Two new methods for obtaining stability derivatives from flight test data

New methods for obtaining stability derivatives from flight dat

Computational aspects of a three dimensional non-intrusive particle motion tracking system

Development of a technique for non-intrusive particle motion tracking in three dimensions is considered. This technique is based on the principle of magnetic induction. In particular, the determination of the position and onentation of the particle from the information gathered is the pnncipal focus of this thesis. The development of such a system is motivated by the need to understand the flow patterns of granular material. This is of cntical importance in dealing with problems associated with bulk solids flows which occur in almost all industries and in natural geological events. A study of the current diagnostic techniques reveals the limitations in their ability to track the motion of an individual particle in a mass flow of other particles. These techniques fail when the particle must be tracked in three dimensions in a non-intrusive manner. The diagnostic technique we consider results in an unconstrained minimization problem of an overdetennined system of nonlinear equations. The Levenberg-Marquardt algorithm is used to solve such a system to predict the location of the particle. The viability of this technique is established through simulated and actual expenmental results. Practical problems such as the effect of noise are considered. Directions for future work are provided

The Linear Least Squares Problem of Bundle Adjustment

A method is described for finding the least squares solution of the overdetermined linear system that arises in the photogrammetric problem of bundle adjustment of aerial photographs. Because of the sparse, blocked structure of the coefficient matrix of the linear system, the proposed method is based on sparse QR factorization using Givens rotations. A reordering of the rows and columns of the matrix greatly reduces the fill-in during the factorization. Rules which predict the fill-in for this ordering are proven based upon the block structure of the matrix. These rules eliminate the need for the usual symbolic factorization in most cases. A subroutine library that implements the proposed method is listed. Timings and populations of a range of test problems are given

Duality in robust linear regression using Huber's M-estimator

Cataloged from PDF version of article.The robust linear regression problem using Huber's piecewise-quadratic M-estimator function is considered. Without exception, computational algorithms for this problem have been primal in nature. In this note, a dual formulation of this problem is derived using Lagrangean duality. It is shown that the dual problem is a strictly convex separable quadratic minimization problem with linear equality and box constraints. Furthermore, the primal solution (Huber's M-estimate) is obtained as the optimal values of the Lagrange multipliers associated with the dual problem. As a result, Huber's M-estimate can be computed using off-the-shelf optimization software

Least-squares methods for identifying biochemical regulatory networks from noisy measurements

<b>Background</b>: We consider the problem of identifying the dynamic interactions in biochemical networks from noisy experimental data. Typically, approaches for solving this problem make use of an estimation algorithm such as the well-known linear Least-Squares (LS) estimation technique. We demonstrate that when time-series measurements are corrupted by white noise and/or drift noise, more accurate and reliable identification of network interactions can be achieved by employing an estimation algorithm known as Constrained Total Least Squares (CTLS). The Total Least Squares (TLS) technique is a generalised least squares method to solve an overdetermined set of equations whose coefficients are noisy. The CTLS is a natural extension of TLS to the case where the noise components of the coefficients are correlated, as is usually the case with time-series measurements of concentrations and expression profiles in gene networks. <b>Results</b>: The superior performance of the CTLS method in identifying network interactions is demonstrated on three examples: a genetic network containing four genes, a network describing p53 activity and <i>mdm2</i> messenger RNA interactions, and a recently proposed kinetic model for interleukin (IL)-6 and (IL)-12b messenger RNA expression as a function of ATF3 and NF-κB promoter binding. For the first example, the CTLS significantly reduces the errors in the estimation of the Jacobian for the gene network. For the second, the CTLS reduces the errors from the measurements that are corrupted by white noise and the effect of neglected kinetics. For the third, it allows the correct identification, from noisy data, of the negative regulation of (IL)-6 and (IL)-12b by ATF3. <b>Conclusion</b>: The significant improvements in performance demonstrated by the CTLS method under the wide range of conditions tested here, including different levels and types of measurement noise and different numbers of data points, suggests that its application will enable more accurate and reliable identification and modelling of biochemical networks

LEPISME

We present a first version of a software dedicated to an application of a classical nonlinear control theory problem to the study of compartmental models in biology. The software is being developed over a new free computer algebra library dedicated to differential and algebraic elimination

Statistical computing support for Lp estimation in augmented linear models under linear inequality restrictions

This research project deals with computationally related problems in the general area of l(,p) (p (GREATERTHEQ) 1) estimation in linear models. Methods for computing l(,p) estimate in linear models are studied. In case of p = 1, descent methods from Bloomfield and Steiger, and Usow are discussed. A proof of convergence of these methods is provided. In case of p \u3e 1, Newton\u27s method and Quasi-Newton method are discussed. A new method is proposed and studied. It performs extremely well for p close to 2. Also, closed form solutions of the l(,p) estimation problem having design matrix of dimension (m + 1) x m or (m +2) x m are derived, and methods of generating test problems for the general l(,p) estimation problem are discussed. In another part of the research project, the objective function for computing l(,p) estimate, augmented by the p(\u27th) power of l(,p) norm of the parameter vector, has been studied. One result of this study is a way to identify the l(,p) estimate having the least l(,p) norm. Finally, branch-and-bound method for computing l(,p) estimate of linear models under linear inequality restrictions are discussed

A Node Elimination Algorithm for Cubatures of High-Dimensional Polytopes

Node elimination is a numerical approach for obtaining cubature rules for the approximation of multivariate integrals over domains in Rn. Beginning with a known cubature, nodes are selected for elimination, and a new, more efficient rule is constructed by iteratively solving the moment equations. In this work, a new node elimination criterion is introduced that is based on linearization of the moment equations. In addition, a penalized iterative solver is introduced that ensures positivity of weights and interiority of nodes. We aim to construct a universal algorithm for convex polytopes that produces efficient cubature rules without any user intervention or parameter tuning, which is reflected in the implementation of our package gen-quad. Strategies for constructing the initial rules for various polytopes in several space dimensions are described. Highly efficient rules in four and higher dimensions are presented. The new rules are compared to those that are obtained by combining transformed tensor products of one dimensional quadrature rules, as well as with known analytically and numerically constructed cubature rules