on dimension of porous measures we introduce a notion of mean porosity for measures and obtain dimensional bounds for mean porous and porous measures as a corollary we generalize to all porous borel measures the estimate obtained recently by j p eckmann e jarvenpaa and m jarvenpaa for porous measures satisfying the doubling condition we also discuss various generalizations of this notion and possible applications

maximum likelihood estimation of a structured covariance matrix with a condition number constraint in this paper we deal with the problem of estimating the disturbance covariance matrix for radar signal processing applications when a limited number of training data is present we determine the maximum likelihood ml estimator of the covariance matrix starting from a set of secondary data assuming a special covariance structure i e the sum of a positive semi definite matrix plus a term proportional to the identity and a condition number upper bound constraint we show that the formulated constrained optimization problem falls within the class of maxdet problems and develop an efficient procedure for its solution in closed form remarkably the computational complexity of the algorithm is of the same order as the eigenvalue decomposition of the sample covariance matrix at the analysis stage we assess the performance of the proposed algorithm in terms of achievable signal to interference plus noise ratio sinr both for a spatial and a doppler processing the results show that interesting sinr improvements with respect to some existing covariance matrix estimation techniques can be achieved

adaptive detection in gaussian interference with unknown covariance after reduction by invariance in this paper we address the problem of adaptive detection in homogeneous gaussian interference with unknown covariance matrix after reduction by invariance starting from a maximal invariant statistic which contains all the information for the synthesis of an invariant detector we devise the rao test generalized likelihood ratio test glrt and durbin test moreover we compare their decision statistics with those of the receivers designed according to the same criteria from the raw data i e before reduction by invariance we prove that the glrt in the original data space is statistically equivalent to the glrt designed after reduction by invariance under a very mild assumption and coincide with the conditional uniformly most powerful invariant c umpi test obtained conditioning on an ancillary part of the maximal invariant statistic as to the rao and durbin criteria when they are applied after reduction by invariance lead to detectors different from the counterparts devised in the raw data domain at the analysis stage the performance of the receivers devised in the invariant domain is analyzed in comparison with that of the counterparts synthesized from the original observations

cfar detection strategies for distributed targets under conic constraints in this paper we deal with the problem of adaptive detection of mismatched mainlobe targets and or sidelobe interfering signals that are distributed in range to this end we investigate the impact of modeling the actual useful signal as a vector belonging to a proper cone with axis the nominal steering vector as a means to improve the robustness of the decision rule in presence of mainlobe targets similarly in order to improve the rejection capabilities of the decision rule in presence of sidelobe interferers we study the effects of replacing the usual noise only hypothesis with a noise plus interferers hypothesis where interferers belong to the complement of a cone with axis the nominal steering vector at the design stage we resort to the two step glrt based design procedure to this end we assume that a set of training data is available namely data free of signal components but sharing the same gaussian distribution of the noise in the cells under test remarkably proposed detectors possess the cfar property under the noise only hypothesis the performance assessment conducted by monte carlo simulation is aimed at assessing the effectiveness of proposed solutions also in comparison to existing ones

the complex parameter rao test the rao test is an important method in signal detection in the presence of unknown parameters the traditional approach to the problem when the unknown parameters are complex valued is to form a corresponding real valued parameter vector and then to use the real rao test alternatively we present a complex parameter rao test by reformulating the calculations with respect to the complex valued quantities directly two important examples of the application of the complex parameter rao test are given to illustrate the procedure

local entropy averages and projections of fractal measures we show that for families of measures on euclidean space which satisfy an ergodic theoretic form of self similarity under the operation of re scaling the dimension of linear images of the measure behaves in a semi continuous way we apply this to prove the following conjecture of furstenberg let m n be integers which are not powers of the same integer and let x y be closed subsets of the unit interval which are invariant respectively under times m mod 1 and times n mod 1 then for any non zero t dim x ty min 1 dim x dim y a similar result holds for invariant measures and gives a simple proof of the rudolph johnson theorem our methods also apply to many other classes of conformal fractals and measures as another application we extend and unify results of peres shmerkin and nazarov and of moreira concerning projections of products self similar measures and gibbs measures on regular cantor sets we show that under natural irreducibility assumptions on the maps in the ifs the image measure has the maximal possible dimension under any linear projection other than the coordinate projections we also present applications to bernoulli convolutions and to the images of fractal measures under differentiable maps

adaptive beamformer orthogonal rejection test research in the area of signal detection in the presence of unknown interference has resulted in a number of adaptive detection algorithms examples of such algorithms include the adaptive matched filter amf the generalized likelihood ratio test glrt and the adaptive coherence estimator ace each of these algorithms results in a tradeoff between detection performance for matched signals and rejection performance for mismatch signals this paper introduces a new detection algorithm we call the adaptive beamformer orthogonal rejection test abort our test decides if an observation contains a multidimensional signal belonging to one subspace or if it contains a multidimensional signal belonging to an orthogonal subspace when unknown complex gaussian noise is present in our analysis we use a statistical hypothesis testing framework to develop a generalized likelihood ratio decision rule we evaluate the performance of this decision rule in both the matched and mismatched signal cases our results show that for constant power complex gaussian noise if the signal is matched to the steering vector abort glrt and amf give approximately equivalent probability of detection higher than that of ace which trades detection probability for an extra invariance to scale mismatch between training and test data of these four tests ace is most selective and therefore least tolerant of mismatch whereas amf is most tolerant of mismatch and therefore least selective abort and glrt offer compromises between these extremes with abort more like ace and with glrt more like amf

adaptive detection of point like targets in spectrally symmetric interference we address adaptive radar detection of targets embedded in ground clutter dominated environments characterized by a symmetrically structured power spectral density at the design stage we leverage on the spectrum symmetry for the interference to come up with decision schemes capable of capitalizing the a priori information on the covariance structure to this end we prove that the detection problem at hand can be formulated in terms of real variables and then we apply design procedures relying on the glrt the rao test and the wald test specifically the estimates of the unknown parameters under the target presence hypothesis are obtained through an iterative optimization algorithm whose convergence and quality guarantee is thoroughly proved the performance analysis both on simulated and on real radar data confirms the superiority of the considered architectures over their conventional counterparts which do not take advantage of the clutter spectral symmetry

adaptive detection of a subspace signal in signal dependent interference this paper deals with the problem of adaptive detection of subspace signals embedded in thermal noise and clutter that depends on the transmitted signal to this end at the design stage we assume that the signal dependent sd clutter shares the same subspace as the target signals as customary a set of secondary data free of signal components is also assumed available two adaptive detectors referred to as the sd rao and sd wald are proposed by resorting to the rao test and wald test design criteria unlike the classical rao and wald tests which are derived by dividing the complex parameter into the real and imaginary parts the proposed detectors treat the complex parameter as a single quantity to reduce the computational burden moreover we derive the theoretical false alarm probabilities and detection probabilities and show that both the two proposed detectors exhibit the constant false alarm rate property numerical results show that the proposed detectors achieve a detection performance improvement over the conventional multidimensional detectors

on existence and uniqueness of solutions to a boussinesq system with nonlinear and mixed boundary conditions abstract we study a boussinesq system in a bounded domain with an outlet boundary portion where fluid can leave or re enter on this boundary part we consider a do nothing condition for the fluid flow and a new artificial condition for the heat transfer that couples nonlinearly the fluid velocity and temperature the latter can be further adjusted if convective or conductive phenomena are dominant we prove existence and in some cases uniqueness of weak solutions to stationary and evolutionary problems by a fixed point strategy under suitable assumptions on the data a variety of numerical tests shows the improved performance of the new artificial condition with respect to other standard choices in the literature

equidistribution from fractal measures we give a fractal geometric condition for a measure on 0 1 to be supported on points x that are normal in base n i e such that n kx k in mathbb n equidistributes modulo 1 this condition is robust under c 1 coordinate changes and it applies also when n is a pisot number rather than an integer as applications we obtain new results and strengthen old ones about the prevalence of normal numbers in fractal sets and new results on measure rigidity specifically completing host s theorem to multiplicatively independent integers and proving a rudolph johnson type theorem for certain pairs of beta transformations

adaptive subspace detectors we use the theory of generalized likelihood ratio tests glrts to adapt the matched subspace detectors msds of scharf 1991 and of scharf and frielander 1994 to unknown noise covariance matrices in so doing we produce adaptive msds that may be applied to signal detection for radar sonar and data communication we call the resulting detectors adaptive subspace detectors asds these include kelly s 1987 glrt and the adaptive cosine estimator ace of kaurt and scharh see ibid vol 47 p 2538 41 1999 and of scharf and mcwhorter see proc 30th asilomar conf signals syst comput pacific grove ca 1996 for scenarios in which the scaling of the test data may deviate from that of the training data we then present a unified analysis of the statistical behavior of the entire class of asds obtaining statistically identical decompositions in which each asd is simply decomposed into the nonadaptive matched filter the nonadaptive cosine or t statistic and three other statistically independent random variables that account for the performance degrading effects of limited training data

performance of the adaptive sidelobe blanker detection algorithm in homogeneous environments the adaptive sidelobe blanker asb algorithm is a two stage detector consisting of a first stage adaptive matched filter amf detector followed by a second stage detector called the adaptive coherence or cosine estimator ace only those data test cells that survive both detection thresholdings are declared signal target bearing we provide exact novel closed form expressions for the resulting probability of detection pd and false alarm pfa for the asb algorithm and demonstrate that under homogeneous data conditions with no signal array response mismatch that i the asb is a constant false alarm rate cfar algorithm ii the asb has a higher or commensurate pd for a given pfa than both the amf and the ace and iii the asb has an overall performance that is commensurate with kelly s 1986 benchmark generalized likelihood ratio test glrt a compact statistical summary is derived providing distributions and dependencies among the glrt amf and the ace decision statistics

adaptive detection and estimation in the presence of useful signal and interference mismatches this paper considers adaptive detection and estimation in the presence of useful signal and interference mismatches we assume a homogeneous environment where the random disturbance components from the primary and secondary data share the same covariance matrix moreover the data under test contains a deterministic interference vector in addition to the possible useful signal we focus on the situation where an energy fraction of both the useful signal and the deterministic interference may lie outside their nominal subspaces conical uncertainty model under these conditions we devise a procedure for the computation of the joint maximum likelihood ml estimators of the useful signal and interference vectors resorting to a suitable rank one decomposition of a semidefinite program sdp problem optimal solution hence we use the aforementioned estimators for the synthesis of adaptive receivers based on different generalized likelihood ratio test glrt criteria at the analysis stage we assess the performance of the new detectors in comparison with some decision rules available in open literature

adaptive double subspace signal detection in gaussian background part ii partially homogeneous environments in this part of the paper we continue to study the problem of detecting a double subspace signal in gaussian noise precisely we address the detection problem in partially homogeneous environments where the primary and secondary data share the same covariance matrix up to an unknown scaling factor we derive the generalized likelihood ratio test glrt rao test wald test and their two step versions we also introduce three spectral norm tests snts all these detectors possess the constant false alarm rate cfar property moreover various kinds of special cases of these detectors are given at the stage of performance evaluation we consider two cases one is the case of no signal mismatch the other is more general namely the case of signal mismatch including the column space signal mismatch and row space signal mismatch

a unifying framework for adaptive radar detection in homogeneous plus structured interference part ii detectors design this paper deals with the problem of adaptive multidimensional multichannel signal detection in homogeneous gaussian disturbance with unknown covariance matrix and structured unknown deterministic interference the aforementioned problem extends the well known generalized multivariate analysis of variance gmanova tackled in the open literature in part i of this paper we have obtained the maximal invariant statistic mis for the problem under consideration as an enabling tool for the design of suitable detectors which possess the constant false alarm rate cfar property herein we focus on the development of several theoretically founded detectors for the problem under consideration first all the considered detectors are shown to be function of the mis thus proving their cfarness property second coincidence or statistical equivalence among some of them in such a general signal model is proved third strong connections to well known simpler scenarios analyzed in adaptive detection literature are established finally simulation results are provided for a comparison of the proposed receivers

tangent measure distributions of fractal measures tangent measure distributions provide a natural tool to study the local geometry of fractal sets and measures in euclidean spaces the idea is loosely speaking to attach to every point of the set a family of random measures called the alpha dimensional tangent measure distributions at the point which describe asymptotically the alpha dimensional scenery seen by an observer zooming down towards this point this tool has been used by bandt ba and graf g to study the regularity of the local geometry of self similar sets but in this paper we show that its scope goes much beyond this situation and in fact it may be used to describe a strong regularity property possessed by every measure we show that for every measure mu on a euclidean space and any dimension alpha at mu almost every point all alpha dimensional tangent measure distributions are palm measures this means that the local geometry of every dimension of general measures can be described like the local geometry of self similar sets by means of a family of statistically self similar random measures we believe that this result reveals a wealth of new and unexpected information about the structure of such general measures and we illustrate this by pointing out how it can be used to improve or generalize recently proved relations between ordinary and average densities

on the navier stokes flows for heat conducting fluids with mixed boundary conditions abstract we consider a coupled model for steady flows of viscous incompressible heat conducting fluids with temperature dependent material coefficients in a fixed three dimensional open cylindrical channel we introduce the banach spaces x and y to be the space of possible solutions of this problem and the space of its data respectively we show that the corresponding operator of the problem acting between x and y is frechet differentiable applying the local diffeomorphism theorem we get the local solvability results for a variational formulation

conical upper density theorems and porosity of measures abstract we study how measures with finite lower density are distributed around n m planes in small balls in r n we also discuss relations between conical upper density theorems and porosity our results may be applied to a large collection of hausdorff and packing type measures

some current cfd issues relevant to the incompressible navier stokes equations abstract the goals of this paper are to carefully define a particular class of well set incompressible navier stokes problems in the continuum partial differential equation pde setting and to discuss some relevant and sometimes poorly understood issues related to these well posed pde problems both in the continuum world and in its computer counterpart emphasized are three common formulations used to generate computer codes the primitive variable velocity pressure formulation and two derived variable formulations pressure poisson equation and vorticity transport equation

false alarm rate of the glrt for subspace signals in subspace interference plus gaussian noise in the presence of interference and gaussian noise with unknown covariance matrix a generalized likelihood ratio test glrt detector has already been developed for detecting a distributed target the target signal and interference are described with subspace models namely the target signals or interference are modeled as linear combinations of the linearly independent columns of a known subspace matrix in this paper we obtain statistical properties of this glrt detector and prove its constant false alarm rate against the noise covariance matrix moreover we derive analytical expressions for the probability of false alarm of the glrt detector specifically exact expressions for the probability of false alarm are obtained for six cases where the target subspace dimension denoted by p is 1 2 and 3 and the number of range cells denoted by h the distributed target occupies is 1 2 and 3 for the general case where p geq 4 and h geq 4 we derive an approximate expression for the probability of false alarm monte carlo simulations show that the exact expressions are valid and the accuracy of the approximate expression is acceptable for moderate or large training data size in practice these expressions can greatly facilitate the threshold setting for the glrt detector for any preassigned probability of false alarm

packing dimension and ahlfors regularity of porous sets in metric spaces let x be a metric measure space with an s regular measure we prove that if a subset x is varrho porous then rm dim p a le s c varrho s where dimp is the packing dimension and c is a positive constant which depends on s and the structure constants of this is an analogue of a well known asymptotically sharp result in euclidean spaces we illustrate by an example that the corresponding result is not valid if is a doubling measure however in the doubling case we find a fixed n subset x with n 0 such that rm dim p a le rm dim p x c log tfrac1 varrho 1 varrho t for all varrho porous sets a subset x setminus n here c and t are constants which depend on the structure constant of finally we characterize uniformly porous sets in complete s regular metric spaces in terms of regular sets by verifying that a is uniformly porous if and only if there is t s and a t regular set f such that a subset f

modified rao test for multichannel adaptive signal detection the problem of detecting a subspace signal is studied in colored gaussian noise with an unknown covariance matrix in the subspace model the target signal belongs to a known subspace but with unknown coordinates we first present a new derivation of the rao test based on the subspace model and then propose a modified rao test mrt by introducing a tunable parameter the mrt is more general which includes the rao test and the generalized likelihood ratio test as special cases moreover closed form expressions for the probabilities of false alarm and detection of the mrt are derived which show that the mrt bears a constant false alarm rate property against the noise covariance matrix numerical results demonstrate that the mrt can offer the flexibility of being adjustable in the mismatched case where the target signal deviates from the presumed signal subspace in particular the mrt provides better mismatch rejection capacities as the tunable parameter increases

a robust and accurate outflow boundary condition for incompressible flow simulations on severely truncated unbounded domains we present a robust and accurate outflow boundary condition and an associated numerical algorithm for incompressible flow simulations on unbounded physical domains aiming at maximizing the domain truncation without adversely affecting the flow physics the proposed outflow boundary condition allows for the influx of kinetic energy into the domain through the outflow boundaries and prevents un controlled growth in the energy of the domain in such situations the numerical algorithm for the outflow boundary condition is developed on top of a rotational velocity correction type strategy to de couple the pressure and velocity computations and a special construction in the algorithmic formulation prevents the numerical locking at the outflow boundaries for time dependent problems extensive numerical tests for flow problems with bounded and semi bounded physical domains demonstrate that this outflow boundary condition and the numerical algorithm produce stable and accurate simulations on even severely truncated computational domains where strong vortices may be present at or exit the outflow boundaries the method developed herein has the potential to significantly expedite simulations of incompressible flows involving outflow or open boundaries and to enable such simulations at reynolds numbers significantly higher than the state of the art

on the invariance coincidence and statistical equivalence of the glrt rao test and wald test three common techniques to discriminate between alternatives in a binary hypothesis testing problem are the generalized likelihood ratio test glrt the rao test and the wald test in this paper we investigate some characteristics of the corresponding decision statistics and provide their expressions for some problems of particular interest in statistical signal processing first of all we focus on the invariance of the rao and wald tests with respect to transformations leaving the testing problem unaltered then we introduce necessary and sufficient conditions in order for their decision statistics to coincide with twice the logarithm of the glrt statistic finally we present some detection problems usually encountered in practical signal processing applications where the decision variables of the three quoted tests are equivalent namely related by strictly monotonic transformations

fast iterative solvers for buoyancy driven flow problems we outline a new class of robust and efficient methods for solving the navier stokes equations with a boussinesq model for buoyancy driven flow we describe a general solution strategy that has two basic building blocks an implicit time integrator using a stabilized trapezoid rule with an explicit adams bashforth method for error control and a robust krylov subspace solver for the spatially discretized system we present numerical experiments illustrating the efficiency of the chosen preconditioning schemes with respect to the discretization parameters

adaptive double subspace signal detection in gaussian background part i homogeneous environments in this two part paper we consider the problem of adaptive multidimensional multichannel signal detection in gaussian noise with unknown covariance matrix the test data primary data is assumed as a collection of sample vectors arranged as the columns of a rectangular data array the rows and columns of the signal matrix are both assumed to lie in known subspaces but with unknown coordinates due to this feature of the signal structure we name this kind of signal as the double subspace signal part i of this paper focuses on the adaptive detection in homogeneous environments while part ii deals with the adaptive detection in partially homogeneous environments precisely in this part we derive the generalized likelihood ratio test glrt rao test wald test as well as their two step variations in homogeneous environments three types of spectral norm tests snts are also introduced all these detectors are shown to possess the constant false alarm rate cfar property moreover we discuss the differences between them and show how they work another contribution is that we investigate various special cases of these detectors remarkably some of them are well known existing detectors while some others are still new at the stage of performance evaluation conducted by monte carlo simulations both matched and mismatched signals are dealt with for each case more than one scenario is considered

invariant adaptive detection of range spread targets under structured noise covariance the invariance principle is adopted to develop an exhaustive study for adaptive detection of range spread targets in gaussian noise sharing a block diagonal covariance structure for this problem the usual generalized likelihood ratio principle is intractable in this paper we first determine the largest group of affine transformations that does not alter the decision problem then a maximal invariant identified by this group is derived which can characterize the totality of the invariant detectors and extends the existing results for the point target case a theoretical performance analysis of the maximal invariant is also given finally we propose two classes of invariant detectors which are distinguished by whether a constant false alarm rate cfar is maintained numerical experiments are provided for a comparison of the proposed detectors where a tradeoff between the cfarness and the improved performance has been observed and studied

adaptive radar detectors based on the observed fim modified versions of rao wald and durbin tests are considered exploiting an estimator of the fisher information matrix fim in place of the exact one they are asymptotically equivalent under some technical conditions to the standard counterparts and rely on the use of the observed fim ofim which is proportional to the negative hessian of the log likelihood the developed framework is applied to the problem of adaptive radar detection of a point like target in homogeneous or partially homogeneous interference remarkably for both the scenarios it is shown that rao wald and durbin tests with ofim are statistically equivalent to the generalized likelihood ratio test glrt for the specific detection problem namely kelly s detector for the homogeneous environment and the adaptive coherence estimator ace s kraut and l l scharf the cfar adaptive subspace detector is a scale invariant glrt ieee trans signal process vol 47 no 9 pp 2538 2541 sep 1999 also known as adaptive normalized matched filter anmf e conte m lops and g ricci asymptotically optimum radar detection in compound gaussian clutter ieee trans aerosp electron syst vol 31 no 2 pp 617 625 apr 1995 for the partially homogeneous scenario this provides a new interpretation of the mentioned glrts laying the foundations for a better understanding of their theoretical validity

invariance theory for adaptive detection in interference with group symmetric covariance matrix this paper describes the adaptive detection of point like targets in a gaussian environment assuming a group symmetric structure for the interference covariance matrix this special configuration enforces block sparsity and permits splitting of the original observation space into lower dimensional subspaces each characterized by its own nuisance parameters hence the principle of invariance is invoked to select decision rules enjoying some symmetry defined by a suitable group of transformations which leave the decision problem unaltered all the invariant tests can be expressed as functions of a maximal invariant statistic whose derivation is among the key results of this paper finally some common design criteria are applied to come up with adaptive architectures that share invariance and their behavior is assessed to highlight the interplay between sample size and detection performance in comparison with conventional decision schemes

a generalized version of ace and performance analysis this paper considers the problem of detecting a signal that belongs to an unknown one dimensional subspace of mathbb c n times 1 in additive interference plus noise whose covariance matrix is unknown the interference plus noise is assumed to be modeled as a complex multivariate zero mean random vector whose covariance matrix bf r is estimated from signal free training vectors the hypothesis test labeled the generalized adaptive coherence estimator gace involves two test vectors both of which contain the unknown signal the test statistic reduces to the ace test statistic as the signal to interference plus noise ratio of any one of the test vectors increases without limit in the limit of large number of training samples the gace test statistic reduces to the magnitude square of the inner product of a signal vector in additive statistically independent white noise vectors analytical expressions for the probability of false alarm and the probability of detection of the gace test are derived and the test is shown to have the constant false alarm rate cfar property sample results to illustrate the performance of the detector are provided and compared with the performance of the generalized likelihood ratio test glrt for the specific problem along with results on the sequential application of the glrt and gace

a maximal invariant framework for adaptive detection with structured and unstructured covariance matrices we introduce a framework for exploring array detection problems in a reduced dimensional space by exploiting the theory of invariance in hypothesis testing this involves calculating a low dimensional basis set of functions called the maximal invariant the statistics of which are often tractable to obtain thereby making analysis feasible and facilitating the search for tests with some optimality property using this approach we obtain a locally most powerful invariant test for the unstructured covariance case and show that all invariant tests can be expressed in terms of the previously published kelly s generalized likelihood ratio glrt and robey s adaptive matched filter amf test statistics applying this framework to structured covariance matrices corresponding to stochastic interferers in a known subspace for which the glrt is unavailable we obtain the maximal invariant and propose several new invariant detectors that are shown to perform as well or better than existing ad hoc detectors these invariant tests are unaffected by most nuisance parameters hence the variation in the level of performance is sharply reduced this framework facilitates the search for such tests even when the usual glrt is unavailable

model order selection rules for covariance structure classification in radar the adaptive classification of the interference covariance matrix structure for radar signal processing applications is addressed in this paper this represents a key issue because many detection architectures are synthesized assuming a specific covariance structure which may not necessarily coincide with the actual one due to the joint action of the system and environment uncertainties the considered classification problem is cast in terms of a multiple hypotheses test with some nested alternatives and the theory of model order selection mos is exploited to devise suitable decision rules several mos techniques such as the akaike takeuchi and bayesian information criteria are adopted and the corresponding merits and drawbacks are discussed at the analysis stage illustrating examples for the probability of correct model selection are presented showing the effectiveness of the proposed rules

performance of a class of adaptive detection algorithms in nonhomogeneous environments a two dimensional 2 d adaptive sidelobe blanker asb detection algorithm was developed through experimentation as an extenuate for false alarms caused by undernulled interference encountered when applying the adaptive matched filter amf in nonhomogeneous environments the algorithm s utility has been demonstrated empirically considering theoretic performance analyses of the asb detection algorithm as well as the amf generalized likelihood ratio test glrt and the adaptive cosine estimator ace under nonideal conditions can become fairly intractable rather quickly especially in an adaptive processing context involving covariance estimation in this paper however we have developed and exploited a theoretic framework through which the performance of these algorithms under nonhomogeneous conditions can be examined theoretically it is demonstrated through theoretic analysis that in the presence of undernulled interference the asb is a pliable false alarm regulatory far detector that maintains good target sensitivity a viable method of asb threshold selection is also presented and demonstrated

generalized cfar property and ump invariance for adaptive signal detection in this paper we consider adaptive detection of a signal embedded in additive disturbance whose multivariate distribution belongs to a very general class including many statistical models commonly adopted for radar disturbance we introduce the concept of generalized constant false alarm rate cfar and show that a class of receivers sharing some invariances complies with the quoted property then we devise the generalized likelihood ratio test glrt and prove that under some mild technical conditions it coincides with that obtained under the gaussian assumption for the observations we also deal with the existence of the uniformly most powerful invariant umpi detector either using the wijsman theorem or directly computing the maximal invariant likelihood ratio lr at the analysis stage we focus on a compound matrix variate model for the disturbance component which is a natural generalization of the spherically invariant random vector sirv in this context we assess the performance of some well known invariant decision rules also in comparison with the most powerful invariant mpi detector the results highlight that some among the analyzed receivers exhibit a performance level very close to the mpi test

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

maximal invariants and performance of some invariant hypothesis tests for an adaptive detection problem maximal invariants for adaptive detection of a signal in unknown interference from multiple observations is derived given coherent samples from p sets of observations it is shown that a maximal invariant statistic for the detection problem is a 2p 1 dimensional vector comprising the eigenvalues of two hermitian positive definite matrices obtained from the data set two invariant detectors well known for p 1 are generalized for the case of multiple observations and closed form expressions for the probability of detection and probability of false alarm are derived along with the distributions of the signal to interference plus noise loss factors several novel invariant detectors are constructed from the maximal invariants and the receiver operating characteristics of the detectors compared

a steady flow through a plane cascade of profiles with an arbitrarily large inflow_the mathematical model existence of a weak solution the paper deals with a mathematical model of a viscous stationary incompressible flow through a cascade of profiles the problem for the navier stokes system is formulated in a domain corresponding to one spatial period of the cascade we consider several types of boundary conditions on various parts of the boundary the inflow the artificial lower and upper boundaries the profile the outflow we solve the problem with an arbitrarily large inflow into the turbine we formulate the artificial boundary condition on the outflow the modification of the so called do nothing condition which enables us to prove the existence of a weak solution for any inflow

rao test for adaptive detection in gaussian interference with unknown covariance matrix this paper deals with the problem of detecting a signal known up to a scaling factor in the presence of gaussian disturbance with unknown covariance matrix a new detector based on the rao test criterion is introduced and its invariance properties and constant false alarm rate cfar behavior are studied at the analysis stage the performance of the new receiver is assessed also in comparison with some classical adaptive radar detectors both in the matched as well as in the mismatched signal case remarkably the rao test may achieve a matched detection performance which is commensurate with that of the generalized likelihood ratio test glrt based detectors if a sufficient number of training data is available moreover it also exhibits better rejection capabilities of mismatched signals than the counterparts in the last part of the work a two stage detector whose second stage coincides with the rao test is devised it represents a suitable means to restore the detection performance of the plain rao test in the presence of a small number of training data finally the performance of the aforementioned two stage processor is analyzed in closed form and the cfar behavior is proved

nonsymmetric conical upper density and k porosity we study how the hausdorff measure is distributed in nonsymmetric narrow cones in n as an application we find an upper bound close to n k for the hausdorff dimension of sets with large k porosity with k porous sets we mean sets which have holes in k different directions on every small scale

differentiability of lipschitz functions in lebesgue null sets we show that if n 1 then there exists a lebesgue null set in mathbb r n containing a point of differentiability of each lipschitz function f mathbb r n rightarrow mathbb r n 1 in combination with the work of others this completes the investigation of when the classical rademacher theorem admits a converse avoidance of sigma porous sets arising as irregular points of lipschitz functions plays a key role in the proof