a new approach to multipath correction of constant modulus signals an adaptive digital filtering algorithm that can compensate for both frequency selective multipath and interference on constant envelope modulated signals is presented the method exploits the fact that multipath reception and various interference sources generate incidental amplitude modulation on the received signal a class of so called constant modulus performance functions is developed which sense this am term but are insensitive to the angle modulation simple adaptive algorithms for finite impulse response fir digital filters are developed which employ a gradient search of the performance function one of the resulting algorithms is simulated for the example of an fm signal degraded by specular multipath propagation substantial improvements in noise power ratio npr are observed e g 25 db with moderately rapid convergence time these results are then extended to include tonal interference on a fm signal and intersymbol interference on a qpsk data signal

conditional scores and optimal scores for generalized linear measurement error models abstract this paper studies estimation of the parameters of generalized linear models in canonical form when the explanatory vector is measured with independent normal error for the functional case i e when the explanatory vectors are fixed constants unbiased score functions are obtained by conditioning on certain sufficient statistics this work generalizes results obtained for logistic regression in the case that the explanatory vectors are independent and identically distributed with unknown distribtuion efficient score functions are obtained using the theory developed in begun et al 1983 keywords conditional score function efficient score function functional model generalized linear model measurement error structural model

some new results in the theory of negative imaginary systems with symmetric transfer matrix function abstract this note represents a first attempt to provide a definition and characterisation of negative imaginary systems for not necessarily rational transfer functions via a sign condition expressed in the entire domain of analyticity along the same lines of the classic definition of positive real systems under the standing assumption of symmetric transfer functions we then derive a necessary and sufficient condition that characterises negative imaginary transfer functions in terms of a matrix sign condition restricted to the imaginary axis once again following the same line of argument of the standard positive real case using this definition even transfer functions with a pole at the origin with double multiplicity as well as with a possibly negative relative degree can be negative imaginary

tracking fast trajectories along a slow dynamics a singular perturbations approach controlled coupled slow and fast motions are examined in a singular perturbations setting the objective is to minimize a cost functional that takes into account both the fast motion supposing say tracking a fast target and the slow dynamics a method is offered to cope with the possibility that the fast flow has nonstationary limits invariant measures of the fast motion are then the controlled objects on the infinitesimal scale optimal amalgamation of them on the slow scale induces the variational limit whose solutions are near optimal solutions of the perturbed system

on errors in variables for binary regression models summary we consider binary regression models when some of the predictors are measured with error for normal measurement errors structural maximum likelihood estimates are considered we show that if the measurement error is large the usual estimate of the probability of the event in question can be substantially in error especially for high risk groups in the situation of large measurement error we investigate a conditional maximum likelihood estimator and its properties

existence and comparison theorems for algebraic riccati equations for continuous and discrete time systems abstract we discuss two comparison theorems for algebraic riccati equations of the form xbr 1 b x x a br 1 c a br 1 c x q c r 1 c 0 simultaneously we give sufficient conditions to obtain the existence of the maximal hermitian solution of a riccati equation from the existence of a hermitian solution of a second riccati equation further similar results are given for discrete algebraic riccati equations

analysis and modification of newton s method for algebraic riccati equations when newton s method is applied to find the maximal symmetric solution of an algebraic riccati equation convergence can be guaranteed under moderate conditions in particular the initial guess need not be close to the solution the convergence is quadratic if the frechet derivative is invertible at the solution in this paper we examine the behaviour of the newton iteration when the derivative is not invertible at the solution we find that a simple modification can improve the performance of the newton iteration dramatically

the effects of pn sequences on the misconvergence of the constant modulus algorithm cma the constant modulus algorithm cma can misconverge when the received two dimensional 2 d signal is derived from encoding a binary pn sequence the distortion of the probabilistic symmetry of the transmitted constellation can be controlled by careful selection of the underlying binary pn sequence thereby influencing the convergence behavior of cma

linear matrix inequalities riccati equations and indefinite stochastic linear quadratic controls this paper deals with an optimal stochastic linear quadratic lq control problem in infinite time horizon where the diffusion term in dynamics depends on both the state and the control variables in contrast to the deterministic case we allow the control and state weighting matrices in the cost functional to be indefinite this leads to an indefinite lq problem which may still be well posed due to the deep nature of uncertainty involved the problem gives rise to a stochastic algebraic riccati equation sare which is however fundamentally different from the classical algebraic riccati equation as a result of the indefinite nature of the lq problem to analyze the sare we introduce linear matrix inequalities lmis whose feasibility is shown to be equivalent to the solvability of the sare moreover we develop a computational approach to the sare via a semi definite programming associated with the lmis finally numerical experiments are reported to illustrate the proposed approach

output feedback negative imaginary synthesis under structural constraints the negative imaginary property is a property that many practical systems exhibit this paper is concerned with the negative imaginary synthesis problem for linear time invariant systems by output feedback control sufficient conditions are developed for the design of static output feedback controllers dynamic output feedback controllers and observer based feedback controllers based on the design conditions a numerical algorithm is suggested to find the desired controllers structural constraints can be imposed on the controllers to reflect the practical system constraints also the separation principle is shown to be valid for the observer based design finally three numerical examples are presented to illustrate the efficiency of the developed theory

stability robustness of a feedback interconnection of systems with negative imaginary frequency response a necessary and sufficient condition expressed simply as the dc loop gain i e the loop gain at zero frequency being less than unity is given in this note to guarantee the internal stability of a feedback interconnection of linear time invariant lti multiple input multiple output systems with negative imaginary frequency response systems with negative imaginary frequency response arise for example when considering transfer functions from force actuators to colocated position sensors and are commonly important in for example lightly damped structures the key result presented here has similar application to the small gain theorem which refers to the stability of feedback interconnections of contractive gain systems and the passivity theorem which refers to the stability of feedback interconnections of positive real or passive systems a complete state space characterization of systems with negative imaginary frequency response is also given in this note and also an example that demonstrates the application of the key result is provided

stability analysis of interconnected systems with mixed negative imaginary and small gain properties in this letter an analytical framework is proposed to examine stability of two stable linear time invariant systems interconnected in positive feedback where the systems have mixed properties of negative imaginary and small gain using the notion of dissipativity the interconnection of systems is guaranteed to be finite gain stable under the condition that the dc loop gain is contractive this work builds on griggs and exploits a new set of frequency dependent triplets that was introduced in above reference to mix two unconditional stability statements i e small gain and passivity unlike the above reference the present work explores the important question of how a conditional stability statement as needed when two negative imaginary systems are connected in a feedback loop can be mixed with an unconditional stability statement as needed when two contractive systems are connected in a feedback loop the usefulness of the proposed analytical framework is demonstrated via a numerical example

an observer based control scheme using negative imaginary theory this paper presents a full order state observer based scheme that transforms a causal lti minimally realized system into a strongly strict negative imaginary system by defining an auxiliary output based on the observed states the auxiliary output is used for closed loop control with positive feedback invoking the internal stability condition of negative imaginary theory a set of lmi conditions is derived that determines the value of a design parameter required for the proposed scheme to transform a given system with a minimal state space realization into a strongly strict negative imaginary system the proposed scheme is applicable for both stable unstable and square non square systems in this paper the framework is further explored for robustness analysis of uncertain systems and numerical examples are given to elucidate effectiveness of the proposed results

homogeneous riccati equations versus quadratic inequalities it is proved that under certain hypotheses the existence of hermitian solutions of a homogenized algebraic riccati equation of continuous type is guaranteed if the corresponding quadratic inequality admits a hermitian solution both finite dimensional matrices and infinite dimensional hilbert space operators riccati equations are considered

correction of logistic regression relative risk estimates and confidence intervals for systematic within person measurement error errors in the measurement of exposure that are independent of disease status tend to bias relative risk estimates and other measures of effect in epidemiologic studies toward the null value two methods are provided to correct relative risk estimates obtained from logistic regression models for measurement errors in continuous exposures within cohort studies that may be due to either random unbiased within person variation or to systematic errors for individual subjects these methods require a separate validation study to estimate the regression coefficient lambda relating the surrogate measure to true exposure in the linear approximation method the true logistic regression coefficient beta is estimated by beta lambda where beta is the observed logistic regression coefficient based on the surrogate measure in the likelihood approximation method a second order taylor series expansion is used to approximate the logistic function enabling closed form likelihood estimation of beta confidence intervals for the corrected relative risks are provided that include a component representing error in the estimation of lambda based on simulation studies both methods perform well for true odds ratios up to 3 0 for higher odds ratios the likelihood approximation method was superior with respect to both bias and coverage probability an example is provided based on data from a prospective study of dietary fat intake and risk of breast cancer and a validation study of the questionnaire used to assess dietary fat intake

the evaluation of integrals of the form f t exp t 2 dt application to logistic normal models abstract logistic normal distributions and related functions arise in a variety of statistical applications of current interest including binary measurement error models and the analysis of teratogenicity experiments analytic intractability has led to the development of numerous approximations to the desired forms often with consequences that have not been well studied a method is developed to compute these forms to arbitrary accuracy and comparative calculations are made that show when the common numerical alternative 20 point gaussian quadrature begins to fail by using a simple matrix transformation this method can be used with multiple covariate regression models of the logistic normal form we conducted a simulation study that compares the ability of 20 point gaussian quadrature and our new method to obtain the maximum likelihood estimator of relative risk in the logistic normal measurement error model using standard subroutines to maximize the likelihood equations 27 of 50 trials failed to

multi stage blind clustering equaliser a multi stage blind clustering algorithm is proposed for equalisation of multi level quadrature amplitude modulation m qam channels a hierarchical decomposition divides the task of equalising a high order qam channel into much simpler sub tasks each sub task can be accomplished fast and reliably using a blind clustering algorithm derived originally for 4 qam signals the constant modulus algorithm cma is used as a benchmark to assess this multi stage blind equaliser it is demonstrated that the new blind algorithm achieves much faster convergence and is very robust when input symbols are not sufficiently white this multi stage clustering equaliser only requires slightly more computations than the cma and like the latter its computational complexity does not increase as the levels of digital symbols increase

a generalized negative imaginary lemma and riccati based static state feedback negative imaginary synthesis abstract in this paper we present a generalized negative imaginary lemma based on a generalized negative imaginary system definition then an algebraic riccati equation method is given to determine if a system is negative imaginary also a state feedback control procedure is presented that stabilizes an uncertain system and leads to the satisfaction of the negative imaginary property the controller synthesis procedure is based on the proposed negative imaginary lemma using this procedure the closed loop system can be guaranteed to be robustly stable against any strict negative imaginary uncertainty such as in the case of unmodeled spill over dynamics in a lightly damped flexible structure a numerical example is presented to illustrate the usefulness of the results

a negative imaginary lemma and the stability of interconnections of linear negative imaginary systems the note is concerned with linear negative imaginary systems first a previously established negative imaginary lemma is shown to remain true even if the system transfer function matrix has poles on the imaginary axis this result is achieved by suitably extending the definition of negative imaginary transfer function matrices secondly a necessary and sufficient condition is established for the internal stability of the positive feedback interconnections of negative imaginary systems meanwhile some properties of linear negative imaginary systems are developed finally an undamped flexible structure example is presented to illustrate the theory

strictly negative imaginary state feedback control with a prescribed degree of stability abstract this paper presents conditions for the synthesis of a strictly negative imaginary closed loop system with a prescribed degree of stability under the assumption of full state feedback a perturbation method is used to ensure the closed loop system has both the strict negative imaginary property and a prescribed degree of stability this approach involves the real schur decomposition of a matrix followed by the solution to two lyapunov equations also we present and clarify the perturbation properties of strictly negative imaginary systems

on non proper negative imaginary systems abstract this paper studies non proper negative imaginary systems first the concept of negative imaginary transfer functions that may have poles at the origin and infinity is introduced then a generalized lemma is presented to provide a sufficient condition to characterize the non proper negative imaginary properties of systems the generalized lemma is given in terms of complex variable s in the quarter domain of analyticity compared to previous results our result removes the symmetric restriction also a new relationship is established between lossless negative imaginary and lossless positive real transfer function matrices by using a minor decomposition the results in this paper give us the possibility to address non proper and non symmetric descriptor systems with negative imaginary frequency response several examples are presented to illustrate the results

cost efficient study designs for binary response data with gaussian covariate measurement error summary when mismeasurement of the exposure variable is anticipated epidemiologic cohort studies may be augmented to include a validation study where a small sample of data relating the imperfect exposure measurement method to the better method is collected optimal study designs i e least expensive subject to specified power constraints are developed that give the overall sample size and proportion of the overall sample size allocated to the validation study if better exposure measurements can be collected on a sample of subjects an optimal design can be suggested that conforms to realistic budgetary constraints the properties of three designs those that include an internal validation study those where the validated subsample is derived from subjects external to the primary investigation and those that use the better method of exposure assessment on all subjects are compared the proportion of overall study resources allocated to the validation substudy increases with increasing sample disease frequency decreasing unit cost of the superior exposure measurement relative to the imperfect one increasing unit cost of outcome ascertainment increasing distance between two alternative values of the relative risk between which the study is designed to discriminate and increasing magnitude of hypothesized values this proportion also depends in a nonlinear fashion on the severity of measurement error and when the validation study is internal measurement error reaches a point after which the optimal design is the smaller fully validated one

on positive realness negative imaginariness and h control of state space symmetric systems this paper studies positive realness and negative imaginariness of state space symmetric systems first a necessary and sufficient condition is provided for a state space symmetric system to be respectively positive real and negative imaginary then an explicit formulation for the infimum of h norm under a mixed h and negative imaginary performance and an explicit solution for the associated optimal static output feedback control gain are developed based on symmetric negative imaginary theorem finally three examples are provided to illustrate the main results of the paper

a generalization of the positive real lemma the positive real lemma also called the kalman yacubovich popov lemma characterizes the positive realness of the transfer function matrix of a linear dynamic system by algebraic conditions in the case of a pole zero cancellation appearing in the transfer function matrix or in other words missing the assumptions of controllability and observability there exist generalized versions which are discussed and proven applying the kalman canonical decomposition

a negative imaginary lemma without minimality assumptions and robust state feedback synthesis for uncertain negative imaginary systems abstract negative imaginary systems have important engineering applications for example in lightly damped flexible structures with collocated position sensors and force actuators this paper proposes a new negative imaginary lemma for generalized negative imaginary systems where the minimality assumption is relaxed the proposed lemma facilitates both analysis and synthesis for negative imaginary systems invoking this result a systematic robust static state feedback synthesis method is proposed in an lmi framework for systems with strictly negative imaginary uncertainty e g unmodeled spill over dynamics in a lightly damped flexible structure assuming all states are available for state feedback two numerical examples are given to show the usefulness of the proposed results

infinite dimensional negative imaginary systems we consider second order infinite dimensional systems with force control and collocated position measurement interconnected with finite dimensional controllers of the same type we show that under assumptions that generalize those in the finite dimensional case the theory of negative imaginary systems asymptotic stability of the closed loop system can be concluded but that the closed loop system may not be exponentially stable nor input output stable

covariate measurement error in generalized linear models summary the em algorithm is used to obtain estimators of regression coefficients for generalized linear models with canonical link when normally distributed covariates are masked by normally distributed measurement errors by casting the true covariates as missing data the em procedure suggests an iterative scheme in which each cycle consists of an e step requiring the computation of approximate first and second conditional moments of the true covariates given the observed data followed by an m step in which regression parameters are updated by iteratively reweighted least squares based on these approximations the proposed procedure is compared numerically with the exact maximum likelihood solution obtained by using gaussian quadrature instead of the approximations in the e step of the em algorithm and with alternative estimators for simple logistic regression with measurement error the results for the proposed procedure are encouraging a procedure is proposed in this paper for estimating regression coefficients in generalized linear models when one or more of the covariates is measured with error this work is related to the paper by carroll et al 1984 in which maximum likelihood estimates are considered for the structural logistic regression model these authors provide estimates for the computationally simpler probit regression model and suggest that the structural logistic regression can be done in principle this paper follows up on that suggestion but differs in detail from similar work by armstrong 1985 other procedures with related aims have been suggested by stefanski carroll 1985 wolter fuller 1982 and prentice 1982 for a quick introduction to the proposed method it is convenient to display the naive estimator which ignores measurement error in its standard computational form if yi is an observed response variable and xi is the observed covariate then for the model which equates the canonical parameter of the distribution of yi to xtf3 the maximum likelihood estimator of f3 can be obtained by iteratively reweighted least squares the estimate of f3 after s 1 cycles is given by

covariate measurement error in logistic regression abstract in a logistic regression model when covariates are subject to measurement error the naive estimator obtained by regressing on the observed covariates is asymptotically biased this document introduces a bias adjusted estimator and two estimators appropriate for normally distributed measurement errors a functional maximum likelihood estimator and an estimator which exploits the consequences of sufficiency the four proposals are studied asymptotically under conditions which are appropriate when the measurement error is small a small monte carlo study illustrates the superiority of the measurement error estimators in certain situations additional keywords mathematical models

pseudo maximum likelihood estimation theory and applications abstract pseudo maximum likelihood estimation easily extends to k parameter models and is of interest in problems in which the likelihood surface is ill behaved in higher dimensions but well behaved in lower dimensions several signal plus noise or convolution models are examined which exhibit such behavior and satisfy the regularity conditions of the asymptotic theory for specific models a numerical comparison of asymptotic variances suggests that a psuedo maximum likelihood estimate of the signal parameter is uniformly more efficient than estimators that have been advanced by previous authors a number of other potential applications are noted

logistic regression for two stage case control data summary samples of diseased cases and nondiseased controls are drawn at random from the population at risk after classification according to the exposure of interest subsamples of cases and controls are selected for purposes of covariable ascertainment a modification of the usual logistic regression analysis yields consistent estimates of covariable adjusted relative risks and their standard errors by balancing the numbers of exposed and nonexposed for whom covariable inforniation is ascertained within case and control samples some efficiency may be gained over the usual single stage design particularly when the exposure is rare and the relative risks associated with the covariables are large the procedure may be useful also when covariable information is missing for a large part of the sample

negative imaginary synthesis via dynamic output feedback and static state feedback a riccati approach abstract this paper is concerned with the study of strictly negative imaginary sni systems and the problem of synthesizing a controller rendering a linear fractional system sni first a set of necessary and sufficient conditions are developed for an sni lemma without imposing minimality assumptions the proposed lemma supports both the analysis and synthesis of sni systems then a set of sufficient conditions based on the solution of algebraic riccati equations is provided for the solution of the sni synthesis problem finally an illustrative example demonstrates the usefulness of the results given herein

feedback stability of negative imaginary systems this paper extends the robust feedback stability theorem of negative imaginary systems by removing restrictive assumptions on the instantaneous gains of the systems that were imposed in the earlier literature and it further generalizes this robust analysis result into the case that allows negative imaginary systems to have poles at the origin in doing so we extend the class of negative imaginary systems for which this robust stability theorem is applicable we also show that this new generalized necessary and sufficient result specializes to the earlier theorems under the same assumptions we additionally prove that the previously known dc gain condition is not only necessary and sufficient for robust feedback stability under the earlier specified instantaneous gain assumptions but is also necessary and sufficient for robust feedback stability under new different and equally simple assumptions the general robust feedback stability theorem for negative imaginary systems with free body dynamics i e poles at the origin derived in this paper also specializes to the case that is only applicable for the negative imaginary system without poles at the origin since the results for negative imaginary systems with free body dynamics developed in this paper depend on the existence of a matrix psi with certain properties we also propose a systematic construction of this matrix psi and show that construction of one such psi is sufficient for determining the feedback stability of the closed loop system finally examples are used to demonstrate the applicability of the results

inference for the proportional hazards model with misclassified discrete valued covariates summary we consider the cox proportional hazards model with discrete valued covariates subject to misclassification we present a simple estimator of the regression parameter vector for this model the estimator is based on a weighted least squares analysis of weighted averaged transformed kaplan meier curves for the different possible configurations of the observed covariate vector optimal weighting of the transformed kaplan meier curves is described the method is designed for the case in which the misclassification rates are known or are estimated from an external validation study a hybrid estimator for situations with an internal validation study is also described when there is no misclassification the regression coefficient vector is small in magnitude and the censoring distribution does not depend on the covariates our estimator has the same asymptotic covariance matrix as the cox partial likelihood estimator we present results of a finite sample simulation study under weibull survival in the setting of a single binary covariate with known misclassification rates in this simulation study our estimator performed as well as or in a few cases better than the full weibull maximum likelihood estimator we illustrate the method on data from a study of the relationship between trans unsaturated dietary fat consumption and cardiovascular disease incidence