a one factor multivariate time series model of metropolitan wage rates abstract the paper formulates and estimates a single factor multivariate time series model the model is a dynamic generalization of the multiple indicator or factor analysis model it is shown to be a special case of the general state space model and can be estimated by maximum likelihood methods using the kalman filter algorithm the model is used to obtain estimates of the unobserved metropolitan wage rate for los angeles based on observations of sectoral wages within the standard metropolitan statistical area hypothesis tests model diagnostics and out of sample forecasts are used to evaluate the model

a hybrid receding horizon control scheme for nonlinear systems a hybrid receding horizon control scheme for nonlinear discrete time systems is proposed whereas a set of optimal feedback control functions is defined at the continuous level a discrete event controller chooses the best control action depending on the current conditions of a plant and on possible external events such a two level scheme is embedded in the structure of abstract hybrid systems thus making it possible to prove a new asymptotic stability result for the hybrid receding horizon control approach

level crossing rate and average fade duration of egc systems with cochannel interference in rayleigh fading both the first order signal statistics e g the outage probability and the second order signal statistics e g the average level crossing rate lcr and the average fade duration afd are important design criteria and performance measures for wireless communication systems including the equal gain combining egc systems in the presence of the cochannel interference cci although the analytical expressions for the outage probability of the coherent egc systems are exposed to cci and various fading channels are already known the respective expressions for the average lcr and the afd are not available in the literature this paper presents such analytical expressions for the rayleigh fading channel which are obtained by utilizing a novel analytical approach that does not require the explicit expression for the joint probability density function pdf of the instantaneous output signal to interference ratio and its time derivative applying the characteristic function method and the beaulieu series we determined the average lcr and the afd at the output of an interference limited egc system with an arbitrary diversity order and an arbitrary number of cochannel interferers in the form of an infinite integral and infinite series for the dual diversity case the respective expressions are derived in closed forms in terms of the gamma and beta functions

exact finite dimensional filters for maximum likelihood parameter estimation of continuous time linear gaussian systems in this paper we derive a new class of finite dimensional filters for integrals and stochastic integrals of moments of the state for continuous time linear gaussian systems apart from being of significant mathematical interest these new filters can be used with the expectation maximization em algorithm to yield maximum likelihood estimates of the model parameters

microdiversity on rician fading channels formats coherent phase shift keying cpsk and noncoherent frequency shift keying ncfsk results using both maximal ratio combining mrc and selection diversity combining sc are presented for comparison our results show that from a feasibility and practical tradeoffs point of view the performance of an eg combiner may be as good as that of a mr combiner the effects of gain unbalance between branches of the eg combiner on the probability distribution of snr and on the bit error rates are also investigated the rician fading model may be used to model both the microcellular environment and the mobile satellite fading channel hence the results of this paper may be useful in both of these areas furthermore in the development of the analysis we present an efficient method for computing the distribution of sums of rich random variables this may be useful for other problems involving rician fading the suitability of modeling a rician fading environment by a properly chosen nakagami model is examined a formula for determining the corresponding values of rician parameter k and nakagami parameter m is also assessed

error rate evaluation of linear equalization and decision feedback equalization with error propagation we propose applying an approximate fourier series to evaluate efficiently the bit error rate ber performance of finite length linear equalization le and decision feedback equalization dfe by extending the fourier series we enable ber calculations for quadrature phase shift keying qpsk transmission on complex channels with in phase and crosstalk intersymbol interference isi the ber calculation is based on determining the residual isi samples and background gaussian noise variance at the equalizer output for static channels or for realizations of quasi static fading channels a simple bound on the series error magnitude in terms of the fourier series parameters ensures the required accuracy and precision improved state transition probability estimates are derived and verified by simulation for an approximate markov model of the dfe error propagation for the case in which residual isi exists even when the previous decisions stored in the feedback filter fbf are correct we demonstrate the ease and widespread applicability of our approach by producing results which elucidate a variety of equalization tradeoffs our analysis includes symbol spaced and fractionally spaced minimum mean square error mmse le zero forcing zf le and mmse dfe with and without error propagation on static isi channels and multipath channels with quasi static rayleigh fading a comparison between suboptimum and optimum receiver filtering in conjunction with equalization and an assessment of the accuracy of some widely used equalization ber approximations and bounds

numerically efficient fourier based technique for calculating error probabilities with intersymbol interference we propose a numerically efficient technique for calculating the probability of symbol error for arbitrary coherent modulation schemes in the presence of intersymbol interference isi and additive noise the probability of error is formulated in terms of an inverse fourier transform of the windowed characteristic function of the random variable representing the interfering symbols and the noise process the integral is evaluated numerically using the sampling theorem

sliding mode control in discrete state and hybrid systems the sliding mode control approach is developed for a class of discrete state systems in a metric space a concept of trajectory continuity is introduced which allows the use of sliding mode design techniques similar to that in continuous state systems this approach is then applied to a class of hybrid systems which consists of a continuous plant an interface and a discrete state controller the introduction of the sliding mode concept leads to a design which is invariant to disturbances and also the solution of the stabilization problem

maximum likelihood estimation of the dynamic shock error model abstract in this paper an efficient estimation technique in the time domain for the dynamic shock error model is developed this approach utilizes a state space representation of the model and the kalman filtering technique to obtain the maximum likelihood estimates the resulting estimates are shown to be consistent and asymptotically normal with the inverse of the information matrix as their precision measure a consistent estimate of the information matrix is suggested to obtain the standard errors of the estimates

stabilizing receding horizon control of nonlinear time varying systems a receding horizon control scheme for nonlinear time varying systems is proposed which is based on a finite horizon optimization problem with a terminal state penalty the penalty is equal to the cost that would be incurred over an infinite horizon by applying a locally stabilizing linear control law to the nonlinear system assuming only stabilizability of the linearized system around the desired equilibrium the new scheme ensures exponential stability of the equilibrium as the length of the optimization horizon goes from zero to infinity the domain of attraction moves from the basin of attraction of the linear controller toward the basin of attraction of the infinite horizon nonlinear controller stability robustness in the face of system perturbations is also established

an analytical method for approximate performance evaluation of binary linear block codes an analytical method for approximate performance evaluation of binary linear block codes using an additive white gaussian noise channel model with binary phase shift keying modulation is presented we focus on the probability density function of the bit log likelihood ratio llr which is expressed in terms of the gram charlier series expansion this expansion requires knowledge of the statistical moments of the bit llr we introduce an analytical method for calculating these moments this is based on some recursive calculations involving certain weight enumerating functions of the code it is proved that the approximation can be as accurate as desired if we use enough terms in the gram charlier series expansion numerical results are provided for some examples which demonstrate close agreement with simulation results

on the distribution of the sum of nakagami m random variables in this paper we investigate the classical problem of finding the probability density function pdf of the sum of nakagami m random variables exact infinite series representations are derived for the sum of three and four identically and independently distributed i i d nakagami m random variables and subsequently it is extended to the sum of general number of random variables a useful pattern emerged as a result of these extensions and a new fourier transform pair that involves parabolic cylinder function and gauss hypergeometric function is obtained bounds on the error resulting from truncation of the infinite series of pdfs are also presented these pdfs are used to analyze the performance of dual triple and quadruple branch predetection equal gain combining egc receivers over nakagami m fading environment furthermore a hypergeometric relation is derived as a result of those derivations subsequently the analysis is extended to the case of l branch egc receiver performance as well selected simulation plots are provided to compare the results with the approximate results available in the literature and to illustrate the validity of the formulation

signaling constellations for fading channels the performance of various coherent 8 ary and 16 ary modulations in additive white gaussian noise awgn and slowly fading channels are analyzed new expressions for the exact symbol error rates ser in fading with diversity combining are derived for any two dimensional signaling format having polygonal decision boundaries maximal ratio combining equal gain combining and selection combining are considered the ser formulas obtained make it possible for the first time to optimize parameters of various constellations precisely and to determine which constellation has the lowest probability of error for example a star constellation such as that specified in the ccitt v 29 standard can be improved by adjusting the amplitude ratios of the points in the constellation to save about 0 63 db power in awgn without sacrificing the phase error tolerance while maintaining the same error rate the sensitivity of each constellation to phase error is presented and comparisons are made six 8 ary signal sets and 11 16 ary signal sets are examined using the new symbol error probability formulas to determine best signal sets for fading channels

on line estimation of dynamic shock error models based on the kullback leibler information measure develops two sequential or on line estimation schemes in the time domain for dynamic shock error models which are special cases of errors in variables models the author s approach utilizes a state space representation of the model kalman filtering techniques and on line algorithms the first on line algorithm is based on the expectation maximization algorithm and uses a recursive gauss newton scheme to maximize the kullback leibler information measure the second on line algorithm the author proposes is a gradient based scheme and uses stochastic approximations to maximize the log likelihood in comparison to the off line maximum likelihood estimation scheme used in ghosh 1989 the author s on line algorithms have significantly reduced computational costs and negligible memory requirements simulations illustrate the satisfactory performance of the algorithms in estimating errors in variables systems with parameters that vary slowly with time or undergo infrequent jump changes

a general method for calculating error probabilities over fading channels signal fading is a ubiquitous problem in mobile and wireless communications in digital systems fading results in bit errors and evaluating the average error rate under fairly general fading models and multichannel reception is often required predominantly to date most researchers perform the averaging using the probability density function method or the moment generating function mgf method this paper presents a third method called the characteristic function chf method for calculating the average error rates and outage performance of a broad class of coherent differentially coherent and noncoherent communication systems with or without diversity reception in a myriad of fading environments unlike the mgf technique the proposed chf method based on parseval s theorem enables us to unify the average error rate analysis of different modulation formats and all commonly used predetection diversity techniques i e maximal ratio combining equal gain combining selection diversity and switched diversity within a single common framework the chf method also lends itself to the averaging of the conditional error probability involving the complementary incomplete gamma function and the confluent hypergeometric function over fading amplitudes which heretofore resisted to a simple form as an aside we show some previous results as special cases of our unified framework

the em approach to the multiple indicators and multiple causes model via the estimation of the latent variable abstract this article considers both likelihood and bayesian estimation procedures for a model with multiple indicators and multiple causes of a single unobservable latent variable the model is complicated by its reduced form which displays a mixture of econometric and psychometric themes we avoid this complexity via the estimation of the unobservable latent variable through direct use of the original structural form this approach not only provides maximum likelihood estimates that are equivalent to those derived from the reduced form but it also permits a feasible bayesian approach which would be technically complex to execute otherwise

alternative algorithms for the estimation of dynamic factor mimic and varying coefficient regression models this paper provides a general approach to the formulation and estimation of dynamic unobserved component models after introducing the general model two methods for estimating the unknown parameters are presented both are algorithms for maximizing the likelihood function the first is based on the method of scoring the second is the em algorithm a derivative free method each iteration of em requires a kalman filter and smoother followed by straightforward regression calculations the paper suggests using the em methods to quickly locate a neighborhood of the maximum scoring can then be used to pinpoint the maximum and calculate the information matrix

exact filters for certain moments and stochastic integrals of the state of systems with benes nonlinearity finite dimensional filters for integrals and stochastic integrals of moments of the state for continuous time nonlinear systems with benes nonlinearity are derived these filters can be used with the expectation maximization algorithm to compute maximum likelihood estimates of the model parameters

towards a stability theory of general hybrid dynamical systems in recent work we proposed a general model for hybrid dynamical systems whose states are defined on arbitrary metric space and evolve along some notion of generalized abstract time for such systems we introduced the usual concepts of lyapunov and lagrange stability we showed that it is always possible to transform this class of hybrid dynamical systems into another class of dynamical systems with equivalent qualitative properties but defined on real time r 0 the motions of this class of systems are in general discontinuous this class of systems may be finite or infinite dimensional for the above discontinuous dynamical systems and hence for the above hybrid dynamical systems we established the principal lyapunov stability theorems as well as lagrange stability theorems for some of these we also established converse theorems we demonstrated the applicability of these results by means of specific classes of hybrid dynamical systems in the present paper we continue the work described above in doing so we first develop a general comparison theory for the class of hybrid dynamical systems resp discontinuous dynamical systems considered herein making use of stability preserving mappings we then show how these results can be applied to establish some of the principal lyaponov stability theorems for the latter we also state and prove a converse theorem not considered previously finally to demonstrate the applicability of our results we consider specific examples throughout the paper

on the convergence properties of the em algorithm two convergence aspects of the em algorithm are studied i does the em algorithm find a local maximum or a stationary value of the incomplete data likelihood function ii does the sequence of parameter estimates generated by em converge several convergence results are obtained under conditions that are applicable to many practical situations two useful special cases are a if the unobserved complete data specification can be described by a curved exponential family with compact parameter space all the limit points of any em sequence are stationary points of the likelihood function b if the likelihood function is unimodal and a certain differentiability condition is satisfied then any em sequence converges to the unique maximum likelihood estimate a list of key properties of the algorithm is included

limit cycle generation for a class of non linear systems with jumps using a low dimensional predictive control in this paper it is shown that using a low dimensional non linear predictive control scheme provably stable limit cycles can be obtained for open loop non linear systems with unstable equilibrium point a particular case where the limit cycle may be reduced to a single point in the state space can be obtained which corresponds to asymptotic stabilization the system may present hybrid nature in the sense that discontinuities jump phenomena on the state evolution may be handled the proposed feedback scheme holds for classical jump free systems as a particular case the proposed strategy is illustrated through two examples a jump free system the ball and beam and a non linear hybrid dynamical system including state jumps the modified impulsive lorenz chaotic system

probability of error calculation of ofdm systems with frequency offset orthogonal frequency division multiplexing ofdm is sensitive to the carrier frequency offset cfo which destroys orthogonality and causes intercarrier interference ici previously two methods were available for the analysis of the resultant degradation in performance firstly the statistical average of the ici could be used as a performance measure secondly the bit error rate ber caused by cfo could be approximated by assuming the ici to be gaussian however a more precise analysis of the performance i e ber or ser degradation is desirable in this letter we propose a precise numerical technique for calculating the effect of the cfo on the ber or symbol error in an ofdm system the subcarriers can be modulated with binary phase shift keying bpsk quaternary phase shift keying qpsk or 16 ary quadrature amplitude modulation 16 qam used in many ofdm applications the bpsk case is solved using a series due to beaulieu 1990 for the qpsk and 16 qam cases we use an infinite series expression for the error function in order to express the average probability of error in terms of the two dimensional characteristic function of the ici

a unified framework for hybrid control model and optimal control theory we propose a very general framework that systematizes the notion of a hybrid system combining differential equations and automata governed by a hybrid controller that issues continuous variable commands and makes logical decisions we first identify the phenomena that arise in real world hybrid systems then we introduce a mathematical model of hybrid systems as interacting collections of dynamical systems evolving on continuous variable state spaces and subject to continuous controls and discrete transitions the model captures the identified phenomena subsumes previous models yet retains enough structure to pose and solve meaningful control problems we develop a theory for synthesizing hybrid controllers for hybrid plants in all optimal control framework in particular we demonstrate the existence of optimal relaxed and near optimal precise controls and derive generalized quasi variational inequalities that the associated value function satisfies we summarize algorithms for solving these inequalities based on a generalized bellman equation impulse control and linear programming

hybrid dynamical systems robust control synthesis problems the paper presents a new approach to robust control synthesis problems for hybrid dynamical systems the hybrid system under consideration is a composite of a continuous plant and a discrete event controller state and output feedback problems are considered the main results are given in terms of the existence of suitable solutions to a dynamic programming equation and a riccati differential equation of the h filtering type these results show a connection between the theories of hybrid dynamical systems and robust and nonlinear control

the evaluation of error probabilities for intersymbol and cochannel interference an efficient series that can be used to calculate the probability of error in a binary symmetric channel with intersymbol interference and additive noise is derived the series is derived by representing the noise complementary probability distribution function by an exact or approximate fourier series bounds on the accuracy of the estimate are derived for gaussian noise examples show that only a small numerical effort may be required to compute error probabilities of interest using the series applications to both finite and infinite intersymbol interference systems are discussed a similar technique is used to derive series representations for the probability of error of additive noise channels with cochannel interference or with combined intersymbol and cochannel interferences the accuracy of the results is bounded for gaussian noise

further results on the beaulieu series a frequent problem in digital communications is the computation of the probability density function pdf and cumulative distribution function cdf given the characteristic function chf of a random variable rv this problem arises in signal detection equalizer performance equal gain diversity combining intersymbol interference and elsewhere often it is impossible to analytically invert the chf to get the pdf and cdf in closed form beaulieu 1990 1991 has derived an infinite series for the cdf of a sum of rvs that has been widely used we rederive his series using the gil pelaez 1951 inversion formula and the poisson sum formula this derivation has several advantages including both the bridging of the well known sampling theorem with beaulieu s series and yielding a simple expression for calculating the truncation error term it is also shown that the pdf and cdf can be computed directly using a discrete fourier transform

precise ber computation for binary data detection in bandlimited white laplace noise investigation into the characteristics and behaviours of laplace noise is of crucial importance for evaluating the performance of communication systems operating in impulsive noise as well as for ultra wideband wireless systems operating in the presence of multi user interference the bit error rate performances of a binary data communication system operating in the presence of additive bandlimited white laplace noise is analyzed theoretically a theoretical expression for the average bit error rate is derived using the beaulieu series for the optimal soft limiting detector and the matched filter detector when arbitrary pulse shapes are used the bit error rate performance of a reduced complexity version of the optimal detector the hard limiting detector and a reduced complexity version of the matched filter detector the sum of samples detector are also analyzed the analytical expressions for the bit error rate are validated by numerical examples

new path generation based receding horizon formulation for constrained stabilization of nonlinear systems in this paper a new formulation of constrained stabilizing receding horizon control is proposed this formulation is based on the use of open loop steering path generators the open loop optimization problem associated to the proposed receding horizon formulation is scalar in which the optimization variable is the prediction horizon length stability is proved in a sampling control scheme a simple example is given to illustrate the main concepts

an infinite series for the computation of the complementary probability distribution function of a sum of independent random variables and its application to the sum of rayleigh random variables the properties of the series are studied for both bounded and unbounded random variables the technique is used to find efficient series for computation of the distributions of sums of uniform random variables and sums of rayleigh random variables a useful closed form expression for the characteristic function of a rayleigh random variable is presented and an efficient method for computing a confluent hypergeometric function is given an infinite series for the probability density function of a sum of independent random variables is also derived the inversion of characteristic functions a trapezoidal rule for numerical integration and the sampling theorem in the frequency domain are related to and interpreted in terms of the results

computing the distribution of sums of random sine waves and of rayleigh distributed random variables by saddle point integration the method of saddle point integration is applied to calculating the cumulative distribution of sums of independent random variables that either have a rayleigh distribution or are sine waves with independently random phases in the presence of gaussian random noise

effects of fading and partial band noise jamming on a fast fh bfsk acquisition receiver with noise normalization combination we present the performance analysis of a fast frequency hopped fh binary orthogonal frequency shift keying acquisition receiver for communication against adverse environments the receiver employs noncoherent noise normalized matched filtered mf correlation detection for rapid acquisition in the search mode our analysis includes four types of communication environments namely additive white gaussian noise awgn channel awgn channel with partial band noise jamming fading channels and fading channels with partial band noise jamming the considered fading channels include nakagami m rician and rayleigh amplitude models based on beaulieu s see ibid vol 38 no 9 p 1463 1990 convergent series approach efficient analytical formulas are developed for performance evaluation example performance results for various environments are presented in terms of two acquisition probabilities namely the detection probability and the false alarm probability of the noise normalized mf detector it is analytically shown that with a short mf correlation length and with a sufficiently large ratio of signal power to noise power the fast fh diversity combining yields noticeable performance improvement for environments with strong fading when the mf correlation is lengthened this improvement tends to fade away and the diversity combining results in performance loss

computation of shot noise probability distributions and densities the computation of the cumulative distribution cdf the complementary cdf ccdf and the density of certain shot noise random variables is discussed after subtracting off a few terms that can be computed in closed form what remains can be approximated by a general method for approximating samples of a cdf or ccdf by summing a fourier series whose coefficients are modulated samples of their characteristic function to approximate the density a spline is fit to the cdf samples and then differentiated when the density has corners it is important that the spline have coincident knots at these locations for shot noise densities these locations are easily identified