honey pot constrained searching with local sensory information in this paper we investigate the problem of searching for a hidden target in a bounded region of the plane using an autonomous robot which is only able to use local sensory information the problem is naturally formulated in the continuous domain but the solution proposed is based on an aggregation refinement approach in which the continuous search space is partitioned into a finite collection of regions on which we define a discrete search problem a solution to the original problem is obtained through a refinement procedure that lifts the discrete path into a continuous one we show that the discrete optimization is computationally difficult np hard but there are computationally efficient approximation algorithms for solving it the resulting solution to the continuous problem is in general not optimal but one can construct bounds to gauge the cost penalty incurred due to i the discretization of the problem and ii the attempt to approximately solve the np hard problem in polynomial time numerical simulations show that the algorithms proposed behave significantly better than naive approaches such as a random walk or a greedy algorithm c 2006 elsevier ltd all rights reserved

theory and design of signal adapted fir paraunitary filter banks we study the design of signal adapted fir paraunitary filter banks using energy compaction as the adaptation criterion we present some important properties that globally optimal solutions to this optimization problem satisfy in particular we show that the optimal filters in the first channel of the filter bank are spectral factors of the solution to a linear semi infinite programming sip problem the remaining filters are related to the first through a matrix eigenvector decomposition we discuss uniqueness and sensitivity issues the sip problem is solved using a discretization method and a standard simplex algorithm we also show how regularity constraints may be incorporated into the design problem to obtain globally optimal in the energy compaction sense filter banks with specified regularity we also consider a problem in which the polyphase matrix implementation of the filter bank is constrained to be dct based such constraints may also be incorporated into our optimization algorithm therefore we are able to obtain globally optimal filter banks subject to regularity and or computational complexity constraints numerous experiments are presented to illustrate the main features that distinguish adapted and nonadapted filters as well as the effects of the various constraints the conjecture that energy compaction and coding gain optimization are equivalent design criteria is shown not to hold for fir filter banks

optimal search among false contacts this paper considers rational methods for the design of search patterns when the intended target is among poisson distributed false contacts attention is restricted to situations in which the searcher must immediately decide based on sensed information whether a contact is the intended target and if the answer is yes end the search and commit to the contact discrimination of false contact from target is modeled as reliable only with given probabilities this research seeks to maximize the probability of finding the intended target in a fixed time most of the paper addresses an optimal search trajectory when intended target and false contacts move according to markov processes the searcher s velocity is taken as the control and it is assumed that his speed is limited and his initial position is given it is proved that an optimal control exists in the space l infty a set of necessary conditions for the optimal control is derived a maximum principle in the form of a two point boundary value pr

a pseudo polynomial heuristic for path constrained discrete time markovian target search we propose a new heuristic for the single searcher path constrained discrete time markovian target search the algorithm minimizes an approximate instead of exact nondetection probability computed from the conditional probability that reflects the search history over the time windows of a fixed length l having a pseudo polynomial complexity it can solve in reasonable time the instances an order of magnitude larger than those solved in the previous studies by an asymptotic analysis relying on the fast mixing markov chain we show that the relative error of the approximation exponentially diminishes as l increases and the experimental results confirm the analysis the experiment also reveals a correlation very close to 1 between the approximate and exact nondetection probability of a search path this means that the heuristic produces near optimal search paths

the role of linear semi infinite programming in signal adapted qmf bank design we consider the problem of designing a perfect reconstruction fir quadrature mirror filter qmf bank h g adapted to input signal statistics with the coding gain as the adaptation criterion maximization of the coding gain has so far been viewed as a difficult nonlinear constrained optimization problem it is shown that the coding gain depends only on the product filter p z h z h z sup 1 and this transformation leads to a stable class of linear optimization problems having finitely many variables and infinitely many constraints termed linear semi infinite programming sip problems the sought for original filter h z is obtained by deflation and spectral factorization of p z with the sip formulation every locally optimal solution is also globally optimal and can be computed using reliable numerical algorithms the natural regularity properties inherent in the sip formulation enhance the performance of these algorithms we present a comprehensive theoretical analysis of the sip problem and its dual characterize the optimal filters and analyze uniqueness and sensitivity issues all these properties are intimately related to those of the input signal and bring considerable insight into the nature of the adaptation process we present discretization and cutting plane algorithms and apply both methods to several examples

the dual parameterization approach to optimal least square fir filter design subject to maximum error constraints this paper is concerned with the design of linear phase finite impulse response fir digital filters for which the weighted least square error is minimized subject to maximum error constraints the design problem is formulated as a semi infinite quadratic optimization problem using a newly developed dual parameterization method in conjunction with the caratheodory s dimensional theorem an equivalent dual finite dimensional optimization problem is obtained the connection between the primal and the dual problems is established a computational procedure is devised for solving the dual finite dimensional optimization problem the optimal solution to the primal problem can then be readily obtained from the dual optimal solution for illustration examples are solved using the proposed computational procedure

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

nonuniform directional filter banks with arbitrary frequency partitioning directional filter banks dfbs are highly desired in directional representation of images in this correspondence we propose a 2 d nonsubsampled nonuniform directional filter bank nudfb and its design method the proposed nudfb has nonuniform wedge shaped subbands and allows arbitrary frequency partitioning schemes it can extract directional information according to the directional distribution of images this attractive advantage cannot be achieved by the existing directional transforms the design method of the proposed nudfb is based upon the pseudopolar fourier transform by utilizing the geometry property of the pseudopolar grid we employ a 1 d nonsubsampled nonuniform filter bank to obtain a set of nonuniform wedge shaped subbands during the design process only 1 d operations are involved and thus the difficulty encountered in the design of 2 d fan filters is avoided to demonstrate the potential of the proposed nudfb an example on image directional decomposition is given

moving target search a real time search for changing goals considers the case of heuristic search where the goal may change during the course of the search for example the goal may be a target that actively avoids the problem solver the authors present a moving target search algorithm mts to solve this problem the authors prove that if the average speed of the target is slower than that of the problem solver then the problem solver is guaranteed to eventually reach the target in a connected problem space the original mts algorithm was constructed with the minimum operations necessary to guarantee its completeness and hence is not very efficient to improve its efficiency the authors introduce ideas from the area of resource bounded planning into mts including 1 commitment to goals and 2 deliberation for selecting plans experimental results demonstrate that the improved mts is 10 to 20 times more efficient than the original mts in uncertain situations

semiparametric crb and slepian bangs formulas for complex elliptically symmetric distributions the main aim of this paper is to extend the semiparametric inference methodology recently investigated for real elliptically symmetric res distributions to complex elliptically symmetric ces distributions the generalization to the complex field is of fundamental importance in all practical applications that exploit the complex representation of the acquired data moreover the ces distributions has been widely recognized as a valuable and general model to statistically describe the non gaussian behaviour of datasets originated from a wide variety of physical measurement processes the paper is divided in two parts in the first part a closed form expression of the constrained semiparametric cramer rao bound cscrb for the joint estimation of complex mean vector and complex scatter matrix of a set of ces distributed random vectors is obtained by exploiting the so called wirtinger or mathbb c mathbb r calculus the second part deals with the derivation of the semiparametric version of the slepian bangs formula in the context of the ces model specifically the proposed semiparametric slepian bangs ssb formula provides us with a useful and ready to use expression of the semiparametric fisher information matrix sfim for the estimation of a parameter vector parametrizing the complex mean and the complex scatter matrix of a ces distributed vector in the presence of unknown nuisance density generator furthermore we show how to exploit the derived ssb formula to obtain the semiparametric counterpart of the stochastic crb for direction of arrival doa estimation under a random signal model assumption simulation results are also provided to clarify the theoretical findings and to demonstrate their usefulness in common array processing applications

performance analysis of direction finding using lag redundancy averaging the lag redundancy averaging lra method for processing linear equispaced arrays is examined lra is a simple procedure for estimating toeplitz covariance matrices which can be computed efficiently by means of spatial fast fourier transform fft algorithms the effect of lra on the performance of the music method for uncorrelated sources is investigated closed form expressions for the asymptotic bearing accuracy are obtained it is shown for the single source case that the lra method is asymptotically efficient for two equipowered sources it is shown that while the resolution threshold of the lra method is superior to that of standard music its asymptotic accuracy is inferior

envelope constrained filter with linear interpolator the envelope constrained ec filtering problem is the minimization of the noise gain of the filter while satisfying the constraint that its noiseless response to a specified input lies within a prescribed envelope using a hybrid filter consisting of an a d converter an fir filter and a linear interpolator the problem is posed as a functional inequality constrained optimization problem a technique for solving this problem is proposed by approximating it with a conventional unconstrained optimization problem that is then solved by a descent direction based algorithm

conditional central algorithms for worst case set membership identification and filtering this paper deals with conditional central estimators in a set membership setting the role and importance of these algorithms in identification and filtering is illustrated by showing that problems like worst case optimal identification and state filtering in contexts in which disturbances are described through norm bounds are reducible to the computation of conditional central algorithms the conditional chebyshev center problem is solved for the case when energy norm bounded disturbances are considered a closed form solution is obtained by finding the unique real root of a polynomial equation in a semi infinite interval

an algorithm for robust pole assignment via polynomial approach a computational method for designing controllers which attempt to place the roots of the characteristic polynomial of an uncertain system inside some prescribed regions is presented the analysis is based on transfer functions of characteristic polynomials and the problem is formulated as one of semi infinite programming an example of an application is given to illustrate this approach

multiresolution analysis on bounded domains for the design of biorthogonal wavelet bases an axiomatic approach to biorthogonal multiresolution analyzes on bounded domains is presented the intervalized multiresolution analysis mra leads to a generalized framework within which one can construct biorthogonal wavelet transforms including many constructions presented in the literature to date the framework also leads naturally to algorithms for calculating and constraining pertinent properties of both the discrete filters and their corresponding continuous basis functions construction of wavelet analysis within the new framework is then illustrated with the design of a basis specifically tailored to reduce the boundary artifacts induced by some wavelet transforms used in image processing

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

an efficient and accurate parallel algorithm for the singular value problem of bidiagonal matrices in this paper we propose an algorithm based on laguerre s iteration rank two divide and conquer technique and a hybrid strategy for computing singular values of bidiagonal matrices the algorithm is fully parallel in nature and evaluates singular values to tiny relative error if necessary it is competitive with qr algorithm in serial mode in speed and advantageous in computing partial singular values error analysis and numerical results are presented

the complexity of the optimal searcher path problem in this note we show that the problem of finding an optimal searcher path that maximizes the probability of detecting a stationary target by the end of a fixed time is np complete we also demonstrate that the problem of finding a path that minimizes mean time to detection is np hard

cramer rao bound for doa estimators under the partial relaxation framework derivation and comparison a class of computationally efficient doa estimators under the partial relaxation pr framework has recently been proposed conceptually different from conventional doa estimation methods in the literature the estimators under the pr framework rely on the non complete relaxation of the array manifold while performing a spectral search in the field of view this particular type of relaxation essentially implies a modified signal model with partial information loss due to the relaxation the information loss and its impact on the doa estimation performance have not yet been analytically quantified in the literature in this paper the information loss induced by the relaxation of the array manifold is investigated through the cramer rao bound crb the closed form expression of the crb for doa estimation under the pr model on the one hand provides insight on the information loss in the asymptotic region where the number of snapshots tends to infinity on the other hand the proposed crb characterizes the lower bound for the doa estimation performance of all pr estimators we prove that under the assumptions of gaussian source signal and noise the crb of the pr signal model is lower bounded by the conventional stochastic crb we also prove that the previously proposed weighted subspace fitting estimator under the pr framework asymptotically achieves the crb of the pr signal model furthermore it is shown that the asymptotic mean squared errors of all weighted subspace fitting estimators under the pr framework for any positive definite weighting matrix are identical

accurate singular values and differential qd algorithms in september 1991 j w demmel and w m kahan were awarded the second siam prize in numerical linear algebra for their paper accurate singular values of bidiagonal matrices 1 referred to as dk hereafter among several valuable results was the observation that the standard bidiagonal qr algorithm used in linpack 2 and in many other svd programs can be simplified when the shift is zero and of greater importance no subtractions occur the last feature permits very small singular values to be found with almost all the accuracy permitted by the data and at no extra cost

gaussian cramer rao bound for direction estimation of noncircular signals in unknown noise fields this paper focuses on the stochastic cramer rao bound crb on direction of arrival doa estimation accuracy for noncircular gaussian sources in the general case of an arbitrary unknown gaussian noise field parameterized by a vector of unknowns explicit closed form expressions of the stochastic crb for doa parameters alone are obtained directly from the slepian bangs formula for general noncircular complex gaussian distributions as a special case the crb under the nonuniform white noise assumption is derived our expressions can be viewed as extensions of the well known results by stoica and nehorai ottersten et al weiss and friedlander pesavento and gershman and gershman et al some properties of these crbs are proved and finally these bounds are numerically compared with the conventional crbs under the circular complex gaussian distribution for different unknown noise field models

one sided reduction to bidiagonal form abstract we present an idea for reducing a rectangular matrix a to bidiagonal form which is based on the implicit reduction of the symmetric positive semidefinite matrix a t a to tridiagonal form in other papers we have shown that a method based upon this idea may become a serious competitor in terms of speed for computing the singular values of large matrices and also that it is well suited for parallel processing however there are still some open questions related to the numerical stability of the method and these will be addressed in this paper the algorithm as it is at present is not backward stable nevertheless we give examples of ill conditioned matrices for which we have been able to produce a bidiagonal form whose singular values are much more accurate than the ones computed with the standard bidiagonalization technique

an optimal branch and bound procedure for the constrained path moving target search problem a searcher and target move among a finite set of cells c 1 2 n in discrete time at the beginning of each time period one cell is searched if the target is in the selected cell j it is detected with probability qj if the target is not in the cell searched it cannot be detected during the current time period after each search a target in cell j moves to cell k with probability pjk the target transition matrix p pjk is known to the searcher the searcher s path is constrained in that if the searcher is currently in cell j the next search cell must be selected from a set of neighboring cells cj the object of the search is to minimize the probability of not detecting the target in t searches

optimal design of nonuniform fir transmultiplexer using semi infinite programming this correspondence considers an optimum nonuniform finite impulse response fir transmultiplexer design problem subject to specifications in the frequency domain our objective is to minimize the sum of the ripple energy for all the individual filters subject to the specifications on amplitude and aliasing distortions and to the passband and stopband specifications for the individual filters this optimum nonuniform transmultiplexer design problem can be formulated as a quadratic semi infinite programming problem the dual parametrization algorithm is extended to this nonuniform transmultiplexer design problem if the lengths of the filters are sufficiently long and the set of decimation integers is compatible then a solution exists since the problem is formulated as a convex problem if a solution exists then the solution obtained is unique and the local solution is a global minimum

frequency selective kyp lemma iir filter and filter bank design for a transfer function f ejomega of order n kalman yakubovich popov kyp lemma characterizes a general intractable semi infinite programming sip condition by a tractable semidefinite programming sdp for the entire frequency range some recent results generalize this lemma for a certain frequency interval all these sdp characterizations are given at the expense of the introduced lyapunov matrix variable of dimension ntimesn consequently formulation and design of high dimensional problem is challenging moreover existing sdp characterizations for frequency selective sip fs sip do not allow to formulate synthesis problems as sdps in this paper we propose a completely new sdp characterization of general fs sip involving sdps of moderate size and free from lyapunov variables furthermore a systematic iir filter and filter bank design is developed in a similar vein with several simulations provided to validate the effectiveness of our sdp formulation

matrix filter design using semi infinite programming with application to doa estimation we propose using a semi infinite programming technique to design a matrix filter the idea is to formulate the design problem into a semi infinite optimization model where the mean square error between the desired response and the designed filter in the passband and stopband is minimized subject to a set of nonlinear functional inequalities these inequality constraints are used to ensure that the stopband attenuation and the passband deviation satisfy the prescribed specifications simulations showed that the proposed method was better than the conventional matrix filter design techniques the matrix filters based on the proposed design method was also applied to the direction of arrival doa estimation problem it was shown that the filter greatly improved the estimation accuracy at low signal to noise ratios snrs

rational suboptimal continuous time controller design we obtain rational suboptimal continuous time solutions to some optimal control problems specified via time domain performance criteria these include spl lscr sub 1 and spl lscr sub spl infin norms and peak overshoot the approach uses linear semi infinite programming to compute weights for a given finite set of rational basis functions and makes the best possible use of the basis the closed loop transfer functions obtained satisfy appropriate interpolation constraints for internal stability and the formulation allows additional linear constraints to be incorporated

constrained optimization methods in hilbert spaces and their applications to optimal control problems with functional inequality constraints this note generalizes constrained optimization methods in a finite dimensional space into hilbert spaces and investigates computational methods for optimal control problems with functional inequality constraints two methods are proposed by applying the feasible direction method and the constrained quasi newton method subsidiary problems for direction finding that are originally linear quadratic programming in a hilbert space can be transformed into linear quadratic ones in rn thus the control problem can be solved by a series of finite dimensional programming problems

efficient algorithm for solving semi infinite programming problems and their applications to nonuniform filter bank designs an efficient algorithm for solving semi infinite programming problems is proposed in this paper the index set is constructed by adding only one of the most violated points in a refined set of grid points by applying this algorithm for solving the optimum nonuniform symmetric antisymmetric linear phase finite impulse response fir filter bank design problems the time required to obtain a globally optimal solution is much reduced compared with that of the previous proposed algorithm

design of high order chebyshev fir filters in the complex domain under magnitude constraints this article discusses the design of fir filters that approximate a complex valued target frequency response in a chebyshev sense additionally the required stopband attenuation can be specified solving the dual of a semi infinite linear program is currently the most efficient way to design such filters but numerical problems prevent the design of high order fir filters modifications are proposed to overcome this limitation furthermore an efficient method is presented for generating starting values that are close to the optimal solution such that the number of iterations is considerably reduced examples of filters with a length up to 250 taps are included

explicit ziv zakai lower bound for bearing estimation the extended ziv zakai bound for vector parameters is used to develop a lower bound on the mean square error in estimating the 2 d bearing of a narrowband planewave signal using planar arrays of arbitrary geometry the bound has a simple closed form expression that is a function of the signal wavelength the signal to noise ratio snr the number of data snapshots the number of sensors in the array and the array configuration analysis of the bound suggests that there are several regions of operation and expressions for the thresholds separating the regions are provided in the asymptotic region where the number of snapshots and or snr are large estimation errors are small and the bound approaches the inverse fisher information this is the same as the asymptotic performance predicted by the local cramer rao bound for each value of bearing in the a priori performance region where the number of snapshots or snr is small estimation errors are distributed throughout the a priori parameter space and the bound approaches the a priori covariance in the transition region both small and large errors occur and the bound varies smoothly between the two extremes simulations of the maximum likelihood estimator mle demonstrate that the bound closely predicts the performance of the mle in all regions

iterative hos sos ihoss algorithm for direction of arrival estimation and sensor localization a new method for joint direction of arrival doa and sensor position estimation is introduced the sensors are assumed to be randomly deployed except two reference sensors the proposed method exploits the advantages of both higher order statistics hos and second order statistics sos with an iterative algorithm namely iterative higher order second order statistics ihoss a new cumulant matrix estimation technique is proposed for the hos approach by converting the multisource problem into a single source one ihoss performs well even in case of correlated source signals due to the effectiveness of the proposed cumulant matrix estimate a cost function is defined for the joint doa and position estimation the iterative procedure is guaranteed to converge the ambiguity problem in sensor position estimation is solved by observing the source signals at least in two different frequencies the conditions on these frequencies are presented closed form expressions are derived for the deterministic cramer rao bound crb for doa and unknown sensor positions for noncircular complex gaussian noise with unknown covariance matrix simulation results show that the performance of ihoss is significantly better than the hos approaches for doa estimation and closely follows the crb for both doa and sensor position estimations

lower bounds for parametric estimation with constraints a chapman robbins form of the barankin bound is used to derive a multiparameter cramer rao cr type lower bound on estimator error covariance when the parameter theta in r sup n is constrained to lie in a subset of the parameter space a simple form for the constrained cr bound is obtained when the constraint set theta sub c can be expressed as a smooth functional inequality constraint it is shown that the constrained cr bound is identical to the unconstrained cr bound at the regular points of theta sub c i e where no equality constraints are active on the other hand at those points theta in theta sub c where pure equality constraints are active the full rank fisher information matrix in the unconstrained cr bound must be replaced by a rank reduced fisher information matrix obtained as a projection of the full rank fisher matrix onto the tangent hyperplane of the full rank fisher matrix onto the tangent hyperplane of the constraint set at theta a necessary and sufficient condition involving the forms of the constraint and the likelihood function is given for the bound to be achievable and examples for which the bound is achieved are presented in addition to providing a useful generalization of the cr bound the results permit analysis of the gain in achievable mse performance due to the imposition of particular constraints on the parameter space without the need for a global reparameterization

direction finding with time varying arrays this paper considers the problem of finding the directions of narrowband signals using a time varying array whose elements move during the observation interval in an arbitrary but known way assuming a gaussian signal model we derive the cramer rao bound crb and the maximum likelihood estimator for the directions of arrival the single source case is studied in detail time varying arrays are shown to be more robust to ambiguity errors than static arrays of comparable dimensions

optimal matrix filter design a matrix filter produces n output values given a block of n input values matrix filters are particularly useful for filtering short data records e g n spl les 20 we introduce a new set of matrix filter design criteria and show that the design of a matrix filter can be formulated as a convex optimization problem several examples are given of lowpass and bandpass designs as well as a hilbert transformer design

optimal sequential search a bayesian approach to the classical model of searching for one object out of n we add uncertainty about the parameters of the distribution of the n objects among the m boxes adopting a bayesian approach we study the optimal sequential search strategy for the case n 1 we obtain a generalization of the fundamental result of blackwell the strategy which searches at each stage in the most inviting box is optimal this strategy is also optimal form 2 and arbitrary n however for n 1 the optimal strategy may be very di erent from that of the classical model even when the uncertainty about is very small ams 1980 subject classi cation primary 90b40

a bayesian approach to array geometry design in this paper we consider the design of planar arrays that optimize direction of arrival doa estimation performance we assume that the single source doa is a random variable with a known prior probability distribution and the sensors of the array are constrained to lie in a region with an arbitrary boundary the crame spl acute r rao bound crb and the fisher information matrix fim for single source doa constitute the basis of the optimality criteria we relate the design criteria to a bayesian crb criterion and to array beamwidth we also derive closed form expressions for the design criteria when the doa prior is uniform on a sector of angles we show that optimal arrays have elements on the constraint boundary thus providing a reduced dimension iterative solution procedure finally we present example designs

accurate polynomial root finding methods for symmetric tridiagonal matrix eigenproblems in this paper we consider the application of polynomial root finding methods to the solution of the tridiagonal matrix eigenproblem all considered solvers are based on evaluating the newton correction we show that the use of scaled three term recurrence relations complemented with error free transformations yields some compensated schemes which significantly improve the accuracy of computed results at a modest increase in computational cost numerical experiments illustrate that under some restriction on the conditioning the novel iterations can approximate and or refine the eigenvalues of a tridiagonal matrix with high relative accuracy

maximum likelihood array processing for stochastic coherent sources maximum likelihood ml estimation in array signal processing for the stochastic noncoherent signal case is well documented in the literature we focus on the equally relevant case of stochastic coherent signals explicit large sample realizations are derived for the ml estimates of the noise power and the singular signal covariance matrix the asymptotic properties of the estimates are examined and some numerical examples are provided in addition we show the surprising fact that the ml estimates of the signal parameters obtained by ignoring the information that the sources are coherent coincide in large samples with the ml estimates obtained by exploiting the coherent source information thus the ml signal parameter estimator derived for the noncoherent case or its large sample realizations asymptotically achieves the lowest possible estimation error variance corresponding to the coherent cramer rao bound

design of nonuniform near allpass complementary fir filters via a semi infinite programming technique in this correspondence we consider the problem of designing a set of nonuniform near allpass complementary finite impulse response fir filters this problem can be formulated as a quadratic semi infinite programming problem where the objective is to minimize the sum of the ripple energy for the individual filters subject to the passband and stopband specifications as well as to the allpass complementary specification the dual parameterization method is used for solving the linear quadratic semi infinite programming problem

on the use of e most active constraints in an exact penalty function method for nonlinear optimization this note presents an algorithm for nonlinear programming problems which utilizes the e most active constraint strategy in an exact penalty function method with trust region the algorithm is particularly suitable for problems containing a large number of constraints the global convergence of the proposed algorithm is proved the results of limited computational experiments for discretized semi infinite programming problems are also reported to demonstrate the effectiveness of the present approach

the optimal search for a moving target when the search path is constrained a search is conducted for a target moving in discrete time among a finite number of cells according to a known markov process the searcher must choose one cell in which to search in each time period the set of cells available for search depends upon the cell chosen in the last time period the problem is to find a searcher path i e a sequence of search cells that maximizes the probability of detecting the target in a fixed number of time periods we formulate the problem as a partially observable markov decision process and present a finite time horizon pomdp solution technique which is simpler than the standard linear programming methods

performance analysis of spatial smoothing with interpolated arrays the interpolated spatial smoothing algorithm is a computationally efficient method for estimating the directions of arrival doas of signals some of which may be perfectly correlated it extends the spatial smoothing method to arbitrary array geometries a statistical performance analysis of the algorithm is presented closed form expressions for the covariance matrix of the doa estimation errors are derived using a perturbation analysis evaluating these expressions for specific cases and comparing them to the cramer rao lower bound for the doa estimates provides insight into the statistical efficiency of this algorithm the formulas for the error covariance are quite general and can be specialized to provide results for other doa estimation algorithms as well

solving convex programs with infinitely many linear constraints by a relaxed cutting plane method abstract one of the major computational bottlenecks of using the conventional cutting plane approach to solve convex programming problems with infinitely many linear constraints lies in finding a global optimizer of a nonlinear and nonconvex program this paper presents a relaxed scheme to generate a new cut in each iteration the proposed scheme chooses a point at which the constraints are violated to a degree rather than at which the violation is maximized a convergence proof is provided the proposed scheme also exhibits the capability of generating an approximate solution to any level of accuracy in a finite number of iterations

a simple computational procedure for optimization problems with functional inequality constraints in this note a simple computational procedure is given for solving a class of optimization problems where an objective function is to be minimized subject to conventional inequality constraints as well as to inequality constraints of the functional type

planning and acting in partially observable stochastic domains in this paper we bring techniques from operations research to bear on the problem of choosing optimal actions in partially observable stochastic domains we begin by introducing the theory of markov decision processes mdps and partially observable mdps pomdps we then outline a novel algorithm for solving pomdps off line and show how in some cases a finite memory controller can be extracted from the solution to a pomdp we conclude with a discussion of how our approach relates to previous work the complexity of finding exact solutions to pomdps and of some possibilities for finding approximate 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

linear periodic systems and multirate filter design we present a systematic procedure for the design of filters intended for multirate systems this procedure is motivated by viewing the equiripple design of filters in linear time invariant systems as a process of obtaining optimum minimax filters for a class of bounded energy input signals the philosophy of designing optimum minimax filters for classes of input signals is extended to multirate systems which are not time invariant we develop a generalized fourier analysis appropriate for linear periodic systems and use it to derive new error criteria for multirate filter design using such criteria yields optimum minimax multirate filters for the input signal class the utility of our method is demonstrated by using it to analyze several multirate systems we give numerical results on the design of a multirate implementation of a narrowband filter and compare our work to previous work on multirate filter design our numerical analysis is based upon a new formulation of the design as a semi infinite linear programming problem

optimal infinite horizon undiscounted control of finite probabilistic systems a finite input finite state finite output stochastic control problem with imperfect state observation and classical information pattern is shown to be meaningful as the horizon increases without bound and the discount rate approaches unity the plant model a finite probabilistic system includes the markov decision and partially observed markov decision problems as special cases under conditions resembling controllability and observability in linear systems we show that an optimal strategy exists it may be realized by a stationary policy on the state estimate its performance does not depend on the initial state distribution and convergence rates for its finite horizon and discounted performances are readily established

discrete sequential search with positive switch cost suppose one object is hidden in one of n boxes according to a known probability distribution p1 pn the boxes are to be searched sequentially the probability of overlooking the object if we search box k and if the object is in box k is denoted by qk the cost of a search of box k amounts to ck if we decide to search box k directly after box k we have to pay some extra cost called switch cost tk k the problem is under some reasonable assumptions to construct a strategy with minimal expected cost if t 0 the problem has a well known solution unfortunately there are many reasons which establish the conjecture that there does not exist an easy construction rule for optimal strategies in the general case we give necessary and sufficient conditions for the existence of optimal strategies which are ultimately periodic u p since we state bounds on the length not only of the transient phase but also of the period of optimal u p strategies we may construct these optimal strategies by comparing finitely many strategies if optimal u p strategies exist we prove some other results to reduce the number of strategies which we have to compare at last we present a numerical example

wavefield modeling and array processing iii resolution capacity for pt ii see ibid vol 42 no 10 p 2560 1994 we use here the wavefield modeling formalism in order to derive some fundamental limitations on the performance of passive arrays we first derive upper bounds on both the ideal and effective resolution capacities and show that the effective resolution capacity is bounded by the effective rank of the relevant sampling matrix i e is determined by the array structure we then study how the resolution capacity is affected when the sources are constrained to lie within an angular sector we also look at the case where the source spectra are known a priori to be flat and show that contrary to the common opinion if the array satisfies the spectral sampling condition the effective wideband resolution capacity is bounded by the same bound as the narrowband one we conclude by examining the interesting phenomenon of resonance in arrays we show that these resonances far from being mathematical artifacts can manifest quite dramatically in the performance of arrays

spatial filtering in ambient noise interferometry theoretically the empirical green s function between a pair of receivers can be extracted from the cross correlation of the received diffuse noise the diffuse noise condition rarely is met in the ocean and directional sources may bias the green s function here matrix based spatial filters are used for removing unwanted contributions in the cross correlations two methods are used for solving the matrix filter design problem first a matrix least square problem is solved with a low rank approximation of the pseudo inverse here derived for linear and planar arrays second a convex optimization approach is used to solve the design problem reformulated with ad hoc constraints the spatial filter is applied to real data cross correlations of elements from a linear array to attenuate the contribution of a discrete interferer in the case of a planar array and simulated data a spatial filter enables a passive upgoing downgoing wavefield separation along with an efficient rejection of horizontally propagating noise the impact of array size and frequency band on the filtered cross correlations is discussed

a search game when a search path is given abstract in this paper we investigate a search game in discrete time and space a searcher is given a search path in advance and his look on the path is determined by a randomized look strategy a target selects a path from some options the searcher gains a value on the detection of the target but expends search cost by the look a pay off function of the game for the searcher is the expected reward which is defined as the expected value minus the expected search cost first we show a recursive relation for the conditional optimal look strategy of the searcher given a target path we prove its np completeness though it looks simple and clarify some characteristics of the solution then our original continuous game is converted to a matrix game from these facts we consider a relationship between the game and the one sided optimizing problem and examine some examples

optimal rejection of persistent disturbances robust stability and mixed sensitivity minimization the problem of optimal disturbance rejection of bounded persistent disturbances is solved in the general nonsquare case the minimum value of the objective function can be obtained by solving a semi infinite linear programming problem and an iterative procedure for obtaining approximate solutions is introduced application of the l sup 1 optimal problem to robustness is discussed a mixed sensitivity problem is formulated and shown to guarantee good disturbance rejection in the presence of plant perturbations

the potential performance gain in using spectral information in passive detection localization of wideband sources we address the problem of detecting the presence of wideband point sources and or estimating their location using data collected by an array of sensors this passive localization problem is typical to applications where the radiated signals do not carry information and are of no interest however knowledge of their waveshape or their cross spectral matrix is essential for applying optimal sub optimal detection localization algorithms in this paper we present results of a study in which we compare the optimal procedures for detection localization and their performance to suboptimal procedures that use no spectral information or only partial spectral information we show that if the number of sensors in the array is larger than the number of sources to be localized or detected then the performance gain of the optimal procedures is potentially significant mainly in conditions of small separation and or high correlation between sources the performance gain is also a function of the spectrum it is potentially higher if the sources are known to be correlated and if their spectra is not smooth if however the number of sources is smaller than the number of sensors then the role of the spectral information in improving detection localization performance becomes major only the use of spectral prior enables reliable localization of more sources than sensors

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

the optimal search for a markovian target when the search path is constrained the infinite horizon case a target moves among a finite number of cells according to a discrete time homogeneous markov chain the searcher is subject to constraints on the search path i e the cells available for search in the current epoch is a function of the cell searched in the previous epoch the aim is to identify a search policy that maximizes the infinite horizon total expected reward earned we show the following structural results under the assumption that the target transition matrix is ergodic 1 the optimal search policy is stationary and 2 there exists spl epsi optimal stationary policies which may be constructed by the standard value iteration algorithm in finite time these results are obtained by showing that the dynamic programming operator associated with the search problem is an m stage contraction mapping on a suitably defined space an upper bound of m and the coefficient of contraction spl alpha is given in terms of the transition matrix and other variables pertaining to the search problem these bounds on m and spl alpha may be used to derive bounds on suboptimal search polices constructed

discounted mean bound for the optimal searcher path problem with non uniform travel times we consider an extension of the optimal searcher path problem osp where a searcher moving through a discretised environment may now need to spend a non uniform amount of time travelling from one region to another before being able to search it for the presence of a moving target in constraining not only where but when the search of each cell can take place the problem more appropriately models the search of environments which cannot be easily partitioned into equally sized cells an existing osp bounding method in literature the mean bound is generalised to provide bounds for solving the new problem in a branch and bound framework the main contribution of this paper is an enhancement discounted mean dmean which greatly tightens the bound for the new and existing problems alike with almost no additional computation we test the new algorithm against existing osp bounding methods and show it leads to faster solution times for moving target search problems

majorization a computational complexity reduction technique in control system design a methodology is presented for transcribing worst case control system design specifications into semi infinite inequalities of low computational complexity which are tractable by semi infinite programming algorithms these algorithms can be used to find a design which satisfies specifications or to find a design which satisfies specifications and minimizes a cost a computational example is given

on the cramer rao bound for direction finding of correlated signals in this paper we present compact closed form formulas for the cramer rao bound corresponding to the joint estimation of the directions of arrival the signal covariance matrix and the noise variance using these formulas we investigate the effect of signal correlation on the achievable accuracy of direction finding system in a correlated signal environment as expected estimation accuracy decreases with increasing correlation magnitude we observe that under certain conditions small aperture high correlation magnitude correlation phase has a strong effect on doa estimation accuracy

optimal strategy of route and look for the path constrained search problem with reward criterion abstract a target is moving among a finite number of cells k 1 k in discrete time t 1 t knowing probability of the target s path selection a searcher is searching for the target with constraints that he can move from cell i to one of the adjacent cells i i the searcher detects the target with the probability pi on the look into cell i in which both the target and the searcher are there he gains a value v t on the detection of the target at time t but expends cost c0 i t on the search in cell i at t the searcher selects his route and determines whether he looks into his current cell on the route or not in this paper our purpose is to find an optimal strategy for the route and the look of the searcher which maximizes the expected reward defined as the expected value minus the expected cost the problem is formulated as an integer programming problem for solving the problem we use a branch and bound procedure with an upper bound estimation

a new computational search technique for ai based on the cantor set abstract this paper discusses the development of a new search algorithm for artificial intelligence systems the search technique is based on the mathematical theory of the cantor set the search algorithm will be efficient for specialized search domains where the distribution of the data elements to be searched is approximately normal the approach uses the iterative procedure of deleted middle thirds this facilitates quick pruning of a search space the new search technique has potential applications in computational systems with large input output data handling extensive experiments comparing the cantor set search css to binary search indicate that the new search technique holds good promise

design of robust envelope constrained filter with orthonormal bases in the continuous time envelope constrained ec filtering problem using an orthonormal filter structure the aim is to synthesize an orthonormal filter such that the noise enhancement is minimized while the noiseless output response of the filter with respect to a specified input signal stays within the upper and lower bounds of the envelope the noiseless output response of the optimum filter to the prescribed input signal touches the output boundaries at some points consequently any disturbance in the prescribed input signal or error in the implementation of the optimal filter will result in the output constraints being violated in this paper we review a semi infinite envelope constrained filtering problem in which the constraint robustness margin of the filter is maximized subject to a specified allowable increase in the optimal noisy power gain using a smoothing technique it is shown that the solution of the optimization problem can be obtained by solving a sequence of strictly convex optimization problems with integral cost an efficient optimization algorithm is developed based on a combination of the golden section search method and the quasi newton method

min norm interpretations and consistency of music mode and ml the multiple signal characterization music approach its generalization to correlated signals known as the method of direction estimation mode and the deterministic maximum likelihood ml approach for bearing estimation in array processing are shown to be signal subspace fitting approaches in a minimum norm sense mode for example is shown to be an approach in which the array manifold is linearly estimated from principal empirical eigenvectors in a minimum weighted frobenius norm sense using the min norm interpretations a unified proof for strong consistency of the three approaches is provided for stationary and ergodic signals

the laguerre iteration in solving the symmetric tridiagonal eigenproblem revisited this paper presents an algorithm for the eigenvalue problem of symmetric tridiagonal matrices the algorithm employs the determinant evaluation split and merge strategy and the laguerre iteration the method directly evaluates eigenvalues and uses inverse iteration as an option when eigenvectors are needed this algorithm combines the advantages of existing algorithms such as qr bisection multisection and cuppen s divide and conquer method it is fully parallel and competitive in speed with the most efficient qr algorithm in serial mode on the other hand the algorithm is as accurate as any standard algorithm for the symmetric tridiagonal eigenproblem and enjoys the flexibility in evaluating partial spectrum

on the resultant property of the fisher information matrix of a vector arma process a matrix is called a multiple resultant matrix associated to two matrix polynomials when it becomes singular if and only if the two matrix polynomials have at least one common eigenvalue in this paper a new multiple resultant matrix is introduced it concerns the fisher information matrix fim of a stationary vector autoregressive and moving average time series process varma the two matrix polynomials are the autoregressive and the moving average matrix polynomials of the varma process in order to show that the fim is a multiple resultant matrix two new representations of the fim are derived to construct such representations appropriate matrix differential rules are applied the newly obtained representations are expressed in terms of the multiple sylvester matrix and the tensor sylvester matrix the representation of the fim expressed by the tensor sylvester matrix is used to prove that the fim becomes singular if and only if the autoregressive and moving average matrix polynomials have at least one common eigenvalue it then follows that the fim and the tensor sylvester matrix have equivalent singularity conditions in a simple numerical example it is shown however that the fim fails to detect common eigenvalues due to some kind of numerical instability whereas the tensor sylvester matrix reveals it clearly proving the usefulness of the results derived in this paper

technical note trading off quick versus slow actions in optimal search we consider the search for a target whose precise location is uncertain the search region is divided into grid cells and the searcher decides which cell to visit next and whether to search it quickly or slowly a quick search of a cell containing the target may damage it resulting in a failed search or it may locate the target safely if the target is not in the cell the search continues over the remaining cells if a slow search is performed on a cell then the search ends in failure with a fixed probability regardless of whether or not the target is in that cell e g because of enemy fire while performing the slow search if the slow search survives this failure possibility then the search ends in success if the target is in that cell otherwise the search continues over the remaining cells we seek to minimize the probability of the search ending in failure and consider two types of rules for visiting cells the unconstrained search in which the searcher may visit cells in any order and the constrained search in which the searcher may only visit adjacent cells e g up down left or right of cells already visited we prove that the optimal policy for the unconstrained search is to search quickly some initial set of cells with the lowest probabilities of containing the target before slowly searching the remaining cells in decreasing order of probabilities for the special case in which a quick search on a cell containing the target damages it with certainty the optimal policy is to search all cells slowly in decreasing order of probabilities we use the optimal solution of the unconstrained search in a branch and bound optimal solution algorithm for the constrained search for larger instances we evaluate heuristics and approximate dynamic programming approaches for finding good solutions

on the deterministic crb for doa estimation in unknown noise fields using sparse sensor arrays the cramer rao bound crb plays an important role in direction of arrival doa estimation because it is always used as a benchmark for comparison of the different proposed estimation algorithms in this correspondence using well known techniques of global analysis and differential geometry four necessary conditions for the maximum of the log likelihood function are derived two of which seem to be new the crb is derived for the general class of sensor arrays composed of multiple arbitrary widely separated subarrays in a concise way via a coordinate free form of the fisher information the result derived in 1 is confirmed

a two state partially observable markov decision process with uniformly distributed observations a controller observes a production system periodically over time if the system is in the good state during one period there is a constant probability that it will deteriorate and be in the bad state during the next period and remains there the true state of the system is unobservable and can only be inferred from observations quality of output two actions are available continue or replace for a fixed cost the objective is to maximize the expected discounted value of the total future income for both the finite and infinite horizon problems the optimal policy is of a control limit clt type continue if the good state probability exceeds the clt and replace otherwise the computation of the clt involves a functional equation an analytical solution for this equation is as yet unknown for uniformly distributed observations we obtain the infinite horizon clt analytically we also show that the finite horizon clts as a function of the time remaining are not necessarily monotone which is counterintuitive

surveillance search for a moving target the surveillance search problem is a generalization of the detection search problem studied by brown and stone among others in the surveillance version of the problem the search terminates only if the time and location of a detection satisfy certain problem specific conditions the objective is to maximize the expected value of a payoff received during and at the end of the search for instance we may wish to maximize the probability of finding the target in a specified subset of the state space or at a specified time consequently we might detect the target several times before the search terminates a search strategy i e an allocation of the available search effort must account for this possibility in this paper we formulate the surveillance search problem for applications in which the target moves according to a not necessarily time homogeneous markov process we then derive a set of necessary conditions for the optimality of a search strategy and develop algorithms based on the algorithm of brown for the detection search problem to find strategies that satisfy these necessary conditions for problems in which the search effort is infinitely divisible

on the achievable localization accuracy of multiple sources at high snr the cramer rao bound crb for the problem of localizing multiple signal sources by an arbitrary passive sensor array is analyzed for the general case where the array is not necessarily simultaneously sampled and where the signals may a priori be known to be uncorrelated it is shown that unlike in the case where the number of samples grows wherein the crb for the localization error always converges to zero in the case where the number of snapshots is kept fixed and the signal to noise ratio snr grows the crb converges to zero only if the number of sensors simultaneously sampled exceeds the signal subspace dimension