geometric polar tracking from bearings only and doppler bearing measurements bearings only tracking bot and doppler bearing tracking dbt perform target motion analysis from measurements of bearings doppler and bearings respectively the state equations are simple for both the target and observer in the rectangular coordinates hence bot and dbt mostly work in that coordinate by developing the trigonometric relations between target and observer postions over time this paper first derives the pseudolinear equations for direct range and bearing estimation it then provides a generalized total least squares gtls and a maximum likelihood solution polar tracking has two advantages over rectangular first for applications that require range and bearing polar output avoids a coordinate conversion at every output instant second polar equations often have a smaller bias than rectangular consequently polar estimates can give a closer to the optimum initialization for iterative algorithms simulation results have validated the theoretical development confirming the near optimality of the gtls and maximum likelihood solutions

some aspects of the spline smoothing approach to non parametric regression curve fitting non parametric regression using cubic splines is an attractive flexible and widely applicable approach to curve estimation although the basic idea was formulated many years ago the method is not as widely known or adopted as perhaps it should be the topics and examples discussed in this paper are intended to promote the understanding and extend the practicability of the spline smoothing methodology particular subjects covered include the basic principles of the method the relation with moving average and other smoothing methods the automatic choice of the amount of smoothing and the use of residuals for diagnostic checking and model adaptation the question of providing inference regions for curves and for relevant properties of curves is approached via a finite dimensional bayesian formulation

an asymptotically unbiased estimator for bearings only and doppler bearing target motion analysis bearings only bo and doppler bearing db target motion analysis tma attempt to obtain a target trajectory based on bearings and on doppler and bearing measurements respectively from an observer to the target the bo tma and db tma problems are nontrivial because the measurement equations are nonlinearly related to the target location parameters the pseudolinear formulation provides a linear estimator solution but the resulting location estimate is biased the instrumental variable method and the numerical maximum likelihood approach can eliminate the bias their convergence behavior however is not easy to control this paper proposes an asymptotically unbiased estimator of the tracking problem the proposed method applies least squares minimization on the pseudolinear equations with a quadratic constraint on the unknown parameters the resulting estimator is shown to be solving the generalized eigenvalue problem the proposed solution does not require initial guesses and does not have convergence problems sequential forms of the proposed algorithms for both bo tma and db tma are derived the sequential algorithms improve the estimation accuracy as a new measurement arrives and do not require generalized eigenvalue decomposition for solution update the proposed estimator achieves the cramer rao lower bound crlb asymptotically for gaussian noise before the thresholding effect occurs

performance analysis of the optimum beamformer in the presence of correlated sources and its behavior under spatial smoothing in this paper we first study the signal cancellation and interference rejection effects of the optimum constrained least squares or minimum variance beamformer in the presence of partially and fully correlated interfering sources in particular we derive expressions for the output power and the gain in the interference direction of the beamformer in terms of the source powers correlation and the sensor noise power and show quantitatively the penalties arising from increasing correlation in several scenarios of interest next we show that spatial smoothing progressively decorrelates the sources at a rate that depends on the spacing and directions of the sources and thus relate the degree of smoothing to the improvement in signal cancellation and interference rejection behavior provided by spatial smoothing results of computer simulations are included to support our analysis

a resolution principle based on first order lattice valued logic lf x abstract in the present paper as a continuous work about resolution principle based on lattice valued propositional logic lp x information sciences 130 2000 1 29 whose algebra of truth values is a relatively general lattice lattice implication algebra lia the lattice valued resolution principle for the corresponding first order lattice valued logic system lf x is focused firstly some concepts about lattice valued resolution principle for lf x are introduced and the herbrand theorem for lf x is proved then an resolution principle which can be used to judge if a first order lattice valued logical formula in lf x is false at a truth valued level i e false is established finally the completeness theorem of this resolution principle and the soundness theorem for the strong resolution are also proved it is hoped that the current work would serve as a foundation for constructing resolution based automated reasoning methods for lattice valued logic capable of dealing with both comparable and incomparable uncertain information

a resolution principle based on lattice valued propositional logic lp x abstract in the present paper resolution based automated reasoning theory in an l type fuzzy logic is focused concretely the resolution principle which is based on lattice valued propositional logic lp x with truth value in a logical algebra lattice implication algebra is investigated finally an resolution principle that can be used to judge if a lattice valued logical formula in lp x is always false at a truth valued level i e false is established and the theorems of both soundness and completeness of this resolution principle are also proved this will become the theoretical foundation for automated reasoning based on lattice valued logical lp x

paraconsistent disjunctive deductive databases abstract databases and knowledge bases could be inconsistent in many ways the semantical characterization of deductive databases that contain disjunctive or indefinite information has been investigated by minker and his co workers 1982 1987 1988 and by henschen and his co workers 1985 1988 in both cases there is one salient feature the databases are assumed to consist of sentences of the form a 1 a n b 1 b m where each a i and each b j is an atom and n 1 thus the database is implicitly assumed to be consistent it is easy to construct a model for any set of such formulas what we study here is a method for reasoning about such databases when they are not necessarily consistent intuitively this occurs when the a i s are restricted not just to atomic formulas but also to negated atoms we use the device of annotated atoms introduced by blair and subrahmanian 1987 1988 to achieve this effect our semantics is closely related to the existing work of newton da costa 1974 1987 whose pioneering work on paraconsistency provides the semantical basis for our formal development

object based 3 d reconstruction of arterial trees from magnetic resonance angiograms by exploiting a priori knowledge of arterial shape and smoothness subpixel accuracy reconstructions are achieved from only four noisy projection images the method incorporates a priori knowledge of the structure of branching arteries into a natural optimality criterion that encompasses the entire arterial tree an efficient optimization algorithm for object estimation is presented and its performance on simulated phantom and in vivo magnetic resonance angiograms is demonstrated it is shown that accurate reconstruction of bifurcations is achievable with parametric models

splitting and composition methods for explicit time dependence in separable dynamical systems we consider splitting methods for the numerical integration of separable non autonomous differential equations in recent years splitting methods have been extensively used as geometric numerical integrators showing excellent performances both qualitatively and quantitatively when applied on many problems they are designed for autonomous separable systems and a substantial number of methods tailored for different structures of the equations have recently appeared splitting methods have also been used for separable non autonomous problems either by solving each non autonomous part separately or after each vector field is frozen properly we show that both procedures correspond to introducing the time as two new coordinates we generalize these results by considering the time as one or more further coordinates which can be integrated following either of the previous two techniques we show that the performance as well as the order of the final method can strongly depend on the particular choice we present a simple analysis which in many relevant cases allows one to choose the most appropriate split to retain the high performance the methods show on the autonomous problems this technique is applied to different problems and its performance is illustrated for several numerical examples

3d pseudolinear target motion analysis from angle measurements the paper presents a new pseudolinear estimator for 3d target motion analysis by a single moving ownship collecting azimuth and elevation angle measurements the 3d pseudolinear estimator is derived as a small noise approximation to the maximum likelihood estimator and consists of a 2d pseudolinear estimator for the xy components of the target motion parameters and a least squares estimator for the z component to improve the poor bias performance of the 3d pseudolinear estimator alternative estimators are proposed employing bias compensation and weighted instrumental variables a selective angle measurement implementation of weighted instrumental variables is presented to maintain a strong correlation between the instrumental variable matrix and the data matrix in the presence of large measurement noise the performance advantages of the selective angle measurement weighted instrumental variable estimator over the conventional maximum likelihood estimator are demonstrated via simulation examples

a novel power bearing approach and asymptotically optimum estimator for target motion analysis the problem of target motion analysis tma has been extensively investigated using bearing only bo doppler bearing db and other measurement data for radio frequency rf emitters signal powers follow the well known path loss law that can be utilized to aid localization and target tracking in bo tma leading to the novel power bearing pb approach as proposed in this paper our main contribution lies in the proof of the asymptotic optimality of the total least squares tls algorithm for pb tma under some mild condition the cramer rao lower bound crlb is employed to demonstrate the performance improvements of the pb tma over the bo tma our work shows the promise of the pb tma approach for rf signals

the value of the four values in his well known paper how computer should think belnap 1977 argues that four valued semantics is a very suitable setting for computerized reasoning in this paper we vindicate this thesis by showing that the logical role that the four valued structure has among ginsberg s bilattices is similar to the role that the two valued algebra has among boolean algebras specifically we provide several theorems that show that the most useful bilattice valued logics can actually be characterized as four valued inference relations in addition we compare the use of three valued logics with the use of four valued logics and show that at least for the task of handling inconsistent or uncertain information the comparison is in favor of the latter

high order imex spectral schemes for computing the dynamics of systems of nonlinear schrodinger gross pitaevskii equations the aim of this paper is to build and validate some explicit high order schemes both in space and time for simulating the dynamics of systems of nonlinear schrodinger gross pitaevskii equations the method is based on the combination of high order implicit explicit imex schemes in time and fourier pseudo spectral approximations in space the resulting imexsp schemes are highly accurate efficient and easy to implement they are also robust when used in conjunction with an adaptive time stepping strategy and appear as an interesting alternative to time splitting pseudo spectral tssp schemes finally a complete numerical study is developed to investigate the properties of the imexsp schemes in comparison with tssp schemes for one and two components systems of gross pitaevskii equations

nonparametric fixed interval smoothing with vector splines a computationally efficient algorithm for nonparametric smoothing of vector signals with general measurement covariances is presented this algorithm provides an alternative to the optimal smoothing algorithms that hinge on possibly inaccurate parametric state space models automatic procedures that use the measurements to determine how much to smooth are developed and compared this adaptation allows the data to speak for itself without imposing a gauss markov model structure a nonparametric approach to covariance estimation for the case of independently identically distributed i i d measurement errors is presented monte carlo simulations demonstrate the performance of the algorithm

three dimensional reconstruction from projections with incomplete and noisy data by object estimation an estimation approach to three dimensional reconstruction from parallel ray projections with incomplete and very noisy data is described using a stochastic dynamic model for an object of interest in a probed domain of known background density the reconstruction problem is reformulated as a n onlinear state estimation problem an approximate minimum mean square error globally optimal algorithm for the solution of this problem is presented the algorithm which is recursive in a hybrid frequency space domain operates directly on the fourier transformed projection data eliminating altogether the attempt to invert the projection integral equation the simulation example considered in this paper demonstrates that good object estimates may be obtained with as few as five views in a limited sector of 90 and at a signal to noise ratio as low as 0 db

constrained maximum likelihood solution of linear equations the total least squares tls is used to solve a set of inconsistent linear equations ax spl ap y when there are errors not only in the observations y but in the modeling matrix a as well the tls seeks the least squares perturbation of both y and a that leads to a consistent set of equations when y and a have a defined structure we usually want the perturbations to also have this structure unfortunately standard tls does not generally preserve the perturbation structure so other methods are required we examine this problem using a probabilistic framework and derive an approach to determining the most probable set of perturbations given an a priori perturbation probability density function while our approach is applicable to both gaussian and non gaussian distributions we show in the uncorrelated gaussian case that our method is equivalent to several existing methods our approach is therefore more general and can be applied to a wider variety of signal processing problems

practical symplectic partitioned runge kutta and runge kutta nystrom methods we present new symmetric fourth and sixth order symplectic partitioned runge kutta and runge kutta nystrom methods we studied compositions using several extra stages optimising the efficiency an effective error ef is defined and an extensive search is carried out using the extra parameters the new methods have smaller values of ef than other methods found in the literature when applied to several examples they perform up to two orders of magnitude better than previously known method which is in very good agreement with the values of ef

a resolution like strategy based on a lattice valued logic as the use of nonclassical logics becomes increasingly important in computer science artificial intelligence and logic programming the development of efficient automated theorem proving based on nonclassical logic is currently an active area of research this paper aims at the resolution principle for the pavelka type fuzzy logic 1979 pavelka showed that the only natural way of formalizing fuzzy logic for truth values in the unit interval 0 1 is by using the lukasiewicz s implication operator a spl rarr b min 1 1 a b or some isomorphic forms of it hence we first focus on the resolution principle for the lukasiewicz logic l sub spl aleph with 0 1 as the truth valued set some limitations of classical resolution and resolution procedures for fuzzy logic with kleene implication are analyzed then some preliminary ideals about combining resolution procedure with the implication connectives in l sub spl aleph are given moreover a resolution like principle in l sub spl aleph is proposed and the soundness theorem of this resolution procedure is also proved second we use this resolution like principle to horn clauses with truth values in an enriched residuated lattice and consider the l type fuzzy prolog

bias compensation for the bearings only pseudolinear target track estimator the bearings only pseudolinear target track estimator is known to suffer from severe bias problems this paper presents a bias analysis for the pseudolinear estimator and develops a method of bias compensation resulting in a closed form reduced bias pseudolinear estimator the reduced bias estimator is then incorporated into an instrumental variable estimator to produce asymptotically unbiased target motion parameter estimates unlike batch iterative estimators the proposed instrumental variable estimator has a closed from solution and therefore avoids the convergence problems associated with iterative estimators the performance of the proposed instrumental variable estimator is illustrated by way of simulation examples and is shown to be almost identical to that of the computationally more demanding iterative maximum likelihood estimator

total least squares for affinely structured matrices and the noisy realization problem structured rank deficient matrices arise in many applications in signal processing system identification and control theory the author discusses the structured total least squares stls problem which is the problem of approximating affinely structured matrices i e matrices affine in the parameters by similarly structured rank deficient ones while minimizing an l sub 2 error criterion it is shown that the optimality conditions lead to a nonlinear generalized singular value decomposition which can be solved via an algorithm that is inspired by inverse iteration next the author concentrates on the so called l sub 2 optimal noisy realization problem which is equivalent with approximating a given data sequence by the impulse response of a finite dimensional time invariant linear system of a given order this can be solved as a structured total least squares problem it is shown with some simple counter examples that classical algorithms such as the steiglitz mcbride 1965 iterative quadratic maximum likelihood and cadzow s 1988 iteration do not converge to the optimal l sub 2 solution despite misleading claims in the literature

fundamental properties and performance of conventional bearings only target motion analysis this paper considers the problem of estimating the position and velocity of an object from noise corrupted bearing measurements obtained by a single moving observation platform the process is inherently nonlinear and exhibits unusual observability properties that are geometry dependent a maximum likelihood estimate mle of the target motion analysis solution is developed and its performance analyzed a comparison is drawn between the mle and two previously reported methods a nonlinear modified instrumental variable estimate miv and the pseudo linear estimate ple both the miv and ple are shown to derive from approximations to the nonlinear measurement equation and therefore share some common properties with the mle the limits on performance that can be expected from processing bearing data are detailed specifically for long range to baseline geometries approximate expressions for the cramer rao bound are derived extension of the results to the practical filters approximately predicts numerically observed behavior for less restrictive geometries bounds are presented incorporation of a target speed constraint on the mle results in a transition to a lower dimensional problem as noise level and range increases monte carlo experimental results are presented and the improvements realized by the mle techniques are evident

some quick and efficient methods for bearing only target motion analysis batch processing estimation methods for a target s trajectory assumed to be linear and uniform based only on the observation of its bearings are presented first the observer is assumed to have constant velocity so that one can only estimate the target s motion up to a multiplicative constant this motion is parameterized by three bearings at three judiciously chosen times and some simple quick yet highly efficient estimators for them are proposed the case of an observer moving nonuniformly is then considered a quadratic estimator that is similar to the pseudolinear estimator but does not have bias is introduced for the case in which the observer s motion can be decomposed into a finite number of constant velocity segments two sets of quasi sufficient statistics that permit considerable saving in computation with no significant loss of efficiency are also introduced expressions for the covariance matrix of the estimators and for their cramer rao bounds are provided

a smoothed newton gauss method with application to bearing only position location the paper deals with a modified newton gauss method in which a smoothing parameter is introduced in order to enhance convergence two practical algorithms are proposed and tested with application to bearing only position location the first algorithm relies on the one step newton minimum search which is used to select a smoothing factor in each newton gauss iteration in the second a smoothing factor is suggested as an appropriate function of the number of iterations

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

utilization of modified polar coordinates for bearings only tracking previous studies have shown that the cartesian coordinate extended kalman filter exhibits unstable behavior characteristics when utilized for bearings only target motion analysis tma in contrast formulating the tma estimation problem in modified polar mp coordinates leads to an extended kalman filter which is both stable and asymptotically unbiased exact state equations for the mp filter are derived without imposing any restrictions on own ship motion thus prediction accuracy inherent in the traditional cartesian formulation is completely preserved in addition these equations reveal that mp coordinates are well suited for bearings only tma because they automatically decouple observable and unobservable components of the estimated state vector such decoupling is shown to prevent covariance matrix ill conditioning which is the primary cause of filter instability further investigation also confirms that the mp state estimates are asymptotically unbiased realistic simulation data are presented to support these findings and to compare algorithm performance with respect to the cramer rao lower bound ideal as well as the cartesian and pseudolinear filters

vector valued lg splines ii smoothing splines abstract in the first paper of this series lg spline theory was extended to the vector valued interpolating case here this work is complemented by giving the extension for smoothing splines the problem is formulated as a constrained minimum norm problem in a reproducing kernel hilbert space and solved recursively using a congruent stochastic estimation model

splitting methods for non autonomous separable dynamical systems a large number of splitting methods for autonomous separable systems exist in the literature which have been designed for many different structures of the vector field however the performance of most of these methods is diminished and their orders of accuracy are frequently reduced when applied to non autonomous problems based on the formal solution obtained from the magnus series expansion we show how to modify a standard splitting method for autonomous problems to treat non autonomous systems with similar or better efficiency we illustrate this technique to build new fourth and sixth order schemes whose performance is then illustrated on several numerical examples

on the numerical integration of ordinary differential equations by symmetric composition methods differential equations of the form dot x x a b are considered where the vector fields a and b can be integrated exactly enabling numerical integration of x by composition of the flows of a and b various symmetric compositions are investigated for order complexity and reversibility free lie algebra theory gives simple formulae for the number of determining equations for a method to have a particular order a new more accurate way of applying the methods thus obtained to compositions of an arbitrary first order integrator is described and tested the determining equations are explored and new methods up to 100 times more accurate at constant work than those previously known are given

the signal extraction approach to nonlinear regression and spline smoothing abstract this article shows how to fit a smooth curve polynomial spline to pairs of data values yi xi prior specification of a parametric functional form for the curve is not required the resulting curve can be used to describe the pattern of the data and to predict unknown values of y given x both point and interval estimates are produced the method is easy to use and the computational requirements are modest even for large sample sizes our method is based on maximum likelihood estimation of a signal in noise model of the data we use the kalman filter to evaluate the likelihood function and achieve significant computational advantages over previous approaches to this problem

a novel location penalized maximum likelihood estimator for bearing only target localization in this paper we present a location penalized maximum likelihood lpml estimator for bearing only target localization we develop a new penalized maximum likelihood cost function by transforming the variables of target position and bearings the new penalized likelihood function can also be recognized as a posterior distribution under a bayesian framework by penalizing a prior we give analysis of the asymptotic properties and show that both traditional bearing maximum likelihood tbml and lpml estimators are asymptotically efficient estimators to compare the performances of the tbml and lpml estimators we analyze the cramer rao lower bound crlb of the two estimators and show that the bound of the lpml estimator is lower than that of the tbml estimator extensive simulations are performed it is observed that the new lpml algorithm consistently outperforms other well known algorithms field experiments are also conducted by applying this method to localize a vehicle using real world data acquired by an acoustic array sensor network the new lpml algorithm demonstrates superior performance in all the field experiments

geometric integrators for odes geometric integration is the numerical integration of a differential equation while preserving one or more of its geometric properties exactly i e to within round off error many of these geometric properties are of crucial importance in physical applications preservation of energy momentum angular momentum phase space volume symmetries time reversal symmetry symplectic structure and dissipation are examples in this paper we present a survey of geometric numerical integration methods for ordinary differential equations our aim has been to make the review of use for both the novice and the more experienced practitioner interested in the new developments and directions of the past decade to this end the reader who is interested in reading up on detailed technicalities will be provided with numerous signposts to the relevant literature

nonparametric fixed interval smoothing of nonlinear vector valued measurements the problem of estimating a smooth vector valued function given noisy nonlinear vector valued measurements of that function is addressed a nonparametric optimality criterion for this estimation problem is presented and a computationally efficient iterative algorithm for its solution is developed the criterion is the natural generalization of previously published work on vector splines with linear measurement models the algorithm provides an alternative to the extended kalman filter as it does not require a parametric state space model an automatic procedure that uses the measurements to determine how much to smooth is presented the algorithm s subpixel estimation accuracy is demonstrated on the estimation of a curved edge in a noisy image and on a biomedical image processing application

sb3a splitting for approximation of invariants in time dependent hamiltonian systems abstract most physical phenomena are described by time dependent hamiltonian systems with qualitative features that should be preserved by numerical integrators used for approximating their dynamics the initial energy of the system together with the energy added or subtracted by the outside forces represent a conserved quantity of the motion for a class of time dependent hamiltonian systems 8 this invariant can be defined by means of an auxiliary function whose dynamics has to be integrated simultaneously with the system s equations we propose splitting procedures featured by a sb 3 a property that allows to construct composition methods with a reduced number of determining order equations and to provide the same high accuracy for both the dynamics and the preservation of the invariant quantity

splitting methods for non autonomous hamiltonian equations abstract we present an algorithm for numerically integrating non autonomous hamiltonian differential equations special attention is paid to the separable case and in particular a new fourth order splitting method is presented which in a certain measure is optimal in combination with a new way of handling non autonomous problems the schemes we present are based on magnus expansions and they show very promising results when applied to hamiltonian odes and pdes