analysis of subspace fitting and ml techniques for parameter estimation from sensor array data it is shown that the multidimensional signal subspace method termed weighted subspace fitting wsf is asymptotically efficient this results in a novel compact matrix expression for the cramer rao bound crb on the estimation error variance the asymptotic analysis of the maximum likelihood ml and wsf methods is extended to deterministic emitter signals the asymptotic properties of the estimates for this case are shown to be identical to the gaussian emitter signal case i e independent of the actual signal waveforms conclusions concerning the modeling aspect of the sensor array problem are drawn

direction finding using noise covariance modeling we consider the problem of direction finding in the presence of colored noise whose covariance matrix is unknown we show that the ambient noise covariance matrix can be modeled by a sum of hermitian matrices known up to a multiplicative scalar using this model we estimate jointly the directions of arrival of the signals and the noise model parameters we show that under certain conditions it is possible to obtain unbiased and efficient estimates of the signal direction the cramer rao bound is used as the principal analysis tool computer simulations using the maximum likelihood estimator provide a validation of the analytical results

paracategories ii adjunctions fibrations and examples from probabilistic automata theory in this sequel to hermida and mateus paracategories i internal paracategories and saturated partial algebras theoret comput sci in press we explore some of the global aspects of the category of paracategories we establish its co completeness and cartesian closure from the closed structure we derive the relevant notion of transformation for paracategories we set up the relevant notion of adjunction between paracategories and apply it to define co completeness and cartesian closure exemplified by the paracategory of bivariant functors and dinatural transformations we introduce partial multicategories to account for partial tensor products we also consider fibrations for paracategories and their indexed paracategory version finally we instantiate all these concepts in the context of probabilistic automata

drinfeld center of enriched monoidal categories abstract we define the drinfeld center of a monoidal category enriched over a braided monoidal category and show that every modular tensor category can be realized in a canonical way as the drinfeld center of a self enriched monoidal category we also give a generalization of this result for important applications in physics

reactive generative and stratified models of probabilistic processes abstract we introduce three models of probabilistic processes namely reactive generative and stratified these models are investigated within the context of pccs an extension of milner s sccs in which each summand of a process summation expression is guarded by a probability and the sum of these probabilities is 1 for each model we present a structural operational semantics of pccs and a notion of bisimulation equivalence which we prove to be a congruence we also show that the models form a hierarchy the reactive model is derivable from the generative model by abstraction from the relative probabilities of different actions and the generative model is derivable from the stratified model by abstraction from the purely probabilistic branching structure moreover the classical nonprobabilistic model is derivable from each of these models by abstraction from all probabilities

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

milnor moore categories and monadic decomposition abstract in this paper monoidal hom lie algebras lie color algebras lie superalgebras and other type of generalized lie algebras are recovered by means of an iterated construction known as monadic decomposition of functors which is based on eilenberg moore categories to this aim we introduce the notion of milnor moore category as a monoidal category for which a milnor moore type theorem holds we also show how to lift the property of being a milnor moore category whenever a suitable monoidal functor is given and we apply this technique to provide examples

algebraic and topological structure of some spaces of set valued maps in this paper we consider possible topological and algebraic structures on some spaces of set valued maps in particular we introduce algebraic operations on the set m x y of all minimal upper semi continuous compact valued maps from a topological space x into a topological group y it is shown that under suitable assumptions on the spaces x and y we may equip the set m x y with a group structure this structure extends the usual pointwise operations on the set of point valued continuous functions we also introduce convergence structures on certain sets of set valued maps in particular we consider the continuous convergence structure on sets of upper semi continuous maps as well as a convergence structure on m x y derived through it which is compatible with the mentioned algebraic structure it is also shown that the generalized compact open topology is compatible with the algebraic structure introduced on m x y

reflection fusion categories abstract we introduce the notion of a reflection fusion category which is a type of a g crossed category generated by objects of frobenius perron dimension 1 and p where p is an odd prime we show that such categories correspond to orthogonal reflection groups over f p this allows us to use the known classification of irreducible reflection groups over finite fields to classify irreducible reflection fusion categories

on quasilinear spaces of convex bodies and intervals algebraic systems abstracting properties of convex bodies and intervals with respect to addition and multiplication by scalars known as quasilinear spaces are studied axiomatically we discuss special quasilinear spaces with group structure called quasivector spaces we show that every quasivector space is a direct sum of a vector space and a symmetric quasivector space a complete characterization of symmetric quasivector spaces in the finite dimensional case is given which permits to reduce computation in quasilinear spaces to computation in familiar vector spaces

solving large classes of nonlinear systems of pdes it is shown that large classes of nonlinear systems of pdes with possibly associated initial and or boundary value problems can be solved by the method of order completion the solutions obtained can be assimilated with hausdorff continuous functions the usual navier stokes equations as well as their various modifications aiming at a realistic modeling are included as particular cases the same holds for the critically important constitutive relations in various branches of continuum mechanics the solution method does not involve functional analysis nor various sobolev or other spaces of distributions or generalized functions the general and type independent existence and regularity results regarding solutions presented here have recently been introduced in the literature provided also if need be that the notion of a solution shall be suitably extended cited from hilbert s 20th problem

paracategories i internal paracategories and saturated partial algebras based on the monoid classifier we give an alternative axiomatization of freyd s paracategories which can be interpreted in any bicategory of partial maps assuming furthermore a free monoid monad t in our ambient category and coequalisers satisfying some exactness conditions we give an abstract envelope construction putting paramonoids and paracategories in the more general context of partial algebras we introduce for the latter the crucial notion of saturation which characterises those partial algebras which are isomorphic to the ones obtained from their enveloping algebras we also set up a factorisation system for partial algebras via epimorphisms and monic kleene morphisms and relate the latter to saturation

spline subdivision schemes for convex compact sets the application of spline subdivision schemes to data consisting of convex compact sets with addition replaced by minkowski sums of sets is investigated these methods generate in the limit set valued functions which can be expressed explicitly in terms of linear combinations of integer shifts of b splines with the initial data as coefficients the subdivision techniques are used to conclude that these limit set valued spline functions have shape preserving properties similar to those of the usual spline functions this extension of subdivision methods from the scalar setting to the set valued case has application in the approximate reconstruction of 3 d bodies from finite collections of their parallel cross sections

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

sensor array processing based on subspace fitting algorithms for estimating unknown signal parameters from the measured output of a sensor array are considered in connection with the subspace fitting problem the methods considered are the deterministic maximum likelihood method ml esprit and a recently proposed multidimensional signal subspace method these methods are formulated in a subspace fitting based framework which provides insight into their algebraic and asymptotic relations it is shown that by introducing a specific weighting matrix the multidimensional signal subspace method can achieve the same asymptotic properties as the ml method the asymptotic distribution of the estimation error is derived for a general subspace weighting and the weighting that provides minimum variance estimates is identified the resulting optimal technique is termed the weighted subspace fitting wsf method numerical examples indicate that the asymptotic variance of the wsf estimates coincides with the cramer rao bound the performance improvement compared to the other techniques is found to be most prominent for highly correlated signals

music maximum likelihood and cramer rao bound the performance of the music and ml methods is studied and their statistical efficiency is analyzed the cramer rao bound crb for the estimation problems is derived and some useful properties of the crb covariance matrix are established the relationship between the music and ml estimators is investigated as well a numerical study is reported of the statistical efficiency of the music estimator for the problem of finding the directions of two plane waves using a uniform linear array an exact description of the results is included

detection and estimation in sensor arrays using weighted subspace fitting the problem of signal parameter estimation of narrowband emitter signals impinging on an array of sensors is addressed a multidimensional estimation procedure that applies to arbitrary array structures and signal correlation is proposed the method is based on the recently introduced weighted subspace fitting wsf criterion and includes schemes for both detecting the number of sources and estimating the signal parameters a gauss newton type method is presented for solving the multidimensional wsf and maximum likelihood optimization problems the global and local properties of the search procedure are investigated through computer simulations most methods require knowledge of the number of coherent noncoherent signals present a scheme for consistently estimating this is proposed based on an asymptotic analysis of the wsf cost function the performance of the detection scheme is also investigated through simulations

extensions of lipschitz selections and an application to differential inclusions we establish in one section of this paper the existence of a lipschitz extension of a lipschitz selection of a lipschitz convex compact set valued map into r that is given a lipschitz selection on a subdomain it can be extended to a lipschitz selection on the entire domain of definition of the set valued map the extension result is applied in the closing section we show that under the minimal natural conditions a lipschitz solution of an autonomous lipschitz differential inclusion is a solution of an autonomous lipschitz ordinary differential equation within the inclusion

performance study of conditional and unconditional direction of arrival estimation a numerical and analytical study of conditional and unconditional direction of arrival doa estimation is presented explicit expressions for the unconditional cramer rao bounds on the doa estimation accuracy and the covariance matrix of the conditional maximum likelihood method are given it is shown that many doa estimation methods have the same asymptotic statistical properties under conditional and unconditional models the situation of two narrowband plane signals impinging on a uniformly spaced linear array is discussed

high resolution direction finding the missing data case this paper considers the problem of estimating the direction of arrival doa of one or more signals using an array of sensors where some of the sensors fail to work before the measurement is completed methods for estimating the array output covariance matrix are discussed in particular the maximum likelihood ml estimate of this covariance matrix and its asymptotic accuracy are derived and discussed different covariance matrix estimates are used for doa estimation together with the music algorithm and with a covariance matching technique in contrast to music the covariance matching technique can utilize information on the estimation accuracy of the array covariance matrix and it is demonstrated that this yields a significant performance gain

maximum likelihood methods for direction of arrival estimation five methods of direction of arrival doa estimation which can be derived from the maximum likelihood ml principle are considered the ml method mlm results from the application of the ml principle to the statistics of the observed raw data the standard multiple signal classification music procedure called music 1 is obtained as a brute force approximation of the mlm an improved music procedure named music 2 is obtained by applying the ml principle to the statistics of certain linear combinations of the sample noise space eigenvectors a procedure which compromises between the good performance of the mlm and the computational simplicity of music is a method of direction estimation mode 1 which is derived as a large sample realization of the mlm a fifth method called mode 2 is obtained by using the ml principle on the statistics of certain linear combinations of the sample eigenvectors mode 2 is computationally less demanding than the mlm it is of the same complexity as mode 1 and statistically more efficient a numerical comparison of these five doa estimation methods is presented it confirms the analytic results on their theoretical performance levels

linear and quasi linear spaces of set valued maps abstract in this paper we investigate the algebraic structure of certain spaces of set valued maps among other results we show that for an arbitrary topological space x and a metrisable topological vector space z the space m x z of minimal upper semi continuous compact valued musco maps from x into z is a linear space this result extends a previously known result on the linear structure of spaces of musco maps previously this result was known only in the case when x is a baire space we also study topologies of uniform convergence on compact sets on m x z