Stabilization of nonlinearly parameterized discrete-time systems by NLS algorithm

The paper gives an overview of non-linear least square method, and presents GPS satellite pseudorange observation equations, which are usually over-determined because there are only 4 unknowns but normally more than 4 satellites being tracked, resulting in more than 4 pseudorange observation equations. Non-linear least squares(NLS) algorithm to solve pseudorange observation equations in order to find position and clock bias solutions are described in detail. There are three tests designed, one vehicle field test and two simulation tests. There are three NovAtel made GPS receivers being used in vehicle field test, while GSS6560 GPS satellite signal generator being used in simulation tests. By employing a set of differential GPS receivers, it is possible to establish rover station receiver to give a relatively high accurate reference to be compared by NLS and another GPS receiver in the vehicle field test. Results from NLS demonstrate that NLS can achieve high accuracy. Experimental study also shows that NLS algorithm possesses similar accuracy level to that of NovAtel Receiver, which represents world leading level.

This article presents a new formulation for attitude-independent calibration of three-axis magnetometers. The proposed solution employs a nonlinear least squares (NLLS) estimator that uses the nonlinear sensor model proposed by Foster and Elkaim in the well-known extended two-step (ETS) algorithm. Our solution has a few advantages over ETS and is more straightforward to implement than many subsequent algorithms. It enables the calculation of the calibration parameters’ uncertainties and does not require the assumption that all magnetometer measurements have a constant magnetic field magnitude. The former is essential for evaluating calibration quality, while the latter may be required for on-orbit magnetometer calibration. However, the NLLS has the drawback of requiring an initial parameter estimation to ensure convergence. Therefore, our work presents a new technique to calculate the scale factors and offsets for initializing the NLLS. Simulations and practical implementations demonstrate that our method performs similar to a recently computed analytical solution of the ETS (ETS-A). Furthermore, a Monte Carlo simulation shows that the NLLS algorithm provides a slightly better estimation of the scale factors than the ETS, in addition to the abovementioned advantages.

Pulse pile-up correction by auto-regression on linear operations (ARLO) method: A comparison with integration-based algorithms

Gradient-based local optimization has been shown to improve results of genetic programming (GP) for symbolic regression. Several state-of-the-art GP implementations use iterative nonlinear least squares (NLS) algorithms such as the Levenberg-Marquardt algorithm for local optimization. The effectiveness of NLS algorithms depends on appropriate scaling and conditioning of the optimization problem. This has so far been ignored in symbolic regression and GP literature. In this study we use a singular value decomposition of NLS Jacobian matrices to determine the numeric rank and the condition number. We perform experiments with a GP implementation and six different benchmark datasets. Our results show that rank-deficient and ill-conditioned Jacobian matrices occur frequently and for all datasets. The issue is less extreme when restricting GP tree size and when using many non-linear functions in the function set.

Oriented patterns in an image often carry important information about the scene represented. Rao and Jain developed a technique to analyze images with oriented texture using phase portraits, where the parameters of a planar first-order phase portrait are locally estimated using a nonlinear least-squares algorithm. The method gives accurate results, but is computationally expensive. Shu and Jain proposed a faster linear method for the estimation of the parameters of the phase portrait. However, their formulation leads to the minimization of a different error measure, which is not as robust as the nonlinear least-squares procedure in the presence of noise, and also makes the implicit assumption that the orientation field was truly generated by a phase portrait model (with an extra weighting factor to compensate for noise sensitivity). We propose a new derivation of Shu and Jain's linear estimator that leads to similar estimation equations, while making explicit the nature of the error measure. Our procedure includes an iterative scheme, of which Shu and Jain's linear estimator is a particular case. We show that our estimator is more robust to noise than Shu and Jain's linear estimator.

Low-rank coals characterized by a high content of sulfur from Mequinenza (type III−S), Calaf (type III), and Utrillas (type III) basins, as well as type I−S oil shales from Ribesalbes were analyzed by thermogravimetry for deriving kinetic parameters from many TG curves recorded with different heating rates (5, 15, and 25 K/min) in maximum temperature of oil generation (Tmax) using a equation defined by Zsakó. These results are contrasted with those obtained by NLS (nonlinear least squares) algorithms which derive kinetic parameters nearby Tmax from single TG curve. Furthermore, analytical determination of organic sulfur has allowed the comparison of different maximum temperatures of oil generation, as well as apparent activation energies, to establish general trends when different types of kerogen are compared. Finally, a method to compare the kinetic parameters at different heating rates (5, 15, and 25 K/min) is applied nearby the maximum temperature of oil generation (Tmax) obtaining similar kinetic values and therefore concluding that the applied method is correct for these selected coals and oil shales.

The Air Force Wright Research and Development Center and the Arnold Engineering Development Center are continuing a program for measuring optical effects of satellite material outgassing products on cryo-optic surfaces. This paper presents infrared (4000 to 700 cm-1) transmittance data for contaminant films condensed on a 77 K geranium window. From the transmittance data, the contaminant film refractive and absorptive indices (n, k) were derived using an analytical thin-film interference model with a nonlinear least-squares algorithm. To date 19 materials have been studied with the optical contants determined for 13 of those. The materials include adhesives, paints, composites, films, and lubricants. This program is continuing and properties for other materials will be available in the future.

Analysis of multi-component fluorescence emission by phase-sensitive detection using one modulation frequency

A method is presented to measure the magnetic field vector in prominences by means of the polarimetric observations in the D3 line of He obtained with the High Altitude Observatory Stokes polarimeter. The characteristics of the observed Stokes profiles are discussed. The theory of the Hanle effect is reformulated in the representation of the irreducible tensors of the density matrix, and is generalized to derive the circular polarization profiles across the spectral line in terms of the intensity and direction of the prominence magnetic field. The circular polarization profile so deduced can be employed to obtain useful information which adds to that carried by the linear polarization observations. A non-linear least-squares algorithm is proposed to derive the measurement of the magnetic field from the observations, and a consistency check is suggested to test the adequacy of the theoretical model to describe the physics of the He I atomic excitation in prominences.

Parameter estimation is an important tool in system modelling. However parameter estimation is difficult in many real-world application where continuous nonlinear dynamics interact with discrete-event dynamics. Nonlinear least-squares algorithms have been successfully applied. The paper establishes a connection between parameter identifiability and ill-conditioning of the least-squares algorithms. It is shown that a set of parameters is only identifiable if the trajectory sensitivities corresponding to those parameters are linearly independent. The importance of an appropriate choice of measurements is established.

A permeability measurement system is developed to quantify the inter-pore connectivity of tissue engineering scaffolds. It uses dry air as the fluid medium and allows rapid measurement operations. The paper analyses the fluid phenomena in porous structures, providing a theoretical background for the developed system. A nonlinear least-squares algorithm is developed to estimate the effective porosity, from which the intrinsic permeability is derived based on the mean pore size of the scaffold. It is shown that the flow in the measurement operations does not have to be within Darcy's region. The developed system can be used to characterize tissue engineering scaffolds with a wide range of permeability values.

Determination of residence-time distribution in i.v. tubing of in-line drug delivery system using deconvolution technique

Among many other uses, positron emission tomography (PET) can be used in studies to estimate the density of a neuroreceptor at each location throughout the brain by measuring the concentration of a radiotracer over time and modeling its kinetics. There are a variety of kinetic models in common usage and these typically rely on nonlinear least-squares (LS) algorithms for parameter estimation. However, PET data often contain artifacts (such as uncorrected head motion) and so the assumptions on which the LS methods are based may be violated. Quantile regression (QR) provides a robust alternative to LS methods and has been used successfully in many applications. We consider fitting various kinetic models to PET data using QR and study the relative performance of the methods via simulation. A data adaptive method for choosing between LS and QR is proposed and the performance of this method is also studied.

Low-rank coals from Mequinenza (type III-S) and Utrillas (type III) basins, characterized by high sulfur content, as well as type I-S oil shales fromRibesalbes were analyzed by thermogravimetry.Process kinetics was studied using the Friedman equation to interpret one point data -temperature of maximum generation of oil and gas (maximum on several experimental and simulated TG curves recorded at heating rates 5, 15 and 25 K⋅min -1 , T max ).These results are contrasted with those obtained by a method based on NLS (nonlinear least-squares) algorithms which derives kinetic parameters from a single TG curve recorded within a temperature interval nearby T max .The final conclusion is that the reliability of kinetic parameters obtained from one point (T max ) at several heating rates is low.On the other hand, the Friedman isoconversional method was used to elucidate the kinetic scheme which is derived from dependencies of apparent activation energy (E) on conversion level (α).Analysis of kinetic data of pyrolysis of Mequinenza coal shows that in this case the dependence of activation energy on conversion level is characteristic of a reversible reaction followed by an irreversible one, whereas in the case of pyrolysis of Utrillas coal and Ribesalbes oil shales such dependence is characteristic of a reversible reaction.

Sparse partial least-squares regression and its applications to high-throughput data analysis