generalized bayesian information criterion for source enumeration in array processing we investigate the problem of enumerating source signals impinging on an array of sensors in an information theoretic framework the conventional bayesian information criterion bic does not yield satisfactory performance for this problem because it only considers the density of the observations in order to remedy the limitations of the bic we propose a generalized bayesian information criterion gbic rule by incorporating the density of the sample eigenvalues or corresponding statistics such a density contains extra information and complements the density of the observations in constructing the gbic as a result two different expressions for the gbic are suggested simulation results validate the superiority of the proposed gbic over the conventional bic in terms of correctly determining the number of sources while their computational costs are comparable

lagrangean decomposition a model yielding stronger lagrangean bounds given a mixed integer programming problem with two matrix constraints it is possible to define a lagrangean relaxation such that the relaxed problem decomposes additively into two subproblems each having one of the two matrices of the original problem as its constraints there is one lagrangean multiplier per variable we prove that the optimal value of this new lagrangean dual dominates the optimal value of the lagrangean dual obtained by relaxing one set of constraints and give a necessary condition for a strict improvement we show on an example that the resulting bound improvement can be substantial we show on a complex practical problem how lagrangean decomposition may help uncover hidden special structures and thus yield better solution methodology

the sample average approximation method for stochastic discrete optimization in this paper we study a monte carlo simulation based approach to stochastic discrete optimization problems the basic idea of such methods is that a random sample is generated and the expected value function is approximated by the corresponding sample average function the obtained sample average optimization problem is solved and the procedure is repeated several times until a stopping criterion is satisfied we discuss convergence rates stopping rules and computational complexity of this procedure and present a numerical example for the stochastic knapsack problem

detection of signals by information theoretic criteria a new approach is presented to the problem of detecting the number of signals in a multichannel time series based on the application of the information theoretic criteria for model selection introduced by akaike aic and by schwartz and rissanen mdl unlike the conventional hypothesis testing based approach the new approach does not requite any subjective threshold settings the number of signals is obtained merely by minimizing the aic or the mdl criteria simulation results that illustrate the performance of the new method for the detection of the number of signals received by a sensor array are presented

a multistage representation of the wiener filter based on orthogonal projections the wiener filter is analyzed for stationary complex gaussian signals from an information theoretic point of view a dual port analysis of the wiener filter leads to a decomposition based on orthogonal projections and results in a new multistage method for implementing the wiener filter using a nested chain of scalar wiener filters this new representation of the wiener filter provides the capability to perform an information theoretic analysis of previous basis dependent reduced rank wiener filters this analysis demonstrates that the cross spectral metric is optimal in the sense that it maximizes mutual information between the observed and desired processes a new reduced rank wiener filter is developed based on this new structure which evolves a basis using successive projections of the desired signal onto orthogonal lower dimensional subspaces the performance is evaluated using a comparative computer analysis model and it is demonstrated that the low complexity multistage reduced rank wiener filter is capable of outperforming the more complex eigendecomposition based methods

mmse based mdl method for robust estimation of number of sources without eigendecomposition it is well known that the conventional eigenvalue based minimum description length mdl approach for source number estimation suffers from high computational load and performs optimally only in the presence of spatially and temporally white noise to improve the robustness of the mdl methodology we propose to utilize the minimum mean square error mmse of the multistage wiener filter to calculate the required description length for encoding the observed data instead of relying on the eigenvalues of the data covariance matrix as there is no need to calculate the covariance matrix and its eigenvalue decomposition our derived mmse based mdl mmdl method is also more computationally efficient than the traditional counterparts numerical examples are included to demonstrate the robustness of the mmdl detector in nonuniform noise

a parametric method for determining the number of signals in narrow band direction finding a novel and more accurate method to determine the number of signals in the multisource direction finding problem is developed the information theoretic criteria of y yin and p krishnaiah 1988 are applied to a set of quantities which are evaluated from the log likelihood function based on proven asymptotic properties of the maximum likelihood estimation these quantities have the properties required by the criteria since the information theoretic criteria use these quantities instead of the eigenvalues of the estimated correlation matrix this approach possesses the advantage of not requiring a subjective threshold and also provides higher performance than when eigenvalues are used simulation results are presented and compared to those obtained from the nonparametric method given by h wax and t kailath 1985

necessary and sufficient conditions for optimal offers in electricity markets in this paper we consider the optimal policy for a generator offering power into a wholesale electricity market operating under a pool arrangement anderson and philpott math oper res 27 2002 pp 82 100 recently discussed necessary conditions for an optimal offer curve when there is uncertainty in the demand and in the behavior of other participants in the market they show that the objective function in these circumstances can be expressed as a line integral along the offer curve of a profit function integrated with respect to a market distribution function in this paper we prove the existence of an optimal offer stack and we extend the analysis of math oper res 27 2002 pp 82 100 to include necessary conditions of a higher order in the presence of horizontal and or vertical sections in an offer curve finally we establish sufficient conditions for an offer curve to be locally optimal

on the differentiability of lipschitz besov functions lr and ordinary differentiability is proved for functions in the lipschitz besov spaces b q 1 0 using certain maximal operators measuring smoothness these techniques allow also the study of lacunary directional differentiability and of tangential convergence of poisson integrals

analysis of the performance and sensitivity of eigendecomposition based detectors a new framework is presented for the analysis of the performance of detection methods such as aic and mdl which are based on the eigenvalues of the sample covariance matrix it is shown that theoretical analysis of the probabilities of overestimation and underestimation can be much more conveniently carried out via a proposed particularly simple sequence of statistics also the breakdown of these detection methods in the presence of model nonidealities is explored by theory simulations and experimentation with real array data for example theoretical arguments are given to demonstrate the high degree of sensitivity of the detectors to unknown deviations of the noise from whiteness

on certain maximal functions and approach regions if f e l ir and u x y is the poisson integral of j a classical theorem of fatou 2 asserts that u has nontangential limits almost everywhere on r littlewood 5 and later zygmund 9 showed that this conclusion is false if nontangential approach is replaced by approach along translates of a curve which approaches the boundary tangentially in this paper we find a necessary and sufficient condition on an approach region for the associated maximal function to be appropriately bounded it then turns out that there are many approach regions which are not contained in any nontangential region but for which the conclusions of fatou s theorem remain true suppose q c ir has the property that whenever xi u e b and whenever x x y y it follows that x v e q then the maximal function associated to such a set is bounded if and only if the cross sectional measure at height y is bounded by a constant times y we also study regions where the cross sectional area is larger than y we introduce a modified maximal function which is again bounded this result leads to a simple proof of the boundedness of certain tangential maximal functions of poisson integrals of potentials studied in 161 the plan of this paper is as follows in section 1 we motivate our main ideas by discussing two particular examples the method of proof here is somewhat different from the proofs of the more general results in section 2 we obtain the necessary and sufficient conditions for fatou s theorem in section 3 we study more general approach regions and the appropriately modified maximal functions in section 4 we show how this maximal function controls the tangential boundary behavior of poisson integrals of potentials

on convergence of an augmented lagrangian decomposition method for sparse convex optimization a decomposition method for large scale convex optimization problems with block angular structure and many linking constraints is analysed the method is based on a separable approximation of the augmented lagrangian function weak global convergence of the method is proved and speed of convergence analysed it is shown that convergence properties of the method are heavily dependent on sparsity of the linking constraints application to large scale linear programming and stochastic programming is discussed

estimation of the number of sources in unbalanced arrays via information theoretic criteria estimating the number of sources impinging on an array of sensors is a well known and well investigated problem a common approach for solving this problem is to use an information theoretic criterion such as minimum description length mdl or the akaike information criterion aic the mdl estimator is known to be a consistent estimator robust against deviations from the gaussian assumption and nonrobust against deviations from the point source and or temporally or spatially white additive noise assumptions over the years several alternative estimation algorithms have been proposed and tested usually these algorithms are shown using computer simulations to have improved performance over the mdl estimator and to be robust against deviations from the assumed spatial model nevertheless these robust algorithms have high computational complexity requiring several multidimensional searches in this paper which is motivated by real life problems a systematic approach toward the problem of robust estimation of the number of sources using information theoretic criteria is taken an mdl type estimator that is robust against deviation from assumption of equal noise level across the array is studied the consistency of this estimator even when deviations from the equal noise level assumption occur is proven a novel low complexity implementation method avoiding the need for multidimensional searches is presented as well making this estimator a favorable choice for practical applications

esprit estimation of signal parameters via rotational invariance techniques an approach to the general problem of signal parameter estimation is described the algorithm differs from its predecessor in that a total least squares rather than a standard least squares criterion is used although discussed in the context of direction of arrival estimation esprit can be applied to a wide variety of problems including accurate detection and estimation of sinusoids in noise it exploits an underlying rotational invariance among signal subspaces induced by an array of sensors with a translational invariance structure the technique when applicable manifests significant performance and computational advantages over previous algorithms such as mem capon s mlm and music

on the variational equilibrium as a refinement of the generalized nash equilibrium we are concerned with a class of games in which the players strategy sets are coupled by a shared constraint a widely employed solution concept for such generalized nash games is the generalized nash equilibrium gne the variational equilibrium ve facchinei kanzow 2007 is a specific kind of gne characterized by the solution of the variational inequality formed from the common constraint and the mapping of the gradients of player objectives our contribution is a theory that provides sufficient conditions for ensuring that the existence of a gne implies the existence of a ve in such an instance the ve is said to be a refinement of the gne for certain games these conditions are shown to be necessary this theory rests on a result showing the equality of the brouwer degree of two suitably defined functions whose zeros are the gne and ve respectively this theory has a natural extension to the primal dual space of strategies and lagrange multipliers corresponding to the shared constraint our results unify some known results pertaining to such equilibria and provide mathematical substantiation for ideas that were known to be appealing to economic intuition

nonparametric detection of signals by information theoretic criteria performance analysis and an improved estimator determining the number of sources from observed data is a fundamental problem in many scientific fields in this paper we consider the nonparametric setting and focus on the detection performance of two popular estimators based on information theoretic criteria the akaike information criterion aic and minimum description length mdl we present three contributions on this subject first we derive a new expression for the detection performance of the mdl estimator which exhibits a much closer fit to simulations in comparison to previous formulas second we present a random matrix theory viewpoint of the performance of the aic estimator including approximate analytical formulas for its overestimation probability finally we show that a small increase in the penalty term of aic leads to an estimator with a very good detection performance and a negligible overestimation probability

optimal offer construction in electricity markets in this paper we study strategies for generators making offers into electricity markets in circumstances where both the demand for electricity and the behaviour of competing generators is unknown but can be represented by a probability distribution given this probability distribution we derive necessary optimality conditions for a broad class of supply offer curves we show how these conditions can be used to construct an optimal solution for a simple example we also consider the case in which a generator is restricted in the number of prices at which power can be offered

on the behavior of information theoretic criteria for model order selection the akaike 1974 information criterion aic and the minimum description length mdl are two well known criteria for model order selection in the additive white noise case our aim is to study the influence on their behavior of a large gap between the signal and the noise eigenvalues and of the noise eigenvalue dispersion our results are mostly qualitative and serve to explain the behavior of the aic and the mdl in some cases of great practical importance we show that when the noise eigenvalues are not clustered sufficiently closely then the aic and the mdl may lead to overmodeling by ignoring an arbitrarily large gap between the signal and the noise eigenvalues for fixed number of data samples overmodeling becomes more likely for increasing the dispersion of the noise eigenvalues for fixed dispersion overmodeling becomes more likely for increasing the number of data samples undermodeling may happen in the cases where the signal and the noise eigenvalues are not well separated and the noise eigenvalues are clustered sufficiently closely we illustrate our results by using simulations from the effective channel order determination area

stochastic power generation unit commitment in electricity markets a novel formulation and a comparison of solution methods we propose a stochastic unit commitment model for a power generation company that takes part in an electricity spot market the relevant feature of this model is its detailed representation of the spot market during a whole week including seven day ahead market sessions and the corresponding adjustment market sessions the adjustment market sessions can be seen as an hour ahead market mechanism this representation takes into account the influence that the company s decisions exert on the market clearing price by means of a residual demand curve for each market session we introduce uncertainty in the form of several possible spot market outcomes for each day which leads to a weekly scenario tree the model also represents in detail the operation of the company s generation units the model leads to large scale mixed linear integer problems that are hard to solve with commercial optimizers this suggests the use of alternative solution methods we test four solution approaches with a realistic numerical example in the context of the spanish electricity spot market the first is a direct solution with a commercial optimizer which illustrates the mentioned limitations the second is a standard lagrangean relaxation algorithm the third and fourth methods are two original variants of benders decomposition for multistage stochastic integer programs the first benders decomposition algorithm builds approximations for the recourse function relaxing the integrality constraints of the subproblems the second variant strengthens these cuts by performing one iteration of the lagrangean of each subproblem we analyze the advantages of these four methods and compare the results

variable metric bundle methods from conceptual to implementable forms to minimize a convex function we combine moreau yosida regularizations quasi newton matrices and bundling mechanisms first we develop conceptual forms using reversal quasi newton formulae and we state their global and local convergence then to produce implementable versions we incorporate a bundle strategy together with a curve search no convergence results are given for the implementable versions however some numerical illustrations show their good behaviour even for large scale problems

detection of the number of coherent signals by the mdl principle an approach is presented to the problem of detecting the number of sources impinging on a passive sensor array that is based on j rissanen s 1983 minimum description length mdl principle the approach is applicable to any type of sources including the case of sources which are fully correlated referred to as the coherent signals case two slightly different detection criteria are derived both requiring the estimation of the locations of the sources the first is tailored to the detection problem per se whereas the second is tailored to the combined detection estimation problem consistency of the two criteria is proved and their performance is demonstrated by computer simulations

finding supply function equilibria with asymmetric firms firms compete in supply functions when they offer a schedule of prices and quantities into a market for example this occurs in many wholesale electricity markets we study the equilibrium behaviour when firms differ both with regard to their costs and their capacities we characterize strong equilibrium solutions in which given the other players supply functions optimal profits are achieved for every demand realisation if the demand can be low enough for it to be met economically with supply from just one firm then the supply function equilibria are ordered in a natural way we consider equilibria in which for the highest levels of demand all but one of the firms have reached their capacity limit we show that there can be at most one supply function equilibrium with this property we also propose a new numerical method to find asymmetric supply function equilibria using piecewise linear approximations and a discretization of the demand distribution we show that this approach has good theoretical convergence behaviour finally we present numerical results from an implementation using gams to demonstrate that the approach is effective in practice

varepsilon optimal bidding in an electricity market with discontinuous market distribution function this paper investigates the optimal bidding strategy supply function for a generator offering power into a wholesale electricity market the model has three characteristics the uncertainties facing the generator are described by a single probability function namely the market distribution function the supply function to be chosen is nondecreasing but need not be smooth the objective function is the expected profit which can be formulated as a stieltjes integral along the generator s supply curve in previous work the market distribution function has been assumed smooth but in practice this assumption may not be satisfied this paper focuses on the case that the market distribution function is not continuous and hence an optimal supply function may not exist we consider a modified optimization problem and show the existence of an optimal solution for this problem then we show constructively how such an optimum can be approximated with an varepsilon optimal supply function by undercutting when

source enumeration for high resolution array processing using improved gerschgorin radii without eigendecomposition accurate detection of sources with low complexity is of considerable interest in practical applications of high resolution array processing this paper addresses a new computationally efficient method for source enumeration by using enhanced gerschgorin radii without eigendecompositofion the proposed method can calculate the gerschgorin radii in a more efficient manner in which the additive background noise can be efficiently suppressed and the computational complexity can be considerably reduced therefore the method is more accurate and computationally attractive furthermore the method does not rely on the eigenvalues of a covariance matrix or the signal noise power making it robust against deviations from the assumption of spatially white noise model numerical results are presented to demonstrate the performance of the method

on the existence of supply function equilibria supply function equilibria are used in the analysis of divisible good auctions with a large number of identical objects to be sold or bought an important example occurs in wholesale electricity markets despite the substantial literature on supply function equilibria the existence of a pure strategy nash equilibria for a uniform price auction in asymmetric cases has not been established in a general setting in this paper we prove the existence of a supply function equilibrium for a duopoly with asymmetric firms having convex non decreasing marginal costs with decreasing concave demand subject to an additive demand shock provided that the second derivative of the demand function is small enough and not increasing the proof is constructive and also gives insight into the structure of the equilibrium solutions

maximum likelihood direction of arrival estimation in the presence of unknown nonuniform noise we consider the problem of estimating directions of arrival doas of multiple sources observed on the background of nonuniform white noise with an arbitrary diagonal covariance matrix a new deterministic maximum likelihood ml doa estimator is derived its implementation is based on an iterative procedure which includes a stepwise concentration of the log likelihood ll function with respect to the signal and noise nuisance parameters and requires only a few iterations to converge new closed form expressions for the deterministic and stochastic direction estimation cramer rao bounds crbs are derived for the considered nonuniform model our expressions can be viewed as an extension of the well known results by stoica and nehorai 1989 1990 and weiss and friedlander 1993 to a more general noise model than the commonly used uniform one in addition these expressions extend the results obtained by matveyev et al see circuits syst signal process vol 18 p 479 87 1999 to the multiple source case comparisons with the above mentioned earlier results help to discover several interesting properties of doa estimation in the nonuniform noise case to compare the estimation performance of the proposed ml technique with the results of our crb analysis and with the performance of conventional uniform ml simulation results are presented additionally we test our technique using experimental seismic array data our simulations and experimental results both validate essential performance improvements achieved by means of the approach proposed

dual applications of proximal bundle methods including lagrangian relaxation of nonconvex problems we exhibit useful properties of proximal bundle methods for finding min sf where f and s are convex we show that they asymptotically find objective subgradients and constraint multipliers involved in optimality conditions multipliers of objective pieces for max type functions and primal and dual solutions in lagrangian decomposition of convex programs when applied to lagrangian relaxation of nonconvex programs they find solutions to relaxed convexified versions of such programs numerical results are presented for unit commitment in power production scheduling

oblique projection based enumeration of mixed noncoherent and coherent narrowband signals in many application scenarios the signals impinging on the array of sensors comprise the noncoherent uncorrelated and or partially correlated signals and the coherent signals with several groups due to multipath propagation in this paper we consider the problem of estimating the number of noncoherent narrowband signals and that of coherent narrowband signals with multiple groups impinging on a planar sensor array composed of two parallel uniform linear arrays ulas and an oblique projection based enumerator for the mixed signals opems is proposed by utilizing the qr decomposition based ratio criterion qrrc for rank determination of a matrix in the opems the number of noncoherent signals and that of coherent signals in each group are estimated separately where only the elevation angles of noncoherent signals are estimated to isolate the coherent signals from the noncoherent ones and the computationally intensive and time consuming eigendecomposition procedure is avoided the consistency of the proposed opems is analyzed and its effectiveness is verified through numerical examples

unit commitment in electricity pool markets we consider an electricity generator making offers of energy into an electricity pool market over a horizon of several trading periods typically a single trading day the generator runs a set of generating units with given start up costs shut down costs and operating ranges at the start of each trading period the generator must submit to the pool system operator a new supply curve defining quantities of offered energy and the prices at which it wants these dispatched the amount of dispatch depends on the supply curve offered along with the offers of the other generators and market demand both of which are random but do not change in response to the actions of the generator we consider after dispatch the generator determines which units to run in the current trading period to meet the dispatch the generator seeks a supply function that maximizes its expected profit we describe an optimization procedure based on dynamic programming that can be used to construct optimal offers in successive time periods over a fixed planning horizon

divide to conquer decomposition methods for energy optimization modern electricity systems provide a plethora of challenging issues in optimization the increasing penetration of low carbon renewable sources of energy introduces uncertainty in problems traditionally modeled in a deterministic setting the liberalization of the electricity sector brought the need of designing sound markets ensuring capacity investments while properly reflecting strategic interactions in all these problems hedging risk possibly in a dynamic manner is also a concern the fact of representing uncertainty and or competition of different companies in a multi settlement power market considerably increases the number of variables and constraints for this reason usually a trade off needs to be found between modeling and numerical tractability the more details are brought into the model the harder becomes the optimization problem for structured optimization and generalized equilibrium problems we explore some variants of solution methods based on lagrangian relaxation and on benders decomposition throughout we keep as a leading thread the actual practical value of such techniques in terms of their efficiency to solve energy related problems

statistical analysis of the performance of information theoretic criteria in the detection of the number of signals in array processing the performances of the akaike 1974 information criterion and the minimum descriptive length criterion methods are examined the events which lead to erroneous decisions are considered and on the basis of these events the probabilities of error for the two criteria are derived the probabilities of the first two events are derived based on the asymptotic distribution of the sample eigenvalues of an estimated hermitian matrix it is further shown that the probabilities of missing and false alarm for these two criteria can be evaluated to a close approximation although the derivation of the probabilities of error is based on an asymptotic analysis the results are confirmed to be in very close agreement with computer simulation results

independent component analysis based source number estimation and its comparison for mechanical systems abstract it has been challenging to correctly separate the mixed signals into source components when the source number is not known a priori in this paper we propose a novel source number estimation based on independent component analysis ica and clustering evaluation analysis we investigate and benchmark three information based source number estimations akaike information criterion aic minimum description length mdl and improved bayesian information criterion ibic all the above methods are comparatively studied in both numerical and experimental case studies with typical mechanical signals the results demonstrate that the proposed ica based source number estimation with nonlinear dissimilarity measures performs more stable and robust than the information based ones for mechanical systems

poisson integrals of regular functions tangential convergence of poisson integrals is proved for certain spaces of regular functions which contain the spaces of bessel potentials of lp functions 1 1

reduced rank mdl method for source enumeration in high resolution array processing this paper proposes a reduced rank minimum description length mdl method to enumerate the incident waves impinging on a uniform linear array ula first a new observation data and a reference signal are formed from sensor data by means of the shift invariance property of the ula a cross correlation between them is calculated which is able to capture signal information and efficiently suppress additive noise second the normalized cross correlation is used as initial information for a recursion procedure to quickly partition the observation data into two orthogonal components in a signal subspace and a reduced rank noise subspace the components in the noise subspace are employed to calculate the total code length that is required to encode the observation data finally the model with the shortest code length namely the minimum description length is chosen as the best model unlike the traditional mdl methods this method partitions the observation data into the cleaner signal and noise subspace components by means of the recursion procedure avoiding the estimation of a covariance matrix and its eigendecomposition thus the method has the advantage of computational simplicity its performance is demonstrated via numerical results

hydroelectric reservoir optimization in a pool market for a price taking generator operating a hydro electric reservoir in a pool electricity market the optimal stack to offer in each trading period over a planning horizon can be computed using dynamic programming however the market trading period usually 1 hour or less may be much shorter than the inherent time scale of the reservoir often many months we devise a dynamic programming model for such situations in which each stage represents many trading periods in this model the decision made at the beginning of each stage consists of a target mean and variance of the water release in the coming stage this decomposes the problem into inter stage and intra stage subproblems

a stabilized structured dantzig wolfe decomposition method we discuss an algorithmic scheme which we call the stabilized structured dantzig wolfe decomposition method for solving large scale structured linear programs it can be applied when the subproblem of the standard dantzig wolfe approach admits an alternative master model amenable to column generation other than the standard one in which there is a variable for each of the extreme points and extreme rays of the corresponding polyhedron stabilization is achieved by the same techniques developed for the standard dantzig wolfe approach and it is equally useful to improve the performance as shown by computational results obtained on an application to the multicommodity capacitated network design problem

solving stochastic complementarity problems in energy market modeling using scenario reduction in this paper we analyze market equilibrium models with random aspects that lead to stochastic complementarity problems while the models presented depict energy markets the results are believed to be applicable to more general stochastic complementarity problems the contribution is the development of new heuristic scenario reduction approaches that iteratively work towards solving the full extensive form stochastic market model the methods are tested on three representative models and supporting numerical results are provided as well as derived mathematical bounds

nonparametric estimation of market distribution functions in electricity pool markets the market distribution function is a probabilistic device that can be used to model the randomness in dispatch and clearing price that generators in electricity pool markets must take account of when submitting offers we discuss techniques for estimating the market distribution function and ways of measuring the quality of these estimators using both classical statistical approaches and an expected foregone revenue approach

source number estimators using transformed gerschgorin radii we introduce effective uses of gerschgorin radii of the unitary transformed covariance matrix for source number estimation there are two approaches likelihood and heuristic used for developing the detection criteria the likelihood approach combines the gerschgorin radii to the well known source number detectors and improves their detection performances for gaussian and white noise processes it is verified that the gerschgorin likelihood estimators gle are consistent the gerschgorin aic yields a consistent estimate and the gerschgorin mdl criterion does not tend to underestimate for small or moderate data samples the heuristic approach applying the gerschgorin disk estimator gde developed from the projection concept overcomes the problem in cases of small data samples an unknown noise model and data dependency furthermore the detection performances of both approaches through the suggested rotations and averaging can be further improved finally the proposed and existing criteria are evaluated in various conditions by using simulated and measured experimental data

on the use of order statistics for improved detection of signals by the mdl criterion the minimum description length mdl criterion for model selection has been successfully applied to the problem of estimating the number of sources in noise we show that by employing an order statistics approach in the existing solution a new processor with uniformly improved performance is constructed at the cost of greater complexity we prove that the resulting mdl based processor is consistent results of simulations of practical scenarios of interest demonstrate how significant the performance improvement can be