decentralized data reduction with quantization constraints a guiding principle for data reduction in statistical inference is the sufficiency principle this paper extends the classical sufficiency principle to decentralized inference i e data reduction needs to be achieved in a decentralized manner we examine the notions of local and global sufficient statistics and the relationship between the two for decentralized inference under different observation models we then consider the impact of quantization on decentralized data reduction which is often needed when communications among sensors are subject to finite capacity constraints the central question we intend to ask is if each node in a decentralized inference system has to summarize its data using a finite number of bits is it still optimal to implement data reduction using global sufficient statistics prior to quantization we show that the answer is negative using a simple example and proceed to identify conditions under which sufficiency based data reduction followed by quantization is indeed optimal they include the well known case when the data at decentralized nodes are conditionally independent as well as a class of problems with conditionally dependent observations that admit conditional independence structure through the introduction of an appropriately chosen hidden variable

non linear quadratic gaussian controlf abstract algebraic necessary conditions for the minimization of a quadratic cost function are derived for non linear stochastic regulator systems on the assumption that the statistics of the state and output random variables can be represented satisfactorily by a gaussian distribution this non linear quadratic gaussian nqg technique is related to the use of statistical linearization and lqg theory in particular the cases of perfect state measurement and incomplete and noisy measurement are addressed

control of non linear stochastic sampled data systems with non quadratic criteria by equivalent lq modelling abstract the control of non linear stochastic sampled data systems with non quadratic performance criteria is approached by development of an equivalent linear system quadratic criterion model using equivalent linearization the resulting control algorithm requires updating as the system trajectory evolves due to the dependence of the equivalent lq model on the trajectory an example illustrates the method and provides comparison with the actual optimal control and the simpler standard lq control based on neglecting the non linear and non quadratic terms altogether

some aspects of fusion in estimation theory the problem of fusing or combining various estimates to obtain a single good estimate is investigated the problem of fusion in estimation theory is addressed and several examples using common distributions in which virtually any method of fusion would be useless in approximating the random variable of interest are presented a theorem which for a very general situation shows that fusion resulting in an almost surely exact approximation is always possible is presented in particular this result addresses the situation in which the data consists of the random variable of interest corrupted by additive gaussian noise and the random variable of interest could be any second order random variable finally an example which illustrates the utility of this result is presented

brief paper an efficient sensor quantization algorithm for decentralized estimation fusion in this paper we consider the design problem of optimal sensor quantization rules quantizers and an optimal linear estimation fusion rule in bandwidth constrained decentralized random signal estimation fusion systems first we derive a fixed point type necessary condition for both optimal sensor quantization rules and an optimal linear estimation fusion rule a fixed point of an integral operation then we can motivate an iterative gauss seidel algorithm to simultaneously search for both optimal sensor quantization rules and an optimal linear estimation fusion rule without gaussian assumptions on the joint probability density function pdf of the estimated parameter and observations moreover we prove that the algorithm converges to a person by person optimal solution in the discretized scheme after a finite number of iterations it is worth noting that the new method can be applied to vector quantization without any modification finally several numerical examples demonstrate the efficiency of our method and provide some reasonable and meaningful observations how the estimation performance is influenced by the observation noise power and numbers of sensors or quantization levels

further results on the optimality of the likelihood ratio test for local sensor decision rules in the presence of nonideal channels in this paper we consider the design of local decision rules for distributed detection systems where decisions from peripheral detectors are transmitted over dependent nonideal channels under the conditional independence assumption among multiple sensor observations we show that the optimal detection performance can be achieved by employing likelihood ratio quantizers lrq as local decision rules under both the bayesian criterion and neyman pearson np criterion even for the cases where the channels between the fusion center and local sensors are dependent and noisy this work generalizes the previous work where independence among such channels was assumed a person by person optimization pbpo procedure to obtain the solution is presented along with an illustrative example

on optimal quantization of noisy sources problems in optimal multidimensional quantization of sources corrupted by noise are addressed expressions for the optimum quantizer values and the optimum quantization rule for the weighted squared error distortion measure are found and calculated for the gaussian signal in additive independent gaussian noise problem some properties of the optimum quantizer and its relations with the optimal estimator for the general problem are derived

canonical fuzzy bags and bag fuzzy measures as a basis for madm with mixed non cardinal data abstract this contribution introduces what will be called sine analysis a new approach to multiple attribute decision making madm with mixed noncardinal data this approach is based upon the notion of canonical fuzzy bags and their scalar evaluations by bag fuzzy measures

use of particle filters in an active control algorithm for noisy nonlinear structural dynamical systems the problem of active control of nonlinear structural dynamical systems in the presence of both process and measurement noises is considered the focus of the study is on the use of particle filters for state estimation in feedback control algorithms for nonlinear structures when a limited number of noisy output measurements are available the control design is done using the state dependent riccati equation sdre method the stochastic differential equations sdes governing the dynamical systems are discretized using explicit forms of ito taylor expansions the bayesian bootstrap filter and that based on sequential important sampling sis are employed for state estimation the simulation results show the feasibility of using particle filters and sdre techniques in control of nonlinear structural dynamical systems

topology for distributed inference on graphs let n decision makers collaborate to reach a decision we consider iterative distributed inference with local intersensor communication which under simplifying assumptions is equivalent to distributed average consensus we show that under appropriate conditions the topology given by the nonbipartite ramanujan graphs optimizes the convergence rate of this distributed algorithm

optimization of disturbance rejection in systems with saturating actuators an extension of the lqr lqg methodology to systems with saturating actuators referred to as slqr slqg is obtained the development is based on the method of stochastic linearization using this method and the lagrange multiplier technique a solution to the slqr slqg problem is derived this solution is given by the standard riccati equations coupled with two transcendental equations which define the variance of the signal at the input of the saturation and the lagrange multiplier associated with the quadratic performance index it is shown that under the standard stabilizability and detectability conditions these equations have a unique solution which can be found by a simple bisection algorithm when the saturation is removed these equations reduce to the standard lqr lqg solution

dynamic quantizer design for hidden markov state estimation via multiple sensors with fusion center feedback this paper considers the state estimation of hidden markov models by sensor networks the objective is to minimize the long term average of the mean square estimation error for the underlying finite state markov chain by employing feedback from the fusion center a dynamic quantization scheme for the sensor nodes is proposed and analyzed by a stochastic control approach dynamic rate allocation is also considered when the sensor nodes generate mode dependent measurements

high rate vector quantization for the neyman pearson detection of correlated processes this paper investigates the effect of quantization on the performance of the neyman pearson test it is assumed that a sensing unit observes samples of a correlated stationary ergodic multivariate process each sample is passed through an n point quantizer and transmitted to a decision device which performs a binary hypothesis test for any false alarm level it is shown that the miss probability of the neyman pearson test converges to zero exponentially as the number of samples tends to infinity assuming that the observed process satisfies certain mixing conditions the main contribution of this paper is to provide a compact closed form expression of the error exponent in the high rate regime i e when the number n of quantization levels tends to infinity generalizing previous results of gupta and hero to the case of nonindependent observations if d represents the dimension of one sample it is proved that the error exponent converges at rate n2 d to the one obtained in the absence of quantization as an application relevant high rate quantization strategies which lead to a large error exponent are determined numerical results indicate that the proposed quantization rule can yield better performance than existing ones in terms of detection error

least squares quantization in pcm it has long been realized that in pulse code modulation pcm with a given ensemble of signals to handle the quantum values should be spaced more closely in the voltage regions where the signal amplitude is more likely to fall it has been shown by panter and dite that in the limit as the number of quanta becomes infinite the asymptotic fractional density of quanta per unit voltage should vary as the one third power of the probability density per unit voltage of signal amplitudes in this paper the corresponding result for any finite number of quanta is derived that is necessary conditions are found that the quanta and associated quantization intervals of an optimum finite quantization scheme must satisfy the optimization criterion used is that the average quantization noise power be a minimum it is shown that the result obtained here goes over into the panter and dite result as the number of quanta become large the optimum quautization schemes for 2 b quanta b 1 2 cdots 7 are given numerically for gaussian and for laplacian distribution of signal amplitudes

optimal resource allocation for detection of a gaussian process using a mac in wsns we analyze a binary hypothesis testing problem built on a wireless sensor network wsn for detecting a stationary random process distributed both in space and time with a circularly symmetric complex gaussian distribution under the neyman pearson np framework using an analog scheme the sensors transmit different linear combinations of their measurements through a multiple access channel mac to reach the fusion center fc whose task is to decide whether the process is present or not considering an energy constraint on each node transmission and a limited amount of channel uses we compute the miss error exponent of the proposed scheme using large deviation theory ldt and show that the proposed strategy is asymptotically optimal when the number of sensors approaches infinity among linear orthogonal schemes we also show that the proposed scheme obtains meaningful energy saving in the low signal to noise ratio regime which is the typical scenario of wsns finally a monte carlo simulation of a 2 dimensional process in space validates the analytical results

a fuzzy bag approach to choosing the best multiattributed potential actions in a multiple judgement and non cardinal data context abstract the present work is concerned with showing how a fuzzy bag construct along with the concept of a positive outstandingness predicate and that of a strict t norm operator can be used to resolve conflicts and aggregation problems in decisions involving multiple judgements and non cardinal data it is also shown how the differential expertness degrees of the judges may be taken into account in the aggregation process the choice device proposed is decisive i e it excludes incomparability

on the optimality of the likelihood ratio test for local sensor decision rules in the presence of nonideal channels distributed detection has been intensively studied in the past in this correspondence we consider the design of local decision rules in the presence of nonideal transmission channels between the sensors and the fusion center under the conditional independence assumption among multiple sensor observations we show that the optimal local decisions that minimize the error probability at the fusion center amount to a likelihood ratio test lrt given a particular constraint on the fusion rule this constraint turns out to be quite general and is easily satisfied for most sensible fusion rules a design example using a parallel sensor fusion structure with binary symmetric channels bscs between local sensors and the fusion center is given to illustrate the usefulness of the result in obtaining optimal thresholds for local sensor observations the study that incorporates the transmission channel in the sensor system design may have potential applications in the emerging field of wireless sensor networks

on some unresolved issues in finding optimum distributed detection schemes optimum distributed detection under the neyman pearson np criterion is considered for a general case with possibly dependent observations from sensor to sensor the focus is on the parallel architecture new necessary conditions are presented that relate the threshold used in the np optimum fusion rule to those used in the np optimum sensor rules these results clearly illustrate that the necessary conditions for np optimality have exactly the same form as those for bayes optimality based on these conditions a new algorithm for finding np optimum distributed detection schemes is developed the algorithm allows randomization at the fusion center which we show is generally needed to achieve optimality the algorithm allows one to attempt to optimize the fusion rule along with the sensor rules or to find the best schemes among those using each of a set of fixed possible fusion rules

a new framework for distributed detection with conditionally dependent observations distributed detection with conditionally dependent observations is known to be a challenging problem in decentralized inference this paper attempts to make progress on this problem by proposing a new framework for distributed detection that builds on a hierarchical conditional independence model through the introduction of a hidden variable that induces conditional independence among the sensor observations the proposed model unifies distributed detection with dependent or independent observations this new framework allows us to identify several classes of distributed detection problems with dependent observations whose optimal decision rules resemble the ones for the independent case the new framework induces a decoupling effect on the forms of the optimal local decision rules for these problems much in the same way as the conditionally independent case this is in sharp contrast to the general dependent case where the coupling of the forms of local sensor decision rules often renders the problem intractable such decoupling enables the use of for example the person by person optimization approach to find optimal local decision rules two classical examples in distributed detection with dependent observations are reexamined under this new framework detection of a deterministic signal in dependent noises and detection of a random signal in independent noises

rate region of the quadratic gaussian two encoder source coding problem we determine the rate region of the quadratic gaussian two encoder source coding problem this rate region is achieved by a simple architecture that separates the analog and digital aspects of the compression furthermore this architecture requires higher rates to send a gaussian source than it does to send any other source with the same covariance our techniques can also be used to determine the sum rate of some generalizations of this classical problem our approach involves coupling the problem to a quadratic gaussian ldquoceo problem rdquo

encoding of correlated observations an important class of engineering problems involves sensing an environment and making estimates based on the phenomena sensed in the traditional model of this problem the sensors observations are available to the estimator without alteration there is growing interest in em distributed sensing systems in which several observations are communicated to the estimator over channels of limited capacity the observations must be separately encoded so that the target can be estimated with minimum distortion two questions are addressed for a special case of this problem wherein there are two sensors which observe noisy data and communicate with a single estimator 1 if the encoder is unlimited in complexity what communication rates and distortions can be achieved 2 if the encoder must be a quantizer a mapping of a single observation sample into a digital output how can it be designed for good performance the first question is treated by the techniques of information theory it is proved that a given combination of rates and distortion is achievable if there exist degraded versions of the observations that satisfy certain formulas the second question is treated by two approaches in the first the outputs of the quantizers undergo a second stage of encoding which exploits their correlation to reduce the output rate algorithms which design the second stage are presented and tested the second approach is based on the em distributional distance a measure of dissimilarity between two probability distributions an algorithm to modify a quantizer for increased distributional distance is derived and tested

resource scalable joint source channel map and mmse estimation of multiple descriptions a joint source channel multiple description jsc md framework for signal estimation and communication in resource constrained lossy networks is presented to keep the encoder complexity at a minimum a signal is coded by a multiple description quantizer mdq with neither entropy nor channel coding the code diversity of mdq and the path diversity of the network are exploited by decoders to combat transmission errors a key design objective is resource scalability powerful nodes in the network can perform jsc md estimation under the criteria of maximum a posteriori probability map or minimum mean square error mmse while primitive nodes resort to simpler md decoding all working with the same mdq code the application of jsc md to distributed estimation of hidden markov models in a sensor network is demonstrated the proposed jsc md map estimator is an algorithm of the longest path in a weighted directed acyclic graph while the jsc md mmse decoder is an extension of the well known forward backward algorithm to multiple descriptions both algorithms simultaneously exploit the source memory the redundancy of the fixed rate mdq and the inter description correlations they outperform the existing hard decision mdq decoders by large margins up to 8 db for gaussian markov sources the complexity of jsc md distributed map sequence estimation can be made as low as that of typical single description viterbi type algorithms

extra an expert system for multicriteria decision making abstract this paper presents an expert system approach to a classical decision making problem aiding in the selection of a preferred action from a list of alternatives evaluated on several criteria in outranking methods the non compensatory aggregation procedure uses an importance relation on criteria subsets in extra the decision maker s knowledge on this importance relation are treated purely formally without converting them into weights therefore each outranking relation may be explained in terms of the input informations and of some simple axioms finally the multicriteria analysis process is illustrated and studied on a real world problem the media selection

quantization for maximin are in distributed estimation we consider the design of optimal quantizers for the distributed estimation of a deterministic parameter in particular we design deterministic scalar quantizers to maximize the minimum asymptotic relative efficiency are between quantized and unquantized ml estimators we first design identical quantizers using the class of score function quantizers sfq we show that the structure of sfqs generally depend on the parameter value but can be expressed as thresholds on the sufficient statistic for a large class of distributions we provide a convergent iterative algorithm to obtain the best sfq that maximizes the minimum are for distributions of that class we compare the performance of the optimal sfq with a general quantizer designed without making any restrictions on the structure this general quantizer is hard to implement due to lack of structure but is optimal if the iterative design algorithm does not encounter local minima through numerical simulations we illustrate that the two quantizers designed are identical in other words the optimal quantizer structure is that of an sfq for a distributed estimation setup designing identical quantizers is shown to be suboptimal we therefore propose a joint multiple quantizer design algorithm based on a person by person optimization technique employing the sfq structure using numerical examples we illustrate the gain in performance due to designing nonidentical quantizers

combining and updating of local estimates and regional maps along sets of one dimensional tracks in this paper we consider the problem of combining and updating estimates that may have been generated in a distributed fashion or may represent estimates generated at different times of the same process sample path the first of these cases has applications in decentralized estimation while the second has applications in updating maps of spatially distributed random quantities given measurements along several tracks the method of solution for the second problem uses the result of the first and the similarity in the formulation and solution of these problems emphasizes the conceptual similarity between many problems in decentralized control and in the analysis of random fields

fusing dependent decisions for hypothesis testing with heterogeneous sensors in this paper we consider a binary decentralized detection problem where the local sensor observations are quantized before their transmission to the fusion center sensor observations and hence their quantized versions may be heterogeneous as well as statistically dependent a composite binary hypothesis testing problem is formulated and a copula based generalized likelihood ratio test glrt based fusion rule is derived given that the local sensors are uniform multilevel quantizers an alternative computationally efficient fusion rule is also designed which involves injecting a deliberate random disturbance to the local sensor decisions before fusion although the introduction of external noise causes a reduction in the received signal to noise ratio snr it is shown that the proposed approach can result in a detection performance comparable to the glrt detector without external noise especially when the number of quantization levels is large

space time code design for mimo detection based on kullback leibler divergence the focus of the paper is on the design of space time codes for a general multiple input multiple output detection problem when multiple observations are available at the receiver the figure of merit used for optimization purposes is the convex combination of the kullback leibler divergences between the densities of the observations under the two hypotheses and different system constraints are considered this approach permits to control the average sample number i e the time for taking a decision in a sequential probability ratio test and to asymptotically minimize the probability of miss in a likelihood ratio test the solutions offer an interesting insight in the optimal transmit policies encapsulated in the rank of the code matrix which rules the amount of diversity to be generated as well as in the power allocation policy along the active eigenmodes a study of the region of achievable divergence pairs whose availability permits optimization of a wide range of merit figures is also undertaken a set of numerical results is finally given in order to analyze and discuss the performance and validate the theoretical results

an lqr lqg theory for systems with saturating actuators an extension of the lqr lqg methodology to systems with saturating actuators referred to as slqr slqg where s stands for saturating is obtained the development is based on the method of stochastic linearization whereby the saturation is replaced by a gain calculated as a function of the variance of the signal at its input using the stochastically linearized system and the lagrange multiplier technique solutions of the slqr slqg problems are derived these solutions are given by standard riccati and lyapunov equations coupled with two transcendental equations which characterize both the variance of the signal at the saturation input and the lagrange multiplier associated with the constrained minimization problem it is shown that under standard stabilizability and detectability conditions these equations have a unique solution which can be found by a simple bisection algorithm when the level of saturation tends to infinity these equations reduce to their standard lqr lqg counterparts in addition the paper investigates the properties of closed loop systems with slqr slqg controllers and saturating actuators in this regard it is shown that slqr slqg controllers ensure semi global stability by appropriate choice of a parameter in the performance criterion finally the paper illustrates the techniques developed by a ship roll damping problem

distributed estimation algorithms for nonlinear systems in this paper we consider the problem of combining the local conditional distributions of a random variable which have been generated by local observers having access to their private information sufficient statistics for the local distributions are communicated to a coordinator who attempts to reconstruct the global centralized distribution using only the communicated statistics we obtain a distributed processing algorithm which recovers exactly the centralized conditional distribution the results can be applied in designing distributed hypothesis testing algorithms for event driven systems

a distributed m ary hypothesis testing problem with correlated observations the distributed m ary hypothesis testing problem of detecting one of m sub 0 events by an n 1 person hierarchical team when the observations are correlated is examined in this problem each of the n subordinate decision makers dms transmits one of a prespecified set of messages based on their data to a primary decision maker who in turn combines the messages with his or her own data to make the final team decision the necessary conditions for the optimal decision rules of the dms are derived a nonlinear gauss seidel iterative algorithm is developed for the person by person optimal decision rules and its monotonic convergence to the person by person optimum is established a fast approximation algorithm is proposed for computing certain conditional probabilities arising in the person by person optimal decision rules the algorithms are illustrated with several examples and implications for distributed organizational designs are pointed out

a multi attribute method for choosing among potential alternatives with ordinal evaluation abstract some concepts are introduced with a view to dealing with the problem of choosing the best potential alternative s in a multi attribute ordinal data context we assume that we know the possibilistic weights of attributes and ordinal evaluations of each potential alternative on all attributes we define what we refer to as positive negative coalitions of attributes and positiveness negativeness numerical bags associated with each potential alternative we also define what will be called positional advantage operators and we describe how all these concepts are used to lay the foundation for the choice method appearing in this paper

binary linear quasi perfect codes are normal whether quasi perfect codes are normal is addressed let c be a code of length n dimension k covering radius r and minimal distance d it is proved that c is normal if d or 2r 1 hence all quasi perfect codes are normal consequently any n k r binary linear code with minimal distance d or 2r 1 is normal

on the optimality of finite level quantizations for distributed signal detection distributed multiple sensor detection problems with quantized observations are investigated for cases of nonbinary hypothesis and possibly statistically dependent observations from sensor to sensor conditioned on the hypothesis the observations available at each sensor are quantized to produce a multiple digit sensor decision which is sent to a fusion center at the fusion center the sensor decisions are combined to form a final decision using a predetermined fusion rule first it is demonstrated that there is a maximum number of digits that should be used to communicate the sensor decision from a given sensor to the fusion center this maximum is based on the number of digits used to communicate the decisions from all the other sensors to the fusion center if more than this maximum number of digits is used the performance of the optimum scheme will not be improved in some special cases of great interest the upper bound on the number of digits that should be used can be made significantly smaller secondly the optimum way to allocate a fixed overall number of digits across sensors is investigated illustrative numerical results are also presented in this correspondence

more binary covering codes are normal it is shown that every optimal binary code with covering radius r 1 is normal this parity proves a conjecture of cohen lobstein and sloane 1986 it is also proved that codes with minimal distance 2r or 2r 1 are normal a generalization of frankl s construction 1987 of abnormal codes is given

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

a framework for multiset merging information fusion is a research area that investigates how to combine information provided by independent sources into one piece of information several aspects of this topic have already been studied leading to amongst others aggregation operators in bounded lattices and merge functions of propositional belief bases in this paper information fusion is investigated in the context of coreferent objects which are pieces of data in an information system that refer to the same real world entity the fundamental operator in our approach is a merge function that maps a multiset of coreferent objects onto a single object which is called the solution we investigate the specific case where objects themselves are multisets which can be applied to problems such as multi document summarization mds and fusion of duplicate graphs e g xml documents our approach involves the definition of quality measures that express the correctness and the completeness of a given solution we show how a solution can be found that optimizes a balance between correctness and completeness merge functions that result in such a solution are called f optimal merge functions and we investigate their properties

ranking alternatives using fuzzy numbers we investigate the problem of employing expert opinion to rank alternatives across a set of criteria the experts use fuzzy numbers to express their preferences and we employ fuzzy arithmetic to compute an issue s fuzzy ranking this leads to a partition of the alternatives into sets h1 h2 where h1 contains the highest ranked issues h2 has all the second highest ranked alternatives etc the total ranking process is shown to possess a number of important properties an example is presented to illustrate the method

unfair coins and necessity measures towards a possibilistic interpretation of histograms this short note defines a bijective mapping which turns a probability measure into a possibility measure this transformation has intuitive grounds especially the converse mapping corresponds to the usual assignment of identical probability values to elementary events of a given set when no information is available

distributed adaptive quantization for wireless sensor networks from delta modulation to maximum likelihood we consider distributed parameter estimation using quantized observations in wireless sensor networks wsns where due to bandwidth constraint each sensor quantizes its local observation into one bit of information a conventional fixed quantization fq approach which employs a fixed threshold for all sensors incurs an estimation error growing exponentially with the difference between the threshold and the unknown parameter to be estimated to address this difficulty we propose a distributed adaptive quantization aq approach which with sensors sequentially broadcasting their quantized data allows each sensor to adaptively adjust its quantization threshold three aq schemes are presented 1 aq fs that involves distributed delta modulation dm with a fixed stepsize 2 aq vs that employs dm with a variable stepsize and 3 aq ml that adjusts the threshold through a maximum likelihood ml estimation process the ml estimators associated with the three aq schemes are developed and their corresponding cramer rao bounds crbs are analyzed we show that our 1 bit aq approach is asymptotically optimum yielding an asymptotic crb that is only pi 2 times that of the clairvoyant sample mean estimator using unquantized observations

the sir method a superiority and inferiority ranking method for multiple criteria decision making abstract in this paper a superiority and inferiority ranking sir method is proposed this new method uses two types of information the superiority and the inferiority information to derive two types of flows the superiority flow and the inferiority flow by which the set of alternatives are ranked partially or completely relationships between the sir method and some of the classical multiple criteria decision making mcdm methods such as saw topsis and promethee are explored it is proved that the sir method is a significant extension of the well known promethee method

linear precoders for the detection of a gaussian process in wireless sensors networks we investigate the performance of neyman pearson detection of a stationary gaussian process in noise using a large wireless sensor network wsn in our model each sensor compresses its observation sequence using a linear precoder and a final decision is taken by a fusion center fc based on the compressed information two families of precoders are studied random i i d precoders and orthogonal precoders we analyse their performance under a regime where both the number of sensors k and the number of samples n per sensor tend to infinity at the same rate that is k n c 0 1 contributions are as follows 1 using results from random matrix theory and large toeplitz matrices we prove that when the above families of precoders are used the miss probability of the neyman pearson detector converges exponentially to zero closed form expressions of the corresponding error exponents are derived 2 in particular we propose a practical orthogonal precoding strategy the principal frequencies strategy pfs which achieves the best error exponent among all orthogonal strategies and which requires very little signaling overhead between the central processor and the nodes of the network 3 when the pfs is used a simplified low complexity testing procedure can be implemented at the fc we show that the proposed suboptimal test enjoys the same error exponent as the neyman pearson test which indicates a similar asymptotic behavior of the performance we illustrate our findings by numerical experiments on several examples

bbtopsis a bag based technique for order preference by similarity to ideal solution abstract this contribution explores the way of accomplishing a topsis ranking of various submitted variants taking into account a our newly developed notions of variant superiority inferiority and noninferiority multiattribute canonical fuzzy bags defined on attributes and b making use of bag metrics to compute the relative closeness of the different variants to an ideal solution in particular we prove the existence and the uniqueness of a bag metric fulfilling a number of interesting properties

statistical inference under multiterminal data compression this paper presents a survey of the literature on the information theoretic problems of statistical inference under multiterminal data compression with rate constraints significant emphasis is put on problems 1 multiterminal hypothesis testing 2 multiterminal parameter estimation and 3 multiterminal pattern classification in either case of positive rates or zero rates in addition the paper includes three new results i e the converse theorems for all problems of multiterminal hypothesis testing multiterminal parameter estimation and multiterminal pattern classification at the zero rate

design of quantizers for decentralized estimation systems the authors consider parameter estimation in decentralized systems with distributed processors they restrict the local processors to be quantizers and consider the optimal design of the systems to minimize the estimation error they present necessary conditions for the optimal system based on the bayes distortion functions and fisher s information the numerical results compare the resulting quantizers obtained by different distortion criteria

iterative procedures in application of the lqg approach to control problems for polynomial stochastic systems the problem of the determination of quasi optimal control for polynomial stochastic dynamic systems using the lqg technique and linearization methods is considered in this paper we present some sufficient conditions of convergence for iterative procedures used in evaluation of quasi optimal control scalar and vector systems are treated separately obtained results are illustrated by numerical examples

fuzzy bags and applications abstract based upon r r yager s concept of bags 1 a definition of fuzzy bags and corresponding operations such as peak value grade of concentration as well as the relative cardinality is introduced here several examples are also given to show the usefulness of fuzzy bags

design of scalable decoders for sensor networks via bayesian network learning minimum mean square error mmse decoding in a large scale sensor network which employs distributed quantization is considered given that the computational complexity of the optimal decoder is exponential in the network size we present a framework based on bayesian networks for designing a near optimal decoder whose complexity is only linear in network size hence scalable in this approach a complexity constrained factor graph which approximately represents the prior joint distribution of the sensor outputs is obtained by constructing an equivalent bayesian network using the maximum likelihood ml criterion the decoder executes the sum product algorithm on the simplified factor graph our simulation results have shown that the scalable decoders constructed using the proposed approach perform close to optimal with both gaussian and non gaussian sensor data

robust distributed maximum likelihood estimation with dependent quantized data in this paper we consider the distributed maximum likelihood estimation mle with dependent quantized data under the assumption that the structure of the joint probability density function pdf is known but it contains unknown deterministic parameters the parameters may include different vector parameters corresponding to marginal pdfs and parameters that describe the dependence of observations across sensors since mle with a single quantizer is sensitive to the choice of thresholds due to the uncertainty of pdf we concentrate on mle with multiple groups of quantizers which can be determined by the use of prior information or some heuristic approaches to fend off against the risk of a poor outlier quantizer the asymptotic efficiency of the mle scheme with multiple quantizers is proved under some regularity conditions and the asymptotic variance is derived to be the inverse of a weighted linear combination of fisher information matrices based on multiple different quantizers which can be used to show the robustness of our approach as an illustrative example we consider an estimation problem with a bivariate non gaussian pdf that has applications in distributed constant false alarm rate cfar detection systems simulations show the robustness of the proposed mle scheme especially when the number of quantized measurements is small

a note on distributed estimation and sufficiency in relation to distributed parameter estimation the notion of local and global sufficient statistics is introduced it is shown that when a sufficiency condition is satisfied by the probability distribution of a random sample a global sufficient statistic is obtainable as a function of local sufficient statistics several standard distributions satisfy the said sufficiency condition

rate distortion theory for gaussian multiterminal source coding systems with several side informations at the decoder in this paper we consider the separate coding problem for l 1 correlated gaussian memoryless sources we deal with the case where l sources work as partial side information at the decoder for the reconstruction of the remaining source the determination problem of the rate distortion region for this system is the so called many help one problem and it has been known as a highly challenging problem for almost 20 years in this paper we give a partial solution to this problem we determine the rate distortion region in the case where the l sources working as partial side information are conditionally independent if the remaining source we wish to reconstruct is given the additive white gaussian noise ceo problem is a special case of this we also discuss the relation of the result previous results of ours

distributed signal detection under the neyman pearson criterion a procedure for finding the neyman pearson optimum distributed sensor detectors for cases with statistically dependent observations is described this is the first valid procedure we have seen for this case this procedure is based on a theorem proven in this paper these results clarify and correct a number of possibly misleading discussions in the existing literature cases with networks of sensors in fairly general configurations are considered along with cases where the sensor detectors make multiple bit sensor decisions

explicit correlation coefficients among random variables ranks and magnitude ranks in this correspondence we address the derivation of joint distributions and correlation coefficients for seven pairs of statistics used commonly in a number of signal detection schemes the upper and lower bounds of the correlation coefficients are obtained and relationships among the correlation coefficients are derived explicit values of the correlation coefficients evaluated for some specific noise distributions are shown for easy reference

distributed estimation of gaussian correlations we study a distributed estimation problem in which two remotely located parties alice and bob observe an unlimited number of i i d samples corresponding to two different parts of a random vector alice can send k bits on average to bob who in turn wants to estimate the cross correlation matrix between the two parts of the vector in the case where the parties observe jointly gaussian scalar random variables with an unknown correlation rho we obtain two constructive and simple unbiased estimators attaining a variance of 1 rho 2 2k ln 2 which coincides with a known but non constructive random coding result of zhang and berger we extend our approach to the vector gaussian case which has not been treated before and construct an estimator that is uniformly better than the scalar estimator applied separately to each of the correlations we then show that the gaussian performance can essentially be attained even when the distribution is completely unknown this in particular implies that in the general problem of distributed correlation estimation the variance can decay at least as o 1 k with the number of transmitted bits this behavior however is not tight we give an example of a rich family of distributions for which local samples reveal essentially nothing about the correlations and where a slightly modified estimator attains a variance of 2 omega k

distributed estimation and quantization an algorithm is developed for the design of a nonlinear n sensor distributed estimation system subject to communication and computation constraints the algorithm uses only bivariate probability distributions and yields locally optimal estimators that satisfy the required system constraints it is shown that the algorithm is a generalization of the classical lloyd max results

on quantizer design for distributed bayesian estimation in sensor networks we consider the problem of distributed estimation under the bayesian criterion and explore the design of optimal quantizers in such a system we show that for a conditionally unbiased and efficient estimator at the fusion center and when local observations have identical distributions it is optimal to partition the local sensors into groups with all sensors within a group using the same quantization rule when all the sensors use identical number of decision regions use of identical quantizers at the sensors is optimal when the network is constrained by the capacity of the wireless multiple access channel over which the sensors transmit their quantized observations we show that binary quantizers at the local sensors are optimal under certain conditions based on these observations we address the location parameter estimation problem and present our optimal quantizer design approach we also derive the performance limit for distributed location parameter estimation under the bayesian criterion and find the conditions when the widely used threshold quantizer achieves this limit we corroborate this result using simulations we then relax the assumption of conditionally independent observations and derive the optimality conditions of quantizers for conditionally dependent observations using counter examples we also show that the previous results do not hold in this setting of dependent observations and therefore identical quantizers are not optimal index terms

a 2 sprt based approach to multiple model hypothesis testing for multi distribution detection this paper presents an approach to multiple model hypothesis testing mmht based on 2 sprt 2 mmsrpt for detecting unknown events that may have multiple possible distributions the sequential probability ratio test sprt based mmht method mmsprt is promising because of its efficiency and theoretical validity however it may suffer from sprt s lack of an upper bound on its stopping time especially in the mis specified case the proposed 2 mmsprt algorithm not only copes with this problem but also is in a setting that can provide efficient detection in the sense of minimizing the maximum expected sample size subject to error probability constraints specifically we prove the theoretical validity of 2 sprt for the problem of testing hypotheses with multivariate normal densities moreover we present a technique of forced independence and identical distribution i i d to map the non i i d likelihood ratio sequence to an i i d one which enables us to apply the sprt and 2 sprt effectively to the dynamic case under the linear gaussian assumption with a non identical distribution also 2 mmsprt s detection efficiency under some assumptions approximations is verified performance of 2 mmsprt is evaluated for signal detection and model set selection problems in several scenarios simulation results demonstrate the detection efficiency of the proposed 2 mmsprt compared with the mmsprt and some traditional tests

diversity integration tradeoffs in mimo detection in this paper a multiple input multiple output mimo detection problem is considered at first we derive the generalized likelihood ratio test glrt for arbitrary transmitted signals and arbitrary time correlation of the disturbance then we investigate design criteria for the transmitted waveforms in both power unlimited and power limited systems and we derive closed form formulas for the probability of false alarm and the detection probability finally we study the interplay among the rank of the optimized space time code i e the number of linearly independent transmitted waveforms the number of transmit diversity paths generated in the signal space and the amount of energy integrated along each path the results confirm that there is an inherent tradeoff between diversity and integration and that no uniformly optimum waveform design strategy exists

dynamic decentralized sequential detection under uniformly distributed observations decentralized sequential detection problems with communicating detectors are solved under the assumptions that the observations are independent and uniformly distributed and that decision errors are uniformly penalized for the cases of one step delayed sequential and nonsequential signaling explicit decision rules are proposed and exact conditions for their member by member optimality are derived these decision rules approximate high performance threshold rules with very strict thresholds when decision errors are heavily penalized

brief an observer for systems with nonlinear output map a nonlinear observer with the feedback gain weighted by the sensitivity of the output with respect to the state is developed for systems with nonlinear output map the observer can be obtained from the extended kalman filter by a special choice of time varying weighting matrices it is shown that the estimation error dynamics are asymptotically stable and a region of attraction is derived the observer is applied to the top blown converter process for estimating the content of impurities in the liquid metal using plant data from the converter at ssab oxelosund ab the observer is shown to provide accurate estimates of the carbon content

the good bad and ugly distributed detection of a known signal in dependent gaussian noise most results about quantized detection rely strongly on an assumption of independence among random variables with this assumption removed little is known thus in this paper bayes optimal binary quantization for the detection of a shift in mean in a pair of dependent gaussian random variables is studied this is arguably the simplest meaningful problem one could consider if results and rules are to be found they ought to make themselves plain in this problem for certain problem parametrizations meaning the signals and correlation coefficient optimal quantization is achievable via a single threshold applied to each observation the same as under independence in other cases one observation is best ignored or is quantized with two thresholds neither behavior is seen under independence further and again in distinction from the case of independence it is seen that in certain situations an xor fusion rule is optimal and in these cases the implied decision rule is bizarre the analysis is extended to the multivariate gaussian problem

extremal properties of likelihood ratio quantizers m hypotheses and a random variable y with a different probability distribution under each hypothesis are considered a quantizer is applied to form a quantized random variable gamma y the extreme points of the set of possible probability distributions of gamma y as gamma ranges over all quantizers is characterized optimality properties of likelihood ratio quantizers are established for a very broad class of quantization problems including problems involving the maximization of an ali silvey 1966 distance measure and the neyman pearson variant of the decentralized detection problem

relational systems of preference with one or more pseudo criteria some new concepts and results this paper proposes new concepts and new results which could lead to a more realistic preference modeling than in classical decision theory sections 1 3 present four fundamental situations of preferences their combinations and the concept of relational system of preferences in 4 a particular case of relational system of preference is studied it is associated with the concept of pseudo criterion derived from the classical concept of criterion by adjunction of two thresholds some results are given generalizing the properties of such well known structures as complete preorders and semiorders sections 5 and 6 emphasize the possibilities given by the preceding concepts to take the imprecisions irresolutions and incomparabilities appearing in every concrete problem where several criteria must be considered into account

distributed estimation constraints on the choice of the local models the following estimation problem is considered a coordinator must reconstruct the global probability density of a nonlinear random process conditioned on the noise corrupted observation history the coordinator can only access the local probability density produced by local processing of the observation history using a local model different from the process model it is shown that if the local model satisfies an algebraic constraint the coordinator can reconstruct the same conditional density of the state process as the one obtained if the observations were processed using the coordinator process model it is assumed that the random process is a nonlinear stochastic differential equation driven by a brownian motion and the observation process is corrupted by additive brownian motion which is identically modeled by the coordinator and the local processor

asymptotic performance of a distributed detection system in correlated gaussian noise the authors consider the detection of a constant signal in noise with a large set of geographically dispersed sensors the noise at the sensors is correlated gaussian two correlation models are considered one where the correlation coefficient between any two sensors decreases geometrically as the sensor separation increases and one in which the correlation coefficient between any two sensors is a constant for both correlation models the asymptotic as the number of sensors becomes large performances of a distributed detection system and a central system are examined

preference relations on actions and criteria in multicriteria decision making abstract let a be a finite set of feasible actions which are judged following several criteria an outranking relation is defined on a by considering preference of the decision maker as a weak order on each criterion and the relation among criteria as a semi order on the given set of criteria several ways of constructing outranking relations have been proposed one of the most popular introduced by b roy for instance electre s is based on the use of weights related to criteria in our approach the knowledge of weights is replaced by the existence of a semi order a case study is developed it deals with a computer selection problem

decentralized estimation with dependent gaussian observations this paper considers decentralized estimation with correlated noises under the bayesian framework for a tandem network with correlated additive gaussian noises we establish that threshold quantizers on local observations are optimal in the sense of maximizing fisher information at the fusion center this is true despite the fact that subsequent estimators may differ at the fusion center depending on the statistical distribution of the parameter to be estimated in addition it is always beneficial to have the better sensor i e the one with higher signal to noise ratio serve as the fusion center in a tandem network finally we identify different correlation regimes in terms of their impact on the estimation performance these include the well known case where negatively correlated noise benefits estimation performance as it facilitates noise cancellation as well as two distinct regimes with positively correlated noises

note a preference ranking organisation method the promethee method for multiple criteria decision making principles for a new family of outranking methods are given the main aim of the proposed promethee approach is to be as easily understood as possible by the decision maker it is based on extensions of the notion of criterion six possible extensions are considered these extensions can easily be identified by the decision maker because the parameters to be defined at most 2 have an economic significance a valued outranking graph is constructed by using a preference index two possibilities are considered to solve the ranking problem by using this valued graph promethee i provides a partial preorder and promethee ii a total preorder on the set of the possible actions

a unified approach for encoding clean and noisy sources by means of waveform and autoregressive model vector quantization data compression by vector quantization is considered for sources which have been degraded by noise it is shown that by appropriately modifying the given distortion measure the problem becomes a standard quantization problem for the noisy source and the modified distortion measure for the special case of sources corrupted by statistically independent additive noise the authors provide sufficient conditions on the original distortion measure and probability distributions of the source and the noise for convergence of the generalized lloyd algorithm in designing the quantizers the results are specialized to waveform and autoregressive model vector quantization using the weighted quadratic and the itakura saito distortion measures respectively

closed form error exponent for the neyman pearson fusion of dependent local decisions in a one dimensional sensor network we consider a distributed detection system formed by a large number of local detectors and a data fusion center that performs a neyman pearson fusion of the binary quantizations of the sensor observations in the analyzed two stage detection system the local decisions are taken with no kind of cooperation among the devices and they are transmitted to the fusion center over an error free parallel access channel in addition the sensors are randomly deployed along a straight line and the corresponding sensor spacings are drawn independently from a common probability density function pdf for both hypothesis h0 and h1 depending on the correlation structure of the observed phenomenon the local decisions might be dependent in the case of being dependent their correlation structure is modelled with a one dimensional markov random field with nearest neighbor dependency and binary state space under this scenario we first derive a closed form error exponent for the neyman pearson fusion of the local decisions when the involved data fusion center only knows the distribution of the sensor spacings second based on a single parameter that captures the mean correlation strength among the local decisions some analytical properties of the error exponent are investigated finally we develop a physical model for the conditional probabilities of the markov random fields that might be present under each hypothesis using this model we characterize the error exponent for two well known models of the sensor spacing i equispaced sensors with failures and ii exponentially spaced sensors with failures