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Filtering and smoothing within a convex and closed family of stationary processes is considered. The performance criterion adopted is the mean square error. Using a saddle point game approach, we develop two classes of lower bounds for this error. Those bounds can be used as evaluation measure in the design of robust filters and smoothers. (Author)

Generalized stationary Markov chains with denumberable state space are considered. For irreducible and aperiodic such chains, some sufficient conditions for ergodicity and steady state equilibrium are developed. The conditions for ergodicity are generalizations of previously proposed such conditions, and they are more tractable for certain applications. (Author)

This paper presents a unified method for the delay analysis of a large class of random multiple-access algorithms. This method is based on a powerful theorem referring to regenerative processes, in conjunction with results from the theory of infinite dimensionality linear systems. The authors apply the method to analyze and compute the per packet expected delays induced by two algorithms, in the presence of the Poisson user model. The considered algorithms are: The controlled ALOHA algorithm, and the 0.487 algorithm. The same method has been previously applied, for the delay analysis of certain limited sensing random access algorithms. Keywords: communications networks; allocations. (Author)

Consider a stationary Gaussian information process transmitted through an additive noise channel. The noise and information processes are mutually independent, and the noise process modeled as nominally Gaussian with additive outliers. For the above system model a theory is developed for outliers resistant filtering and smoothing operations. We then design specific such nonlinear operations, and we study their performance. The performance criteria are the asymptotic mean squared error at the Gaussian nominal model, the breakdown point, and the influence function. The proposed operations combine excellent performance at the nominal model with strong resistance to outliers.

In this paper the analysis of estimates operating on dependent data is considered. Special dependent data structures are considered and the analysis is made for three different choices of contamination and performance distance measures. For contamination and performance measures both being Levy (Hampel model), an analysis that is particularly oriented toward fast convergence of the estimate to value that is stable (robust) inside the contaminated family is undertaken. The minimum sample size to satisfy certain performance is investigated and it is found that the problem reduces to finding continuous, absolutely bounded estimates with logarithms of their moment generating function slowly increasing with the absolute value of the argument for all data distributions considered.

The authors consider packet radio multi-user spread-spectrum environments, where frequency hopping spread spectrum techniques are deployed for protection against intelligent adversaries. When the users in such environments are mobile and bursty, random access frequency hopping transmission algorithms should be adopted, for efficiency in throughput and delay control. This paper proposes and analyzes such an algorithm, named Collision Resolution Algorithm for Frequency Hopping (CRAFH). The CRAFH is a limited sensing random access algorithm utilizing receiver oriented frequency hopping patterns. In its design, the experience from random access algorithms for non spread spectrum multi-user channels is utilized. Utilizing the regenerative character of the induced by the algorithm transmission process, the authors compute throughputs and expected per packet delays. In the presence of interferences between transmissions to different receivers, we compute throughputs, subject to an upper bound on the probability of erroneous data decoding. The CRAFH induces uniformly good delays within its stability region, and is particularly appropriate for environments where the users are highly mobile.

In relatively recent years, several algorithms for smoothing of time series have been proposed by statisticians. Some of the simpler such algorithms have been also applied in several engineering applications such as Image Processing. The smoothing problem and the implied objective have not been formalized and stated, however. This fact presents a serious handicap when different smoothing algorithms are to be compared in terms of their performance. In this paper, we take a fresh and daring approach to the whole smoothing problem. We formalize the problem as the extraction of a low entropy process from a high entropy process, and as a result we present a constructive theory of parametric and robust data smoothers. We claim that parametric data smoothers are analog-to-digital converters, and that robust data smoothers are stochastic such converters. (Author)

In this paper, we are concerned with the per packet transmission delays induced by the Capetabakis collision resolution protocol for infinitely large number of identical bursty users. We first correct the existing lower and upper bounds on the expected per packet transmission delay E(D). Then, we proceed by developing a new upper bound on E(D). This new bound is much tighter approaching the lower bound for large arrival rates. (Author)

The authors present and discuss a class of continuous operations on the family of discrete time stochastic processes, which serves as a guide to construct qualitatively robust operations for a given class of processes, namely the one induced by a nominal process and a substitutive contaminating process. The results are general enough to help develop any robust statistical procedure, but the authors have concentrated their attention on detection of a change from one class of processes to another (disjoint) class of processes, while both classes consist of not necessarily Markov processes and satisfy certain mixing conditions in addition to stationarity and ergodicity. Two quantitative measures of robustness, breakdown point and influence functions are also developed for few examples.

A theory for robust filtering and smoothing is formulated that combines the qualitative robustness theory with the theory of saddle point games. This theory finds robust filters for certain contaminated classes of stochastic processes. Robust predictors, interpolators, and filters are designed for various classes of vector stationary processes with contaminated spectra. Measures of breakdown points and curves, efficiency, and performance variation within the classes are produced. A variety of multiple access transmission protocols are designed for various levels of available feedback and feedback sensing. The studies include asymptotically many user models. Limited sensing algorithms are devised with the with the highest existing throughput, to this point in time, and with robust characteristics in the presence of feedback errors. A unified methodology for the delay analysis of a big variety of random access algorithms is devised.

The object of this grant is the analysis and design of decision procedures that have stable, good performance in statistically ill-defined environments. Such procedures indicate the way to design powerful receivers for systems whose statistical behavior cannot be described precisely (due to incomplete availability of data about the system behavior). Different distance measures have been studied for use as performance criteria for robust estimates. Careful evaluation and comparison of these distances was done and their similarities, advantages and disadvantages were carefully stated. A thorough study of the work already accomplished (by the author as well as other investigators) on nonparametric statistical procedures in the presence of small number of discrete data was done and included in a book on the use of nonparametric procedures in Communication Systems. A feature selection problem was studied, when several distance measures are used as discrimination criteria. A sequential procedure for clustered data was proposed and analyzed. Hampel's general qualitative definition of robustness of sequences of estimators on memoryless observation processes was generalized to stationary processes. The constructive analysis of robustness completed by the author is being used now in the performance analysis of communication Networks at Bell Laboratories.

Consider prediction for stationary processes, in environments where data outliers may be present. Two sequences are developed for outliers resistant prediction operations, which are uniformly qualitatively robust. The asymptotic mean-squared performance of the developed operations are studied in the absence of data outliers. Important performance characteristics studied include the breakdown point and the influence function. Included are numerical results, for some autoregressive nominal processes.