periodic shadowing sensitivity analysis of chaotic systems abstract the sensitivity of long time averages of a hyperbolic chaotic system to parameter perturbations can be determined using the shadowing direction the uniformly bounded in time solution of the sensitivity equations although its existence is formally guaranteed for certain systems methods to determine it are hardly available one practical approach is the least squares shadowing lss algorithm wang 2014 18 whereby the shadowing direction is approximated by the solution of the sensitivity equations with the least square average norm here we present an alternative potentially simpler shadowing based algorithm termed periodic shadowing the key idea is to obtain a bounded solution of the sensitivity equations by complementing it with periodic boundary conditions in time we show that this is not only justifiable when the reference trajectory is itself periodic but also possible and effective for chaotic trajectories our error analysis shows that periodic shadowing has the same convergence rates as lss when the time span t is increased the sensitivity error first decays as 1 t and then asymptotically as 1 t we demonstrate the approach on the lorenz equations and also show that as t tends to infinity periodic shadowing sensitivities converge to the same value obtained from long unstable periodic orbits lasagna 2018 14 for which there is no shadowing error finally finite difference approximations of the sensitivity are also examined and we show that subtle non hyperbolicity features of the lorenz system introduce a small yet systematic bias

the milne and kramers problems for the boltzmann equation of a hard sphere gas existence uniqueness and properties of asymptotic behavior are proved for solutions of the milne and kramers problems for the linearized boltzmann equation for a gas of hard spheres the proof uses energy like estimates and follows the analysis of bardos santos and sentis for the equations of neutron transport

a divergence free chebyshev collocation procedure for incompressible flows with two non periodic directions abstract the enforcement of divergence free condition in the interior and on the boundaries of an incompressible flow with two non periodic directions is discussed for a chebyshev collocation formulation an influence matrix technique along with a correction methodology is used to satisfy the continuity equation everywhere in the domain details of implementing this procedure in a collocation method are presented an efficient solution procedure based on matrix diagonalization has been used to solve the resulting full matrices two test problems a flow in a driven square cavity and b fully developed laminar flow in a square duct subject to a three dimensional perturbation are studied run time statistics cpu memory mflops of the solution procedure are presented for representative grid sizes

differentiation of srb states correction and complements taking into account criticism by d dolgopyat and m jiang we present here an improved derivation of the formula for the derivative of an srb measure with respect to parameters

a preconditioned multiple shooting shadowing algorithm for the sensitivity analysis of chaotic systems abstract we propose a preconditioner that can accelerate the rate of convergence of the multiple shooting shadowing mss method 1 this recently proposed method can be used to compute derivatives of time averaged objectives also known as sensitivities to system parameter s for chaotic systems we propose a block diagonal preconditioner which is based on a partial singular value decomposition of the mss constraint matrix the preconditioner can be computed using matrix vector products only i e it is matrix free and is fully parallelised in the time domain two chaotic systems are considered the lorenz system and the 1d kuramoto sivashinsky equation combination of the preconditioner with a regularisation method leads to tight bracketing of the eigenvalues to a narrow range this combination results in a significant reduction in the number of iterations and renders the convergence rate almost independent of the number of degrees of freedom of the system and the length of the trajectory that is used to compute the time averaged objective this can potentially allow the method to be used for large chaotic systems such as turbulent flows and optimal control applications the singular value decomposition of the constraint matrix can also be used to quantify the effect of the system condition on the accuracy of the sensitivities in fact neglecting the singular modes affected by noise we recover the correct values of sensitivity that match closely with those obtained with finite differences for the kuramoto sivashinsky equation in the light turbulent regime we notice a similar improvement for the lorenz system as well

least squares shadowing sensitivity analysis of chaotic limit cycle oscillations abstract the adjoint method among other sensitivity analysis methods can fail in chaotic dynamical systems the result from these methods can be too large often by orders of magnitude when the result is the derivative of a long time averaged quantity this failure is known to be caused by ill conditioned initial value problems this paper overcomes this failure by replacing the initial value problem with the well conditioned least squares shadowing lss problem the lss problem is then linearized in our sensitivity analysis algorithm which computes a derivative that converges to the derivative of the infinitely long time average we demonstrate our algorithm in several dynamical systems exhibiting both periodic and chaotic oscillations

sensitivity analysis of limit cycle oscillations many unsteady problems equilibrate to periodic behavior for these problems the sensitivity of periodic outputs to system parameters are often desired and must be estimated from a finite time span or frequency domain calculation sensitivities computed in the time domain over a finite time span can take excessive time to converge or fail altogether to converge to the periodic value additionally finite span outputs can exhibit local extrema in parameter space which the periodic outputs they approximate do not hindering their use in optimization we derive a theoretical basis for this error and demonstrate it using two examples a van der pol oscillator and vortex shedding from a low reynolds number airfoil we show that output windowing enables the accurate computation of periodic output sensitivities and may allow for decreased simulation time to compute both time averaged outputs and sensitivities we classify two distinct window types long time over a large not necessarily integer number of periods and short time over a small integer number of periods finally from these two classes we investigate several examples of window shape and demonstrate their convergence with window size and error in the period approximation respectively

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

direct numerical simulation of flow past elliptic cylinders flow over elliptic cylinders can be considered prototypical of flow over a range of bluff bodies since the geometry allows one to study the effect of both thickness and angle of attack on the flow field therefore a careful study of this flow should provide valuable insight into the phenomenon of unsteady separation and the structure of bluff body wakes with this in mind a spectral collocation technique has been developed to simulate the full three dimensional incompressible flow over elliptic cylinders and unlike spectral element and spectral multidomain techniques here the flow is solved in a single domain the equations are discretized on a body fitted elliptic cylindrical grid and properties of the metric associated with this coordinate system are used to solve the governing equations in an efficient manner key issues including the inflow and outflow boundary conditions and time discretization are discussed in detail with the hope that this will facilitate future simulations of similar flows finally we present results of two and three dimensional simulations for a range of flow and geometric parameters the results are compared with available experimental data and it is found that important quantities like strouhal numbers and drag coefficients match well with established values

least squares shadowing method for sensitivity analysis of differential equations for a parameterized hyperbolic system frac du dt f u s the derivative of the ergodic average langle j rangle lim t to infty frac 1 t int 0 t j u t s to the parameter s can be computed via the least squares shadowing lss algorithm we assume that the system is ergodic which means that langle j rangle depends only on s not on the initial condition of the hyperbolic system the algorithm solves a constrained least squares problem and from the solution to this problem computes the desired derivative frac d langle j rangle ds the purpose of this paper is to prove that the value given by the lss algorithm approaches the exact derivative when the timespan used to formulate the least squares problem grows to infinity it then illustrates the convergence result through a numerical example

the local structure of turbulence in incompressible viscous fluid for very large reynolds numbers 1 we shall denote by u p u x 1 x 2 x 3 t 1 2 3 the components of velocity at the moment t at the point with rectangular cartesian coordinates x 1 x 2 x 3 in considering the turbulence it is natural to assume the components of the velocity u p at every point p x 1 x 2 x 3 t of the considered domain g of the four dimensional space x 1 x 2 x 3 t are random variables in the sense of the theory of probabilities cf for this approach to the problem millionshtchikov 1939 denoting by the mathematical expectation of the random variable a we suppose that 2 and d u d x 2 are finite and bounded in every bounded subdomain of the domain g

on use of the em algorithm for penalized likelihood estimation summary the em algorithm is a popular approach to maximum likelihood estimation but has not been much used for penalized likelihood or maximum a posteriori estimation this paper discusses properties of the em algorithm in such contexts concentrating on rates of conver gence and presents an alternative that is usually more practical and converges at least as quickly the em algorithm is a general approach to maximum likelihood estimation rather than a specific algorithm dempster et al 1977 discussed the method and derived basic properties demonstrating that a variety of procedures previously developed rather informally could be unified the common strand to problems where the approach is applicable is a notion of incomplete data this includes the conventional sense of missing data but is much broader than that the em algorithm demon strates its strength in situations where some hypothetical experiment yields data from which estimation is particularly convenient and economical the incomplete data actually at hand are regarded as observable functions of these complete data the resulting algorithms while usually slow to converge are often extremely simple and remain practical in large problems where no other approaches may be feasible dempster et al 1977 briefly refer to the use of the same approach to the problem of finding the posterior mode maximum a posteriori estimate in a bayesian estima

forward and adjoint sensitivity computation of chaotic dynamical systems this paper describes a forward algorithm and an adjoint algorithm for computing sensitivity derivatives in chaotic dynamical systems such as the lorenz attractor the algorithms compute the derivative of long time averaged statistical quantities to infinitesimal perturbations of the system parameters the algorithms are demonstrated on the lorenz attractor we show that sensitivity derivatives of statistical quantities can be accurately estimated using a single short trajectory over a time interval of 20 on the lorenz attractor

simplified least squares shadowing sensitivity analysis for chaotic odes and pdes abstract this paper develops a variant of the least squares shadowing lss method which has successfully computed the derivative for several chaotic odes and pdes the development in this paper aims to simplify least squares shadowing method by improving how time dilation is treated instead of adding an explicit time dilation term as in the original method the new variant uses windowing which can be more efficient and simpler to implement especially for pdes

2d and 3d exact shock wave solutions with specular reflection to the discrete boltzmann models the authors construct exact solutions which are 2d two spatial coordinates for the four velocity planar model 3d for the cubic broadwell models and p dimensional for the p dimensional hypercubic discrete boltzmann model these solutions are shock waves which satisfy a specular reflection boundary condition at a wall

a framework for simultaneous aerodynamic design optimization in the presence of chaos abstract integrating existing solvers for unsteady partial differential equations into a simultaneous optimization method is challenging due to the forward in time information propagation of classical time stepping methods this paper applies the simultaneous single step one shot optimization method to a reformulated unsteady constraint that allows for both forward and backward in time information propagation especially in the presence of chaotic and turbulent flow solving the initial value problem simultaneously with the optimization problem often scales poorly with the time domain length the new formulation relaxes the initial condition and instead solves a least squares problem for the discrete partial differential equations this enables efficient one shot optimization that is independent of the time domain length even in the presence of chaos

multiple shooting shadowing for sensitivity analysis of chaotic dynamical systems abstract sensitivity analysis methods are important tools for research and design with simulations many important simulations exhibit chaotic dynamics including scale resolving turbulent fluid flow simulations unfortunately conventional sensitivity analysis methods are unable to compute useful gradient information for long time averaged quantities in chaotic dynamical systems sensitivity analysis with least squares shadowing lss can compute useful gradient information for a number of chaotic systems including simulations of chaotic vortex shedding and homogeneous isotropic turbulence however this gradient information comes at a very high computational cost this paper presents multiple shooting shadowing mss a more computationally efficient shadowing approach than the original lss approach through an analysis of the convergence rate of mss it is shown that mss can have lower memory usage and run time than lss

convergence of the least squares shadowing method for computing derivative of ergodic averages for a parameterized hyperbolic system u i 1 f u i s the derivative of an ergodic average langle j rangle lim n rightarrow infty frac1n sum 1 n j u i s to the parameter s can be computed via the least squares shadowing method this method solves a constrained least squares problem and computes an approximation to the desired derivative frac d langle j rangle ds from the solution this paper proves that as the size of the least squares problem approaches infinity the computed approximation converges to the true derivative

characterizing dynamics with covariant lyapunov vectors a general method to determine covariant lyapunov vectors in both discrete and continuous time dynamical systems is introduced this allows us to address fundamental questions such as the degree of hyperbolicity which can be quantified in terms of the transversality of these intrinsic vectors for spatially extended systems the covariant lyapunov vectors have localization properties and spatial fourier spectra qualitatively different from those composing the orthonormalized basis obtained in the standard procedure used to calculate the lyapunov exponents

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

discrete second order adjoints in atmospheric chemical transport modeling atmospheric chemical transport models ctms are essential tools for the study of air pollution for environmental policy decisions for the interpretation of observational data and for producing air quality forecasts many air quality studies require sensitivity analyses i e the computation of derivatives of the model output with respect to model parameters the derivatives of a cost functional defined on the model output with respect to a large number of model parameters can be calculated efficiently through adjoint sensitivity analysis while the traditional first order adjoint models give the gradient of the cost functional with respect to parameters second order adjoint models give second derivative information in the form of products between the hessian of the cost functional and a vector representing a perturbation in sensitivity analysis a search direction in optimization an eigenvector etc in this paper we discuss the mathematical foundations of the discrete second order adjoint sensitivity method and present a complete set of computational tools for performing second order sensitivity studies in three dimensional atmospheric ctms the tools include discrete second order adjoints of runge kutta and of rosenbrock time stepping methods for stiff equations together with efficient implementation strategies numerical examples illustrate the use of these computational tools in important applications like sensitivity analysis optimization uncertainty quantification and the calculation of directions of maximal error growth in three dimensional atmospheric ctms

sensitivity of long periodic orbits of chaotic systems the properties of long numerically determined periodic orbits of two low dimensional chaotic systems the lorenz equations and the kuramoto sivashinsky system in a minimal domain configuration are examined the primary question is to establish whether the sensitivity of period averaged quantities with respect to parameter perturbations computed over long orbits can be used as a sufficiently good proxy for the response of the chaotic state to finite amplitude parameter perturbations to address this question an inventory of thousands of orbits at least two orders of magnitude longer than the shortest admissible cycles is constructed the expectation of period averages floquet exponents and sensitivities over such set is then obtained it is shown that all these quantities converge to a limiting value as the orbit period is increased however while period averages and floquet exponents appear to converge to analogous quantities computed from chaotic trajectories the limiting value of the sensitivity is not necessarily consistent with the response of the chaotic state similar to observations made with other shadowing algorithms

measure solutions of the steady boltzmann equation in a slab it is shown that the steady boltzmann equation in a slab 0 a has solutionsx x such that the ingoing boundary measures 0 0 and 0 can be prescribed a priori the collision kernel is truncated such that particles with smallx component of the velocity have a reduced collision rate

tracking the direction of arrival of multiple moving targets by passive arrays algorithm we propose a maximum likelihood ml approach for tracking the direction of arrival doa of multiple moving targets by a passive array a locally linear model is assumed for the target motion and the multiple target states mtss are defined to describe the states of the target motion the locally linear model is shown to be strongly locally observable almost everywhere the approach is to estimate the initial mts by maximizing the likelihood function of the array data the tracking is implemented by prediction through the target motion dynamics using the initial mts estimate by incorporating the target motion dynamics the algorithm is able to eliminate the spread spectrum effects due to target motion a modified newton type algorithm is also presented which ensures fast convergence of the algorithm finally numerical simulations are included to show the effectiveness of the proposed algorithm

differentiation of srb states abstract let f be a diffeomorphism of a manifold m and f a generalized srb state for f if supp f is a hyperbolic compact set we show that the map is differentiable in a suitable functional setup and we compute the derivative when supp f is an attractor the derivative is given by where x is the vector field this formula can be extended to time dependent situations and also at least formally to nonuniformly hyperbolic situations the above results will find their use in the study of the onsager reciprocity relations and the fluctuation dissipation formula of nonequilibrium statistical mechanics

sensitivity analysis on chaotic dynamical systems by non intrusive least squares shadowing nilss abstract this paper develops the non intrusive least squares shadowing nilss method which computes the sensitivity for long time averaged objectives in chaotic dynamical systems in nilss we represent a tangent solution by a linear combination of one inhomogeneous tangent solution and several homogeneous tangent solutions next we solve a least squares problem using this representation thus the resulting solution can be used for computing sensitivities nilss is easy to implement with existing solvers in addition for chaotic systems with many degrees of freedom but few unstable modes nilss has a low computational cost nilss is applied to two chaotic pde systems the lorenz 63 system and a cfd simulation of flow over a backward facing step in both cases the sensitivities computed by nilss reflect the trends in the long time averaged objectives of dynamical systems

space alternating generalized expectation maximization algorithm the expectation maximization em method can facilitate maximizing likelihood functions that arise in statistical estimation problems in the classical em paradigm one iteratively maximizes the conditional log likelihood of a single unobservable complete data space rather than maximizing the intractable likelihood function for the measured or incomplete data em algorithms update all parameters simultaneously which has two drawbacks 1 slow convergence and 2 difficult maximization steps due to coupling when smoothness penalties are used the paper describes the space alternating generalized em sage method which updates the parameters sequentially by alternating between several small hidden data spaces defined by the algorithm designer the authors prove that the sequence of estimates monotonically increases the penalized likelihood objective derive asymptotic convergence rates and provide sufficient conditions for monotone convergence in norm two signal processing applications illustrate the method estimation of superimposed signals in gaussian noise and image reconstruction from poisson measurements in both applications the sage algorithms easily accommodate smoothness penalties and converge faster than the em algorithms

recursive expectation maximization em algorithms for time varying parameters with applications to multiple target tracking we investigate the application of expectation maximization em algorithms to the classical problem of multiple target tracking mtt for a known number of targets conventional algorithms which deal with this problem have a computational complexity that depends exponentially on the number of targets and usually divide the problem into a localization stage and a tracking stage the new algorithms achieve a linear dependency and integrate these two stages three optimization criteria are proposed using deterministic and stochastic dynamic models for the targets

efficient sensitivity analysis method for chaotic dynamical systems the direct differentiation and improved least squares shadowing methods are both developed for accurately and efficiently calculating the sensitivity coefficients of time averaged quantities for chaotic dynamical systems the key idea is to recast the time averaged integration term in the form of differential equation before applying the sensitivity analysis method an additional constraint based equation which forms the augmented equations of motion is proposed to calculate the time averaged integration variable and the sensitivity coefficients are obtained as a result of solving the augmented differential equations the application of the least squares shadowing formulation to the augmented equations results in an explicit expression for the sensitivity coefficient which is dependent on the final state of the lagrange multipliers the lu factorization technique to calculate the lagrange multipliers leads to a better performance for the convergence problem and the computational expense numerical experiments on a set of problems selected from the literature are presented to illustrate the developed methods the numerical results demonstrate the correctness and effectiveness of the present approaches and some short impulsive sensitivity coefficients are observed by using the direct differentiation sensitivity analysis method

a boundary value problem for the two dimensional broadwell model it is shown that a certain boundary value problem for the steady two dimensional broadwell model on a rectangle has a solution the boundary conditions specify the ingoing particle densities on each side of the rectangle

tracking the direction of arrival of multiple moving targets by passive arrays asymptotic performance analysis in the companion paper of zhou yip and leung see ibid vol 47 no 10 p 2655 66 1999 the maximum likelihood ml algorithm for tracking the doas of multiple moving targets by passive arrays is presented in this paper we provide an asymptotic performance analysis of the algorithm the statistical consistency of the ml estimates is discussed and their asymptotic covariances are derived the cramer rao bounds for the ml estimates are investigated and their relative efficiency conditions are discussed the asymptotic performance of the ml tracking algorithm is compared with that of the extended kalman filter ekf under the assumption that the target waveforms are known finally numerical simulation results are used to verify the theoretical results

minimal repetition dynamic checkpointing algorithm for unsteady adjoint calculation adjoint equations of differential equations have seen widespread applications in optimization inverse problems and uncertainty quantification a major challenge in solving adjoint equations for time dependent systems has been the need to use the solution of the original system in the adjoint calculation and the associated memory requirement in applications where storing the entire solution history is impractical checkpointing methods have frequently been used however traditional checkpointing algorithms such as revolve require a priori knowledge of the number of time steps making these methods incompatible with adaptive time stepping we propose a dynamic checkpointing algorithm applicable when the number of time steps is a priori unknown our algorithm maintains a specified number of checkpoints on the fly as time integration proceeds for an arbitrary number of time steps the resulting checkpoints at any snapshot during the time integration have the optimal repetition number the efficiency of our algorithm is demonstrated both analytically and experimentally in solving adjoint equations this algorithm also has significant advantage in automatic differentiation when the length of execution is variable

tracking the direction of arrival of multiple moving targets the authors focus on the problem of tracking the direction of arrival doa of multiple moving targets the targets are assumed to be moving with constant accelerations subject to minor random perturbations and emitting narrow band signals that impinge on an array of passive sensors estimates of the doa vector of the targets are obtained from the sensor data based on the maximum likelihood ml principle in such a way that the association between the estimates made at different time points is maintained at each stage the current ml estimates of doa are treated as measurements and refined via a kalman filter tracking is accomplished without the need to perform unduly heavy computations an efficient strategy for dealing with closely spaced targets is also presented finally the performance of the tracking algorithm is illustrated via computer simulations

sensitivity analysis on chaotic dynamical systems by finite difference non intrusive least squares shadowing fd nilss abstract we present the finite difference non intrusive least squares shadowing fd nilss algorithm for computing sensitivities of long time averaged quantities in chaotic dynamical systems fd nilss does not require tangent solvers and can be implemented with little modification to existing numerical simulation software we also give a formula for solving the least squares problem in fd nilss which can be applied in nilss as well finally we apply fd nilss for sensitivity analysis of a chaotic flow over a 3 d cylinder at reynolds number 525 where fd nilss computes accurate sensitivities and the computational cost is in the same order as the numerical simulation

on nonlinear stationary half space problems in discrete kinetic theory we show that every steady discrete velocity model of the boltzmann equation on the real line i d dx fi ci f which satisfies anh theorem and for which all i 0 has solutions on the half line 0 which take prescribed non negativefi o if i 0 and approach a certain manifold of maxwellians asx such solutions give the density distribution in a knudsen boundary layer in the discrete velocity case

adjoint sensitivity analysis of chaotic dynamical systems with non intrusive least squares shadowing abstract this paper presents a discrete adjoint version of the recently developed non intrusive least squares shadowing nilss algorithm which circumvents the instability that conventional adjoint methods encounter for chaotic systems the nilss approach involves solving a smaller minimization problem than other shadowing approaches and can be implemented with only minor modifications to preexisting tangent and adjoint solvers adjoint nilss is demonstrated on a small chaotic ode a one dimensional scalar pde and a direct numerical simulation dns of the minimal flow unit a turbulent channel flow on a small spatial domain this is the first application of an adjoint shadowing based algorithm to a three dimensional turbulent flow

entropy adjoint p adaptive discontinuous galerkin method for the under resolved simulation of turbulent flows this paper presents an approach to mesh adaptation suitable for scale resolving simulations the methodology is based on the entropy adjoint approach which corresponds to a standard output based a

a pseudospectral method for solution of the three dimensional incompressible navier stokes equations abstract a new chebyshev pseudospectral technique based on the projection method that was previously applied by the authors to the solution of two dimensional incompressible navier stokes equations in primitive variables for nonperiodic boundary conditions is extended to solve the three dimensional navier stokes equations the crucial point of the method is the requirement that the continuity equation be satisfied everywhere in the domain on the boundaries as well as in the interior the key feature of the work presented in this paper is that the computer storage requirements of the full matrix inversion resulting from direct solution of the pressure poisson equation in three dimensions is greatly reduced by considering an eigenfunction decomposition the method was tested on a two dimensional driven cavity flow and the results were compared with those of the most accurate finite difference calculation the three dimensional driven cavity flow was then calculated at the same reynolds numbers as the two dimensional cases i e re 100 400 and 1000 in the calculated results three dimensional boundary effects were observed in all cases and became more apparent with increasing reynolds number

the analytical solutions of 2d stationary broadwell kinetic model the present communication is devoted to the calculation of some explicit stationary solutions of the four velocity broadwell kinetic model in two spatial dimensions the method of the truncated painleve expansion is employed and two classes of solutions are constructed it is shown that these solutions satisfy the special boundary value problem in a rectangle

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

subspace based adaptive method for estimating direction of arrival with luenberger observer in this paper we propose a computationally simple and efficient subspace based adaptive method for estimating directions of arrival amend for multiple coherent narrowband signals impinging on a uniform linear array ula where the previously proposed qr based method is modified for the number determination a new recursive least squares rls algorithm is proposed for null space updating and a dynamic model and the luenberger state observer are employed to solve the estimate association of directions automatically the statistical performance of the rls algorithm in stationary environment is analyzed in the mean and mean squares senses and the mean square error mse and mean square derivation msd learning curves are derived explicitly furthermore an analytical study of the rls algorithm is carried out to quantitatively compare the performance between the rls and least mean square lms algorithms in the steady state the theoretical analyses and effectiveness of the proposed rls algorithm are substantiated through numerical examples

maximum likelihood narrow band direction finding and the em algorithm generalized em expectation maximization algorithms have been derived for the maximum likelihood estimation of the direction of arrival of multiple narrowband signals in noise both deterministic and stochastic signal models are considered the algorithm for the deterministic model yields estimates of the signal amplitudes while that for the stochastic model yields estimates of the powers of the signal both algorithms have the properties that their limit points are stable and satisfy the necessary maximizer conditions for maximum likelihood estimators it is shown via simulation that the maximum likelihood method allows for the resolution of the directions of arrival of signals at angular separation and noise levels for which other high resolution methods will not work algorithm convergence does depend on initial conditions however convergence to a global maximum has been observed in simulation when the initial estimates are within a significant fraction if one beamwidth componentwise of this maximum simulations also show that the deterministic model has a significant impact on the angle estimator performance

numerical convergence of the lyapunov spectrum computed using low mach number solvers abstract in the dynamical systems approach to describing turbulent or otherwise chaotic flows an important quantity is the lyapunov exponents and vectors that characterize the strange attractor of the flow in particular knowledge of the lyapunov exponents and vectors will help identify perturbations that the system is most sensitive to and quantify the dimension of the attractor however reliably computing these quantities requires robust numerical algorithms while several perturbation based techniques are available in literature their application to commonly used turbulent flow solvers as well the numerical convergence properties have not been studied in detail the goal of this work is to examine the convergence properties of the lyapunov exponents when computed using a low mach number solver for a series of progressively complex flow problems in particular a manufactured solutions approach is devised using the orr sommerfeld os perturbation theory to extract lyapunov exponents and vectors from os eigen solutions overall the spatial convergence rates of lyapunov exponents follow the truncation order for the discretization scheme however temporal convergence rates were found to be only a weak function of timestep used additionally for some configurations the convergence properties are found to depend on the lyapunov exponent itself these results indicate that convergence properties do not follow universal rates and require careful analysis for specific configurations considered

a boundary value problem for discrete velocity models on considere deux problemes aux valeurs limites non lineaires concernant un ecoulement stationnaire a une dimension entre des plaques paralleles