maximization and minimization of the rank and inertia of the hermitian matrix expression a bx bx with applications abstract we give in this paper a group of closed form formulas for the maximal and minimal ranks and inertias of the linear hermitian matrix function a bx bx with respect to a variable matrix x as applications we derive the extremal ranks and inertias of the matrices x x where x is a solution to the matrix equation axb c and then give necessary and sufficient conditions for the matrix equation axb c to have hermitian definite and re definite solutions in addition we give closed form formulas for the extremal ranks and inertias of the difference x 1 x 2 where x 1 and x 2 are hermitian solutions of two matrix equations a 1 x 1 a 1 c 1 and a 2 x 2 a 2 c 2 and then use the formulas to characterize relations between hermitian solutions of the two equations

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

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

the signal subspace approach for multiple wide band emitter location the rational vector space generalization of the signal subspace approach is presented and applied to the estimation of multiple wide band emitter locations from the signals received at multiple sensors the signal subspace and array manifold concepts first introduced by schmidt are generalized to rational vector space these concepts are used to develop the rational signal subspace theory and prove the signal subspace theorem on which signal subspace algorithms are based the theory is applied in discrete time to derive a class of rational signal subspace algorithms for source location and spectral estimation using unit circle eigendecomposition of multivariate rational models of sensor outputs simulation results are presented for an algorithm in this class including sample statistics from monte carlo trials and comparisons with the cramer rao bound

grouped coordinate ascent algorithms for penalized likelihood transmission image reconstruction presents a new class of algorithms for penalized likelihood reconstruction of attenuation maps from low count transmission scans we derive the algorithms by applying to the transmission log likelihood a version of the convexity technique developed by de pierro for emission tomography the new class includes the single coordinate ascent sca algorithm and lange s convex algorithm for transmission tomography as special cases the new grouped coordinate ascent gca algorithms in the class overcome several limitations associated with previous algorithms 1 fewer exponentiations are required than in the transmission maximum likelihood expectation maximization ml em algorithm or in the sca algorithm 2 the algorithms intrinsically accommodate nonnegativity constraints unlike many gradient based methods 3 the algorithms are easily parallelizable unlike the sca algorithm and perhaps line search algorithms we show that the gca algorithms converge faster than the sca algorithm even on conventional workstations an example from a low count positron emission tomography pet transmission scan illustrates the method

estimation of spatial and spectral parameters of multiple sources the problem of estimating spatial and spectral parameters of multiple sources by sensor arrays is considered a parametric model is derived for the multichannel measurement vector tbe model parameters are the time delays and the autoregressive moving average parameters of all the sources a suboptimal parameter estimation procedure is proposed and simulation results are presented to illustrate its performance

a quick method for estimation of parameters of individual pulses in a multipath signal abstract consider a multipath signal whose individual signals are deterministic known increasing or decreasing pulses the problem is to estimate the amplitudes and delay times of individual signals several methods have been devoted to the solution of these unknown parameters the maximum likelihood ml estimation and the estimate maximize em algorithm are commonly used but they are computationally intensive and still insufficient to obtain accurate estimations the method can provide a quick and accurate estimate of the amplitudes and arrival delay times even in the closely spaced multipaths and heavy noise

a unified method for measurement and tracking of contacts from an array of sensors a multiple target track estimation method that operates directly from array data is presented the maximum a posteriori map estimator for contact states is derived for temporally uncorrelated signals and uncorrelated contact tracks where the number of contacts is assumed known this estimator is an iterative algorithm employing a nonlinear programming nlp penalty method in conjunction with an expectation maximization em algorithm the nlp technique is used to find the map track estimate based on the synthetic signal estimates produced by the em algorithm this method eliminates the data association step of traditional multitarget tracking approaches by conditioning the measurement process on individual target state distributions it results in a process similar to the em algorithm for direction finding with an additional penalty term imposed by the track distributions the algorithm is derived as a batch method an extension to support sequential tracking is also developed simulation results for a relevant submarine towed array scenario are presented and discussed

estimation of time differences of arrival by pole decomposition time differences of arrival tdoa s of emitter wave fronts to a spatially distributed array of sensors can be used to determine the source location in this paper we suggest a new method of tdoa estimation for multiple unknown autoregressive moving average arma sources and additive noise that may be correlated between the sensors we derive a theoretical formula that only uses the receiver cross spectra and the source poles for the tdoa determination the poles are estimated by a least squares technique and two methods are suggested for the estimation of the cross spectra which allow tradeoffs between computational complexity and accuracy a new time delay model is derived and used to show the applicability of the methods for noninteger tdoa s results from simulations illustrate the performance of the algorithm by monte carlo trials and compare it to the cramer rao bound

em based recursive estimation of channel parameters recursive online expectation maximization em algorithm along with stochastic approximation is employed in this paper to estimate unknown time invariant variant parameters the impulse response of a linear system channel is modeled as an unknown deterministic vector process and as a gaussian vector process with unknown stochastic characteristics using these models which are embedded in white or colored gaussian noise different types of recursive least squares rls kalman filtering and smoothing and combined rls and kalman type algorithms are derived directly from the recursive em algorithm the estimation of unknown parameters also generates new recursive algorithms for situations such as additive colored noise modeled by an autoregressive process the recursive em algorithm is shown as a powerful tool which unifies the derivations of many adaptive estimation methods

on the inertia of sums of hermitian matrices abstract given n n hermitian matrices h1 hp a complete description is found for the possible inertias of the sum h1 hp in terms of the inertias of hi i 1 p we also consider and solve other related problems

the inertia of hermitian block matrices with zero main diagonal abstract let n 1 n 2 n 3 be nonnegative integers we consider partitioned hermitian matrices of the form h 0 x 12 x 13 3pt x 12 0 x 23 5pt x 13 x 23 0 where each x ij is n i n j and we characterize the set of the inertias in h r ij rank x ij r ij for 1 i in terms of r ij r ij and the block orders

a maximum likelihood digital receiver using coordinate ascent and the discrete wavelet transform in this paper a maximum likelihood ml method is presented for joint estimation of amplitude phase time delay and data symbols in a single user direct sequence spread spectrum communication system since maximization of the likelihood function is analytically intractable a novel coordinate ascent algorithm is used to obtain sequential updates of the data symbols and all unknown nuisance parameters the novelty of the algorithm is due to the use of a multiresolution expansion of the received signal and the use of polynomial rooting in the complex plane in place of a line search over the signal delay parameter the multiresolution structure of the algorithm is exploited to reduce sensitivity to impulsive noise via wavelet thresholding computer simulations of the single user system show that the algorithm has fast convergence and comparison with theoretical lower bounds establishes that the algorithm achieves nearly optimal error performance

parameter estimation of superimposed signals using the em algorithm a computationally efficient algorithm for parameter estimation of superimposed signals based on the two step iterative em estimate and maximize with an e step and an m step algorithm is developed the idea is to decompose the observed data into their signal components and then to estimate the parameters of each signal component separately the algorithm iterates back and forth using the current parameter estimates to decompose the observed data better and thus increase the likelihood of the next parameter estimates the application of the algorithm to the multipath time delay and multiple source location estimation problems is considered

the inertia of certain hermitian block matrices abstract we characterize sets of inertias of some partitioned hermitian matrices by a system of inequalities involving the orders of the blocks the inertias of the diagonal blocks and the ranks of the nondiagonal blocks the main result generalizes some well known characterizations of sa and cain and others

on the convergence properties of the em algorithm two convergence aspects of the em algorithm are studied i does the em algorithm find a local maximum or a stationary value of the incomplete data likelihood function ii does the sequence of parameter estimates generated by em converge several convergence results are obtained under conditions that are applicable to many practical situations two useful special cases are a if the unobserved complete data specification can be described by a curved exponential family with compact parameter space all the limit points of any em sequence are stationary points of the likelihood function b if the likelihood function is unimodal and a certain differentiability condition is satisfied then any em sequence converges to the unique maximum likelihood estimate a list of key properties of the algorithm is included

the inertia sets of symmetric tridiagonal sign patterns abstract we give a complete description of the possible inertias of real symmetric matrices with a given arbitrarily prescribed tridiagonal symmetric sign pattern the inertia set of such a pattern is a subset of z 2 given by a system of linear inequalities whose parameters are determined from the sign sequence of the pattern s diagonal entries

the inertia of certain hermitian skew triangular block matrices abstract let n1 n2 n3 be nonnegative integers we consider hermitian matrices h of the form h h 11 h 12 h 13 h 21 h 22 h 23 h 31 h 32 h 33 where each hij is ni nj we characterize the set of inertias in h in hii i vi i and r1 i 1 rank h1 i 1 r1 i 1 for i 1 2 in terms of 1 v1 1 2 v2 2 n3 r12 r13 r12 r 12 and we discuss the implications of this characterization for the determination of the inertia of other types of hermitian skew triangular block matrices

une base explicite de symboles modulaires sur les corps de fonctions modular symbols for the congruence subgroup gamma 0 mathfrak n of gl 2 mathbf f q t have been defined by teitelbaum they have a presentation given by a finite number of generators and relations in a formalism similar to manin s for classical modular symbols we completely solve the relations and get an explicit basis of generators when mathfrak n is a prime ideal of odd degree as an application we give a non vanishing statement for l functions of certain automorphic cusp forms for mathbf f q t the main statement also provides a key step for a result towards the uniform boundedness conjecture for drinfeld modules of rank 2

a fast improvement to the em algorithm on its own terms the em algorithm is a numerical technique for the evaluation of maximum likelihood estimates for parameters describing incomplete data models it is easy to apply in many problems and is stable but slow the algorithm fails to provide a consistent estimator of the standard errors of the maximum likelihood estimates unless the additional analysis required by the louis method is performed newton type or other gradient methods are faster and provide error estimates but tend to be unstable and require the analytical evaluation of likelihoods to derive expressions for the score function and at least approximations to the fisher information matrix the purpose of this paper is to expand on a result by fisher that permits a unification of em methodology and newton methods the evaluation of the individual observation by observation score functions of the incomplete data is a byproduct of the application of the e step of the em algorithm once these become available the fisher information matrix may be consistently estimated and the m step may be replaced by a fast newton type step

equalities and inequalities for inertias of hermitian matrices with applications abstract the inertia of a hermitian matrix is defined to be a triplet composed of the numbers of the positive negative and zero eigenvalues of the matrix counted with multiplicities respectively in this paper we show some basic formulas for inertias of 2 2 block hermitian matrices from these formulas we derive various equalities and inequalities for inertias of sums parallel sums products of hermitian matrices submatrices in block hermitian matrices differences of outer inverses of hermitian matrices as applications we derive the extremal inertias of the linear matrix expression a bxb with respect to a variable hermitian matrix x in addition we give some results on the extremal inertias of hermitian solutions to the matrix equation ax b as well as the extremal inertias of a partial block hermitian matrix