gevd based low rank approximation for distributed adaptive node specific signal estimation in wireless sensor networks in this paper we address the problem of distributed adaptive estimation of node specific signals for signal enhancement or noise reduction in wireless sensor networks with multi sensor nodes the estimation is performed by a multi channel wiener filter mwf in which a low rank approximation based on a generalized eigenvalue decomposition gevd is incorporated in non stationary or low snr conditions this gevd based mwf has been demonstrated to be more robust than the original mwf in a centralized realization where a fusion center has access to all the nodes sensor signal observations the network wide sensor signal correlation matrices and the low rank approximation can be directly estimated and used to compute the network wide gevd based mwf however in this paper we aim to avoid centralizing the sensor signal observations in which case the network wide sensor signal correlation matrices cannot be estimated to this end we start from the so called distributed adaptive node specific signal estimation danse algorithm and include gevd based low rank approximations in the per node local computations remarkably the new algorithm is able to significantly compress the signal observations transmitted between the nodes while still converging to the network wide gevd based mwf as if each node would have access to all sensor signal observations even though the low rank approximations are applied locally at each node we provide a theoretical convergence analysis which shows that the algorithm converges to the network wide gevd based mwf under conditions that are less strict than in the original danse algorithm the convergence and performance of the algorithm are further investigated via numerical simulations

on scaling laws of diversity schemes in decentralized estimation this paper is concerned with decentralized estimation of a gaussian source using multiple sensors we consider a diversity scheme where only the sensor with the best channel sends their measurements over a fading channel to a fusion center using the analog amplify and forwarding technique the fusion centre reconstructs a minimum mean squared error mmse estimate of the source based on the received measurements a distributed version of the diversity scheme where sensors decide whether to transmit based only on their local channel information is also considered we derive asymptotic expressions for the expected distortion of the mmse estimate at the fusion centre of these schemes as the number of sensors becomes large for comparison asymptotic expressions for the expected distortion for a coherent multiaccess scheme and an orthogonal access scheme are derived it is seen that as opposed to the coherent multiaccess scheme and the orthogonal scheme where the expected distortion decays as 1 m m being the number of sensors the expected distortion decays only as 1 ln m for the diversity schemes this reduction of the decay rate can be seen as a tradeoff between the simplicity of the diversity schemes and the strict synchronization and large bandwidth requirements for the coherent multiaccess and the orthogonal schemes respectively we study for the diversity schemes the optimal power allocation for minimizing the expected distortion subject to average power constraints the effect of optimizing the probability of transmission on the expected distortion in the distributed scenario is also studied it is proved that for rayleigh fading optimal sensor transmit power allocation achieves the same asymptotic scaling law as the constant power allocation scheme whereas it is observed that optimizing the sensor transmission probability with or without optimal power allocation in the distributed case makes very little difference to the asymptotic scaling laws

kalman filtering with scheduled measurements this paper is concerned with the design of transmission scheduler and estimator for linear discrete time stochastic systems to reduce the number of measurements to be transmitted from sensor to estimator to this purpose both controllable and uncontrollable scheduling schemes are considered respectively a controllable scheduler is designed as a deterministic function of system measurements and sequentially decides the transmission of each element of a measurement vector to the estimator we derive an approximate minimum mean square error mmse estimator on the other hand an uncontrollable scheduler means that the transmission of the measurement vector is driven by a random process which is independent of system evolution the mmse estimator under this scheduler is cast as the kalman filtering with intermittent observations some stability conditions are established for both the estimators finally illustrative examples are included to validate the theoretical results

linear dimensionality reduction for margin based classification high dimensional data and sensor networks low dimensional statistics of measurements play an important role in detection problems including those encountered in sensor networks in this work we focus on learning low dimensional linear statistics of high dimensional measurement data along with decision rules defined in the low dimensional space in the case when the probability density of the measurements and class labels is not given but a training set of samples from this distribution is given we pose a joint optimization problem for linear dimensionality reduction and margin based classification and develop a coordinate descent algorithm on the stiefel manifold for its solution although the coordinate descent is not guaranteed to find the globally optimal solution crucially its alternating structure enables us to extend it for sensor networks with a message passing approach requiring little communication linear dimensionality reduction prevents overfitting when learning from finite training data in the sensor network setting dimensionality reduction not only prevents overfitting but also reduces power consumption due to communication the learned reduced dimensional space and decision rule is shown to be consistent and its rademacher complexity is characterized experimental results are presented for a variety of datasets including those from existing sensor networks demonstrating the potential of our methodology in comparison with other dimensionality reduction approaches

greedy adaptive linear compression in signal plus noise models in this paper we examine adaptive compression policies when the sequence of vector valued measurements to be compressed is noisy and the compressed variables are themselves noisy the optimization criterion is information gain in the case of sequential scalar compressions the unit norm compression vectors that greedily maximize per stage information gain are eigenvectors of an a priori error covariance matrix and the greedy policy selects them according to eigenvalues of a posterior covariance matrix these eigenvalues depend on all previous compressions and are computed recursively a water filling solution is given for the optimum compression policy that maximizes net information gain under a constraint on the average norm of compression vectors we provide sufficient conditions under which the greedy policy for maximizing stepwise information gain actually is optimal in the sense of maximizing the net information gain in the case of scalar compressions our examples and simulation results illustrate that the greedy policy can be quite close to optimal when the noise sequences are white

decomposable principal component analysis in this paper we consider principal component analysis pca in decomposable gaussian graphical models we exploit the prior information in these models in order to distribute pca computation for this purpose we reformulate the pca problem in the sparse inverse covariance concentration domain and address the global eigenvalue problem by solving a sequence of local eigenvalue problems in each of the cliques of the decomposable graph we illustrate our methodology in the context of decentralized anomaly detection in the abilene backbone network based on the topology of the network we propose an approximate statistical graphical model and distribute the computation of pca

sensor centric data reduction for estimation with wsns via censoring and quantization consider a wireless sensor network wsn with a fusion center fc deployed to estimate signal parameters from noisy sensor measurements if the wsn has a large number of low cost battery operated sensor nodes with limited transmission bandwidth then conservation of transmission resources power and bandwidth is paramount to this end the present paper develops a novel data reduction method which requires no inter sensor collaboration and results in only a subset of the sensor measurements transmitted to the fc using interval censoring as a data reduction method each sensor decides separately whether to censor its acquired measurements based on a rule that promotes censoring of measurements with least impact on the estimator mean square error mse leveraging the statistical distribution of sensor data the censoring mechanism and the received uncensored data fc based estimators are derived for both deterministic via maximum likelihood estimation and random parameters via maximum a posteriori probability estimation for a linear gaussian model quantization of the uncensored measurements at the sensor nodes offers an additional degree of freedom in the resource conservation versus estimator mse reduction tradeoff cramer rao bound analysis for the different censor estimators and censor quantizer estimators is also provided to benchmark and facilitate mse based performance comparisons numerical simulations corroborate the analytical findings and demonstrate that the proposed censoring estimation approach performs competitively with alternative methods under different sensing conditions while having lower computational complexity

on a theorem of castelnuovo and the equations defining space curves introduction 491 w notat ion and conventions 493 w a regularity theorem 494 w a rationality theorem 498 w the existence of secant lines 501 w open problems 505 references 506

dimensionality reduction for distributed estimation in the infinite dimensional regime distributed estimation of an unknown signal is a common task in sensor networks the scenario usually envisioned consists of several nodes each making an observation correlated with the signal of interest the acquired data is then wirelessly transmitted to a fusion center that aims at estimating the desired signal within a prescribed accuracy motivated by the obvious processing limitations inherent to such distributed infrastructures we seek to find efficient compression schemes that account for limited available power and communication bandwidth in this paper we propose a transform based approach to this problem where each sensor provides the fusion center with a low dimensional approximation of its local observation by means of a suitable linear transform under the mean squared error criterion we derive the optimal solution to apply at one sensor assuming all else being fixed this naturally leads to an iterative algorithm whose optimality properties are exemplified using a simple though illustrative correlation model the stationarity issue is also investigated under restrictive assumptions we then provide an asymptotic distortion analysis as the size of the observed vectors becomes large our derivation relies on a variation of the toeplitz distribution theorem which allows us to provide a reverse ldquowater fillingrdquo perspective to the problem of optimal dimensionality reduction we illustrate with a first order gauss markov model how our findings allow for the computation of analytical closed form distortion formulas that provide an accurate estimation of the reconstruction error obtained in the finite dimensional regime

sensors optimal dimensionality compression matrix in estimation fusion when there exists the limitation of communication bandwidth between sensors and a fusion center one needs to optimally pre compress sensor outputs sensor observations or estimates before sensors transmission to obtain a constrained optimal estimation at the fusion center in terms of the linear minimum error variance criterion this paper will give an analytic solution of the optimal linear dimensionality compression matrix for the single sensor case and analyze the existence of the optimal linear dimensionality compression matrix for the multisensor case as well as how to implement a gauss seidel algorithm to search for an optimal solution to linear dimensionality compression matrix

linear coherent decentralized estimation we consider the distributed estimation of an unknown vector signal in a resource constrained sensor network with a fusion center due to power and bandwidth limitations each sensor compresses its data in order to minimize the amount of information that needs to be communicated to the fusion center in this context we study the linear decentralized estimation of the source vector where each sensor linearly encodes its observations and the fusion center also applies a linear mapping to estimate the unknown vector signal based on the received messages we adopt the mean squared error mse as the performance criterion when the channels between sensors and the fusion center are orthogonal it has been shown previously that the complexity of designing the optimal encoding matrices is np hard in general in this paper we study the optimal linear decentralized estimation when the multiple access channel mac is coherent for the case when the source and observations are scalars we derive the optimal power scheduling via convex optimization and show that it admits a simple distributed implementation simulations show that the proposed power scheduling improves the mse performance by a large margin when compared to the uniform power scheduling we also show that under a finite network power budget the asymptotic mse performance when the total number of sensors is large critically depends on the multiple access scheme for the case when the source and observations are vectors we study the optimal linear decentralized estimation under both bandwidth and power constraints we show that when the mac between sensors and the fusion center is noiseless the resulting problem has a closed form solution which is in sharp contrast to the orthogonal mac case while in the noisy mac case the problem can be efficiently solved by semidefinite programming sdp

hyperplane based vector quantization for distributed estimation in wireless sensor networks this paper considers distributed estimation of a vector parameter in the presence of zero mean additive multivariate gaussian noise in wireless sensor networks due to stringent power and bandwidth constraints vector quantization is performed at each sensor to convert its local noisy vector observation into one bit of information which is then forwarded to a fusion center where a final estimate of the vector parameter is obtained within such a context this paper focuses on a class of hyperplane based vector quantizers which linearly convert the observation vector into a scalar by using a compression vector and then carry out a scalar quantization it is shown that the key of the vector quantization design is to find a compression vector for each sensor under the framework of the cramer rao bound crb analysis the compression vector design problem is formulated as an optimization problem that minimizes the trace of the crb matrix such an optimization problem is extensively studied in particular an efficient iterative algorithm is developed for the general case along with optimal and near optimal solutions for some specific but important noise scenarios performance analysis and simulation results are carried out to illustrate the effectiveness of the proposed scheme

optimal dimensionality reduction of sensor data in multisensor estimation fusion when there exists the limitation of communication bandwidth between sensors and a fusion center one needs to optimally precompress sensor outputs sensor observations or estimates before the sensors transmission in order to obtain a constrained optimal estimation at the fusion center in terms of the linear minimum error variance criterion or when an allowed performance loss constraint exists one needs to design the minimum dimension of sensor data this paper will answer the above questions by using the matrix decomposition pseudo inverse and eigenvalue techniques

liaison equivalence classes we will work in ip n 2 over an algebraically closed field the notion of liaison among subvarieties of ip was introduced in 3 we will consider here liaison in codimension two generalizing results in 4 recall therefore that two subschemes v 1 v 2 of ip that are locally cohenmacaulay and equidimensional of codimension two are said to be linked algebraically via the complete intersection x of two hypersurfaces denoted v l v z via x if d e v j x v r o v x t j they are said to be linked geometrically if i 1 and v2 in the above definition have no components in common according to 4 theorem 1 7 the two notions of linkage generate the same equivalence relation among those subschemes v which are also generically locally complete intersections we will hence consider only algebraic linkage

reduced dimension linear transform coding of correlated signals in networks a model called the linear transform network ltn is proposed to analyze the compression and estimation of correlated signals transmitted over directed acyclic graphs dags an ltn is a dag network with multiple source and receiver nodes source nodes transmit subspace projections of random correlated signals by applying reduced dimension linear transforms the subspace projections are linearly processed by multiple relays and routed to intended receivers each receiver applies a linear estimator to approximate a subset of the sources with minimum mean squared error mse distortion the model is extended to include noisy networks with power constraints on transmitters a key task is to compute all local compression matrices and linear estimators in the network to minimize end to end distortion the nonconvex problem is solved iteratively within an optimization framework using constrained quadratic programs qps the proposed algorithm recovers as special cases the regular and distributed karhunen loeve transforms klts cut set lower bounds on the distortion region of multi source multi receiver networks are given for linear coding based on convex relaxations cut set lower bounds are also given for any coding strategy based on information theory the distortion region and compression estimation tradeoffs are illustrated for different communication demands e g multiple unicast and graph structures

optimum compression of a noisy measurement for transmission over a noisy channel this paper is motivated by sensing and wireless communication where data compression or dimension reduction may be used to reduce the required communication bandwidth high dimensional measurements are converted into low dimensional representations through linear compression our aim is to compress a noisy sensor measurement allowing for the fact that the compressed measurement will then be transmitted over a noisy channel we give the closed form expression for the optimal compression matrix that minimizes the trace or determinant of the error covariance matrix we show that the solutions share a common architecture consisting of a canonical coordinate transformation scaling by coefficients which account for canonical correlations and channel noise variance followed by a coordinate transformation into the sub dominant invariant subspace of the channel noise furthermore we explore the design problem with respect to more general criteria and provide a unified factorization for the corresponding optimal compression matrix a necessary condition is obtained for the optimal compression

a simple and efficient extension of a class of substructure based preconditioners to heterogeneous structural mechanics problems several domain decomposition methods with lagrange multipliers have been recently designed for solving iteratively large scale systems of finite element equations while these methods differ typically by implementational details they share in most cases the same substructure based preconditioners that were originally developed for the feti method the success of these preconditioners is due to the fact that for homogeneous structural mechanics problems they ensure a computational performance that scales with the problem size in this paper we address the suboptimal behaviour of these preconditioners in the presence of material and or discretization heterogeneities we propose a simple and virtually no cost extension of these preconditioners that exhibits scalability even for highly heterogeneous systems of equations we consider several intricate structural analysis problems and demonstrate numerically the optimal performance delivered by the new preconditioners for problems with discontinuities copyright 1999 john wiley sons ltd

asymptotically optimal parameter estimation with scheduled measurements to reduce the communication cost of a sensor node this paper is concerned with an estimation framework with scheduled measurements for a linear system a scheduler is designed to control the transmission of measurements from sensor to estimator which results in that only a subset of measurements is transmitted to the estimator we propose an innovation based scheduler and derive an analytical expression for the cramer rao lower bound crlb for the given scheduling strategy under a communication constraint an adaptive scheduler and a corresponding recursive estimator are jointly designed to asymptotically attain the crlb the structure of the estimator bears close resemblance to the standard least square estimator lse with the full set of sensor measurements moreover we prove that the estimation performance in terms of mean square estimation error is comparable to the standard lse even under a moderate communication cost the theoretical results are verified by simulations

universal decentralized estimation in a bandwidth constrained sensor network consider a situation where a set of distributed sensors and a fusion center wish to cooperate to estimate an unknown parameter over a bounded interval u u each sensor collects one noise corrupted sample performs a local estimation and transmits a message to the fusion center while the latter combines the received messages to produce a final estimate this correspondence investigates optimal local estimation and final fusion schemes under the constraint that the communication from each sensor to the fusion center must be a one bit message such a binary message constraint is well motivated by the bandwidth limitation of the communication links fusion center and by the limited power budget of local sensors in the absence of bandwidth constraint and assuming the noises are bounded to the interval u u additive independent but otherwise unknown the classical estimation theory suggests that a total of o u2 epsi2 sensors are necessary and sufficient in order for the sensors and the fusion center to jointly estimate the unknown parameter within epsi root mean squared error mse it is shown in this correspondence that the same remains true even with the binary message constraint furthermore the optimal decentralized estimation scheme suggests allocating 1 2 of the sensors to estimate the first bit of the unknown parameter 1 4 of the sensors to estimate the second bit and so on

the hilbert function of generic plane sections of curves of ℙ3 a characteristic condition is given on a zero dimensional differentiable 0 sequenceh hi i 0 h1 3 in order to be the hilbert function of a generic plane section of a reduced irreducible curve of 3 hence of points of 2 with the uniform position property in this way an answer is given to some question stated by harris in ha2

bandwidth constrained distributed estimation for wireless sensor networks part ii unknown probability density function wireless sensor networks wsns deployed to perform surveillance and monitoring tasks have to operate under stringent energy and bandwidth limitations these motivate well distributed estimation scenarios where sensors quantize and transmit only one or a few bits per observation for use in forming parameter estimators of interest in a companion paper we developed algorithms and studied interesting tradeoffs that emerge even in the simplest distributed setup of estimating a scalar location parameter in the presence of zero mean additive white gaussian noise of known variance herein we derive distributed estimators based on binary observations along with their fundamental error variance limits for more pragmatic signal models i known univariate but generally non gaussian noise probability density functions pdfs ii known noise pdfs with a finite number of unknown parameters iii completely unknown noise pdfs and iv practical generalizations to multivariate and possibly correlated pdfs estimators utilizing either independent or colored binary observations are developed and analyzed corroborating simulations present comparisons with the clairvoyant sample mean estimator based on unquantized sensor observations and include a motivating application entailing distributed parameter estimation where a wsn is used for habitat monitoring

fundamentals of statistical signal processing estimation theory minimum variance unbiased estimation cramer rao lower bound linear models general minimum variance unbiased estimation best linear unbiased estimators maximum likelihood estimation least squares method of moments the bayesian philosophy general bayesian estimators linear bayesian estimators kalman filters summary of estimators extension for complex data and parameters

distributed state estimation with dimension reduction preprocessing system state estimation relies heavily on the measurements with the advance of sensing technology the ability to measure is no longer a bottleneck in many systems and more and more researchers now focus on the rich information setting i e big data however although information never hurts it does not help unconditionally how to make the most of it depends on whether we can process the data efficiently in some systems the inherent constraint such as the bandwidth and cost makes it necessary to reduce the dimension of the measurement before further processing the problem that the raw measurements are first preprocessed to reduce size and then used for estimation is addressed in this paper it is shown that there is a lower bound on the size of the preprocessed data such that if the size is beyond the bound there exists a closed form estimator design that the linear minimum mean square estimation can be obtained moreover we propose an algorithm that is guaranteed to converge to a stationary point to design an estimator in the conditions that the lower bound cannot be reached besides convergence the proposed algorithm guarantees bounded performance loss compared with the global optimal solution under some additional conditions finally simulation results in three different applications are shown to demonstrate the effectiveness of the proposed algorithm

the distributed karhunen loeve transform the karhunen loeve transform klt is a key element of many signal processing and communication tasks many recent applications involve distributed signal processing where it is not generally possible to apply the klt to the entire signal rather the klt must be approximated in a distributed fashion this paper investigates such distributed approaches to the klt where several distributed terminals observe disjoint subsets of a random vector we introduce several versions of the distributed klt first a local klt is introduced which is the optimal solution for a given terminal assuming all else is fixed this local klt is different and in general improves upon the marginal klt which simply ignores other terminals both optimal approximation and compression using this local klt are derived two important special cases are studied in detail namely the partial observation klt which has access to a subset of variables but aims at reconstructing them all and the conditional klt which has access to side information at the decoder we focus on the jointly gaussian case with known correlation structure and on approximation and compression problems then the distributed klt is addressed by considering local klts in turn at the various terminals leading to an iterative algorithm which is locally convergent sometimes reaching a global optimum depending on the overall correlation structure for compression it is shown that the classical distributed source coding techniques admit a natural transform coding interpretation the transform being the distributed klt examples throughout illustrate the performance of the proposed distributed klt this distributed transform has potential applications in sensor networks distributed image databases hyper spectral imagery and data fusion

distributed fusion estimation with communication bandwidth constraints this technical note is concerned with the distributed kalman filtering problem for a class of networked multi sensor fusion systems nmfss with communication bandwidth constraints to satisfy finite communication bandwidth only partial components of the local vector estimation signals are transmitted to the fusion center fc at each time step where multiple binary variables are introduced to model this component transmitting process a novel compensation strategy is proposed to restructure the untransmitted components of each local estimate at the fc end and a recursive distributed fusion kalman filter dfkf is designed in the linear minimum variance sense moreover a simple suboptimal judgement criterion is proposed to determine a group of binary variables such that the mean square error of the designed dfkf is minimal at each time step an illustrative example is given to show the effectiveness of the proposed methods

distributed estimation using reduced dimensionality sensor observations we derive linear estimators of stationary random signals based on reduced dimensionality observations collected at distributed sensors and communicated to a fusion center over wireless links dimensionality reduction compresses sensor data to meet low power and bandwidth constraints while linearity in compression and estimation are well motivated by the limited computing capabilities wireless sensor networks are envisioned to operate with and by the desire to estimate random signals from observations with unknown probability density functions in the absence of fading and fusion center noise ideal links we cast this intertwined compression estimation problem in a canonical correlation analysis framework and derive closed form mean square error mse optimal estimators along with coordinate descent suboptimal alternatives that guarantee convergence at least to a stationary point likewise we develop estimators based on reduced dimensionality sensor observations in the presence of fading and additive noise at the fusion center nonideal links performance analysis and corroborating simulations demonstrate the merits of the novel distributed estimators relative to existing alternatives

numerical invariants of liaison classes 302 c huneke intersection what properties are then enjoyed by v for instance buchweitz was able to show that all such v are strongly nonobstructed see 5 for details the two questions above have been completely answered if x spec r with r a regular local ring and if codim v 2 in this case