Least-squares Fitting Approach Research Articles

Demonstration of orbit determination for LEO objects using the Murchison Widefield Array

The rapidly increasing number of satellites in Earth’s orbit motivates the development of Space Domain Awareness (SDA) capabilities using wide field-of-view sensor systems that can perform simultaneous detections. This work demonstrates preliminary orbit determination capability for Low Earth Orbit objects using the 36°×36° field-of-view of the Murchison Widefield Array (MWA) at commercial Frequency Modulated (FM) frequencies (transmitters in 88-108 MHz range). Non-coherent passive radar techniques with the MWA produce spatially smeared detections, due to time averaging in the MWA’s standard signal processing chain. The work develops methods to extract time-stamped measurements of a satellite’s angular coordinates from these data. The developed method was tested on observations of 32 satellite passes and the extracted measurements were used to perform orbit determination for the targets using a least-squares fitting approach. The target satellites span a range in altitude and Radar Cross Section, providing examples of both high and low signal-to-noise detections. The estimated orbital elements for the satellites are validated against the publicly available Two Line Element (TLE) updates provided by the Space Surveillance Network (SSN) and the preliminary estimates are found to be in close agreement. The work also tests for re-acquisition for one target using the orbital elements and finds the trajectory predicted by the method to coincide within 0.2° cross-track and 0.3° in-track for a subsequent pass, reduced to approximately 0.1° cross-track (less than one kilometre) if two passes are used to predict the subsequent pass (using simple two-body propagation). The median uncertainty in the angular position for objects in LEO (range less than 1000 km) is found to be 860 m in the cross-track direction and 780 m in the in-track direction, which are comparable to the typical uncertainty of ∼1000 m in the publicly available TLE information. The techniques, therefore, demonstrate the MWA to be capable of being a valuable contributor to the global SDA community. Based on the understanding of the MWA SDA system, this paper also briefly describes methods to mitigate the impact of FM-reflecting LEO satellites on radio astronomy observations, and how maintaining a catalog of FM-reflecting LEO objects is in the best interests of both SDA and radio astronomy.

Accuracy and precision of depth-resolved estimation of attenuation coefficients in optical coherence tomography.

Parametric imaging of the attenuation coefficient using optical coherence tomography (OCT) is a promising approach for evaluating abnormalities in tissue. To date, a standardized measure of accuracy and precision of by the depth-resolved estimation (DRE) method, as an alternative to least squares fitting, is missing. We present a robust theoretical framework to determine accuracy and precision of the DRE of . We derive and validate analytical expressions for the accuracy and precision of determination by the DRE using simulated OCT signals in absence and presence of noise. We compare the theoretically achievable precisions of the DRE method and the least-squares fitting approach. Our analytical expressions agree with the numerical simulations for high signal-to-noise ratios and qualitatively describe the dependence on noise otherwise. A commonly used simplification of the DRE method results in a systematic overestimation of the attenuation coefficient in the order of , where is the pixel stepsize. When , is reconstructed with higher precision by the depth-resolved method compared to fitting over the length of an axial fitting range . We derived and validated expressions for the accuracy and precision of DRE of . A commonly used simplification of this method is not recommended as being used for OCT-attenuation reconstruction. We give a rule of thumb providing guidance in the choice of estimation method.

High-Precision Measuring System for Internal Deformation Monitoring Pipeline of Rockfill Dams: Design and Validation

The monitoring of internal deformation in rockfill dams using pre-buried flexible pipelines is a promising technique; however, achieving precise measurements over a long-range pipeline is crucial and challenging. In this paper, we present a high-precision pipeline measuring system for monitoring internal deformation in rockfill dams, which can simultaneously measure the pipeline centerline and cross-section geometry. The system leverages the inertial measurement principle to perform positioning by fusing an inertial measurement unit (IMU) with odometers. It utilizes a Kalman filter and Rauch-Tung-Striebel (RTS) smoothing to estimate the optimal 3D curves of the pipeline. The pipeline’s inner diameter is measured using three wheel swing arms and a set of load-bearing wheels, and the pipeline cross-section geometry is fitted using a direct least-square ellipse fitting approach. Finally, we validated the measuring system through both model and on-site experiments and compared the measurements with the Leica AT-960LR absolute tracker and hydraulic overflow settlement gauge. The results indicate that the measuring system has excellent accuracy for measuring pipeline curves and deformation, and the settlement trend is consistent with the hydraulic overflow settlement gauge. We also assessed the cross-section deformation of the deformation monitoring pipeline in the Lianghekou dam for six months, and the results showed that if deployed in strict accordance with the design requirements, the monitoring pipeline buried inside the rockfill dam would not deform significantly. These findings provide a tremendous incentive for the continued development of rockfill dam internal deformation monitoring.

An AI-Based Newly Developed Analytical Formulation for Discharging Behavior of Supercapacitors with the Integration of a Review of Supercapacitor Challenges and Advancement Using Quantum Dots

A supercapacitor is a type of electrical component that has larger capacitance, due to asymmetric behavior with better power density, and lower ESR (effective series resistance) than conventional energy-storage components. Supercapacitors can be used with battery technology to create an effective energy storage system due to their qualities and precise characterization. Studies have shown that the use of quantum dots as electrodes in supercapacitors can significantly increase their effectiveness. In this research article, we have used a Drude model based on free electrons (asymmetric nature) to describe the supercapacitor’s discharging characteristics. Commercially available Nippon DLA and Green-cap supercapacitors were used to verify the Drude model by discharging them through a constant current source using a simple current mirror circuit. The parameters of both the fractional-order models and our suggested method were estimated using the least-squares regression fitting approach. An intriguing finding from the Drude model is the current-dependent behavior of the leakage-parallel resistance in the constant current discharge process. Instead of using the traditional exponential rule, supercapacitors discharge according to a power law. This work reflects the strong symmetry of different aspects of designing a hybrid supercapacitor with high efficiency and reliability.

Modeling and Parameter Estimation of Radar Sea-Clutter with Trimodal Gamma Population

Real radar data often consist of a mixture of Gaussian and non-Gaussian clutter. Such a situation creates one or more inflexion points in the curve of the empirical cumulative distributed function (CDF). In order to obtain an accurate fit with sea reverberation data, we propose, in this paper, a trimodal gamma disturbance model and two parameter estimators. The non-linear least-squares (NLS) fit approach is used to avoid computational issues associated with the maximum likelihood estimator (MLE) and moments-based estimator for parameters of the mixture model. For this purpose, a combination of moment fit and complementary CDF (CCDF) NLS fit methods is proposed. The simplex minimization algorithm is used to simultaneously obtain all parameters of the model. In the case of a single gamma probability density function, a zlog(z) method is derived. Firstly, simulated life tests based on a gamma population with different shape parameter values are worked out. Then, numerical illustrations show that both MLE and zlog(z) methods produce closer results. The proposed trimodal gamma distribution with moments NLS fit and CCDF NLS fit estimators is validated to be in qualitative agreement with different cell resolutions of the available IPIX database.

Generalized Frequency Dependent Small Signal Model for High Frequency Analysis of AlGaN/GaN MOS-HEMTs

Traditional lumped small signal equivalent circuit models of AlGaN/GaN metal oxide semiconductor high electron mobility transistors (MOS-HEMTs) are made up of constant valued circuit elements. Such models are unable to capture the high frequency behavior (above 20 GHz) of the device. In this work, a modified small signal equivalent circuit model of AlGaN/GaN MOS-HEMTs is presented. The key feature of the proposed model is that the values of the different circuit elements in the model are considered to be frequency dependent in nature and not constants. The frequency dependent value of each circuit element is mathematically represented using polynomial functions where the coefficients of the functions are determined via a least-square curve fitting approach. This frequency dependent attribute of the circuit element values ensures that the proposed model is very accurate at high frequencies without sacrificing the compactness of the model topology. The accuracy of the proposed model has been verified up to 50 GHz using experimentally measured Y-parameters of AlGaN/GaN MOS-HEMTs having a different gate dielectric and gate length.

Methods to Evaluate Airway Resistance and Lung Compliance During Mechanical Ventilation: A Comparative Study

Mechanical ventilation is a lifesaving activity that is used in critical care management. In such case, monitoring of airway resistance(Raw) and lung compliance(CL) play a major role for diagnosing the lung condition, setting the ventilator parameters, can act as a decision parameter for weaning the patient from the ventilator. Several methods have been described for estimating these respiratory parameters. In this work, a study is conducted to compare two different methods used to calculate airway resistance and lung compliance during mechanical ventilation. Michigan Adult/Infant lung simulator is used to simulate different compliance conditions and Michigan Pneuflo Resistors to simulate different resistance conditions. Flow, volume and pressure data were logged for different set parameters i.e. for different resistance and compliance combinations. Later these data were used to calculate the respiratory system resistance and compliance. Two methods were used to calculate lung parameters, dynamic approach and Least Square fitting(LSF) method(using respiratory system equation of motion). Both methods gave accurate estimate of Raw and CL. But the dynamic approach required respiratory maneuver whereas LSF approach required large datasets to carry out the calculation and the patient should not show any active breathing during evaluation

Derivation of input-output functions from distortion-product otoacoustic emission level maps.

Distortion-product otoacoustic emissions (DPOAEs) emerge from the cochlea when elicited with two tones of frequencies f1 and f2. DPOAEs mainly consist of two components, a nonlinear-distortion and a coherent-reflection component. Input-output (I/O) functions of DPOAE pressure at the cubic difference frequency, fDP=2f1-f2, enable the computation of estimated distortion-product thresholds (EDPTs), offering a noninvasive approach to estimate auditory thresholds. However, wave interference between the DPOAE components and suboptimal stimulus-level pairs reduces the accuracy of EDPTs. Here, the amplitude P of the nonlinear-distortion component is extracted from short-pulse DPOAE time signals. DPOAE level maps representing the growth behavior of P in L1,L2 space are recorded for 21 stimulus-level pairs and 14 frequencies with f2=1 to 14 kHz (f2/f1=1.2) from 20 ears. Reproducing DPOAE growth behavior using a least-squares fit approach enables the derivation of ridge-based I/O functions from model level maps. Objective evaluation criteria assess the fit results and provide EDPTs, which correlate significantly with auditory thresholds (p < 0.001). In conclusion, I/O functions derived from model level maps provide EDPTs with high precision but without the need of predefined optimal stimulus-level pairs.

Signal Processing Approach for Spectral Interferometry Immune to $\lambda$ /2 Errors

The paper develops a least-squares fitting approach for demodulating optical path difference (OPD) in spectral interferometric sensors. The proposed signal processing approach enables to substantially decrease the probability of abrupt λ/2 demodulation errors. This is achieved by excluding from analysis a part of spectrum samples, providing less information, responsible for distinguishing the spectra of interferometrs, which OPDs differ at λ/2. The amount of excluded samples is controlled by a numeric parameter. The dependency of optimal value of signal processing parameter on signal to noise ratio (SNR) of optical spectrum is derived. The proposed signal processing approach is tested experimentally, it's efficiency in suppressing the λ/2 demodulation errors and optimal parameter dependency on SNR were confirmed. It was demonstrated to provide a 4 dB effort in terms of minimal SNR providing error-free OPD demodulation.

Revisiting the Scale-Invariant, Two-Dimensional Linear Regression Method

The scale-invariant way to analyze two-dimensional experimental and theoretical data with statistical errors in both the independent and dependent variables is revisited by using what we call the triangular linear regression method. This is compared to the standard least-squares fit approach by applying it to typical simple sets of example data from the actual chemical literature. A new add-in for Microsoft Excel, LinEstXY, and ready-to-use formulas for the scale-invariant method are provided.

Structural determination and population transfer of 4-nitroanisole by broadband microwave spectroscopy and tailored microwave pulses.

The rotational spectrum of 4-nitroanisole was recorded via chirped-pulse Fourier transform microwave spectroscopy in the frequency range of 2-8 GHz. The spectra of the parent molecule and all of its 13C-, 15N-, and 18O-monosubstituted species in their natural abundance were assigned, and the molecular structure was determined using Kraitchman's equations as well as a least-square fitting approach. 4-nitroanisole has a large dipole moment of 6.15 D along the inertial a-axis and a smaller dipole moment of 0.78 D along the b-axis. The large dipole moment component makes this molecule a potential candidate for deceleration experiments using static electric fields or electromagnetic radiation. Using tailored microwave pulses, we investigate the possibility of transferring population between the rotational states of 4-nitroanisole. Such a technique could be applied to selectively increase the population for specific rotational states of interest, which are then accessible for further, more advanced experiments, such as deceleration.

Hierarchical predictive system for the neural integration of incoming somatosensory stimulations

Hierarchical predictive system for the neural integration of incoming somatosensory stimulations

Characterizing the dynamics of amino acid racemization using time-dependent reaction kinetics: A Bayesian approach to fitting age-calibration models

Robust estimates of specimen age and associated precision are critical to the study of many palaeobiological and sedimentological processes. While recent work has explored a variety of methods for calibrating the rate of amino acid racemization using paired radiocarbon analyses, and for assessing the precision of age estimates obtained using these models, the calibration models themselves, and the underlying assumptions used to construct them, have not yet been rigorously evaluated. Here we use a Bayesian model fitting procedure to compare three previously proposed calibration functions (“apparent parabolic kinetics” [APK], “simple power-law kinetics” [SPK], and “constrained power-law kinetics” [CPK]), and we propose a new function, “time-dependent reaction kinetics” (TDK), which has a mechanistic basis in first-order reversible kinetics. We then evaluate which of three statistical distributions – normal, lognormal, gamma – best describes the prediction uncertainty associated with each age-calibration function. The Bayesian fitting method outlined here is superior to the least-squares fitting approach commonly used because it allows greater flexibility in modelling this uncertainty and its effects on the precision of age estimates. To facilitate the adoption of this methodology, we provide an analytical script that can be implemented on a variety of computer platforms using freely available software.Regardless of the fitted calibration function, we find that the gamma and lognormal distributions more accurately describe prediction uncertainty than to the normal distribution. Three of the four calibration functions perform well (the exception being APK), but no single function performs best in all situations. In general, TDK and CPK (which we show to be a special case of TDK) yield superior model fits to SPK when d/l is close to saturation, and moreover provide useful mechanistically-based functions for calibrating amino acid racemization datasets.

Relationship of distortion product otoacoustic emission components to psychoacoustic measures of noise induced hearing loss

Distortion product otoacoustic emissions (DPOAEs) have promise as a tool to detect and monitor cochlear hair cell damage in noise-induced hearing loss (NIHL). However, variability in OAE amplitudes and thresholds across individuals limits their potential for detecting the early impact of NIHL. The DPOAE has two components, one generated at the point of interaction between the primaries (generator), the second reflected from the characteristic place of the DPOAE frequency (reflected). This study investigated the components of the DPOAE and how they correlate with injury. A total of 109 men, including 54 with varying degrees of occupational noise exposure, were tested. We recorded DPOAEs using logarithmically swept pure-tones and extracted the components of the DPOAE using a least-squares fit approach. Audiometry was conducted at 1.5 and 4kHz with 1dB resolution. Compressive nonlinearity was evaluated psychoacoustically with 1.5 and 4kHz pure-tones using Schroeder-phase maskers. Overall there were associations between the generator component and the psychoacoustic measures: stronger DPOAE amplitudes were associated with better thresholds and greater difference in Schroeder-phase masking threshold. Associations were stronger at 4kHz than 1.5kHz. Similar, but weaker effects were observed for the reflected component. Findings suggest that separation of DPOAE components enhances the assessment of cochlear noise-induced injury.

Noise-induced hearing loss and strategies for its prevention in the New Zealand population: The Kiwi connection

Celebrating Glenis Long’s outstanding contribution to auditory physiology and psychoacoustics, this presentation covers the New Zealand connection and particularly her involvement in our research program into the monitoring and prevention of noise-induced hearing loss (NIHL) in the country. A large multidisciplinary project is being undertaken to investigate the nature of occupational hearing loss in New Zealand and establish a national approach to prevent NIHL. This includes estimates of NIHL prevalence and the design and evaluation of education and prevention programs to reduce the impact of noise. Using a modeling approach, we have estimated that NIHL contributes to 17–25% of cases of hearing impairment in New Zealand and is therefore a significant modifiable risk factor. A key component of our project is monitoring of noise injury and we have also studied distortion product otoacoustic emissions (DPOAE) as a measure of early injury. To assess DPOAEs as a measure of injury, we recorded them using swept pure tones and extracted DPOAE components using a least-squares fit approach in noise and non-noise exposed individuals. OAE findings were compared with measures of auditory function. We found that the generator component correlated more strongly with auditory threshold and thus may be a better physiological index of noise injury. Overall, these findings have informed a national strategy involving government and community agencies to mitigate the effects of noise.

A study of the derailment mechanism of a high speed train due to an earthquake

In order to investigate the mechanism of derailment of high-speed trains due to an earthquake, a coupled vehicle/track dynamic model considering the earthquake effect is developed. The vehicle is modelled as a multi-body system of 35 degrees of freedom and the nonlinear suspension characteristic is considered. The slab track model considers the deformable rails, the discrete support of fasteners and the deformable slabs. Rails are assumed to be Timoshenko beams supported by the rail fasteners discretely, and the slabs are modelled with solid finite elements. The coupling of the vehicle and the track considers the track moving with respect to the vehicle running at a constant speed, and such a coupling model can simulate the effect of the periodical discrete rail supports on the vehicle/track interaction. The least-square curve fitting (LSCF) approach is introduced to integrate the originally recorded earthquake acceleration to acquire the velocity and displacement-time series of the earthquake. The system motion equations are solved by means of an explicit integration method in the time domain. The present paper analyses in detail the effect of the earthquake characteristic on dynamical behaviour of the vehicle and the track and the transient derailment criteria. The considered derailment criteria include the ratio of the wheel/rail lateral force to the vertical force, the wheel loading reduction, and the wheel/rail contact point traces on the wheel tread and the wheel rise with respect to the rail top, respectively. The present investigation includes the effect of lateral earthquake motion, vertical earthquake motion, operation speed, and their combined effect on the existing derailment criteria, respectively.

Regulatory component analysis: A semi-blind extraction approach to infer gene regulatory networks with imperfect biological knowledge

With the advent of high-throughput biotechnology capable of monitoring genomic signals, it becomes increasingly promising to understand molecular cellular mechanisms through systems biology approaches. One of the active research topics in systems biology is to infer gene transcriptional regulatory networks using various genomic data; this inference problem can be formulated as a linear model with latent signals associated with some regulatory proteins called transcription factors (TFs). As common statistical assumptions may not hold for genomic signals, typical latent variable algorithms such as independent component analysis (ICA) are incapable to reveal underlying true regulatory signals. Liao et al. [1] proposed to perform inference using an approach named network component analysis (NCA), the optimization of which is achieved by a least-squares fitting approach with biological knowledge constraints. However, the incompleteness of biological knowledge and its inconsistency with gene expression data are not considered in the original NCA solution, which could greatly affect the inference accuracy. To overcome these limitations, we propose a linear extraction scheme, namely regulatory component analysis (RCA), to infer underlying regulatory signals even with partial biological knowledge. Numerical simulations show a significant improvement of our proposed RCA over NCA, not only when signal-to-noise ratio (SNR) is low but also when the given biological knowledge is incomplete and inconsistent to gene expression data. Furthermore, real biological experiments on Escherichia coli are performed for regulatory network inference in comparison with several typical linear latent variable methods, which again demonstrates the effectiveness and improved performance of the proposed algorithm.

Synoptic relationships between surface Chlorophyll-&amp;lt;i&amp;gt;a&amp;lt;/i&amp;gt; and diagnostic pigments specific to phytoplankton functional types

Abstract. Error-quantified, synoptic-scale relationships between chlorophyll-a (Chl-a) and phytoplankton pigment groups at the sea surface are presented. A total of ten pigment groups were considered to represent three Phytoplankton Size Classes (PSCs, micro-, nano- and picoplankton) and seven Phytoplankton Functional Types (PFTs, i.e. diatoms, dinoflagellates, green algae, prymnesiophytes (haptophytes), pico-eukaryotes, prokaryotes and Prochlorococcus sp.). The observed relationships between Chl-a and PSCs/PFTs were well-defined at the global scale to show that a community shift of phytoplankton at the basin and global scales is reflected by a change in Chl-a of the total community. Thus, Chl-a of the total community can be used as an index of not only phytoplankton biomass but also of their community structure. Within these relationships, we also found non-monotonic variations with Chl-a for certain pico-sized phytoplankton (pico-eukaryotes, Prokaryotes and Prochlorococcus sp.) and nano-sized phytoplankton (Green algae, prymnesiophytes). The relationships were quantified with a least-square fitting approach in order to enable an estimation of the PFTs from Chl-a where PFTs are expressed as a percentage of the total Chl-a. The estimated uncertainty of the relationships depends on both PFT and Chl-a concentration. Maximum uncertainty of 31.8% was found for diatoms at Chl-a = 0.49 mg m−3. However, the mean uncertainty of the relationships over all PFTs was 5.9% over the entire Chl-a range observed in situ (0.02 &lt; Chl-a &lt; 4.26 mg m−3). The relationships were applied to SeaWiFS satellite Chl-a data from 1998 to 2009 to show the global climatological fields of the surface distribution of PFTs. Results show that microplankton are present in the mid and high latitudes, constituting only ~10.9% of the entire phytoplankton community in the mean field for 1998–2009, in which diatoms explain ~7.5%. Nanoplankton are ubiquitous throughout the global surface oceans, except the subtropical gyres, constituting ~45.5%, of which prymnesiophytes (haptophytes) are the major group explaining ~31.7% while green algae contribute ~13.9%. Picoplankton are dominant in the subtropical gyres, but constitute ~43.6% globally, of which prokaryotes are the major group explaining ~26.5% (Prochlorococcus sp. explaining 22.8%), while pico-eukaryotes explain ~17.2% and are relatively abundant in the South Pacific. These results may be of use to evaluate global marine ecosystem models.

Compositional breast imaging using a dual‐energy mammography protocol

Mammography has a low sensitivity in dense breasts due to low contrast between malignant and normal tissue confounded by the predominant water density of the breast. Water is found in both adipose and fibroglandular tissue and constitutes most of the mass of a breast. However, significant protein mass is mainly found in the fibroglandular tissue where most cancers originate. If the protein compartment in a mammogram could be imaged without the influence of water, the sensitivity and specificity of the mammogram may be improved. This article describes a novel approach to dual-energy mammography, full-field digital compositional mammography (FFDCM), which can independently image the three compositional components of breast tissue: water, lipid, and protein. Dual-energy attenuation and breast shape measures are used together to solve for the three compositional thicknesses. Dual-energy measurements were performed on breast-mimicking phantoms using a full-field digital mammography unit. The phantoms were made of materials shown to have similar x-ray attenuation properties of the compositional compartments. They were made of two main stacks of thicknesses around 2 and 4 cm. Twenty-six thickness and composition combinations were used to derive the compositional calibration using a least-squares fitting approach. Very high accuracy was achieved with a simple cubic fitting function with root mean square errors of 0.023, 0.011, and 0.012 cm for the water, lipid, and protein thicknesses, respectively. The repeatability (percent coefficient of variation) of these measures was tested using sequential images and was found to be 0.5%, 0.5%, and 3.3% for water, lipid, and protein, respectively. However, swapping the location of the two stacks of the phantom on the imaging plate introduced further errors showing the need for more complete system uniformity corrections. Finally, a preliminary breast image is presented of each of the compositional compartments separately. FFDCM has been derived and exhibited good compositional thickness accuracy on phantoms. Preliminary breast images demonstrated the feasibility of creating individual compositional diagnostic images in a clinical environment.

Acoustomotive optical coherence elastography for measuring material mechanical properties

Acoustomotive optical coherence elastography (AM-OCE), a dynamic and internal excitation optical coherence elastography technique, is reported. Acoustic radiation force was used for internal mechanical excitation, and spectral-domain optical coherence tomography was used for detection. Mechanical properties of gelatin tissue phantoms were measured by AM-OCE and verified using rheometry results. Measured mechanical properties including shear moduli and shear damping parameters of the gelatin samples double when their polymer concentration increases from 3% to 4%. Spectral analysis was also performed on the acquired data, which improved the processing speed by a factor of 5 compared with a least-square fitting approach. Quantitative measurement, microscale resolution, and remote excitation are the main features of AM-OCE, which make the technique promising for measuring biomechanical properties.