Total Least Squares Research Articles

Reliability, Validity, and Comparison of Barbell Velocity Measurement Devices during the Jump Shrug and Hang High Pull.

This study examined the reliability, potential bias, and practical differences between the GymAware Powertool (GA), Tendo Power Analyzer (TENDO), and Push Band 2.0 (PUSH) during the jump shrug (JS) and hang high pull (HHP) performed across a spectrum of loads. Fifteen resistance-trained men performed JS and HHP repetitions with 20, 40, 60, 80, and 100% of their 1RM hang power clean, and mean (MBV) and peak barbell velocity (PBV) were determined by each velocity measurement device. Least-products regression and Bland-Altman plots were used to examine instances of proportional, fixed, and systematic bias between the TENDO and PUSH compared to the GA. Hedge's g effect sizes were also calculated to determine any meaningful differences between devices. The GA and TENDO displayed excellent reliability and acceptable variability during the JS and HHP while the PUSH showed instances of poor-moderate reliability and unacceptable variability at various loads. While the TENDO and PUSH showed instances of various bias, the TENDO device demonstrated greater validity when compared to the GA. Trivial-small differences were shown between the GA and TENDO during the JS and HHP exercises while trivial-moderate differences existed between GA and PUSH during the JS. However, despite trivial-small effects between the GA and PUSH devices at 20 and 40% 1RM during the HHP, practically meaningful differences existed at 60, 80, and 100%, indicating that the PUSH velocity outputs were not accurate. The TENDO appears to be more reliable and valid than the PUSH when measuring MBV and PBV during the JS and HHP.

Estimating the target DOA, range and velocity using subspace methods in a MIMO OFDM DFRC system

Dual-function Radar communication (DFRC) systems implement Radar detection and communication using the same hardware simultaneously. Significant attention has been paid to a multiple-input multiple-output DFRC system based on orthogonal frequency division multiplexing (OFDM). So far, the directions of arrival of the targets have been well estimated using subspace methods. In this paper, the ranges and/or velocities are estimated using the subspace methods. To this end, the Radar waveform must be based on the data symbols that are replicated over a few sub-carriers and/or during a few OFDM symbols. To avoid data replication, the target ranges and velocities can be estimated based on a least-squares (LS) or total LS method. After giving a few practical considerations, simulation results show that the proposed approaches outperform the existing ones based on the Fourier transform and/or Lasso algorithm. The performance of the proposed approaches is compared with the Cramer–Rao bound. Moreover, we show how the performance of the DFRC system (in terms of the accuracy of the estimated target parameters and data rate) evolves when modifying the system parameters, such as the number of sub-carriers and the number of OFDM symbols.

Comparison of meteoric water lines at different temporal scales and regression methods in inland monsoon region, Northwest China.

The local meteoric water line (LMWL) is an important basis for tracing the regional hydrological processes with stable isotopes. The establishment of LMWL, which can represent the overall characteristics of stable isotopes of local precipitation, is crucial for accurately revealing the hydrological processes. The influences of different temporal scales and regression methods on the established LMWL were analyzed and compared based on nine years of stable isotopic data of precipitation in Changwu Tableland, a typical area of the inland monsoon region of Northwest China. The results showed that, for different regression methods, the LMWL established by stable isotopes of annual precipitation was basically stable, whereas the LWML established by each precipitation event and the monthly precipitation data showed significant differences with different regression methods. The LMWL from the ordinary least squares regression (OLSR), major axis regression (MA) and reduced major axis regression (RMA) methods were significantly different based on the data of precipitation event, monthly precipitation data, and annual precipitation data, respectively. Only when OLSR, MA and RMA considering precipitation weighting were used, the LMWL established by these scale data was relatively close. This suggested that special attention should be paid to the selection of precipitation stable isotope data scale and regression method when LMWL was established in areas with temporal heterogeneity of precipitation and stable isotopic characteristics. For regions where stable isotope observations of precipitation were difficult and data were limited, the precipitation weighted major axis regression or reduced major axis regression methods are recommended during the establishment of representative LMWL.

A Fractional-Order Gradient-Descent Total Least Mean P-Norm Adaptive Filtering Algorithm in Impulsive Noise Environments

As a widely used method in the errors-in-variables (EIV) model, total least square (TLS) can work well for both input and output signals disturbed with noises. The TLS based adaptive filtering algorithms also have better performance than the least square based ones in the EIV system. However, their performance will deteriorate seriously in impulsive noise environments, since TLS cannot effectively suppress the large outliers in the noise. To address this problem, we present a cost function, called total least mean <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$p$ </tex-math></inline-formula> -norm (TLMP), and develop a fractional-order gradient-descent TLMP (FOGD-TLMP) algorithm in this brief. With the proposed cost function and the fractional-order derivative, FOGD-TLMP can deal well with impulsive noises in the EIV system. Furthermore, the local stability and computational complexity of the proposed algorithm are analyzed. Simulation results show that the proposed algorithm has better convergence performance than previous algorithms when the input and output signals are contaminated with impulsive noises.

Partial Discharge Location Algorithm Based on Total Least-Squares With Matérn Kernel in Cable Systems

Partial discharge (PD) location techniques are a useful tool for condition monitoring of electrical apparatus in power systems. However, the noisy PD measurements may significantly degrade the performance of location algorithms. This article deals with the PD location problem by using adaptive filtering techniques. Heretofore, scarce literature focuses on addressing the PD location based on such method. A novel adaptive algorithm, termed as total least-squares (TLS)-Matérn kernel (TLS-MK), is proposed. Benefiting from the merits of the Matérn kernel, the TLS model can effectively suppress the noise from the direct and reflected waves of the PD source. Meanwhile, the TLS-MK algorithm is used to estimate the time difference, which is used in the PD location. Moreover, the convergence behavior of the TLS-MK algorithm is analyzed. Simulations and experiments show that the proposed algorithm can enhance the location accuracy as compared to state-of-the-art methods for various PD signals.

A New Gain-Phase Error Pre-Calibration Method for Uniform Linear Arrays.

In this paper, we consider the gain-phase error calibration problem for uniform linear arrays (ULAs). Based on the adaptive antenna nulling technique, a new gain-phase error pre-calibration method is proposed, requiring only one calibration source with known direction of arrival (DOA). In the proposed method, a ULA with M array elements is divided into M-1 sub-arrays, and the gain-phase error of each sub-array can be uniquely extracted one by one. Furthermore, in order to obtain the accurate gain-phase error in each sub-array, we formulate an errors-in-variables (EIV) model and present a weighted total least-squares (WTLS) algorithm by exploiting the structure of the received data on sub-arrays. In addition, the solution to the proposed WTLS algorithm is exactly analyzed in the statistical sense, and the spatial location of the calibration source is also discussed. Simulation results demonstrate the efficiency and feasibility of our proposed method in both large-scale and small-scale ULAs and the superiority to some state-of-the-art gain-phase error calibration approaches.

Carpal allometry of African apes among mammals.

Morphological variation in African ape carpals has been used to support the idea that Pan and Gorilla evolved knuckle-walking independently. Little work, however, has focused on the effect of body mass on carpal morphology. Here, we compare carpal allometry in Pan and Gorilla to that of other quadrupedal mammals with similar body mass differences. If allometric trends in Pan and Gorilla carpals mirror those of other mammals with similar body mass variation, then body mass differences may provide a more parsimonious explanation for African ape carpal variation than the independent evolution of knuckle-walking. Three linear measurements were collected on the capitate, hamate, lunate, and scaphoid (or scapholunate) of 39 quadrupedal species from six mammalian families/subfamilies. Relationships between linear measurements and estimated body mass were analyzed using reduced major axis regression. Slopes were compared to 0.33 for isometry. Within Hominidae, higher body mass taxa (Gorilla) have relatively anteroposteriorly wider, mediolaterally wider, and/or proximodistally shorter capitates, hamates, and scaphoids than low body mass taxa (Pan). These allometric relationships are mirrored in most, but not all, mammalian families/subfamilies included in the analysis. Within most mammalian families/subfamilies, carpals of high body mass taxa are proximodistally shorter, anteroposteriorly wider, and mediolaterally wider than those of low body mass taxa. These distinctions may be caused by the need to accommodate relatively higher forelimb loading associated with greater body mass. Because these trends occur within multiple mammalian families/subfamilies, some carpal variation in Pan and Gorilla is consistent with body mass differences.

Predicting riverine fish production using empirical models and the metabolic theory of ecology

AbstractFish production integrates many different measures of community performance, such as abundance, biomass, growth, and reproduction, into one valuable quantitative metric but requires resource intensive data for empirical estimation. While published empirical models and the metabolic theory of ecology (MTE) represent alternative methods to estimate fish production, few studies have focused on productivity models for stream fish assemblages. The goal of our study was to determine whether existing empirical models and elements of the metabolic theory of ecology can reliably estimate stream fish productivity. We used production estimates from the literature (n = 107) to parameterize models based on the metabolic theory of ecology and new estimates of stream fish production from North America (n = 78) to compare and validate all models. Using major axis regression, we determined that while all models had strongly correlated production estimates relative to the observed values (r2 range: [0.496, 0.815]), not all the models produced accurate estimates. The MTE model with the temperature component had a poorer predictive performance (RMSE = 0.502) relative to models based solely on allometric scaling (RMSE range: [0.299, 0.380]). We conclude that standard production models can generate relative estimates of production using general fish sample data, however, the accuracy and precision of the estimates can vary among the models. Our study highlights the need for productivity estimates for stream fish assemblages from different geographic regions, to test empirical models with novel datasets, and for further investigation of temperature effects on fish productivity.

Adaptive Two-Stage Monte Carlo Algorithm for Accuracy Estimation of Total Least Squares

The existing theory of the total least squares (TLS) accuracy estimation contains the following problems: (1) the approximation function method based on the Taylor series expansion cannot avoid the derivative operation; (2) the selection of the number of simulations for the Monte Carlo method is subjective; and (3) the adaptive Monte Carlo algorithm is complex. Aiming at these problems, we introduce the adaptive two-stage Monte Carlo (ATMC) algorithm into the theory of accuracy estimation of the TLS. In order to consider the biases of estimation for parameters, residuals, and the estimation of the variance of unit weight, the computing process for accuracy estimation of the TLS contains bias estimation and accuracy estimation, and the algorithm is provided. In addition, based on the quasi-Monte Carlo method, an adaptive two-stage quasi-Monte Carlo (ATQMC) algorithm is proposed for the calculation of the expected bias in parameter estimates, and the algorithm flow is given. The experimental results verified the effectiveness of the ATMC and ATQMC algorithms. Compared with the ATMC algorithm, the ATQMC algorithm proposed in this paper is more efficient in the calculation of the expected bias in parameter estimates.

Recursive Variational Inference for Total Least-Squares

Recursive Variational Inference for Total Least-Squares

A framework for automating the parameter determination of crack growth models

Motivated by the need for an efficient fatigue crack growth prediction infrastructure for both legacy and novel materials, we have initiated the development of an automated computational framework capable of determining crack growth model parameters for an equationally defined model. As a first step in addressing this need, the present paper focuses on the Hartman-Schijve crack growth variant of the NASGRO equation by exploring and comparing various global optimization methods for parameter determination and evaluating their performance by using both synthetic and actual data. It also introduces the concept of the total least-squares minimization criterion within the context of crack growth modeling. The development of an open-source software library and an application implementing the approach are also described and are available for distribution to the technical community.

Modeling the spatial distribution of the meteoric water line of modern precipitation across the broader Mediterranean region

The covariance of stable hydrogen (δ2H) and oxygen (δ18O) isotopes in local precipitation (the local meteoric water line – LMWL) serves as a benchmark in isotope hydrological or paleoclimatological applications. However, the isotope hydrometeorological monitoring network is still sparse in many parts of the Mediterranean, and the degree of spatial data coverage is insufficient to address current needs. To remedy this weakness a spatially continuous interpolated geostatistical product of the LMWLs of modern precipitation across the Mediterranean has been developed. The LMWLs of the stations with data for more than four years between 2000 and 2015 were calculated using reduced major axis regression, and then interpolated across the region using statistical and machine learning methods. Random forest interpolation with buffer distance and elevation gave the best performance in the out-of-sample verification, and was thus used to derive the final interpolated product. The slope and intercept of the LMWLs ranged between ∼5.9 to 8.2 and −3.9 to 16.1‰, respectively. A detailed comparison with previous local/regional estimations showed that the model presented here concurs with those, albeit with minor deviations in certain regions. With the present results, it then becomes possible to assess how well grounded the ‘Eastern- and Western Mediterranean Meteoric Water Lines’ (EMMWL and WMMWL) for the 21st century are. In the eastern Mediterranean, the current model shows a slope (∼6.9) and the intercept (∼15‰) concurring with local studies, but does not reproduce the frequently cited benchmark values of the EMMWL; slope: 8, intercept ≥20‰. The EMMWL may be considered an idealized isotope-hydrological benchmark useful in regional studies; nonetheless, it cannot be taken as a valid representation of the actual empirical description of the δ2H – δ18O covariance of local precipitation in the eastern Mediterranean. Defining a uniform regional MWL in the western Mediterranean is not supported by the spatial heterogeneity of LMWL parameters based on the present estimations, calling into question the utility of the ‘WMMWL’ as an isotope hydrological benchmark.

A spreadsheet for determining critical soil test values using the modified arcsine‐log calibration curve

AbstractSoil test correlation data are often used to identify a critical soil test value (CSTV), above which crop response to added fertilizer is not expected. Oftentimes, models are used to determine the CSTV from soil test correlation data, yet most commonly used models have inherent assumptions that may not be valid for these data. The arcsine‐log calibration curve (ALCC) was developed in response to the statistical limitations of other commonly used models. A modified ALCC model using standardized major axis regression further improves this model's applicability to soil test correlation data. Here, we describe a Microsoft Excel spreadsheet for calculating CSTV from soil test correlation data using the modified ALCC model. The spreadsheet is available for download providing an accessible and easy‐to‐use tool for those who would like to use this method but who lack the experience with more sophisticated coding programs. The spreadsheet is available for download at http://www.ars.usda.gov/ALCC.

A Polynomial Fitting Problem: The Orthogonal Distances Method

The classical curve-fitting problem to relate two variables, x and y, deals with polynomials. Generally, this problem is solved by the least squares method (LS), where the minimization function considers the vertical errors from the data points to the fitting curve. Another curve-fitting method is total least squares (TLS), which takes into account errors in both x and y variables. A further method is the orthogonal distances method (OD), which minimizes the sum of the squares of orthogonal distances from the data points to the fitting curve. In this work, we develop the OD method for the polynomial fitting of degree n and compare the TLS and OD methods. The results show that TLS and OD methods are not equivalent in general; however, both methods get the same estimates when a polynomial of degree 1 without an independent coefficient is considered. As examples, we consider the calibration curve-fitting problem of a R-type thermocouple by polynomials of degrees 1 to 4, with and without an independent coefficient, using the LS, TLS and OD methods.

A Variable Step Size Gradient-Descent TLS Algorithm for Efficient DOA Estimation

The direction-of-arrival (DOA) estimation model of this brief is based on deviation compensation model with input noise, and the performance of the traditional Least mean square (LMS) adaptive algorithm shows poor performance. Instead, total least squares (TLS) algorithm is widely used in models which contains input noise. Therefore, we present TLS algorithm for DOA estimation, which is used to update weight coefficient by searching the peak of the spatial spectrum to estimate the direction of the angle of arrival. Due to the unsatisfactory DOA estimation performance on fixed step algorithms, a variable step-size gradient descent total least-squares (VSS-GDTLS) is proposed. The variable step size strategy is derived by applying the instantaneous augmented weight vector and the estimated signal power. Moreover, the convergence of the proposed algorithm is analyzed. Finally, simulation results show the superiority of the VSS-GDTLS algorithm than GDTLS and the other adaptive algorithms.

Latrine counts to estimate wild rabbit (Oryctolagus cuniculus) density as a tool for biodiversity conservation and management

The recovery of European wild rabbit (Oryctolagus cuniculus) populations in Spain is of great interest for wildlife conservation. Large-scale management and conservation programmes aimed to determine current population abundance.Most methods for censusing rabbits only offer estimates of relative abundance. However, we lack accurate studies about how latrine counts index is related to population density. The aim of this study is twofold: 1) to test the suitability of counting rabbit latrines as a relative abundance index and; 2) to explore if the number of latrines is a useful predictor of wild rabbit density.We compared latrine surveys conducted in 2 km-length paths with density estimates obtained from distance-based estimates. The study was conducted during two years in central Spain in mixed agriculture-woodland landscapes. Sites covered all potential range of rabbit densities in natural landscapes. Density estimates were obtained by using Distance software.We used type II major axis regression to evaluate the relationship between rabbit density and latrine counting. The predictive ability of the regression equation was performed by several predictive metrics.Results show that the number of latrines counted is a very good abundance index. We also found that latrine counts had a high predictive power to estimate rabbit density. Therefore, latrine surveys are not only a proxy of abundance, but can be used as a cost-effective tool to estimate rabbit population density at low and intermediate densities, which are the most important for the conservation practitioners. Furthermore, the method needs to be tested in other seasons and habitats to prove its generality.

Indo-western Pacific Ocean capacitor events recorded by coral proxies in the South China Sea

The Indo-western Pacific Ocean capacitor (IPOC) effect induces coherent climate variations over the Indo-western Pacific Ocean with significant sea-surface temperature (SST) anomalies over the South China Sea (SCS). Most IPOC events are related to El Nin∼o-Southern Oscillation (ENSO), occurring in the post-ENSO years. The coral δ18O and Sr/Ca precisely recorded climate variations as proxies for SST. This study investigated the IPOC via a reduced major axis (RMA) regression analysis based on coral records in the SCS. The coral records of Yongxing Island show a double SST peak during El Niño events after the 1960s, one in the mature phase and the other in the post-El Nin∼o summer. Tropical Indian Ocean warming persists into summer and anchors an anomalous anticyclonic circulation over the western North Pacific, extending the ENSO effect on the SCS SST through the IPOC effect, despite the decay of El Nin∼o. The corals from Yongle Atoll, Dongsha Atoll, and the region off central Vietnam well recorded the IPOC impacts associated with two strong El Nin∼o events (2009–2010 and 1997–1998) on SST anomalies in summer. According to coral records off central Vietnam, the 1959 IPOC effect occurred without an antecedent El Nin∼o event. The results show that coral proxies could capture the IPOC events in the SCS and prove that IPOC could act as an intrinsic climate mode in the Indo-western Pacific Ocean.

An inter-laboratory comparison of elemental loadings of PM2.5 samples using energy-dispersive XRF and magnetic-sector ICP-MS

We performed an inter-laboratory study comparing elemental loadings of atmospheric particulate matter (PM) samples, determined using Energy Dispersive X-ray Fluorescence (XRF) and Sector Field-Inductively Coupled Plasma-Mass Spectrometry (SF-ICP-MS) techniques. Three hundred archived samples collected on polytetrafluoroethylene (PTFE) filters from four sites of the IMPROVE network in the United States were included in the comparison. Regression analyses were utilized to compare the techniques. For elements measured well above the respective method detection limits (MDLs), agreement between methods was typically within ±20%. Major axis regression analysis between the techniques revealed very strong correlations (r2 > 0.9) for 13 out of 20 elements (Na, Mg, Al, S, K, Ca, Ti, V, Mn, Fe, Cu, Zn and Sr), strong correlations (0.8 < r2 < 0.9) for 3 elements (Cr, Ni and Pb), a weak correlation (r2 = 0.69) for one element (Zr), and very weak correlations (r2 < 0.4) for three elements (P, As and Rb). All the elements with strong or very strong correlations yielded regression slopes within 20% of unity, except Zn, indicating that absolute element recoveries of the two techniques were similar. Inter-elemental correlations for several element pairs with common environmental sources (e.g., Ni versus V from shipping emissions) were examined with both measurement platforms, and the comparisons verify that SF-ICP-MS has better detection limits than XRF for several elements. However, one of the four selected IMPROVE sites, a coastal site with high levels of sea salt, presented poor correlations between the two methods for elements Z < 20. Although independent ion chromatography (IC) confirmed the validity of the XRF measurements, without a shared Reference Method for PM elemental content, it is challenging to determine which analytical technique is more accurate in all cases. Laboratory-prepared reference materials (RM) were analyzed by both approaches in an effort to address the relative accuracy of the methods; however, the results were not consistent with the patterns observed in the ambient samples. Further inter-comparisons on real-world environmental samples, incorporating additional analytical techniques are necessary to better assess the measurements. This study highlights the need for shared reference materials that challenge all aspects of the measurement process for the atmospheric PM monitoring community.

Midline growth of the sphenoid bone in primates: A histological and microcomputed tomography study

AbstractObjectivesThe aim of the present study is to broaden our knowledge of the ontogeny of cranial base cartilaginous joints in primates.Materials and MethodsA cross‐sectional age sample of 66 specimens from four platyrrhine and three strepsirrhine genera were studied using microcomputed tomography, histology, and immunohistochemistry. Specimens were segmented, reconstructed, and measured using Amira software. Ontogenetic scaling of palatal, presphenoid, and basisphenoid length relative to cranial length was examined using standardized major axis regression. After histological sectioning, selected specimens were examined using immunohistochemistry of antibodies to proliferating cell nuclear antigen.ResultsOur results support the hypothesis that the presphenoid in platyrrhines grows more rapidly compared with strepsirrhines, but this study establishes that most or all of this growth discrepancy occurs prenatally, and mostly at the presphenoseptal synchondrosis (PSept). All species have prolonged patency (here meaning absence of any bony bridging across the synchondrosis) of the intrasphenoidal and spheno‐occipital synchondroses (ISS). However, immunohistochemical results suggest growth is only rapid throughout infancy, and mitotic activity is slowing during juvenile ages. The same is indicated for the PSept.DiscussionThese results demonstrate that platyrrhines and strepsirrhines do not follow the pattern of early fusion of ISS seen in humans. In addition, these primates have a more prolonged patency and growth at PSept compared with humans. Finally, results reveal that in bushbabies and tamarins, as in humans, synchondroses remain cartilaginous for a prolonged period after chondrocyte proliferation has slowed or ceased. In light of these results, it is time to reassess related processes, such as differences in timing of brain expansion.

Determination of Helmert transformation parameters for continuous GNSS networks: a case study of the Géoazur GNSS network

ABSTRACT In this paper, we propose an approach to determine seven parameters of the Helmert transformation by transforming the coordinates of a continuous GNSS network from the World Geodetic System 1984 (WGS84) to the International Terrestrial Reference Frame. This includes (1) converting the coordinates of common points from the global coordinate system to the local coordinate system, (2) identifying and eliminating outliers by the Dikin estimator, and (3) estimating seven parameters of the Helmert transformation by least squares (LS) estimation with the “clean” data (i.e. outliers removed). Herein, the local coordinate system provides a platform to separate points’ horizontal and vertical components. Then, the Dikin estimator identifies and eliminates outliers in the horizontal or vertical component separately. It is significant because common points in a continuous GNSS network may contain outliers. The proposed approach is tested with the Géoazur GNSS network with the results showing that the Dikin estimator detects outliers at 6 out of 18 common points, among which three points are found with outliers in the vertical component only. Thus, instead of eliminating all coordinate components of these six common points, we only eliminate all coordinate components of three common points and only the vertical component of another three common points. Finally, the classical LS estimation is applied to “clean” data to estimate seven parameters of the Helmert transformation with a significant accuracy improvement. The Dikin estimator’s results are compared to those of other robust estimators of Huber and Theil-Sen, which shows that the Dikin estimator performs better. Furthermore, the weighted total least-squares estimation is implemented to assess the accuracy of the LS estimation with the same data. The inter-comparison of the seven estimated parameters and their standard deviations shows a small difference at a few per million levels (E-6).