Representations for multivariate reciprocal Gaussian processes

Multivariate reciprocal Gaussian processes are represented as a sum of two independent processes: a piecewise Markov process, which is also represented in terms of a Wiener-type process, and a time-dependent linear transformation of a normally distributed random vector. This result is then applied to the first-passage time problem     

Discrete-index Markov-type random processes

Discrete-index Markov-type random processes in one and two dimensions are considered, with emphasis on two-dimensional processes (or fields). Important classes of Markov-type models, their properties, and their relationship are described. Although some new results are given, the authors mainly present a systematic study and grouping of processes according to two fundamental Markov-type properties: strict-sense Markov, defined in terms of conditional probabilities, and wide-sense Markov, defined in terms of linear minimum-mean-square error estimates. Classes of models having special cases of the fundamental properties, including many models which are widely used to represent images are obtained by specifying the index set, the conditioning set used to define the Markov property, and the process distribution. The relationships between unilateral and bilateral models in each class are carefully investigated. Particular attention is given to simultaneous autoregressive models which are shown to be both strict-sense and wide-sense Markov. Classification of processes according to their Markov-type properties helps to clarify the consequences of and relationships between different model assumptions     

Distribution of absolute maximum of mean square differentiable Gaussian stationery process

In this paper it is obtained the distribution of absolute maximum of mean square differentiable stationery Gaussian process by means of integration of the results of the second Kolmogorov equation solution. It is shown the way simplifying integration and its interrelation to integro-differential equation obtained before. The second Kolmogorov equation is solved first for the boundary conditions allowing to obtain the results in form of infinite series with coefficients obtained by means of solution of Sturm–Liouville problem and reducing to the simple expression. It is analyzed the correlation of obtained results with known before. It is carried out a comparative analysis of correlation functions and expressions for distribution of absolute maximums of mean square differentiable and single-component Markov processes. In spite of correlation function of single-component Markov process can be considered as limit expression for correlation function of mean square differentiable process, the expression for distribution of their absolute maximums are essentially different. It shows practical meaning of the results since real processes in radio engineering systems can be mean square differentiable only.     

A matched-filter-based reverse-time migration algorithm forground-penetrating radar data

Ground-penetrating radar (GPR) is a remote sensing technique used to obtain information on subsurface features from data collected over the surface. The process of collecting data may be viewed as mapping from the object space to an image space. Since most GPRs use broad beam width antennas, the energy reflected from a buried structure is recorded over a large lateral aperture in the image spare, migration algorithms are used to reconstruct an accurate scattering map by refocusing the recorded scattering events to their true spatial locations through a backpropagation process. The goal of this paper is to present a pair of finite-difference time-domain (FDTD) reverse-time migration algorithms for GPR data processing. Linear inverse scattering theory is used to develop a matched-filter response for the GPR problem. The reverse-time migration algorithms, developed for both bistatic and monostatic antenna configurations, are implemented via FDTD in the object space. Several examples are presented     

Error-probability bounds for continuous-time decision problems

The evaluation of error-probability bounds for binary detection problems involving continuons-time stochastic processes as signals is considered. These bounds are of interest because, in even the simplest detection problems, the computation of the exact probabilities of error is usually mathematically intractable. The method used consists of applying some results from martingale theory to detection and estimation problems. Only discontinuous observations that contain the rate process associated with a counting process are considered. The problem addressed is to evaluate Chernoff bounds on error probabilities for the likelihood-ratio test. The solution procedure consists of a measure transformation technique that makes it possible to obtain an expression for the Chernoff bound in terms of an expectation of a multiplicative functional of the conditional mean signal (rate process) estimates. If the processes involved are Markov, it is then possible to represent the above expression as a solution to a partial differential equation that is derived from the backward equation of Kolmogorov. The above procedure is repeated when the optimal estimates are replaced by suboptimal estimates. Examples are given to illustrate the technique.     

Particle filters for state estimation of jump Markov linear systems

Jump Markov linear systems (JMLS) are linear systems whose parameters evolve with time according to a finite state Markov chain. In this paper, our aim is to recursively compute optimal state estimates for this class of systems. We present efficient simulation-based algorithms called particle filters to solve the optimal filtering problem as well as the optimal fixed-lag smoothing problem. Our algorithms combine sequential importance sampling, a selection scheme, and Markov chain Monte Carlo methods. They use several variance reduction methods to make the most of the statistical structure of JMLS. Computer simulations are carried out to evaluate the performance of the proposed algorithms. The problems of on-line deconvolution of impulsive processes and of tracking a maneuvering target are considered. It is shown that our algorithms outperform the current methods     

A mixed MAP/MLSE receiver for convolutional coded signalstransmitted over a fading channel

This paper addresses the problem of estimating a rapidly fading convolutionally coded signal such as might be found in a wireless telephony or data network. We model both the channel gain and the convolutionally coded signal as Markov processes and, thus, the noisy received signal as a hidden Markov process (HMP). Two now-classical methods for estimating finite-state hidden Markov processes are the Viterbi (1967) algorithm and the a posteriori probability (APP) filter. A hybrid recursive estimation procedure is derived whereby one hidden process (the encoder state in our application) is estimated using a Viterbi-type (i.e., sequence based) cost and the other (the fading process) using an APP-based cost such as maximum a posteriori probability. The paper presents the new algorithm as applied specifically to this problem but also formulates the problem in a more general setting. The algorithm is derived in this general setting using reference probability methods. Using simulations, performance of the optimal scheme is compared with a number of suboptimal techniques-decision-directed Kalman and HMP predictors and Kalman filter and HMP filter per-survivor processing techniques     

Introduction to Cyclic Replacement Systems

A fundamental and unified treatment of problems akin to the classical Swedish Machine Problem is presented. Section I describes the nature of the systems known as cyclic replacement systems. In Section II pertinent facts about Markov processes are gathered. In Section III, it is shown that a certain class of cyclic systems behave as homogeneous Markov processes. The special class of homogeneous Markov processes known as homogeneous birth and death processes is considered in Section IV. Results of Section IV are applied to some cyclic replacement systems in Section V. In Section VI some systems are treated which cannot be represented as birth and death processes.     

Risk-sensitive filtering and smoothing for continuous-time Markov Processes

We consider risk sensitive filtering and smoothing for a dynamical system whose output is a vector process in /spl Ropf//sup 2/. The components of the observation process are a Markov process observed through a Brownian motion and a Markov process observed through a Poisson process. Risk-sensitive filters for the robust estimation of an indirectly observed Markov state processes are given. These filters are stochastic partial differential equations for which robust discretizations are obtained. Computer simulations are given which demonstrate the benefits of risk sensitive filtering.     

On the approximation of the output process of multiuserrandom-access communication networks

Bernoulli and first-order Markov processes are used to approximate the output process of a class of slotted multiuser random-access communication networks. The output process is defined as the process of the successfully transmitted packets within the network. The parameters of the approximating processes are analytically calculated for a network operating under a specific random access algorithm. The applied methods are general and can be used to calculate these parameters in the case of any random access algorithm within a class. To evaluate the accuracy of the approximations, a star topology of interconnected multiuser random-access communication networks is considered. The mean time that a packet spends in the central node of the star topology is calculated under the proposed approximations of the output processes of the interconnected networks. The results are compared to simulation results of the actual system. It turns out that the memoryless approximation gives satisfactory results up to a certain per network traffic load. Beyond that per network traffic load, the first-order Markov process performs better     

Über die Entropierate von Quellen mit Gedächtnis

Various entropy rates of stochastic processes with statistical dependencies are shortly presented. We introduce the concept of mapped Markov chains and discuss the properties of their joint probability distributions. We develop a distinctive chain rule resembling the well-known one for genuine Markov chains which allows computing the value of any feasible probability distribution, however, our rule is now based on matrix calculus. A diversity of equivalent Markov chains which finely defines a mapped process with designed characteristics can be seen. Mapped Markov chains are proposed as excellent and flexible means for modeling any general sources with memory. A binary process with non-Markovian properties is set up as an example, the various entropy rates are evaluated and their estimated relationships are proved.     

Characterization and estimation of two-dimensional ARMA models

A class of finite-order two-dimensional autoregressive moving average (ARMA) is introduced that can represent any process with rational spectral density. In this model the driving noise is correlated and need not be Gaussian. Currently known classes of ARMA models or AR models are shown to be subsets of the above class. The three definitions of Markov property are discussed, and the class of ARMA models are precisely stated which have the noncausal and semicausal Markov property without imposing any specific boundary conditions. Next two approaches are considered to estimate the parameters of a model to fit a given image. The first method uses only the empirical correlations and involves the solution of linear equations. The second method is the likelihood approach. Since the exact likelihood function is difficult to compute, we resort to approximations suggested by the toroidal models. Numerical experiments compare the quality of the two estimation schemes. Finally the problem of synthesizing a texture obeying an ARMA model is considered.     

Utilizing Multitemporal Data by a Stochastic Model

In remote sensing, a principle objective is to produce an accurate ground cover thematic classification map. In this paper a new classifier which makes use of multitemporal data is described. Ground cover types are considered as stochastic systems with nonstationary Gaussian processes as input and temporal variation of reflected and emitted electromagnetic energy as output. Then, by assumption that the behavior of these stochastic systems are governed by first-order Markov processes, multitemporal information is utilized. As a result of this approach for characterizing multitemporal data, a new processor, the Markov classifier, is developed. Experimental results from Landsat MSS data are included.     

Stability of Markovian Jump Systems over Networks via Delta Operator Approach

This paper investigates the problem of stability for a class of linear uncertain Markovian jump systems over networks via the delta operator approach. The sensor-to-controller random network-induced delay and arbitrary packet losses are considered for mode-dependent time delays. That is, a Markov process is used to model the time-varying delays which are dependent on the system mode. Based on the Lyapunov–Krasovskii functional in the delta domain, a new sufficient condition for the solvability of the stability problem is presented in terms of linear matrix inequalities. A numerical example is given to illustrate the effectiveness of the techniques developed.     

Minimum delay routing in stochastic network

The authors consider the problem of traveling with least expected delay in networks whose link delays change probabilistically according to Markov chains. This is a typical routing problem in dynamic computer communication networks. Several optimization problems, posed on infinite and finite horizons, are formulated, and they are considered with and without using memory in the decision-making process. It is proved that all these problems are, in general, intractable. However, for networks with nodal stochastic delays, a simple polynomial optimal solution is presented. This is typical of high-speed networks, in which the dominant delays are incurred by the nodes. For more general networks, a tractable ∈-optimal solution is presented     

Two-Layer multistate Markov model for modeling a 1.8 GHz narrow-band wireless propagation channel in urban Taipei city

An accurate propagation channel model is crucial for evaluating the performance of a communication system. A propagation channel can be described by a Markov model with a finite number of states, each of which is considered to be quasi-stationary over a short period. This work proposes a two-layer multistate Markov model. Instead of a large Markov transition matrix used in a conventional single-layer Markov model, two small Markov transition matrices are employed by a two-layer Markov model to reduce the computational complexity of the model without increasing the memory requirements. The proposed approach characterizes the multiplicative processes of a propagation channel as shadowing and fast fading. Each type of fading is considered as several channel states and each of the states corresponds to a specific mixed Rayleigh-lognormal distribution. Numerical results reveal that the statistical properties of the simulated data are quite close to those obtained from the measurements; indeed, the proposed two-layer Markov model is more accurate and less complex, and requires less memory than the single-layer Markov model. Furthermore, the proposed two-layer Markov model enables the fading statistics and error probability performance of a quadrature phase-shift keying modulation scheme in a typical urban Taipei environment to be more accurately predicted. Besides, it can easily be applied to similar environmental scenarios.     

An averaging principle for filtering a jump process with pointprocess observations

A proof of the following result is given. Le X_t and Y_t be two jump processes which modulate the intensity of a multivariate point process N _t, and suppose that the process X_t is a fast' Markov chain with a unique invariant probability distribution. Then the filtering equations for Y_t can be obtained by considering, instead of the original problem, the averaged problem where the intensity is replaced by the averaged intensity     

Finite-state Markov modeling of correlated Rician-fading channels

Stochastic properties of the binary channel that describe the successes and failures of the transmission of a modulated signal over a time-correlated flat-fading channel are considered for investigation. This analysis is employed to develop Kth-order Markov models for such a burst channel. The order of the Markov model that generates accurate analytical models is estimated for a broad range of fading environments. The parameterization and accuracy of an important class of hidden Markov models, known as the Gilbert-Elliott channel (GEC), are also investigated. Fading rates are identified in which the Kth-order Markov model and the GEC model approximate the fading channel with similar accuracy. The latter model is useful for approximating slowly fading processes, since it provides a more compact parameterization.     

Stochastic differential equations: an approach to the generation ofcontinuous non-Gaussian processes

The generation of continuous random processes with jointly specified probability density and covariation functions is considered. The proposed approach is based on the interpretation of the simulated process as a stationary output of a nonlinear dynamic system, excited by white Gaussian noise and described by a system of a first-order stochastic differential equations (SDE). The authors explore how the statistical characteristics of the equation's solution depends on the form of its operator and on the intensity of the input noise. Some aspects of the approximate synthesis of stochastic differential equations and examples of their application to the generation of non-Gaussian continuous processes are considered. The approach should be useful in signal processing when it is necessary to translate the available a priori information on the real random process into the language of its Markov model as well as in simulation of continuous correlated processes with the known probability density function     

Markov Approach to Percolation Theory Based Propagation in Random Media

For line-of-sight links in random media or urban areas, propagation may be approximated through sequential reflections of an optical ray in a two-dimensional medium of disordered lossless scatterers. Franceschetti approximated such percolation-based optical-ray propagation by a Markov process with two absorbing barriers, provided numerical solutions for the probability of a ray passing through the percolation lattice and solved-both approximately and exactly-a corresponding problem based on the theory of martingales. In this paper we solve exactly the Markov-theoretical formulation of the problem and prove that both the Markov and martingale approaches are equivalent. Our proof is an application of the Perron-Frobenius theory which provides an elegant framework for the study of the asymptotic behavior of stochastic processes. We demonstrate that for a wide range of vacancies and incident angles the exact solution of the Markov-theoretical formulation performs significantly better than the commonly used Wald approximation in the martingale approach. This has a number of implications on the accuracy of the model, especially for low density propagation media.