Showing papers on "Discrete time and continuous time published in 1974"
TL;DR: Estimation of the parameters of a single-frequency complex tone from a finite number of noisy discrete-time observations is discussed and appropriate Cramer-Rao bounds and maximum-likelihood estimation algorithms are derived.
Abstract: Estimation of the parameters of a single-frequency complex tone from a finite number of noisy discrete-time observations is discussed. The appropriate Cramer-Rao bounds and maximum-likelihood (MI.) estimation algorithms are derived. Some properties of the ML estimators are proved. The relationship of ML estimation to the discrete Fourier transform is exploited to obtain practical algorithms. The threshold effect of one algorithm is analyzed and compared to simulation results. Other simulation results verify other aspects of the analysis.
1,878 citations
TL;DR: In this paper, the Chandrasekhar-type Riccati-type difference equation is replaced by another set of difference equations, which are then used for recursive estimation in constant continuous-time linear systems.
Abstract: Certain recently developed fast algorithms for recursive estimation in constant continuous-time linear systems are extended to discrete-time systems. The main feature is the replacement of the Riccati-type difference equation that is generally used for such problems by another set of difference equations that we call of Chandrasekhar-type. The total number of operations in the new algorithm is in general less than with the Riccati-equation based Kalman filter, with significant reductions being obtained in several important special cases. The algorithms are derived via a factorization of increments of the Riccati equation variable, a method that can be extended to nonsymmetric Riccati equations as well.
215 citations
TL;DR: In this paper, the authors generalize the results obtained for models which assume a discrete state-space or discrete time or both, to a model with both state space and time continuous.
Abstract: Results on the behaviour of Markov branching processes as time goes to infinity, hitherto obtained for models which assume a discrete state-space or discrete time or both, are here generalised to a model with both state-space and time continuous. The results are similar but the methods not always so.
180 citations
TL;DR: In this article, limit properties of the Riccati operator difference equation with a quadratic cost functional were investigated. But the limit properties were not investigated in the context of infinite-dimensional control systems.
Abstract: The aim of this paper is to investigate limit properties of the infinite-dimensional control system described by a difference equation with a quadratic cost functional Some related results of independent interest concerning stability and the Riccati operator difference equation are given also
168 citations
126 citations
TL;DR: In this paper, an algorithm for computing the gain matrices of the Kalman filter is presented, which does not involve the usual Riccati-type equation, and the number of nonlinear equations to be solved in each step is of order k rather than $k^2$ as by the usual procedure.
Abstract: An algorithm (which does not involve the usual Riccati-type equation) for computing the gain matrices of the Kalman filter is presented. If the dimension k of the state space is much larger than that of the observation process, the number of nonlinear equations to be solved in each step is of order k rather than $k^2$ as by the usual procedure.
96 citations
TL;DR: Approximate expressions for the steady-state phase error probability density, phase error variance, and a theoretical prediction of threshold are obtained in discrete time analyses of firstand second-order digital phase lock loops.
Abstract: The present paper considers discrete time analyses of firstand second-order digital phase lock loops. These loops are characterized by the fact that they track the zero crossings of the incoming signal; consequently, the sampling intervals are nonuniform. The firstorder loop is analyzed for phase step and frequency step inputs; mean time to skip cycle is also considered. For phase step input, approximate expressions are obtained for the steady-state phase error probability density and phase error variance, the second of which leads directly to a theoretical prediction of threshold. The second-order loop is analyzed for frequency step input. Approximate expressions for the steady-state phase error probability density, phase error variance, and a theoretical prediction of threshold are obtained. The analyses are confirmed by numerical results and simulation.
94 citations
TL;DR: A technique for simulating GI/G/s queues is shown to apply to simulations of discrete and continuous-time Markov chains and to address questions of simulation run duration and of starting and stopping simulations because of the existence of a random grouping of observations.
Abstract: A technique for simulating GI/G/s queues is shown to apply to simulations of discrete and continuous-time Markov chains. It is possible to address questions of simulation run duration and of starting and stopping simulations because of the existence of a random grouping of observations which produces independent identically distributed blocks from the start of the simulation. This grouping allows confidence intervals to be obtained for a general function of the steady-state distribution of the Markov chain. The technique is illustrated with simulation of an (s, S) inventory model in discrete time and the classical repairman problem in continuous time. Consideration is also given to determining system sensitivity to errors and uncertainty in the input parameters.
93 citations
TL;DR: The relationship between the continuous and the discrete parameters yields a simple method of maximum likelihood estimation of the continuous parameters from a discretely sampled data.
Abstract: Discretization of a continuous autoregressive moving average process at an equispaced sampling interval results in a discrete autoregressive moving average process The relationship between the continuous and the discrete parameters yields a simple method of maximum likelihood estimation of the continuous parameters from a discretely sampled data A technique is described for modeling of continuous processes from discrete observations and is illustrated with analysis of the yearly Wolfer's sunspot numbers data
84 citations
TL;DR: In this article, the continued fraction and time-moments methods for the reduction in order of linear continuous-time systems are extended for use in reducing the order of the linear discrete-time system, and simple numerical examples are given to illustrate the methods.
Abstract: The continued fraction and time-moments methods for the reduction in order of linear continuous-time systems are extended for use in reducing the order of linear discrete-time systems- Simple numerical examples are given to illustrate the methods
79 citations
TL;DR: In this article, the authors tighten these bounds by modifying an argument used to prove the Sain-Massey result, which is a modification of the argument used in this paper.
Abstract: Sain and Massey [1] have obtained necessary and sufficient conditions for the invertibility of continuous and discrete time linear systems and have also found bounds for what they termed the "inherent integration" (continuous time) or the "inherent delay" (discrete time) of an invertible linear system. In this note, we tighten these bounds by modifying an argument used to prove the Sain-Massey result.
TL;DR: In this paper, single step discrete time Galerkinetic methods for the mixed initial-boundary value problem for the heat equation are studied and two general theories leading to error estimates are developed.
Abstract: Single step discrete time Galerkin methods for the mixed initial-boundary value problem for the heat equation are studied. Two general theories leading to error estimates are developed. Among the examples analyzed in the application of these theories are methods in which the related quadratic form is required to be definite only on the subspace of approximating functions and two classes containing methods of arbitrary given order of accuracy, one requiring satisfaction of certain boundary conditions by the elements of the subspace, the other making no such requirements.
Proceedings Article•
01 Jan 1974
01 Jan 1974
TL;DR: In this article, the authors generalize the results obtained for models which assume a discrete state-space or discrete time or both, to a model with both state space and time continuous.
Abstract: Results on the behaviour of Markov branching processes as time goes to infinity, hitherto obtained for models which assume a discrete state-space or discrete time or both, are here generalised to a model with both state-space and time continuous. The results are similar but the methods not always so.
TL;DR: In this paper, the authors studied the role of upper record values and times and inter-record times as embedded structures in discrete time extremal processes and showed that they converge to limiting continuous time processes as T -- oo under suitable assumptions on the underlying CDF F, for example, when 1 -F varies regularly at oo and more generally.
Abstract: Upper record values and times and inter-record times are studied in their roles as embedded structures in discrete time extremal processes. Various continuous time approximations to the discrete-time processes are analysed, especially as processes over their state spaces. Discrete time processes, suitably normalized after crossing a threshold T, are shown to converge to limiting continuous time processes as T -- oo under suitable assumptions on the underlying CDF F, for example, when 1 - F varies regularly at oo, and more generally. Discrete time extremal processes viewed as processes over their state spaces are noted to have an interesting interpretation in terms of processes of population growth.
TL;DR: A method for determining the optimum control for distributed parameter systems is presented, restricted to systems which can be represented by discrete time models having coefficients which are functions of the spatial variables.
Abstract: A method for determining the optimum control for distributed parameter systems is presented. The method is based upon mathematical programming and is restricted to systems which can be represented by discrete time models having coefficients which are functions of the spatial variables. The control function is assumed to be spatially concentrated. A closed form Bolutton is given which is valid when no constraints exist. An illustrative example is provided.
TL;DR: It is shown for those systems with a single-input and the diagonalizable transition matrix that reachability properties are heavily influenced by the integral characteristics of eigenvalues.
Abstract: The concept of reachability of discrete-time quantized control systems is introduced and the relations between reachability properties and structures of linear, time-invariant, discrete-time quantized control systems are discussed. It is shown for those systems with a single-input and the diagonalizable transition matrix that reachability properties are heavily influenced by the integral characteristics of eigenvalues.
TL;DR: A method is presented for estimating the system matrix triple {F,G,H} from noisy measurements of the input and output signals that enables the estimation to be carried out without having to first estimate the output structural indices.
Abstract: A method is presented for estimating the system matrix triple {F,G,H} from noisy measurements of the input and output signals. The algorithm which is derived considering stationary, discrete time systems possessing cyclic state space, enables the estimation to be carried out without having to first estimate the output structural indices. The proposed consistent estimator can be easily implemented.
TL;DR: In this article, an approximate model is proposed for stochastic differencedifferential equations with non-integral lags, which is consistent with respect to the true model under some conditions.
Abstract: As an alternative to conventional discrete time models for stochastic processes that fluctuate within the sampling interval, we propose difference equations containing non-integral lags. We discuss the problems of stability, identification and estimation, for which an approximate model is needed. Least squaresa pplied to an approximateF ourier-transformedm odel yields estimators of the coefficients that are consistent with respect to the true model under some conditions. The conditions are weak when the model contains predetermined variables that obey an "aliasing condition"; estimators of the lags as well as coefficients can then be found that are consistent, efficient and satisfy a central limit theorem. Optimal estimators for stochastic differencedifferential equations are also available.
TL;DR: In this article, a discrete time version of a generalized one-type age-dependent branching process is considered in relation to stable population theory in demography, and confidence bounds for the projected number of individuals in any age group by utilizing the covariance functions of the process and the central limit theorem are derived.
Abstract: A discrete time version of a generalized one-type age-dependent branching process is considered in relation to stable population theory in demography. The motivation underlying the discrete time version of the theory is to make it amenable to computations involving demographic data. After giving a brief discussion of the foundations underlying the process, discrete type renewal equations for the mean and covariance functions of the process are derived. It is then shown how those renewal type equations may be used for making population projections with respect to age-specific birth rates, rates of population growth, and the number of live individuals in each age group, given an initial population with an arbitrary age distribution. A novel feature of the method of population projection introduced in this paper is that it is possible to derive confidence bounds for the projected number of individuals in any age group by utilizing the covariance functions of the process and the central limit theorem.
TL;DR: The diffusion of information models developed by Funkhouser and McCombs (1972) are expanded to include situations involving simple interaction processes and more complicated situations involving both mass mediated messages and interactively mediated messages.
Abstract: This paper expands the diffusion of information models developed by Funkhouser and McCombs (1972) to include situations involving simple interaction processes and more complicated situations involving both mass mediated messages and interactively mediated messages. This paper develops discrete time models of information diffusion as opposed to the continuous time models developed by Coleman (1964) and Bartholomew (1967) and others.
TL;DR: In this paper, the joint plant and measurement control problem of linear, unknown, discrete time systems excited by white Ganssian noise is considered, and the performance criterion is quadratic in the state and is additive in the plant and control.
Abstract: In this paper, the joint plant and measurement control problem of linear, unknown, discrete time systems excited by white Ganssian noise is considered. The performance criterion is quadratic in the state and is additive in the plant and measurement control. The adaptive control solution is obtained by approximating the dynamic programming equation-the approximation amounts to replacing the optimal adaptive cost-to-go in the dynamic programming equation by the average value of the truly optimum cost-to-go for each admissible model. In our solution, the adaptive plant and measurement control schemes can be separated. The adaptive plant control is given by the product of the weighted integrals with the a posteriori probability of the parameter as weights. The adaptive measurement control scheme is obtained as the solution of a constrained nonlinear, optimization problem for each time; the constraint equations being the error covatiance matrix equations in the Kalman filter. An illustrative example of the optimum timing of measurements is discussed where the joint adaptive control scheme is simulated and its performance is compared with the optimum value of the performance if the system parameters were completely known.
01 Jan 1974
TL;DR: Sometimes an insight may be gained by reasoning in terms of channel capacity, amount of information and redundancy, but this language again seems more successful in the analysis of peripheral sensory events than in the study of central processes.
Abstract: Situations within the central nervous system are elusive when we try to render them in anything more abstract than approximate verbal descriptions. A description in terms of ionic movements through cell membranes, for example, might be useful when dealing with information transmission in sense cells but becomes unwieldy if applied to situations involving many neurons of the brain. Attempts at applying the formalism of a logical calculus, inspired by the success of binary algebra in dealing with switching networks, seem to impose a restriction on the working of neurons (e.g. by assuming discrete time) which is not justified by electrophysiology. Occasionally an insight may be gained by reasoning in terms of channel capacity, amount of information and redundancy, but this language again seems more successful in the analysis of peripheral sensory events than in the study of central processes.
TL;DR: A method is presented to synthesize a quadratic state regulator for analytic nonlinear discrete-time systems and the applicability of the method is tested in practice in computer control of a laboratory scaled process.
Abstract: A method is presented to synthesize a quadratic state regulator for analytic nonlinear discrete-time systems The applicability of the method is tested in practice in computer control of a laboratory scaled process
Posted Content•
Posted Content•
01 Jan 1974
TL;DR: In this paper, the authors discuss the multivariate spectral models and their applications and present the stochastic models for which the components are stationary processes, either all in continuous time or all in discrete time, possessing power spectra.
Abstract: This chapter discusses the multivariate spectral models and their applications. Only those multivariate time series models are presented in the chapter for which the components are univariate time series, either all in continuous time or all in discrete time, possessing power spectra. The chapter presents the stochastic models for which the components are stationary processes. These models apply quite well to a variety of real phenomena. In geophysics, they are used, for example, to describe wind velocities, the oscillation of the earth at a given location, and sea state over a given region. Economic systems characteristically require several descriptive variables, such as price, available supply, and demand among others. Under stable conditions, the stationary models are reasonably accurate. Even when conditions are not stable, these models provide useful results over restricted time periods.
TL;DR: Using the criterion of minimum variance of the output concentration, it is shown that blender performance depends only on the residence time distribution of the blender and the autocovariance function of the input concentration.
TL;DR: The algorithm leads to the solution of a Boolean linear programming problem, for which many computer codes are available commercially, and an application to a time-shared sampled-data control system is presented.
Abstract: A computer algorithm is described for the optimization of discrete-time pulse frequency modulated systems with state and control constraints. The algorithm, based on a modified maximum principle [1], leads to the solution of a Boolean linear programming problem, for which many computer codes are available commercially. An application to a time-shared sampled-data control system is presented. Numerical examples are given.