Showing papers on "Robustness (computer science) published in 1977"

Levenberg--Marquardt algorithm: implementation and theory

Abstract: The nonlinear least-squares minimization problem is considered. Algorithms for the numerical solution of this problem have been proposed in the past, notably by Levenberg (Quart. Appl. Math., 2, 164-168 (1944)) and Marquardt (SIAM J. Appl. Math., 11, 431-441 (1963)). The present work discusses a robust and efficient implementation of a version of the Levenberg--Marquardt algorithm and shows that it has strong convergence properties. In addition to robustness, the main features of this implementation are the proper use of implicitly scaled variables and the choice of the Levenberg--Marquardt parameter by means of a scheme due to Hebden (AERE Report TP515). Numerical results illustrating the behavior of this implementation are included. 1 table. (RWR)

On the use of autocorrelation analysis for pitch detection

Abstract: One of the most time honored methods of detecting pitch is to use some type of autocorrelation analysis on speech which has been appropriately preprocessed. The goal of the speech preprocessing in most systems is to whiten, or spectrally flatten, the signal so as to eliminate the effects of the vocal tract spectrum on the detailed shape of the resulting autocorrelation function. The purpose of this paper is to present some results on several types of (nonlinear) preprocessing which can be used to effectively spectrally flatten the speech signal The types of nonlinearities which are considered are classified by a non-linear input-output quantizer characteristic. By appropriate adjustment of the quantizer threshold levels, both the ordinary (linear) autocorrelation analysis, and the center clipping-peak clipping autocorrelation of Dubnowski et al. [1] can be obtained. Results are presented to demonstrate the degree of spectrum flattening obtained using these methods. Each of the proposed methods was tested on several of the utterances used in a recent pitch detector comparison study by Rabiner et al. [2] Results of this comparison are included in this paper. One final topic which is discussed in this paper is an algorithm for adaptively choosing a frame size for an autocorrelation pitch analysis.

Robust statistical procedures

Abstract: Background - Why Robust Procedures? Qualitative and Quantitative Robustness, Qualitative Robustness, Quantitative Robustness, Breakdown, Infinitesimal Robustness, Influence Function M-L and R-Estimates, L-Estimates, R-Estimates, Asymptotic Properties of M-Estimates, Asymptotically Efficient M-L, R-Estimates, Scaling Question Asymptotic Minimax Theory, Minimax Asymptotic Bias, Minimax Asymptotic Variance Multiparameter Problems, Generalities, Regression, Robust Covariances - the Affinely Invariant Case, Robust Covariances - the Coordinate Dependent Case Finite Sample Minimax Theory, Robust Tests and Capacities, Finite Sample Minimax Estimation Adaptive Estimates, Adaptive Estimates Robustness - Where Are We Now?, The First Ten Years - Influence Functions and Pseudovalues, Breakdown and Outlier Detection, Studentizing, Shrinking Neighbourhoods, Some Persistent Misunderstandings, Future Directions.

Levenberg--Marquardt algorithm: implementation and theory

Abstract: The nonlinear least-squares minimization problem is considered. Algorithms for the numerical solution of this problem have been proposed in the past, notably by Levenberg (Quart. Appl. Math., 2, 164-168 (1944)) and Marquardt (SIAM J. Appl. Math., 11, 431-441 (1963)). The present work discusses a robust and efficient implementation of a version of the Levenberg--Marquardt algorithm and shows that it has strong convergence properties. In addition to robustness, the main features of this implementation are the proper use of implicitly scaled variables and the choice of the Levenberg--Marquardt parameter by means of a scheme due to Hebden (AERE Report TP515). Numerical results illustrating the behavior of this implementation are included. 1 table. (RWR)

Robustness and computational aspects of nonlinear stochastic estimators and regulators

Abstract: Robustness properties of nonlinear extended Kalman filters with constant gains and modeling errors are presented. Sufficient conditions for the nondivergence of state estimates generated by such nonlinear estimators are given. In addition, the overall robustness and stability properties of closed-loop stochastic regulators, based upon the linear-quadratic Gaussian design methodology using linearized dynamics, are presented; the sufficient conditions for closed-loop stability have a "separation-type" property.

Robust Location Estimates

Abstract: Measures of location differentiable at every density in the Hellinger metric are constructed in this paper. Differentiability entitles these location functionals to the label "robust," even though their influence curves need not be bounded and continuous. The latter properties are, in fact, associated with functionals differentiable in the Prokhorov metric. A Hellinger metric concept of minimax robustness of a location measure at a density shape $f$ is developed. Asymptotically optimal estimators are found for minimax robust location measures. Since, at $f$, their asymptotic variance equals the reciprocal of Fisher information, asymptotic efficiency at $f$ and robustness near $f$ prove compatible.

The current state-of-the-art of algorithms and computer software for geometric programming

Abstract: This paper attempts to consolidate over 15 years of attempts at designing algorithms for geometric programming (GP) and its extensions. The pitfalls encounteres when solving GP's and some proposed remedies are discussed in detail. A comprehensive summary of published software for the solution of GP problems is included. Also included, is a numerical comparison of some of the more promising recently developed computer codes for geometric programming, on a specially chosen set of GP test problems. The relative performance of these codes is measured in terms of their robustness as well as speed of computation. The performance of some general nonlinear programming (NLP) codes on the same set of test problems is also given and compared with the results for the GP codes. The paper concludes with some suggestions for future research.

A note on robust density estimation for spatial point patterns

Abstract: SUMMARY The author's earlier analytical results on the robustness of distance-based estimators of density are supplemented by a simulation study, with particular attention being given to various types of aggregated spatial point patterns. In addition, some remarks on heterogeneous patterns are made. Finally, the results of an application to data on tree locations are described.

Robustness of stability conditions for linear time-invariant feedback systems

Abstract: The robustness of stability conditions for linear time-invariant feedback systems is examined, assuming three different types of representations: state space representation, coprime matrix fraction representation, and transfer function representation. We stress the importance of certain details of the representation used and, even more, the importance of making sure that the allowed perturbations be relevant to the physical situation under study.

Robustness in parameter estimation

Abstract: A constructive approach to robust parameter estimation that carries over naturally to the nonparametric estimation is presented. Vagueness in previous notions of "robustness" has prevented such a connection from being made. To eliminate vagueness, robustness is defined in a precise mathematical way that leads to isolation of constructive analytical properties which characterize robust parameter estimators. The approach used in this paper is an extension of the qualitative approach introduced by Hampel.

Multidimension scaling for multiobjective policies

Abstract: This paper develops and expands the use of multidimension scaling techniques (MDSCAL) as applied in the two separate fields of psychological testing and archaeology to the problem of multiple criteria decision making. Other work by the author published elsewhere shows that it is feasible to use MDSCAL for drawing maps of separate policies using very weak input information from which deductions as to most preferred and least preferred policies may be drawn. An application of this method is made, to show its use and a comparison made with the utility approach. The final, and main, part of the paper examines the robustness of the method for both deterministic and probabilistic input criteria. In this examination it is seen that the mapping method performs very well in picking up extremes of preference even under severe tests of robustness.

Robust properties of solutions to linear-quadratic estimation and control problems

Abstract: In this note we demonstrate a minimax robustness property for linear-quadratic estimation and control problems and discuss the importance of this result as well as the relevance of the general philosophy of robust design in estimation and control.

On the relationship between reliability and linear quadratic optimal control

Abstract: The linear quadratic optimal control method is used today to solve many complex systems problems. As system complexity increases, and as linear quadratic optimal control is used in more demanding situations, the extension of the design methodology to cover system failures, robustness and reliability is of crucial importance. This paper documents is the progress toward a theory which incorporates reliability in the performance index; a linear quadratic control problem is formulated which accounts for system effectiveness and gives an offline Procedure for comparing two linear quadratic control systems on the basis of both reliability and performance.

Automatic numerical quadrature

Abstract: An automatic numerical quadrature routine (anqr) attempts to evaluate $\in_{a}^{b} f(x) dx$ to absolute accuracy ∊, given only ∊, a, b, and a user-supplied subroutine which calculates f(x) for any x in [a,b]. An anqr which guarantees success is impossible to construct, even disregarding the effects of finite computer precision, but the problem is nonetheless of interest. A reliable and efficient anqr is a necessary part of any mathematical subroutine library. New single- and double-precision anqrs, quad and dquad, have been constructed and tested. They are based on adaptive Romberg extrapolation, with cautious error estimation. An important practical feature is the automatic recognition of endpoint singularities, and a change of variable to handle them. quad and dquad also recognize the presence of noise in the function being integrated, and limit the attempted accuracy accordingly. Since guaranteed anqrs are impossible, extensive testing of dquad is presented to demonstrate its efficiency and robustness. Comparable testing is not available for competitive anqrs, but performance on a standard set of test integrals is presented for dquad and nine other anqrs. dquad is generally better. quad and dquad are written in pfort, a subset of American National Standard (ans) Fortran. Machine-dependent constants are obtained from the port library machine-constants programs. A portable package of storage allocation routines is used.

Robustness properties for a simple class of rank estimates

Abstract: Robustness properties of a family of rank estimates to compete with trimmed means and other robust estimates for the one sample location problem are investigated. In particular, the influence curve and breakdown point are developed, as well as their finite sample equivalents, the sensitivity curve and tolerance. The estimates are formulated from a one sample rank test rather than the customary two sample rank test approach. In addition, a functional is implicitly defined for the asymptotic version of the estimate. Computational problems are considered and a simple iterative procedure for finding the estimate is given.

Model-Based Scene Matching

Abstract: : Results form this work on model-based scene-matching schemes lead us to believe that our approach is sufficiently sound and robust to perform adequately with complex real imagery appropriate to various possible mission scenarios Some of these results were given in this report; in particular, schemes include: the feasibility demonstration of the vertex-based model- matching system for registering two scenes Many parts of this system have already been perfected--interfacing and feedback loops between the different parts remain to be developed The needed modifications are outlined in this section Experimental results on scene matching using vertex models are reported The results illustrate the robustness and inherent power of mode-based matching techniques The approach has the advantage that the reference model is simple and has low data requirements The reference model is constructed before it is needed; it is often only necessary to store a list of points (vertices) and their interconnections, and it is feasible to store multiple references Also, any modifications or changes needed to update the reference model can be conveniently specified In a software implementation on a general-purpose machine of the model construction and matching techniques, the majority of computing required was at the lowest level (eg, edge detection) Edges are currently detected by the Hueckel operator, which is a complex, time-consuming process However, the Hueckel operator apparently can be replaced with a simpler edge-detection technique This technique can be implemented in hardware for real-time operation

Further Progress on Robust/Resistant Widthers.

Abstract: : This report describes work on the development of robust estimators of width. An earlier technical report, an Interim Report of a Monte Carlo Study of Robust Estimators of Width describes previous work undertaken in connection with this project. Essentially a single faimly of estimators (together with a few obvious variations) was investigated for sample sizes n=10 and n=20, using Monte Carlo methods. The authors were motivated by considerations of conceptual and computational simplicity as well as a desire to achieve high robustness of efficiency. Moderate success was achieved on both counts. In fact apparent triefficiencies of 89% were obtained for sample size 10.

Robustness in linear quadratic feedback design with application to an aircraft control problem

Abstract: Some new results concerning robustness and asymptotic properties of error bounds of a linear quadratic feedback design are applied to an aircraft control problem. An autopilot for the flare control of the Augmentor Wing Jet STOL Research Aircraft (AWJSRA) is designed based on Linear Quadratic (LQ) theory and the results developed in this paper. The variation of the error bounds to changes in the weighting matrices in the LQ design is studied by computer simulations, and appropriate weighting matrices are chosen to obtain a reasonable error bound for variations in the system matrix and at the same time meet the practical constraints for the flare maneuver of the AWJSRA. Results from the computer simulation of a satisfactory autopilot design for the flare control of the AWJSRA are presented.

A robustness property of the separation principle

Abstract: We consider the stochastic linear regulator problem when the observation and driving noises are random processes with large, but finite, bandwidths. We show that as the bandwidth of the noise tends to infinity there is a natural limiting stochastic regulator problem which involves Gaussian white noise disturbances. The optimal control law of this problem, for which the Separation Principle holds, is suboptimal for the original problem. We obtain a power series expansion of the suboptimal cost of this control law in terms of the correlation time (inverse of the bandwidth) of the noise. From this expansion we conclude that as the bandwidth of the disturbances approaches infinity the suboptimal cost approaches the optimal cost of the limiting regulator problem, and so, that the Separation Principle is robust. Both finite and infinite time (steady state) problems are considered.