Least-squares Processing Research Articles

Narrow-Band Least-Squares Infrasound Array Processing

Abstract Infrasound data from arrays can be used to detect, locate, and quantify a variety of natural and anthropogenic sources from local to remote distances. However, many array processing methods use a single broad frequency range to process the data, which can lead to signals of interest being missed due to the choice of frequency limits or simultaneous clutter sources. We introduce a new open-source Python code that processes infrasound array data in multiple sequential narrow frequency bands using the least-squares approach. We test our algorithm on a few examples of natural sources (volcanic eruptions, mass movements, and bolides) for a variety of array configurations. Our method reduces the need to choose frequency limits for processing, which may result in missed signals, and it is parallelized to decrease the computational burden. Improvements of our narrow-band least-squares algorithm over broad-band least-squares processing include the ability to distinguish between multiple simultaneous sources if distinct in their frequency content (e.g., microbarom or surf vs. volcanic eruption), the ability to track changes in frequency content of a signal through time, and a decreased need to fine-tune frequency limits for processing. We incorporate a measure of planarity of the wavefield across the array (sigma tau, στ) as well as the ability to utilize the robust least trimmed squares algorithm to improve signal processing and insight into array performance. Our implementation allows for more detailed characterization of infrasound signals recorded at arrays that can improve monitoring and enhance research capabilities.

Through-Plane and In-Plane Thermal Diffusivity Determination of Graphene Nanoplatelets by Photothermal Beam Deflection Spectrometry.

In this work, in-plane and through-plane thermal diffusivities and conductivities of a freestanding sheet of graphene nanoplatelets are determined using photothermal beam deflection spectrometry. Two experimental methods were employed in order to observe the effect of load pressures on the thermal diffusivity and conductivity of the materials. The in-plane thermal diffusivity was determined by the use of a slope method supported by a new theoretical model, whereas the through-plane thermal diffusivity was determined by a frequency scan method in which the obtained data were processed with a specifically developed least-squares data processing algorithm. On the basis of the determined values, the in-plane and through-plane thermal conductivities and their dependences on the values of thermal diffusivity were found. The results show a significant difference in the character of thermal parameter dependence between the two methods. In the case of the in-plane configuration of the experimental setup, the thermal conductivity decreases with the increase in thermal diffusivity, whereas with the through-plane variant, the thermal conductivity increases with an increase in thermal diffusivity for the whole range of the loading pressure used. This behavior is due to the dependence of heat propagation on changes introduced in the graphene nano-platelets structure by compression.

Prediction of Cutting Material Durability by T = f(vc) Dependence for Turning Processes

This article is focused on the prediction of cutting material durability by Taylor’s model. To create predictive models of the durability of cutting materials in the turning process, tools made of high-speed steel, sintered carbide without coating and with Titanium nitride (TiN) coating, cutting ceramics without coating and with TiN coating were applied. The experimental part was performed on reference material C45 using conventional lathe—type of machine SU50A and computer numerical control machine—CNC lathe Leadwell T-5 in accordance with International Organization for Standardization—ISO 3685. Implementation of the least-squares method and processing of regression analysis made predictions of cutting tool behaviour in the turning process. Using the method of regression analysis, a correlation index of 93.5% was obtained, indicating the functional dependence of the predicted relationship.

A Better Method of Applying OLS to the CAPM, Prediction, and Forecasting

This paper formulates a weighting function from conventional least squares (LS) and combines it with estimation theory to provide the statistical estimate, expected value, and variance of any point on the polynomial constructed for fitting a set of existing data. This solves the problem of the missing variance at arbitrary points on the polynomial from LS derived by Gauss. The method includes three LS tricks: (a) Reframing LS from creating a polynomial for fitting existing data to estimating an already existing polynomial corrupted with statistically described sampling errors. (b) Restructuring LS processing from approximating polynomial coefficients to creating a weighting function for estimating the independent variable at any point on the LS polynomial. (c) Averaging the statistical deviations from the estimated LS polynomial to estimate the variance of sampling errors. The method is based on two cold hard CAPM data sets: (a) samples of the asset corrupted by statistically described errors and (b) deterministic samples of the corresponding market. Hand-waving arguments about market forces and investor behavior apply only after LS processing, not before or during. An example of the technique applied to fictitious sales as a function of GNP shows the technique applies to virtually any problem addressed by polynomial LS.

Rank defect analysis and the realization of proper singularity in normal equations of geodetic networks

The singularity of input normal equations (NEQ) is a crucial element for their optimal handling in the context of terrestrial reference frame (TRF) estimation under the minimal-constraint framework. However, this element is often missing in the recovered NEQ from SINEX files after the usual deconstraining based on the stated information for the stored solutions. The same setback also occurs with the original NEQ that are formed by the least-squares processing of space geodetic data due to the datum information which is carried by various modeling choices and/or software-dependent procedures. In the absence of this datum-related singularity, it is not possible to obtain genuine minimally constrained solutions because of the interference between the input NEQ’s content and the external datum conditions, a fact that may alter the geometrical information of the original measurements and can cause unwanted distortions in the estimated solution. The main goal of this paper is the formulation of a filtering scheme to enforce the proper (or desired) singularity in the input NEQ with regard to datum parameters that will be handled by the minimal-constraint setting in TRF estimation problems. The importance of this task is extensively discussed and justified with the help of several numerical examples in different GNSS networks.

Ionospheric corrections for single-frequency tracking of GNSS satellites by VLBI based on co-located GNSS

Tracking L-band signals of GNSS satellites by radio telescopes became a new observation type in recent years and will be used to improve reference system realizations and links between Earth- and space-fixed frames. First successful test observations were done, with the drawback of being single-frequency only. In order to correct the ionospheric delay by using GNSS phase observations from co-located receivers, the L4R approach was developed. Based on residuals derived by a least-squares processing of the GNSS geometry-free linear combination corresponding corrections could be derived. As a first validation step L4R corrections were applied to GNSS $$L_1$$ data analysis. Station coordinate repeatibilities at the 1-cm level were obtained for baselines of a few thousand kilometers. Comparing the derived delay corrections to VLBI ionospheric delays for quasars located in same directions, differences with a standard deviation of 2.2 TECU could be achieved.

Dynamic PV Model Parameter Identification by Least-Squares Regression

This paper proposes a method for parameter identification of a photovoltaic (PV) source dynamic model. The identification procedure is based on a suitable time-domain step response and on a least-squares regression-based data processing algorithm. The considered equivalent circuit models the PV source as seen at load terminals; it is composed of a four-parameter static model and a dynamic part, which includes a capacitor with a series resistance and an inductance. The identification technique determines all three dynamic parameters with a single measurement. The proposed approach allows the appropriate dynamic modeling of the PV source and its connection cables, obtaining a better accuracy with respect to other methods in the technical literature. A practical case of parameter identification is presented.

A Fractal Approach to Assess the Risks of Nitroamine Explosives

To the best of our knowledge, this work represents the first thermal conductivity theory for fractal energetic particle groups to combine fractal and hot-spot theories. We considered the influence of the fractal dimensions of particles on their thermal conductivity and even on the sensitivity of the explosive. Based on this theory, two types of nitroamine explosives (hexahydro-1,3,5-trinitro-1,3,5-triazine [RDX] and hexanitrohexaazaisowurtzitane [HNIW]) with different sizes, size distributions, and microscale morphologies were prepared using wet milling, solvent/nonsolvent, and ridding methods. The dependence of the explosive sensitivity on the fractal characteristics of the particles was investigated. Specifically, the size distributions and scanning electron microscopy (SEM) images of the samples were used to obtain the fractal dimension (D) and surface fractal dimension (Ds), respectively, by using a least-squares method and fractal image processing software (FIPS). The mechanical sensitivity and thermal stability of the samples were characterized using mechanical sensitivity tests and differential scanning calorimetry (DSC) and were further compared with the previous results upon the investigation about HMX (octahydro-1.3.5.7-tetranitro-1,3,5,7-tetrazocine). The results indicate that the sensitivity of nitroamine explosives largely depends on the fractal dimensions of the particles. Specifically, the sample with a higher D value is more insensitive to impact action, whereas the sample with a higher Ds value is more sensitive to friction action. In addition, the sample with both higher D and Ds values has less heat release and a slower rate of thermal decomposition. All of the above observations can be attributed to the alternation of the formation of hot spots that was controlled by heat mass and thermal conductivity due to the increase of D and Ds values caused by changes in parameters such as fine particle content, specific surface area, porosity content, surface protruding points, and surface roughness. Therefore, the data in these studies were used to develop a thermal conductivity theory for fractal energetic particle groups that could be applied to the prediction of the sensitivity of energetic materials.

Three-dimensional fluence rate measurement and data acquisition system for minimally invasive light therapies

Light based therapies such as photodynamic therapy are in need of advanced tools for light fluence rate dosimetry and monitoring within the context of therapy planning and light delivery to ensure maximum treatment efficacy. The use of a single, multisensor fiber-based fluorescent probe capable of performing spatially resolved fluence rate measurements along an axis was demonstrated. This work extends the previous technique and describes a fluence rate quantification system able to employ up to 12 multisensor probes to simultaneously measure fluence rate distribution throughout a 3D treatment volume. The system optoelectronics provides for sensor calibration, data acquisition, and weighted least-squares processing to extract localized fluence rate information in real-time. Core components include an integrating cylinder for source sensor calibration, a 2D back thin CCD detector for sensor signal detection from multiple probes, high-speed data acquisition card, and custom software for real-time extraction of fluence rate information from all sensors.

Characterization and Quantification of Grape Variety by Means of Shikimic Acid Concentration and Protein Fingerprint in Still White Wines

Protein profiles, obtained by high-performance capillary electrophoresis (HPCE) on white wines previously dialyzed, combined with shikimic acid concentration and multivariate analysis, were used for the determination of grape variety composition of a still white wine. Six varieties were studied through monovarietal wines elaborated in the laboratory: Chardonnay (24 samples), Chenin (24), Petit Manseng (7), Sauvignon (37), Semillon (24), and Ugni Blanc (9). Homemade mixtures were elaborated from authentic monovarietal wines according to a Plackett-Burman sampling plan. After protein peak area normalization, a matrix was elaborated containing protein results of wines (mixtures and monovarietal). Partial least-squares processing was applied to this matrix allowing the elaboration of a model that provided a varietal quantification precision of around 20% for most of the grape varieties studied. The model was applied to commercial samples from various geographical origins, providing encouraging results for control purposes.

Analysis of the paramagnetic properties of pyrite, arsenopyrite, and chalcopyrite at high temperatures

The Faraday method is used to measure the temperature dependence of magnetic susceptibility χ(T) of pyrite and arsenopyrite in the temperature interval 20–800°C and the magnetic susceptibility of chalcopyrite in the temperature interval 500–900°C. The complicated character of dependence χ(T) is interpreted. The paramagnetic characteristic of the samples is determined via the least-squares processing. It is demonstrated that dependence χ−1(T) of the samples in the paramagnetic phase obeys the Curie-Weiss law and that the magnetic properties of iron weaken in the presence of nonmagnetic elements (S, As, and Cu).

Analysis of the magnetic properties of (La1 − x Sr x )0.93MnO3 manganites at high temperatures

For the first time, the Faraday method is used to measure the temperature dependence of paramagnetic susceptibility χ(T) of (La1 − x Sr x )0.93MnO3 (x = 0.2, 0.25, or 0.3) manganites in the temperature interval 60–850°C. It is demonstrated that the dependences have two kinks and three linear sections. The kink of curve χ−1(T) is related to polymorphic transformations (Q′ → Q* and Q* → R) that take place in the crystal lattices of the samples. The main magnetic characteristics of the samples are determined with the least-squares processing of curve χ−1. Is is demonstrated that dependence χ−1(T) obeys the Curie-Weiss law. The energy state of the magnetoactive manganese atom in the Q′-and Q*-phase samples is close to the energy state of a free Mn2+ ion. In the R phase, this state is close to the state of a free Mn3+ ion.

Pressure dependence of the sound velocity in distilled water

The sound velocity is measured in distilled water in the pressure range 0.1–60 MPa and in the temperature range 0–40°C. The results are given in the form of tables and an equation derived by least-squares processing of the experimental data.

Feasibility and Performances of a New, Multiplexed, Fast and Low-Cost Fiber-Optic NIR Spectrometer for the On-Line Measurement of Sugar in Fruits

This paper describes an attempt to develop a new NIR spectrometer to sort fruits according to the sugar content in the conditioning stations. This spectrometer, ranging from 800 to 1050 nm, is based on diode array technology. It is coupled with fiber optics, which allow multiplexing; 20 fibers have been detected by the camera, showing the potential multiplexing of 20 different points. The acquisition time is 40 ms per image (i.e., 2 ms per spectrum). A good signal-to-noise ratio has been recorded in the 820–1010 nm range. This spectrometer has been tested with a set of 79 peaches. Partial least-squares processing is applied to different wavelength ranges. The best coefficient of correlation, achieved with a reduced wavelength range (from 847 to 977 nm), is 0.81, and the standard error of prediction is 1.04°Brix. With this calibration, the fruits can be sorted into three maturity classes with a reliability of 76%. This performance, as well as the other characteristics of the instrument, is in accordance with the requirements of the conditioning station managers.

Accurate d-spacings from zero-order Laue zone patterns.

Experimental d-spacing values are criteria towards the identification of crystallites by electron diffraction. Conclusive identifications often rely on accurate d-spacings. It is shown here that accurate orthogonal components (in mm) for the primitive unit vectors of a zero-level diffraction pattern can be obtained through least-squares processing of (x,y) coordinates for all spots on the film. Valid vectors from the origin spot to any spot in the plane of the film are integer linear combinations of the two selected unit vectors. Accurate lengths and standard deviations for such vectors therefore can be calculated from the least-squares results. Corresponding d-spacings can then be calculated from the vector lengths on the film and the camera constant. In order to obtain d-spacing values that are not only precise, but also accurate, an accurate value of the camera constant should be used. This requires calibration of the experimental setup with reference materials in the same experimental conditions, with careful control of the sample height. For the same quality of measurements, the improvement in the accuracy of the d-spacings obtained with the proposed method is approximately proportional to the square root of the number of measurements taken. Practically, typical improvement in accuracy is about threefold, and accuracies of a fraction of a percent in d-spacings are achievable in this way. The above approach has been programmed as an option in the NRCBED program.

Universal FFT/matrix method for processing Mössbauer spectra

A new method for least-squares processing of Mossbauer spectra is presented applicable not only to the common spectra with superposition of bound Lorentzians or to a simple model of hyperfine field distribution, but allowing to use the transmission integral as well. A FORTRAN IV implementation comprises, among others, a computer-aided matrix model design and extensive postprocessing involving velocity scale calibration and area analysis. As an illustration, fitting of spectra of partially crystallized amorphous alloys having both crystalline and amorphous contributions is presented.

A unified scheme for processing GPS dual-band phase observations

A unified computational scheme is presented for sequential least-squares processing ofGPS dual-band carrier-beat-phase observations in network-mode positioning with orbit relaxation, and in orbit determination applications. This scheme is applicable to any spatial and temporal distribution of stations and satellites during a particularGPS experiment. Full covariance matrices can be specified for carrier-beat-phases and for weighted constraints on the ionosphere in order to improve phase ambiguity resolution. Physically meaningful choices for these covariance matrices are developed.

Evaluation of multiwavelength first- and second-derivative spectra for the quantitation of mixtures of polynuclear aromatic hydrocarbons

This paper describes the use of multiwavelength first- and second-derivative spectra with matrix least-squares data processing to resolve mixtures of components with overlapping absorption spectra. Procedures are evaluated for polynuclear aromatic hydrocarbons in the presence of a light-scattering component. Results show that the multiwavelength first- and second-derivative spectra offer higher degrees of selectivity than absorption spectra, permit the resolution of mixtures of components with overlapping spectra, and yield an improved signal-to-noise ratio relative to single-wavelength derivative data. Polynuclear aromatic hydrocarbons in two- and three-component mixtures are quantified in the range from 0.2 to 2.0 ..mu..g/mL with uncertainties in the range of 0.005 ..mu..g/mL. 4 references, 2 figures, 3 tables.

Application of a systolic array to adaptive beamforming

The paper describes a new technique for adaptive antenna beamforming. By analysing the adaptive antenna as a least-squares problem, it is possible to organise the control processor around a recursive minimisation procedure operating in the data domain. This avoids the explicit computation of the covariance matrix estimate as required by the method known as sample matrix inversion (SMI). The paper further shows how the least-squares processing algorithm may be implemented in an efficient pipeline architecture using a triangular systolic array. Computer simulation results are presented which show the performance of this new technique compared with sample matrix inversion.

Discussion on “Least-squares array processing for signals of unknown form”

Discussion on “Least-squares array processing for signals of unknown form”