Rabinder N. Madan

Functional characterization of fault tolerant integration in distributed sensor networks

Fault-tolerance is an important issue in network design because sensor networks must function in a dynamic, uncertain world. A functional characterization of the fault-tolerant integration of abstract interval estimates is proposed. This model provides a preliminary version for a general framework that is hoped to develop to address the general problem of fault-tolerant integration of abstract sensor estimates. A scheme for narrowing the width of the sensor output in a specific failure model is proposed and given a functional representation. The main distinguishing feature of the model over the original model of K. Marzullo (1989) is in reducing the width of the output interval estimate significantly in most cases where the number of sensors involved is large. >

Robust estimation of sinusoidal signals with colored noise using decentralized processing

We develop a new technique for the estimation of the number of signals and their central frequencies by using the decentralized processing, when it is known a priori that the observations consist of a finite number of source signals corrupted by additive colored random noise process. Our decentralized processing scheme is that each sensor estimates the frequency and the covariance matrix of the observations, and sends the estimated results to the fusion center. For the parameter estimation at each sensor, we use the earlier work of [1]. At the fusion center, we utilize the Robust estimation technique to combine the estimates obtained from individual sensors. The overall performance does not deteriorate very quickly even if some of the sensors are destroyed.

Robust decentralized direction-of-arrival estimation in contaminated noise

A novel scheme for direction-of-arrival (DOA) estimation is presented. The procedure provides estimates that are robust against outliers and distributional uncertainties. It also employs decentralized processing in which each subarray site provides a robust estimate of the number of sources accompanied by its corresponding reliability statistics, so that only the reliable estimates of the number of sources are combined at the fusion center. A robust technique is used to combine the corresponding DOA estimates from the subarray sites. Simulation results show that the scheme performs consistently when the outlier noise is present, whereas the performance of the corresponding nonrobust method deteriorates quickly even with a slight change of the noise environment. This is especially significant at a low signal-to-noise ratio. >

Robust estimation of sinusoidal signal with colored noise using decentralized processing

We develop a new technique for the estimation of the number of signals and their central frequencies by using the decentralized processing, when it is known a priori that the observations consist of a finite number of source signals corrupted by additive colored random noise process. Our decentralized processing scheme is that each sensor estimates the frequency and the covariance matrix of the observations, and sends the estimated results to the fusion center. For the parameter estimation at each sensor, we use the earlier work of [1]. At the fusion center, we utilize the Robust estimation technique to combine the estimates obtained from individual sensors. The overall performance does not deteriorate very quickly even if some of the sensors are destroyed.

Cyber-physical trade-offs in distributed detection networks

We consider a network of sensors that measure the scalar intensity due to the background or a source combined with background, inside a two-dimensional monitoring area. The sensor measurements may be random due to the underlying nature of the source and background or due to sensor errors or both. The detection problem is infer the presence of a source of unknown intensity and location based on sensor measurements. In the conventional approach, detection decisions are made at the individual sensors, which are then combined at the fusion center, for example using the majority rule. With increased communication and computation costs, we show that a more complex fusion algorithm based on measurements achieves better detection performance under smooth and non-smooth source intensity functions, Lipschitz conditions on probability ratios and a minimum packing number for the state-space. We show that these conditions for trade-offs between the cyber costs and physical detection performance are applicable for two detection problems: (i) Poisson radiation sources amidst background radiation, and (ii) sources and background with Gaussian distributions.

Maximum Entropy Method and Digital Filter Design

A new procedure that makes use of the maximum entropy method (MEM) for the design of linear phase FIR digital filters is described here. It is shown here that by applying MEM to the inverse of the desired gain function or its square root function, it is possible to generate linear phase FIR filters that match the given gain function to any desired degree of accuracy. Moreover, an iterative algorithm makes the design procedure very efficient, since the higher order filters can be recursively generated from the lower order ones. To minimize the effect of any residual passband distortion, a final averaging scheme on the lower order filters generates a class of passband distortion-free linear phase FIR filters. Simulation results that compare the present procedure with other well known methods are also presented here.

A Perspective on Information Fusion Problems

Information fusion problems have a rich history spanning four centuries and several disciplines as diverse as political economy, reliability engineering, target tracking, bioinformatics, forecasting, distributed detection, robotics, cyber security, nuclear engineering, distributed sensor networks, and others. Over the past decade, the area of information fusion has been established as a discipline by itself with several contributions to its foundations as well as applications. In a basic formulation of the information fusion problem, each component is characterized by a probability distribution. The goal is to estimate a fusion rule for combining the outputs of components to achieve a specified objective such as better performance or functionality compared to the components. If the sensor error distributions are known, several fusion rule estimation problems have been formulated and solved using deterministic methods. In the area of pattern recognition a weighted majority fuser was shown to be optimal in combining outputs from pattern recognizers under statistical independence conditions. A simpler version of this problem corresponds to the Condorcet Jury theorem proposed in 1786. This result was rediscovered since then in other disciplines including by von Neumann in 1959 in building reliable computing devices. The distributed detection problem, studied extensively in the target tracking area, can be viewed as a generalization of the above two problems. In these works, the underlying distributions are assumed to be known, which is quite reasonable in the areas these methods are applied. In a different formulation, we consider estimating the fuser based on empirical data when no information is available about the underlying distributions of components. Using the empirical estimation methods, this problem is shown to be solvable in principle, and the fuser performance may be sharpened based on the specific formulation. The isolation fusers perform at least as good as best component, and the projective fusers perform as good as best combination of components. In a special case of function estimation, each component could be a potential function estimator, radial basis function, nearest neighbor estimator, regressogram, kernel estimator, regression tree or another estimator. A projective fuser based on a nearest neighbor concept has been proposed based on Voronoi regions in this case. Under fairly general smoothness and non-smoothness conditions on the individual estimators, the expected fuser error is close to optimal with a specified probability. This result is purely sample-based and distribution-free in that it does not require the knowledge of underlying distributions and can be computed only using measurements.

Maximum entropy method and the design of linear phase FIR filters

A procedure that makes use of the maximum-entropy method (MEM) for the design of linear-phase FIR digital filters is described. It is shown that by applying MEM to the inverse of the desired gain function or its square root function, it is possible to generate linear phase FIR filters that match the given gain function to any desired degree of accuracy. Further, an iterative algorithm makes the design procedures very efficient, since the higher-order filters can be recursively generated from the lower-order ones. To minimize any residual distortion in the passband region, a final averaging scheme on the lower-order filters generates a class of linear phase FIR filters that are practically distortion free in the passband as well as the stopband. Simulation results that compare the present procedure with other well-known methods are also presented. >

Tree-structured sensor fusion architecture for distributed sensor networks

An assessment of numerous activities in the field of multisensor target recognition reveals several trends and conditions which are cause for concern. .These concerns are analyzed in terms of their potential impact on the ultimate employment of automatic target recognition in military systems. Suggestions for additional investigation and guidance for current activities are presented with respect to some of the identified concerns.

Robust Models for Time Series

This paper introduces the concept of robust models in time series. A model is said to be robust if the accuracies of the inferences derived from it such as 1 step ahead or k step ahead forecasts are not affected even if the given process y does not exactly obey the given model. Specifically consider a stationary process y (.) about which we know only its autocorrelations of order k, k⩽m. Suppose we want to construct a model y(.) for obtaining inferences such as k step ahead forecastes of y (t) based on the past values of y (.). The criterion for the choice of the model in that optimal k-step ahead forecasts derived from the model are robust, ie, the mean square error of forecast computed from the model does not alter appreciably even if the given process y(.) does not obey the model. We show that the robust model is the mth order autoregressive model whose coefficients are chosen so that its autocorrelations of order k⩽m equal the corresponding specified values.Next we consider the robust modeling of a pr...