George V. Moustakides

Fast and Stable Subspace Tracking

We consider the problem of adaptive subspace tracking, when the rank of the subspace we seek to estimate is assumed to be known. Starting from the data projection method (DPM), which constitutes a simple and reliable means for adaptively estimating and tracking subspaces, we develop a fast and numerically robust implementation of DPM, which comes at a considerably lower computational cost. Most existing schemes track subspaces corresponding either to the largest or to the smallest singular values, while our DPM version can switch from one subspace type to the other with a simple change of sign of its single parameter. The proposed algorithm provides orthonormal vector estimates of the subspace basis that are numerically stable since they do not accumulate roundoff errors. In fact, our scheme constitutes the first numerically stable, low complexity, algorithm for tracking subspaces corresponding to the smallest singular values. Regarding convergence towards orthonormality our scheme exhibits the fastest speed among all other subspace tracking algorithms of similar complexity.

Fast Newton transversal filters-a new class of adaptive estimation algorithms

A class of adaptive algorithms for the estimation of FIR (finite impulse response) transversal filters is presented. The main characteristic of this class is the fast computation of the gain vector needed for the adaptation of the transversal filters. The method for deriving these algorithms is based on the assumption that the input signal is autoregressive of order M, where M can be much smaller than the order of the filter to be estimated. Under this assumption the covariance matrix of the input signal is estimated by extending in a min-max way the M order sample covariance matrix. This estimate can be regarded as a generalization of the diagonal covariance matrix used in LMS and leads to an efficient computation of the gain needed for the adaptation. The new class of algorithms contains the LMS and the fast versions of LS as special cases. The complexity changes linearly with M, starting from the complexity of the LMS (for M=0) and ending at the complexity of the fast versions of LS. >

A Bayesian decision model for cost optimal record matching

Abstract. In an error-free system with perfectly clean data, the construction of a global view of the data consists of linking - in relational terms, joining - two or more tables on their key fields. Unfortunately, most of the time, these data are neither carefully controlled for quality nor necessarily defined commonly across different data sources. As a result, the creation of such a global data view resorts to approximate joins. In this paper, an optimal solution is proposed for the matching or the linking of database record pairs in the presence of inconsistencies, errors or missing values in the data. Existing models for record matching rely on decision rules that minimize the probability of error, that is the probability that a sample (a measurement vector) is assigned to the wrong class. In practice though, minimizing the probability of error is not the best criterion to design a decision rule because the misclassifications of different samples may have different consequences. In this paper we present a decision model that minimizes the cost of making a decision. In particular: (a) we present a decision rule: (b) we prove that this rule is optimal with respect to the cost of a decision: and (c) we compute the probabilities of the two types of errors (Type I and Type II) that incur when this rule is applied. We also present a closed form decision model for a certain class of record comparison pairs along with an example, and results from comparing the proposed cost-based model to the error-based model, for large record comparison spaces.

Detection and diagnosis of changes in the eigenstructure of nonstationary multivariable systems

Abstract The two problems of detection and diagnosis of changes in the state transition matrix of a multivariable system with nonstationary unknown state noise are addressed. New instrumental tests are derived and shown to be numerically powerful, even for small changes. The application to vibration monitoring of offshore platforms is described.

Blind adaptive channel estimation in ofdm systems

We consider the problem of blind channel estimation in zero padding OFDM systems, and propose blind adaptive algorithms in order to identify the impulse response of the multipath channel. In particular, we develop RLS and LMS schemes that exhibit rapid convergence combined with low computational complexity and numerical stability. Both versions are obtained by properly modifying the orthogonal iteration method used in numerical analysis for the computation of singular vectors. With a number of simulation experiments we demonstrate the satisfactory performance of our adaptive schemes under diverse signaling conditions

Decentralized Sequential Hypothesis Testing Using Asynchronous Communication

An asymptotically optimum test for the problem of decentralized sequential hypothesis testing is presented. The induced communication between sensors and fusion center is asynchronous and limited to 1-bit data. When the sensors observe continuously stochastic processes with continuous paths, the proposed test is order-2 asymptotically optimal, in the sense that its inflicted performance loss is bounded. When the sensors take discrete time observations, the proposed test achieves order-1 asymptotic optimality, i.e., the ratio of its performance over the optimal performance tends to 1. Moreover, we show theoretically and corroborate with simulations that the performance of the suggested test in discrete time can be significantly improved when the sensors sample their underlying continuous time processes more frequently, a property which is not enjoyed by other centralized or decentralized tests in the literature.

Detecting IEEE 802.11 MAC layer misbehavior in ad hoc networks: Robust strategies against individual and colluding attackers

Selfish behavior at the Medium Access (MAC) Layer can have devastating side effects on the performance of wireless networks, with effects similar to those of Denial of Service (DoS) attacks. In this paper we consider the problem of detection and prevention of node misbehavior at the MAC layer, focusing on the back-off manipulation by selfish nodes. We first propose an algorithm that ensures honest behavior of non-colluding participants. Furthermore, we analyze the problem of colluding selfish nodes, casting the problem within a minimax robust detection framework and providing an optimal detection rule for the worst-case attack scenarios. Finally, we evaluate the performance of single and colluding attackers in terms of detection delay. Although our approach is general and can be used with any probabilistic distributed MAC protocol, we focus our analysis on the IEEE 802.11 MAC.

Joint Detection and Estimation: Optimum Tests and Applications

We consider a well-defined joint detection and parameter estimation problem. By combining the Bayesian formulation of the estimation subproblem with suitable constraints on the detection subproblem, we develop optimum one- and two-step test for the joint detection/estimation setup. The proposed combined strategies have the very desirable characteristic to allow for the trade-off between detection power and estimation quality. Our theoretical developments are, then, applied to the problems of retrospective changepoint detection and multiple-input multiple-output (MIMO) radar. In the former case, we are interested in detecting a change in the statistics of a set of available data and provide an estimate for the time of change, while in the latter in detecting a target and estimating its location. Intense simulations in the MIMO radar example demonstrate that by using jointly optimum schemes, we can experience significant improvement in estimation quality, as compared to generalized the likelihood ratio test or the test that treats the two subproblems separately, with only small sacrifices in detection power.

Study of the transient phase of the forgetting factor RLS

We investigate the convergence properties of the forgetting factor RLS algorithm in a stationary data environment. Using the settling time as our performance measure, we show that the algorithm exhibits a variable performance that depends on the particular combination of the initialization and noise level. Specifically when the observation noise level is low (high SNR) RLS, when initialized with a matrix of small norm, it has an exceptionally fast convergence. Convergence speed decreases as we increase the norm of the initialization matrix. In a medium SNR environment, the optimum convergence speed of the algorithm is reduced as compared with the previous case; however, RLS becomes more insensitive to initialization. Finally, in a low SNR environment, we show that it is preferable to initialize the algorithm with a matrix of large norm.

Adaptive Sampling for Linear State Estimation

When a sensor has continuous measurements but sends limited messages over a data network to a supervisor which estimates the state, the available packet rate fixes the achievable quality of state estimation. When such rate limits turn stringent, the sensors messaging policy should be designed anew. What are the good causal messaging policies ? What should message packets contain ? What is the lowest possible distortion in a causal estimate at the supervisor ? Is Delta sampling better than periodic sampling ? We answer these questions under an idealized model of the network and the assumption of perfect measurements at the sensor. For a scalar, linear diffusion process, we study the problem of choosing the causal sampling times that will give the lowest aggregate squared error distortion. We stick to finite-horizons and impose a hard upper bound on the number of allowed samples. We cast the design as a problem of choosing an optimal sequence of stopping times. We reduce this to a nested sequence of problems each asking for a single optimal stopping time. Under an unproven but natural assumption about the least-square estimate at the supervisor, each of these single stopping problems are of standard form. The optimal stopping times are random times when the estimation error exceeds designed envelopes. For the case where the state is a Brownian motion, we give analytically: the shape of the optimal sampling envelopes, the shape of the envelopes under optimal Delta sampling, and their performances. Surprisingly, we find that Delta sampling performs badly. Hence, when the rate constraint is a hard limit on the number of samples over a finite horizon, we should should not use Delta sampling.