach provides quite accurate parameter estimates for the two parameter Weibull distribution with respect to deficiency criteria.

This article presents the application of weighted least squares (WLS) extrapolation and vector autoregressive (VAR) modeling in polar motion prediction. A piecewise weighting function is developed for the least squares (LS) adjustment in consideration of the effect of intervals between observation and prediction epochs on WLS extrapolation. Furthermore, the VAR technique is used to simultaneously model and predict the residuals of x p, y p pole coordinates for WLS misfit. The simultaneous predictions of x p, y p pole coordinates are subsequently computed by the combination of WLS extrapolation of harmonic models for the linear trend, Chandler and annual wobbles, and VAR stochastic prediction of the residuals (WLS+VAR). The 365-day-ahead x p, y p predictions are compared with those generated by LS extrapolation+univariate AR prediction and LS extrapolation+VAR modeling. It is shown that the x p, y p predictions based on WLS+VAR taking into consideration both the interval effect and correlation between x p and y p outperform those generated by two others. The accuracies of the x p predictions are 13.97 mas, 18.47 mas, and 20.52 mas, respectively for the 150-, 270-, and 365-day horizon in terms of the mean absolute error statistics, 36%, 24.8%, and 33.5% higher than LS+AR, respectively. For the y p predictions, the 150-, 270-, and 365-day accuracies are 15.41 mas, 21.17 mas, and 21.82 mas respectively, 27.4%, 11.9%, and 21.8% higher than LS+AR respectively. Moreover, the absolute differences of the WLS+VAR predictions and observations are smaller than the differences from LS+VAR and LS+AR, which is practically important to practical and scientific users, although the improvement in accuracies is no more than 10% relative to LS+VAR. The further comparison with the predictions submitted to the 1st Earth Orientation Parameters Prediction Comparison Campaign (1st EOP PCC) shows that while the accuracy of the predictions within 30 days is comparable with that by the most accurate prediction techniques including neural networks and LS+AR participating in the campaign for x p, y p pole coordinates, the accuracy of the predictions up to 365 days into the future are better than accuracies by the other techniques except best LS+AR used in the EOP PCC. It is therefore concluded that the medium- and long-term prediction accuracy of polar motion can be improved by modeling x p, y p pole coordinates together.

A Fuzzy clustering based fusion location method is presented for acoustic source direction estimation in underwater wireless sensor network. This method based on acoustic signal energy measurements taken at the received acoustic signal of a stationary sensor. Using fuzzy K-Means clustering, we could get centers of clusters with different orders. According to the new centers with their coordinates calculated, three least-square methods of source localization based on energy decay model(LS, WLS and F-WLS) are used to estimate the direction of the source. Numerous simulation results show that weighted least-square (WLS) method of localization outperforms least-square (LS) localization for different SNR. The experimental results shown that this direction method could also perform well in lower SNR. The average error of F-WLS yield the approximately same direction accuracy, but outperforms WLS in lower SNR. And for a certain network, the optimal order of clusters could be found not the bigger the better.

Meta-analysis is a statistical method for synthesizing quantitative data from multiple related studies, yet heterogeneity among studies often complicates interpretation. Meta-regression extends this approach by incorporating study-level covariates to explain variations in outcomes. With the global increase in depression, Acceptance and Commitment Therapy(ACT) has attracted attention as an effective psychological intervention. Therefore, a deeper understanding of the factors that influence its effectiveness across studies is needed. However, to date, only a few meta-analyses have quantitatively examined moderator variables that influence ACT outcomes using a random effects meta-regression approach. This study aims to fill this gap. This study estimated the model parameters using the Weighted Least Squares (WLS) method. Thirty-three published studies testing the effectiveness of ACT in reducing depression were collected from PubMed, Google Scholar, and Science Direct. The homogeneity test results showed significant heterogeneity, supporting the use of a random effects model. The combined effect size of -0.321 indicates that ACT significantly reduces depression levels compared to the control group. Meta-regression analysis revealed that variation in effect size was significantly influenced by differences in the average age of patients and duration of therapy. These findings provide new insights into the conditions and characteristics that make ACT therapy more effective.

Uncertainty calculation applied to different regression methods in the quasi-dynamic collector test

We investigate herein the problem of amplitude estimation of sinusoidal signals from observations corrupted by colored noise. A relatively large number of amplitude estimators are described which encompass least squares (LS) and weighted least squares (WLS) methods. Additionally, filterbank approaches, which are widely used for spectral analysis, are extended to amplitude estimation. Specifically, we consider the matched-filterbank (MAFI) approach and show that, by appropriately designing the prefilters, the MAFI approach includes the WLS approach. The amplitude estimation techniques discussed in this paper do not model the noise, and yet they are all asymptotically statistically efficient. It is their different finite-sample properties that are of particular interest to this study. Numerical examples are provided to illustrate the differences among the various estimators. Though amplitude estimation applications are numerous, we focus on system identification using sinusoidal probing signals.

One of the major questions in high-density transcranial electrical stimulation (TES) is: given a region of interest (ROI) and electric current limits for safety, how much current should be delivered by each electrode for optimal targeting of the ROI? Several solutions, apparently unrelated, have been independently proposed depending on how “optimality” is defined and on how this optimization problem is stated mathematically. The least squares (LS), weighted LS (WLS), or reciprocity-based approaches are the simplest ones and have closed-form solutions. An extended optimization problem can be stated as follows: maximize the directional intensity at the ROI, limit the electric fields at the non-ROI, and constrain total injected current and current per electrode for safety. This problem requires iterative convex or linear optimization solvers. We theoretically prove in this work that the LS, WLS and reciprocity-based closed-form solutions are specific solutions to the extended directional maximization optimization problem. Moreover, the LS/WLS and reciprocity-based solutions are the two extreme cases of the intensity-focality trade-off, emerging under variation of a unique parameter of the extended directional maximization problem, the imposed constraint to the electric fields at the non-ROI. We validate and illustrate these findings with simulations on an atlas head model. The unified approach we present here allows a better understanding of the nature of the TES optimization problem and helps in the development of advanced and more effective targeting strategies.

This study presents the Kumaraswamy Marshal–Olkin Flexible Weibull Extension (KMO-FWE) distribution, a newly developed probability model designed to extend existing lifetime distributions. This extension enhances the ability to model various hazard rate patterns with greater flexibility. The study explores the fundamental properties of this distribution, including the cumulative distribution function (CDF), probability density function (PDF), survival function, hazard function, moments, moment generating function, quantile function, and order statistics. To estimate the distribution’s parameters, several statistical methods are assessed, with a primary focus on Maximum Likelihood Estimation (MLE). Additionally, alternative estimation techniques such as Maximum Product Spacing (MPS), Least Squares (LS), Weighted Least Squares (WLS), and Percentile Estimation (PE) are considered. A Monte Carlo simulation study is conducted to evaluate the accuracy and efficiency of these estimation approaches under both complete data and Type-II censoring conditions. The results indicate that MLE is highly effective for large sample sizes but may introduce bias in smaller samples. In contrast, MPS provides stable parameter estimates under more complex conditions. While LS and WLS are computationally straightforward, their performance diminishes in the presence of censoring. Meanwhile, PE proves beneficial in reliability analysis based on percentile estimation. Overall, the findings highlight the KMO-FWE distribution as a versatile and reliable model, suitable for applications in reliability engineering, survival analysis, and biomedical research.

Asymptotically efficient GNSS trilateration

Precise dynamic parameters are of great significance to the model-based controller of industrial robots. The least square (LS) method is widely used to identify the dynamic parameters in reality, but it is sensitive to the measurement noise and may obtain a biased solution. Besides, the nonlinear dynamics are the key and difficult point of identification, such as the nonlinear friction and the coupling effect of adjacent joint, but they are seldom solved simply and effectively. To cope with the above issues, we propose a backpropagation learning (BPL) method for parameter identification. The mean square error between the measured torque and the calculated torque from the dynamic model is taken as the loss function. The gradient of the loss function with respect to the parameters is computed, and the parameters are updated in the negative gradient direction to minimize the loss function until finding the optimal parameters with the minimum loss function. The optimal parameters will not only fit the modeled torque but also compensate for the torque caused by the unmodeled factors, thus improving the parameter accuracy. The proposed method is essentially a supervised learning method, so the impact of measurement noise is reduced by continuous training with a large amount of valid data. The proposed method is verified in an industrial robot platform, and the experimental results show that the proposed method has smaller errors than the weighted least squares (WLS) method and achieves similar accuracy to the semiparametric model (SPM) but has a better generalization ability.