convex optimization approaches for blind sensor calibration using sparsity we investigate a compressive sensing framework in which the sensors introduce a distortion to the measurements in the form of unknown gains we focus on blind calibration using measures performed on multiple unknown but sparse signals and formulate the joint recovery of the gains and the sparse signals as a convex optimization problem we divide this problem in 3 subproblems with different conditions on the gains specifially i gains with different amplitude and the same phase ii gains with the same amplitude and different phase and iii gains with different amplitude and phase in order to solve the first case we propose an extension to the basis pursuit optimization which can estimate the unknown gains along with the unknown sparse signals for the second case we formulate a quadratic approach that eliminates the unknown phase shifts and retrieves the unknown sparse signals an alternative form of this approach is also formulated to reduce complexity and memory requirements and provide scalability with respect to the number of input signals finally for the third case we propose a formulation that combines the earlier two approaches to solve the problem the performance of the proposed algorithms is investigated extensively through numerical simulations which demonstrates that simultaneous signal recovery and calibration is possible with convex methods when sufficiently many unknown but sparse calibrating signals are provided

direction finding with partly calibrated uniform linear arrays a new method for direction finding with partly calibrated uniform linear arrays ulas is presented it is based on the conventional estimation of signal parameters via rotational invariance techniques esprit by modeling the imperfections of the ulas as gain and phase uncertainties for a fully calibrated array it reduces to the conventional esprit algorithm moreover the direction of arrivals doas unknown gains and phases of the uncalibrated sensors can be estimated in closed form without performing a spectral search hence it is computationally very attractive the cramer rao bounds crbs of the partly calibrated ulas are also given simulation results show that the root mean squared error rmse performance of the proposed algorithm is better than the conventional methods when the number of uncalibrated sensors is large it also achieves satisfactory performance even at low signal to noise ratios snrs

controllability observability and duality in singular systems the concepts of controllability and observability for systems of the form e dot x ax bu y cx e singular are considered a theory is presented which unifies the three main approaches to this topic already existing in the literature the development includes a generalization of the duality theorem from state space theory

multisource self calibration for sensor arrays calibration of a sensor array is more involved if the antennas have direction dependent gains and multiple calibrator sources are simultaneously present we study this case for a sensor array with arbitrary geometry but identical elements i e elements with the same direction dependent gain pattern a weighted alternating least squares wals algorithm is derived that iteratively solves for the direction independent complex gains of the array elements their noise powers and their gains in the direction of the calibrator sources an extension of the problem is the case where the apparent calibrator source locations are unknown e g due to refractive propagation paths for this case the wals method is supplemented with weighted subspace fitting wsf direction finding techniques using monte carlo simulations we demonstrate that both methods are asymptotically statistically efficient and converge within two iterations even in cases of low snr

re estimating the sample size of an on going blinded trial based on the method of randomization block sums we extend a method we had previously described statist med 2005 to estimate the within group variance of a continuous endpoint without breaking the blind in a randomized clinical trial specifically we a explain how the method may be used for a wider set of designs than we had previously indicated b obtain a within group covariate adjusted blinded variance estimator c illustrate use of the method for sample size re estimation and d describe a procedure to determine whether or not the blinded variance estimator works well not just on average but for the data set at hand the proposed method is simple to use and makes no additional assumptions than is made for unblinded analysis simulations show that for realistic sample sizes there is virtually no inflation in the type i error rate when weighing the burden imposed by interim unblinded re estimation with the loss in precision with blinded re estimation it may be advantageous for some trials to use the blinded method

a general approach for sample size calculation for the three arm gold standard non inferiority design in the three arm gold standard non inferiority design an experimental treatment an active reference and a placebo are compared this design is becoming increasingly popular and it is whenever feasible recommended for use by regulatory guidelines we provide a general method to calculate the required sample size for clinical trials performed in this design as special cases the situations of continuous binary and poisson distributed outcomes are explored taking into account the correlation structure of the involved test statistics the proposed approach leads to considerable savings in sample size as compared with application of ad hoc methods for all three scale levels furthermore optimal sample size allocation ratios are determined that result in markedly smaller total sample sizes as compared with equal assignment as optimal allocation makes the active treatment groups larger than the placebo group implementation of the proposed approach is also desirable from an ethical viewpoint

multiple emitter location and signal parameter estimation processing the signals received on an array of sensors for the location of the emitter is of great enough interest to have been treated under many special case assumptions the general problem considers sensors with arbitrary locations and arbitrary directional characteristics gain phase polarization in a noise interference environment of arbitrary covariance matrix this report is concerned first with the multiple emitter aspect of this problem and second with the generality of solution a description is given of the multiple signal classification music algorithm which provides asymptotically unbiased estimates of 1 number of incident wavefronts present 2 directions of arrival doa or emitter locations 3 strengths and cross correlations among the incident waveforms 4 noise interference strength examples and comparisons with methods based on maximum likelihood ml and maximum entropy me as well as conventional beamforming are included an example of its use as a multiple frequency estimator operating on time series is included

a studentized permutation test for three arm trials in the gold standard design the gold standard design for three arm trials refers to trials with an active control and a placebo control in addition to the experimental treatment group this trial design is recommended when being ethically justifiable and it allows the simultaneous comparison of experimental treatment active control and placebo parametric testing methods have been studied plentifully over the past years however these methods often tend to be liberal or conservative when distributional assumptions are not met particularly with small sample sizes in this article we introduce a studentized permutation test for testing non inferiority and superiority of the experimental treatment compared with the active control in three arm trials in the gold standard design the performance of the studentized permutation test for finite sample sizes is assessed in a monte carlo simulation study under various parameter constellations emphasis is put on whether the studentized permutation test meets the target significance level for comparison purposes commonly used wald type tests which do not make any distributional assumptions are included in the simulation study the simulation study shows that the presented studentized permutation test for assessing non inferiority in three arm trials in the gold standard design outperforms its competitors for instance the test based on a quasi poisson model for count data the methods discussed in this paper are implemented in the r package threearmedtrials which is available on the comprehensive r archive network cran copyright 2016 john wiley sons ltd

direction of arrival estimates in the presence of wavelength gain and phase errors direction of arrival doa estimation using an array of sensors relies on an accurate characterization of the array manifold in the absence of characterization errors established techniques like music can be shown to perform well both theoretically and in simulation however in the presence of unknown sensor and or source characteristics the performance of most methods degrades significantly we consider the problem of estimating gain and phase errors of an array of sensors whose physical positions are known our algorithm assumes that the gain and phase characteristics of the sensors are independent of doa and employs multiple calibration sources with known doa s it differs from other algorithms in that the signal wavelengths are unknown a least squares formulation of the problem is then shown to be np complete implying that an efficient solution is unlikely to exist an implicit enumerative technique is used to obtain the exact solution for the special case of collinear sensors we further show that an inherent ambiguity in the model prevents exact phase characterization unless the wavelength of one calibration source is assumed known a theorem is presented relating the error in doa to the difference between the assumed and true wavelengths of this calibration source simulation results are presented for both noncollinear and collinear arrays

a compact cramer rao bound expression for parametric estimation of superimposed signals the problem of parameter estimation of superimposed signals in white gaussian noise is considered closed form expressions of the cramer rao bound for real or complex signals with vector parameters are derived extending recent results by p stoica and a nehorai 1989

a unified framework and sparse bayesian perspective for direction of arrival estimation in the presence of array imperfections self calibration methods play an important role in reducing the negative effects of array imperfections during direction of arrival doa estimation however the dependence of most such methods on the eigenstructure techniques greatly degrades their adaptation to demanding scenarios such as low signal to noise ratio snr and limited snapshots this paper aims at formulating a unified framework and sparse bayesian perspective for array calibration and doa estimation a comprehensive model of the array output is presented first when a single type of array imperfection is considered with mutual coupling gain phase uncertainty and sensor location error treated as typical examples the spatial sparsity of the incident signals is then exploited and a bayesian method is proposed to realize array calibration and source doa estimation the array perturbation magnitudes are assumed to be small according to most application scenarios and the geometries of mutually coupled arrays are assumed to be uniform linear and those of arrays with sensor location errors are assumed to be linear cramer rao lower bounds crlbs for the array calibration and doa estimation precisions are also obtained the sparse bayesian method is finally extended to deal with the doa estimation problem when more than one type of array perturbation coexists

joint 2 d doa estimation and phase calibration for uniform rectangular arrays a precise model of the array response is required to maintain the performance of direction of arrival doa estimation when modeling errors are present or the sensor environment is time varying autocalibration becomes necessary in this paper the problem of phase autocalibration for uniform rectangular array ura geometries is considered for the case with a single source a simple and robust least squares algorithm for joint 2 d doa estimation and phase calibration is presented when performing phase autocalibration with a ura the phase and doa parameters cannot be identified together without ambiguity this problem is discussed and a suitable remedy is suggested an approximate cramer rao bound and analytical expressions for the mean squared error performance of the proposed estimator are presented the proposed algorithm for phase autocalibration is extended for the case with multiple sources the results are evaluated using a representative body of simulations

an improved double sampling procedure based on the variance summary sample size calculations for a continuous outcome require specification of the anticipated variance inaccurate specification can result in an underpowered or overpowered study for this reason adaptive methods whereby sample size is recalculated using the variance of a subsample have become increasingly popular the first proposal of this type stein 1945 annals of mathematical statistics16 243 258 used all of the data to estimate the mean difference but only the first stage data to estimate the variance stein s procedure is not commonly used because many people perceive it as ignoring relevant data this is especially problematic when the first stage sample size is small as would be the case if the anticipated total sample size were small a more naive approach uses in the denominator of the final test statistic the variance estimate based on all of the data applying the helmert transformation we show why this naive approach underestimates the true variance and how to construct an unbiased estimate that uses all of the data we prove that the type i error rate of our procedure cannot exceed

array shape calibration using sources in unknown locations a maximum likelihood approach sensor location uncertainty can severely degrade the performance of direction finding systems an iterative maximum likelihood method for simultaneously estimating directions of arrival doa and sensor locations is developed to alleviate this problem the case of nondisjoint sources i e sources observed in the same frequency cell and at the same time is emphasized the algorithm converges to the global maximum of the likelihood function if the initial conditions are sufficiently good numerical examples are presented illustrating the performance of the proposed technique a distinctive feature of the algorithm is its ability to locate the sensors accurately without deploying calibration sources at known locations

observability of singular systems with commensurate time delays and neutral terms this paper deals with the observability problem of a sort of singular systems with commensurate time delays in the trajectories of the system in the time derivative of the trajectories neutral terms and in the output system by using a recursive algorithm sufficient conditions easy testable are proposed for guaranteeing the backward and the algebraic observability of the system this condition implies that the trajectories of the system can be reconstructed by using the actual and past values of the system output

doa estimation and detection in colored noise using additional noise only data in a typical array processing scenario noise acting on the array can not be assumed spatially white it is in many cases necessary to use quiet periods when only noise is received to estimate the noise covariance if estimation of the signal parameters and noise covariance is performed jointly performance can be improved this is especially true when stationarity considerations limit the amount of available valid noise only data an asymptotically valid approximative maximum likelihood method aml for the estimation problem is derived in this work the resulting criterion is when concentrated with respect to the signal parameters relatively simple in numerical experiments aml shows promising small sample performance compared to earlier methods the criterion function is also well suited for numerical optimization the new criterion function allows for the development of a novel mode like non iterative estimation procedure if the array belongs to the important class of uniform linear arrays the resulting procedure retains the asymptotic properties of maximum likelihood and numerical simulations indicate superior threshold performance when compared to an optimally weighted subspace fitting wsf formulation of mode for the detection problem no method has been presented that takes the unknown noise covariance into account here a well known detection scheme for wsf is extended to work in this scenario as well the derivations of this scheme further stress the importance of using the correct weighting in wsf when the noise covariance is unknown it is also shown that the minimum value of the criterion function associated with aml can be used for the detection purpose numerical experiments indicate very promising performance for the aml detection scheme

solvability controllability and observability of continuous descriptor systems in this paper we investigate the properties of the continuous descriptor system e dot x t ax t bu t 0 leqt leqb where e a and b are complex and possibly singular matrices and u t is a complex function differentiable sufficiently many times the traditional approach to such systems is to separate the state equations from the algebraic equations however such algorithms usually destroy the natural physically based sparsity and structure of the original system therefore we consider descriptor systems in their original form such systems possess numerous properties not shared by the well known state variable systems first we relate classical theories of matrix pencils to the solvability of descriptor systems then we extend the concepts of reachability controllability and observability of state variable systems to descriptor systems and describe the set of reachable states for descriptor systems

a method to estimate the variance of an endpoint from an on going blinded trial blinded estimation of variance allows for changing the sample size without compromising the integrity of the trial some of the methods that estimate the variance in a blinded manner either make untenable assumptions or are only applicable to two treatment trials we propose a new method for continuous endpoints that makes minimal assumptions the method uses the enrollment order of subjects and the randomization block size to estimate the variance it can be applied to normal or non normal data trials with two or more treatments equal or unequal allocation schemes fixed or random randomization block sizes and single or multi centre trials the variance estimator is unbiased and performs best when the randomization block size is the smallest simulation results suggest that for many commonly used randomization block sizes the proposed estimator is expected to perform well the proposed method is used to estimate the variance of the endpoint for two trials and is shown to perform well by comparison with its unblinded counterpart

doa estimation for mixed signals in the presence of mutual coupling in this paper a new direction of arrival doa estimation method is proposed in the presence of unknown mutual coupling the impinging signals are a mixture of signals in different correlation degrees which are uncorrelated partially correlated or coherent with each other the method proceeds in three steps the noncoherent uncorrelated or partially correlated signals are firstly estimated with unknown mutual coupling then these estimates are utilized to get the mutual coupling coefficients finally by eliminating the contributions of the noncoherent signals and compensating the mutual coupling effect only coherent signals remain to be estimated this method is simple but effective and does not need iterative processing simulation results demonstrate the effectiveness and performance of the proposed method

blinded sample size re estimation in three arm trials with gold standard design in this article we study blinded sample size re estimation in the gold standard design with internal pilot study for normally distributed outcomes the gold standard design is a three arm clinical trial design that includes an active and a placebo control in addition to an experimental treatment we focus on the absolute margin approach to hypothesis testing in three arm trials at which the non inferiority of the experimental treatment and the assay sensitivity are assessed by pairwise comparisons we compare several blinded sample size re estimation procedures in a simulation study assessing operating characteristics including power and type i error we find that sample size re estimation based on the popular one sample variance estimator results in overpowered trials moreover sample size re estimation based on unbiased variance estimators such as the xing ganju variance estimator results in underpowered trials as it is expected because an overestimation of the variance and thus the sample size is in general required for the re estimation procedure to eventually meet the target power to overcome this problem we propose an inflation factor for the sample size re estimation with the xing ganju variance estimator and show that this approach results in adequately powered trials because of favorable features of the xing ganju variance estimator such as unbiasedness and a distribution independent of the group means the inflation factor does not depend on the nuisance parameter and therefore can be calculated prior to a trial moreover we prove that the sample size re estimation based on the xing ganju variance estimator does not bias the effect estimate copyright 2017 john wiley sons ltd

esprit estimation of signal parameters via rotational invariance techniques an approach to the general problem of signal parameter estimation is described the algorithm differs from its predecessor in that a total least squares rather than a standard least squares criterion is used although discussed in the context of direction of arrival estimation esprit can be applied to a wide variety of problems including accurate detection and estimation of sinusoids in noise it exploits an underlying rotational invariance among signal subspaces induced by an array of sensors with a translational invariance structure the technique when applicable manifests significant performance and computational advantages over previous algorithms such as mem capon s mlm and music

causal observability of descriptor systems observability analysis for descriptor systems by using a matrix pencil approach is presented systems under consideration are the most general class of linear continuous descriptor systems a few practically relevant notions of observability particularly the causal observability which corresponds to the existence of a luenberger observer and the corresponding necessary and sufficient test conditions are provided the interpretation of various observabilities in terms of matrix pencils offers insights into the physical meaning of these concepts

array shape calibration using sources in unknown locations part i far field sources this paper deals with source localization using a two dimensional array of sensors whose locations are not known precisely if only a single source is observed uncertainties in sensor location increase errors in source bearing and range by an amount which is independent of signal to noise ratio and which can easily dominate over all localization accuracy major performance gains could therefore result from successful calibration of array geometry the paper derives cramer rao bounds on calibration and source location accuracies achievable with far field sources whose bearings are not initially known the sources are assumed to radiate gaussian noise and to be spectrally disjoint of each other when the location of one sensor and the direction to a second sensor is known three noncollinear sources are sufficient to calibrate sensor positions with errors which decrease to zero as calibrating source strength or time bandwidth products tend to infinity the sole exception to this statement is a nominally linear array for which such calibration is not possible when one sensor location is known but no directional reference is available three noncollinear sources can determine array shape but there remains a residual error in angular orientation which is irremovable by the calibration procedure when no sensor locations are known a priori one adds to the residual error in rotation a translational component in the far field the latter should be unimportant in addition to the asymptotic results cramer rao bounds are computed for finite signal to noise ratios and observation times one finds that calibration permits significant reductions in localization errors for parameter values well within the practical range

a novel online mutual coupling compensation algorithm for uniform and linear arrays in this paper a novel online mutual coupling compensation algorithm especially tailored to uniform and linear arrays is presented it is conceived to simultaneously compensate for mutual coupling and estimate the direction of arrivals doas of signals impinging on the array since the estimated calibration matrix can be embedded within any classical super resolution direction finding method an alternating minimization procedure based on closed form solutions is performed to estimate the mutual coupling matrix in the field of complex symmetric toeplitz matrices unlike many existing array calibration methods it requires neither the presence of calibration sources nor previous calibration information as initialization computer simulations show the effectiveness of the proposed technique and prove that the nice statistical properties of classical super resolution doa estimation algorithms can be restored despite the presence of mutual coupling

on the asymptotic performance analysis of subspace doa estimation in the presence of modeling errors case of music this paper provides a new analytic expression of the bias and rms error root mean square error of the estimated direction of arrival doa in the presence of modeling errors in first order approximations of the rms error are derived which are accurate for small enough perturbations however the previously available expressions are not able to capture the behavior of the estimation algorithm into the threshold region in order to fill this gap we provide a second order performance analysis which is valid in a larger interval of modeling errors to this end it is shown that the doa estimation error for each signal source can be expressed as a ratio of hermitian forms with a stochastic vector containing the modeling error then an analytic expression for the moments of such a hermitian forms ratio is provided finally a closed form expression for the performance bias and rms error is derived simulation results indicate that the new result is accurate into the region where the algorithm breaks down

a sensitivity analysis of the music algorithm a first order analysis of the sensitivity of the music algorithm to system errors which cause differences between the array manifold used by music and the true array manifold is presented the effect of such errors on the direction of arrival estimates is investigated the ability of the music algorithm to resolve two closely spaced sources in the presence of phase and gain errors in the array elements or the receivers or errors in the element locations is analyzed a formula for computing the failure threshold of music as a function of source separation and other system parameters is derived and tested by simulation the analysis assumes that the exact covariance matrix of array element outputs is known the infinite data case

analysis of the asymptotic relative efficiency of the music algorithm an analytical performance evaluation of the errors of the direction of arrival estimates obtained by the music algorithm for uncorrelated sources is provided explicit asymptotic formulas are derived for the means and the covariance of the estimates the covariances are then compared to the cramer rao lower bound it is shown that for a single course the music algorithm is asymptotically efficient for multiple sources the algorithm is not efficient in general however it approaches asymptotic efficiency when the snrs signal to noise ratios of all sources tend to infinity it is illustrated by several test cases that the relative efficiency of the music algorithm is nearly one under a wide range of parameter variations the analytic performance evaluation thus confirms empirical evidence to the excellent performance of the music algorithm for narrowband signals

consensus of networked mechanical systems with communication delays a unified framework this technical note addresses the consensus problem of networked uncertain mechanical systems which interact on directed graphs containing a spanning tree and are subjected to nonuniform communication delays the challenge lies in the unclear input output property of a linear networked system containing communication delays and the unclear convergent property of this system under an external input we establish a new input output property of this linear networked system and moreover its convergent property under an external input upon which we establish a unified framework to resolve the consensus problem of multiple mechanical systems the proposed consensus framework unifies extends the existing results and in addition yields a fully cascaded closed loop system with lyapunov like analysis and frequency domain input output analysis we show that the proposed unified consensus control scheme ensures consensus without the integral action of the sliding vector and scaled weighted average consensus with the integral action of the sliding vector simulation results are provided to demonstrate the performance of the proposed consensus schemes

unknown inputs functional observers designs for delay descriptor systems new time and frequency domain designs of unknown inputs functional observers uifo for a class of descriptor systems with a constant time delay are investigated in this paper the unknown inputs are present in both the state and the measurement equations the time procedure design is based on the unbiasedness of the estimation error and the lyapunov krasovskii stability theory after given the existence condition of such observers the gain implemented in the functional observer with internal delay design is obtained in terms of linear matrix inequalities the particular cases where the observer is independent of internal delay and where it is independent of delay are also investigated a design algorithm that summarises the different steps of the uifo design is proposed then the frequency procedure design is derived from time domain results by applying the factorisation approach where we define some useful matrix fraction descriptions note that the order of this unknown input observers is equal to

consistency and mse performance of music based doa of a single source in white noise with randomly missing data music is a popular algorithm for estimating the direction of arrival doa in array signal processing applications in this paper we analyze the performance of the music algorithm for a single source system in the presence of noisy and missing data when only a random subset of the entries in the data matrix are observed we prove consistency of the doa estimate when signal from a single source is impinging on low coherence arrays and derive an analytic expression for the mean squared error mse performance of music for the case of uniform linear arrays in the large array and relatively large sample setting our analysis is mathematically justified in both the sample rich and deficient regimes the expression for the mse is a simple function of array geometry signal to noise ratio snr the fraction of entries observed and the ratio of the number of sensors to number of snapshots we derive a phase transition threshold which separates a regime where music is consistent from a regime where music is inconsistent this threshold depends upon the snr the probability of observing entries in the data matrix and number of sensors and snapshots in a simple manner which we make explicit

the statistical performance of the music and the minimum norm algorithms in resolving plane waves in noise this paper presents an asymptotic statistical analysis of the null spectra of two eigen assisted methods music 1 and minimum norm 2 for resolving independent closely spaced plane waves in noise particular attention is paid to the average deviation of the null spectra from zero at the true angles of arrival for the plane waves these deviations are expressed as functions of signal to noise ratios number of array elements angular separation of emitters and the number of snapshots in the case of music an approximate expression is derived for the resolution threshold of two plane waves with equal power in noise this result is validated by monte carlo simulations

an eigenstructure method for estimating doa and sensor gain phase errors in this paper we consider the problem of direction of arrival doa estimation in the presence of sensor gain phase errors under some mild assumptions we propose a new doa estimation method based on the eigendecomposition of a covariance matrix which is constructed by the dot product of the array output vector and its conjugate by combining the new doa estimation with the conventional gain phase error estimation a method is proposed to simultaneously estimate the doa and gain phase errors without joint iteration theoretical analysis shows that the proposed method performs independently of phase errors and thus behaves well regardless of phase errors however the resolution capability of the proposed method is lower than that of the method in a j weiss and b friedlander eigenstructure methods for direction finding with sensor gain and phase uncertainties circuits systems signal process vol 9 no 3 pp 271 300 1990 named as the wf method in order to improve the resolution capability and maintain phase error independence a combined strategy is developed using the proposed and wf methods the advantage of the proposed methods is that they are independent of phase errors leading to the cancellation of phase error calibration during the operation life of an array moreover the proposed methods avoid the problem of suboptimal convergence which occurs in the wf method the drawbacks of the proposed methods are their high computational complexity and their requirement for the condition that at least two signals are spatially far from each other and they are not applicable to a linear array simulation results verify the effectiveness of the proposed methods

maximum likelihood array processing in spatially correlated noise fields using parameterized signals this paper deals with the problem of estimating signal parameters using an array of sensors this problem is of interest in a variety of applications such as radar and sonar source localization a vast number of estimation techniques have been proposed in the literature during the past two decades most of these can deliver consistent estimates only if the covariance matrix of the background noise is known in many applications the aforementioned assumption is unrealistic recently a number of contributions have addressed the problem of signal parameter estimation in unknown noise environments based on various assumptions on the noise herein a different approach is taken we assume instead that the signals are partially known the received signals are modeled as linear combinations of certain known basis functions the exact maximum likelihood ml estimator for the problem at hand is derived as well as computationally more attractive approximation the cramer rao lower bound crb on the estimation error variance is also derived and found to coincide with the crb assuming an arbitrary deterministic model and known noise covariance

single antenna power measurements based direction finding in this paper the problem of estimating direction of arrival doa of multiple uncorrelated sources from single antenna power measurements is addressed utilizing the fact that the antenna pattern is bandlimited and can be modeled as a finite sum of complex exponentials we first show that the problem can be transformed into a frequency estimation problem then we explain how the annihilating filter method can be used to solve for the doa in the noiseless case in the presence of noise we propose to use cadzow denoising that is formulated as an iterative algorithm derived from exploiting the matrix rank and linear structure properties furthermore we have also derived the cramer rao bound crb and reviewed several alternative approaches that can be used as a comparison to the proposed approach from the simulation and experimental results we demonstrate that the proposed approach significantly outperforms other approaches it is also evident from the monte carlo analysis that the proposed approach converges to the crb

performance prediction of maximum likelihood direction of arrival estimation in the presence of modeling errors this paper provides new analytic expressions for the root mean square rms error and bias of the maximum likelihood ml direction of arrival doa estimator in the presence of steering vector modeling errors previous work has provided a first order approximation of these performance measures which is valid for small modeling errors in order to take into account larger errors and provide tools for designing an experimental setup a more accurate but still easy to use performance analysis is necessary for such an investigation the doa estimation errors are expressed as a hermitian form with a stochastic vector composed of the modeling errors closed form expressions relating the bias and rms errors to the statistical moments of the modeling error are then deduced from the statistics of this hermitian form simulations are provided to illustrate the usefulness of the theoretical results

a novel approach to array manifold calibration using single direction information for accurate direction of arrival estimation a method of array manifold calibration using one steering vector measured in a single direction is proposed the phase information of the measured steering vector is used to derive a novel calibration matrix that is proposed to compensate for the relative phase distortion rpd at each antenna port we also present a metric function defined as a standard deviation of the rpd to determine the optimum calibration angle which provides intuition for the cause of the accuracy degradation in the direction of arrival estimation to verify the feasibility a seven element circular array with identical microstrip patch antennas is fabricated for calibrating its array manifold using a single steering vector measured in a full anechoic chamber the calibrated array manifold is then used to estimate the direction of arrival and its accuracy is compared to the calibrated result obtained from the traditional least squares method the results demonstrate that the estimation error can be improved by 54 9 compared to the traditional least squares method when the number of measured steering vectors is extremely limited

parametric sensor array calibration using measured steering vectors of uncertain locations we consider the problem of sensor array calibration using a set of unique measured steering vectors of uncertain locations to estimate the unknown deterministic array perturbation parameters in a maximum likelihood framework the array perturbations are parameterized by the sensor locations mutual coupling coefficients and receiver channel mismatch we introduce a hybrid optimizer based on the amalgamation of gradient based algorithms and the genetic algorithm this optimizer is capable of coping with the problem of local extrema attractors particularly initial estimates with large deviations from their true values numerical examples are provided to demonstrate the effectiveness and behavior of the proposed algorithms

asymptotically perfect wideband focusing of multiring circular arrays the concept of coherent focusing of sensor arrays introduced by wang and kaveh led to the development of high performance and computationally efficient algorithms for wideband direction finding and beamforming nonetheless the quality of focusing depends on the understanding and the proper exploitation of specific array manifold properties circular arrays exhibit uniform isotropic performance over the entire azimuthal range and allow the use of fast algorithms originally developed for uniform linear arrays by decomposing the manifold into circular harmonics coherent wideband focusing of circular arrays suffers from ambiguities noise warping and numerical ill conditioning in this work it is shown that a fast orthonormal beamspace transformation combining the responses of two concentric rings can perfectly focus wideband sources at all azimuth angles in the circular harmonic domain in the limit of infinite number of sensors the information loss after focusing is minimized through an analytical approach the proposed focusing scheme is computationally very efficient and can be directly extended to multiring circular arrays that are arranged into a set of nested two ring subarrays to cover very large bandwidths

observability and related structural results for linear hereditary systems new results on the theory of observability and deterministic observers for linear time invariant systems with delays are presented the results have been established only for the case of point delays which are commensurable however most of the results can be generalized to the situation with distributed delays and to the ease with non commensurate delays

observability of linear systems with commensurate delays and unknown inputs this paper investigates the observability analysis for linear time systems whose outputs are affected by unknown inputs three different definitions of observability are proposed by introducing the smith form and comparing the invariant factors a sufficient condition is deduced for each proposed definition observability several examples are given for the purpose of highlighting the effectiveness of the proposed approach

a performance analysis of subspace based methods in the presence of model errors i the music algorithm application of subspace based algorithms to narrowband direction of arrival doa estimation requires that both the array response in all directions of interest and the spatial covariance of the noise must be known in practice however neither of these quantities is known precisely depending on the degree to which they deviate from their nominal values serious performance degradation can result the performance of the music algorithm is examined for situations in which the noise covariance and array response are perturbed from their assumed values theoretical expressions for the error in the music doa estimates are derived and compared with simulations performed for several representative cases and with the appropriate cramer rao bound an optimally weighted version of music is proposed for a particular class of array errors

sensor array calibration using a maximum likelihood approach high resolution array processing algorithms for source localization are known to be sensitive to errors in the model for the sensor array spatial response in particular unknown gain phase and mutual coupling as well as errors in the sensor positions can seriously degrade the performances of array processing algorithms this paper describes a calibration algorithm that estimates the calibration matrix consisting of the unknown gain phase and mutual coupling coefficients as well as the sensor positions using a set of calibration sources in known locations the estimation of the various parameters is based on a maximum likelihood approach cramer rao lower bound crb expressions for the sensor positions and the calibration matrix parameters are also derived numerical results are shown to illustrate the potential usefulness of the proposed calibration algorithm toward better accuracy and resolution in parametric array processing algorithms

music maximum likelihood and cramer rao bound further results and comparisons the problem of determining the direction of arrival of narrowband plane waves using sensor arrays and the related problem of estimating the parameters of superimposed signals from noisy measurements are studied a number of results have been recently presented by the authors on the statistical performance of the multiple signal characterization music and the maximum likelihood ml estimators for the above problems this work extends those results in several directions first it establishes that in the class of weighted music estimators the unweighted music achieves the best performance i e the minimum variance of estimation errors in large samples next it derives the covariance matrix of the ml estimator and presents detailed analytic studies of the statistical efficiency of music and ml estimators these studies include performance comparisons of music and mle with each other as well as with the ultimate performance corresponding to the cramer rao bound finally some numerical examples are given which provide a more quantitative study of performance for the problem of finding two directions with uniform linear sensor arrays

simple procedures for blinded sample size adjustment that do not affect the type i error rate for normally distributed data determination of the appropriate sample size requires a knowledge of the variance because of the uncertainty in the planning phase two stage procedures are attractive where the variance is reestimated from a subsample and the sample size is adjusted if necessary from a regulatory viewpoint preserving blindness and maintaining the ability to calculate or control the type i error rate are essential recently a number of proposals have been made for sample size adjustment procedures in the t test situation unfortunately none of these methods satisfy both these requirements we show through analytical computations that the type i error rate of the t test is not affected if simple blind variance estimators are used for sample size recalculation furthermore the results for the expected power of the procedures demonstrate that the methods are effective in ensuring the desired power even under initial misspecification of the variance a method is discussed that can be applied in a more general setting and that assumes analysis with a permutation test this procedure maintains the significance level for any design situation and arbitrary blind sample size recalculation strategy

efficient quadratic detection in perturbed arrays via fourier transform techniques matched field beamforming used in combination with a generalized likelihood ratio test is the most common detector structure in array processing situations unfortunately various array perturbations caused by phase calibration propagation effects or modeling errors can cause the sensor observations to become only partially correlated limiting the performance of traditional matched field beamformers that assume perfect coherence of the signal wavefronts quadratic array processing is optimal for many perturbed array problems however direct implementation poses a significant computational burden we show that under certain conditions the optimal quadratic detector for dealing with perturbed arrays can be approximately realized efficiently and robustly employing only discrete fourier transforms to deal with spatial processing in addition we show that the proposed spatial processing allows for convenient integration of conventional frequency domain methods for angle of arrival searches our proposed array detection structure provides the robustness and performance benefits of complicated quadratic processing at a computational cost comparable with that of traditional matched field beamforming

identifiability analysis of local oscillator phase self calibration based on hybrid cramer rao bound in mimo radar the identifiability of self calibration of local oscillator phase perturbation in multiple input multiple output mimo radar is analyzed in this paper four cases are considered the absolute phase perturbation app and phase perturbation differences ppds in mimo radar with widely separated antennas smimor and the app and ppds in co located mimo radar cmimor the tightness of the hybrid cramer rao bound hcrb is proved in all four cases it is interesting that the problem in this paper is a special case in which hcrb is asymptotically tight for nonlinear observation models containing unknown deterministic and random parameters for each case a signal model for multiple stationary targets is constructed the closed form hcrb of phase perturbation is derived and used to analyze the identifiability of phase perturbation it is proven that only the ppds in cmimor in the above mentioned four cases are identifiable numerical simulations verify the conclusion

maximum likelihood localization of multiple sources by alternating projection an algorithm referred to as apm for computing the maximum likelihood estimator of the locations of simple sources in passive sensor arrays is presented the algorithm is equally applicable to the case of coherent signals and to the case of a single snapshot the algorithm is iterative the maximum of the likelihood function is computed by successive approximations the convergence of the algorithm to the global maximum is demonstrated for a variety of scenarios the key to this global convergence is the initialization scheme

estimation in flexible two stage designs adaptive test designs for clinical trials allow for a wide range of data driven design adaptations using all information gathered until an interim analysis the basic principle is to use a test statistics which is invariant with respect to the design adaptations under the null hypothesis this allows for a control of the type i error rate for the primary hypothesis even for adaptations not specified a priori in the study protocol estimation is usually another important part of a clinical trial however is more difficult in adaptive designs in this research paper we give an overview of point and interval estimates for flexible designs and compare methods for typical sample size rules we also make some proposals for confidence intervals which have nominal coverage probability also after an unforeseen design adaptation and which contain the maximum likelihood estimate and the usual unadjusted confidence interval

2 d doa estimation in the presence of mutual coupling we present a 2 d direction of arrival doa estimation algorithm in the presence of unknown mutual coupling for the uniform rectangular array ura based on the multiple signal classification music algorithm by setting the sensors on the boundary of the ura as auxiliary sensors it can accurately estimate the doas without any calibration sources or iterative operations we prove that the effect of mutual coupling can be eliminated by the inherent mechanism of the proposed method twice search technique is used to reduce the computation of the 2 d spectrum search moreover we provide a method to estimate the mutual coupling coefficients after getting the doa estimates simulation results confirm the effectiveness of the proposed algorithm

state feedback impulse elimination for singular systems over a hermite domain we reduce the problem of impulse elimination via state feedback in singular differential equations to algebra our results are developed for systems over an arbitrary hermite domain we show that the established theories for the time invariant and the real analytic time varying settings can be unified in this way besides the constant and real analytic functions several other function rings are considered our algebraic theory is applied to these cases providing solutions to the impulse elimination problem for classes of systems not previously studied in particular our work allows the restriction of the feedback matrix to certain function rings

the assessment of non inferiority in a gold standard design with censored exponentially distributed endpoints the objective of this paper is to develop statistical methodology for non inferiority hypotheses to censored exponentially distributed time to event endpoints motivated by a recent clinical trial in depression we consider a gold standard design where a test group is compared to an active reference and to a placebo group the test problem is formulated in terms of a retention of effect hypothesis thus the proposed wald type test procedure assures that the effect of the test group is better than a pre specified proportionof the treatment effect of the reference group compared to the placebo group a sample size allocation rule to achieve optimal power is presented which only depends on the pre specifiedand the probabilities for the occurrence of censoring in addition a pretest is presented for either the reference or the test group to ensure assay sensitivity in the complete test procedure the actual type i error and the sample size formula of the proposed tests is explored asymptotically and by means of a simulation study showing good small sample characteristics to illustrate the procedure a randomized double blind clinical trial in depression is evaluated an r package for implementation of the proposed tests and for sample size determination accompanies this paper on the author s web page

optimal utilization of signal free samples for array processing in unknown colored noise fields many algorithms for direction of arrival doa estimation require the noise covariance matrix to be known or to possess a known structure in many cases the noise covariance is in fact estimated from separate measurements this paper addresses the combined effects of finite sample sizes both in the estimated noise covariance matrix and in the data with signals present it is assumed that a batch of signal free samples is available in addition to the signal containing samples no assumption is made on the structure of the noise covariance in this paper the asymptotic covariance of the weighted subspace fitting wsf algorithm is derived for the case in which the data are whitened using an estimated noise covariance the expression obtained suggests an optimal weighting that improves performance compared to the standard choice in addition a new method based on covariance matching is proposed both methods are asymptotically statistically efficient the cramer rao lower bound crb on the covariance of the estimate for the data model is also derived monte carlo simulations show promising small sample performance for the two new methods and confirm the asymptotic results

observability and detectability of singular linear systems with unknown inputs in this paper the strong observability and strong detectability of a general class of singular linear systems with unknown inputs are tackled the case when the matrix pencil is non regular is comprised i e more than one solution for the differential equation is allowed it is shown that under suitable assumptions the original problem can be studied by means of a regular non singular linear system with unknown inputs and algebraic constraints thus it is shown that for purposes of analysis the algebraic equations can be included as part of an extended system output based on this analysis we obtain necessary and sufficient conditions guaranteeing the observability or detectability of the system in terms of the zeros of the system matrix corresponding algebraic conditions are given in order to test the observability and detectability a formula is provided that expresses the state as high order derivative of a function of the output which allows for the reconstruction of the actual state vector it is shown that the unknown inputs may be reconstructed also

performance analysis of root music the authors analyze the performance of root music a variation of the music algorithm for estimating the direction of arrival doa of plane waves in white noise in the case of a linear equispaced sensor array the performance of the method is analyzed by examining the perturbation in the roots of the polynomial formed in the intermediate step of root music in particular asymptotic results for the mean squared error in the estimates of the direction of arrival are derived simplified expressions are presented for the one and two source case and compared to those obtained for least squares esprit computer simulations are also presented and they are in close agreement with the theory an important outcome of this analysis is the fact that the error in the signal zeros has a largely radial component this provides an explanation as to why the root music is superior to the spectral music algorithm

assessing non inferiority of a new treatment in a three arm clinical trial including a placebo in non inferiority trials where non inferiority of a new experimental drug compared to an active control has to be shown it may be advisable to use an additional placebo group for internal validation if ethically justifiable the focus of this paper is on such designs assuming normality and homogeneity of variances we will derive a statistical test procedure which turns out to be equivalent to the assessment based on fieller s confidence interval based on the power function of this test sample size calculations are carried out to achieve a given power additionally the optimal allocation of the total sample size is derived as an alternative to this parametric procedure the bootstrap percentile interval is discussed and finally compared with fieller s confidence interval in a study on mildly asthmatic patients

asymptotically optimal blind calibration of uniform linear sensor arrays for narrowband gaussian signals an asymptotically optimal blind calibration scheme of uniform linear arrays for narrowband gaussian signals is proposed rather than taking the direct maximum likelihood ml approach for joint estimation of all the unknown model parameters which leads to a multi dimensional optimization problem with no closed form solution we revisit paulraj and kailath s p k s classical approach in exploiting the special toeplitz structure of the observations covariance however we offer a substantial improvement over p k s ordinary least squares ls estimates by using asymptotic approximations in order to obtain simple non iterative quasi linear optimally weighted ls owls estimates of the sensors gains and phases offsets with asymptotically optimal weighting based only on the empirical covariance matrix of the measurements moreover we prove that our resulting estimates are also asymptotically optimal w r t the raw data and can therefore be deemed equivalent to the ml estimates mle which are otherwise obtained by joint ml estimation of all the unknown model parameters after deriving computationally convenient expressions of the respective cramer rao lower bounds we also show that our estimates offer improved performance when applied to non gaussian signals and or noise as quasi mle in a similar setting the optimal performance of our estimates is demonstrated in simulation experiments with a considerable improvement reaching an order of magnitude and more in the resulting mean squared errors w r t p k s ordinary ls estimates we also demonstrate the improved accuracy in a multiple sources directions of arrivals estimation task

observer design for linear singular time delay systems this paper investigates the problem of observer design for a general class of linear singular time delay systems in which the time delays are involved in the state and its derivatives the output and the known input if there exists the involvement of the delay could be multiple which however is rarely studied in the literature sufficient conditions are proposed which guarantees the existence of a luenberger like observer for the general system

estimating the sample size for a t test using an internal pilot if the sample size for a t test is calculated on the basis of a prior estimate of the variance then the power of the test at the treatment difference of interest is not robust to misspecification of the variance we propose a t test for a two treatment comparison based on stein s two stage test which involves the use of an internal pilot to estimate variance and thus the final sample size required we evaluate our procedure s performance and show that it controls the type i and ii error rates more closely than existing methods for the same problem we also propose a rule for choosing the size of the internal pilot and show that this is reasonable in terms of the efficiency of the procedure

a subspace method for estimating sensor gains and phases the problem of array signal processing under model errors is studied a signal subspace constraint is used to obtain a simple way for computing a set of sensor gains and phases consistent with a given set of doa angles then the issue of uniqueness of the set of sensor gains and phases and doa angles is addressed

planning and analysis of three arm non inferiority trials with binary endpoints three arm trials including an experimental treatment an active control and a placebo group are frequently preferred for the assessment of non inferiority in contrast to two arm non inferiority studies these designs allow a direct proof of efficacy of a new treatment by comparison with placebo as a further advantage the test problem for establishing non inferiority can be formulated in such a way that rejection of the null hypothesis assures that a pre defined portion of the unknown effect the reference shows versus placebo is preserved by the treatment under investigation we present statistical methods for this study design and the situation of a binary outcome variable asymptotic test procedures are given and their actual type i error rates are calculated approximate sample size formulae are derived and their accuracy is discussed furthermore the question of optimal allocation of the total sample size is considered power properties of the testing strategy including a pre test for assay sensitivity are presented the derived methods are illustrated by application to a clinical trial in depression

a performance analysis of subspace based methods in the presence of model error ii multidimensional algorithms for pt i see ibid vol 40 no 7 p 1758 74 1992 in pt i the performance of the music algorithms for narrowband direction of arrival doa estimation when the array manifold and noise covariance are not correctly modeled was investigated this analysis is extended to multidimensional subspace based algorithms including deterministic or conditional maximum likelihood md music weighted subspace fitting wsf mode and esprit a general expression for the variance of the doa estimates that can be applied to any of the above algorithms and to any of a wide variety of scenarios is presented optimally weighted subspace fitting algorithms are presented for special cases involving random unstructured errors of the array manifold and noise covariance it is shown that one dimensional music outperforms all of the above multidimensional algorithms for random angle independent array perturbations

the effects of array calibration errors on df based signal copy performance this paper studies the effect of array calibration errors on the performance of various direction finding df based signal copy algorithms unlike blind copy methods this class of algorithms requires an estimate of the directions of arrival doas of the signals in order to compute the copy weight vectors under the assumption that the observation time is sufficiently long the following algorithms are studied classical beamforming least squares total least squares linearly constrained minimum variance beamforming and structured stochastic estimation expressions for the mean square error of the signal estimates are derived as a function of the calibration errors for both the case where the doas are known precisely and for the case where the doas must be estimated

doa estimation via manifold separation for arbitrary array structures in this paper we consider the manifold separation technique mst which stems from the wavefield modeling formalism developed for array processing mst is a method for modeling the steering vector of antenna arrays of practical interest with arbitrary 2 d or 3 d geometry it is the product of a sampling matrix dependent on the antenna array only and a vandermonde structured coefficients vector depending on the wavefield only this allows fast direction of arrival doa algorithms designed for linear arrays to be used on arrays with arbitrary configuration in real world applications the calibration measurements used to determine the sampling matrix are corrupted by noise this impairs the performance of mst based algorithms in particular we study the effect of noisy calibration measurements on subspace based doa algorithms using mst expressions describing the error in the doa estimates due to calibration noise and truncation are derived this allows predicting the performance of mst based algorithms in real world applications the analysis is verified by simulations we established a link between the optimal number of selected modes and the statistics of calibration noise we analyze the modeling error when mst is used for 1 d azimuth doa estimation

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

performance analysis of the enhanced minimum variance spatial spectrum estimator the performance of the enhanced minimum variance emv spatial spectrum estimator is studied expressions are presented fur the variance and bias of direction of arrival estimators based on general functions of the covariance matrix and these expressions are then used to study the emv estimator finite data effects and random perturbations on the ideal modeling assumptions are studied separately

on the angular resolution limit for array processing in the presence of modeling errors in this correspondence we study the impact of modeling errors on the angular resolution limit arl for two closely spaced sources in the context of array processing particularly we follow two methods based on the well known lee and smith s criteria using the cramer rao lower bound crb to derive closed form expressions of the arl with respect to w r t the error variance we show that as the signal to noise ratio increases the arl does not fall into zero contrary to the classical case without modeling errors and converge to a fixed limit depending on the method for which we give a closed form expression one can see that at high snr the arl in the lee and smith sense are linear as a function of the error variance we also investigate the influence of the array geometry on the arl based on the lee s and smith s criteria

statistical resolution limit of the uniform linear cocentered orthogonal loop and dipole array among the family of polarization sensitive arrays we can find the so called cocentered orthogonal loop and dipole uniform linear array cold ula the cold ula exhibits some interesting properties e g the insensibility of the polarization vector with respect to the source localization in the plan of the array in this correspondence we derive the statistical resolution limit srl characterizing the minimal separation in terms of direction of arrivals to resolve two closely spaced known polarized sources impinging on a cold ula toward this end nonmatrix closed form expressions of the deterministic cramer rao bound crb are derived and thus the srl is deduced a comparison between the srl of the cold ula and the classical ula are given particularly it is shown that in the case of orthogonal known signal sources the srl of the cold ula is equal to the srl of the ula meaning that it is not a function of polarization parameters furthermore due to the derived srl it is shown that under some general conditions the srl of the cold ula is smaller than the one of the ula

geometric algebra of euclidean 3 space for electromagnetic vector sensor array processing part i modeling a new mathematical tool the geometric algebra of euclidean 3 space g3 is introduced for electromagnetic vector sensor array processing herein this paper focuses on modeling the six component outputs of a vector sensor holistically by an entry called as a multivector in g3 a compact polarized model for the array termed as a geometric algebra model g model is then presented using the g model a novel data covariance matrix model is defined by the geometric products in g3 and then analyzed the analytical results show that the six component measurement noise of a vector sensor can naturally be whitened if the noise cross correlations between the different axial electric and magnetic components are equal to one another compared with the known best quad quaternion model the new covariance matrix model results in a reduction of half memory requirements while the amount of divisions is reduced to 1 2 multiplications and additions reduced to almost 1 7

internal pilot studies ii comparison of various procedures the two stage design involves sample size recalculation using an interim variance estimate stein proposed the design in 1945 biostatisticians recently have shown renewed interest in it wittes and brittain proposed a modification aimed at greater efficiency gould and shih proposed a similar procedure but with a different interim variance estimate based on blinded data we compare the power of stein s original test an idealized version of the wittes brittain test and a theoretical optimal test which can be approximated in practice we also compare two procedures that control the conditional type i error rate given the actual final sample size gould and shih s procedure and a newly proposed second segment procedure the comparison among the first three procedures indicates that the stein test is unexpectedly the test of choice under the original design alternative whereas the approximate optimal and wittes brittain procedures appear to have superior power for detecting smaller treatment differences as between the latter two procedures the second segment procedure is more powerful when many observations are likely to be taken after the interim resizing whereas otherwise the gould shih procedure is superior

the resolution threshold of a direction finding algorithm for diversely polarized arrays subspace based algorithms for narrowband direction of arrival doa estimation require detailed knowledge of the array response the array manifold and assume that the noise covariance matrix is known up to a scaling factor in practice these quantities are not known precisely resolution and estimation accuracy can degrade significantly when the array response or the noise covariance deviate from their nominal values we examine the resolution threshold of a recently proposed subspace based algorithm for direction finding with diversely polarized arrays we study finite sample effects and the effects of modeling errors errors in the array manifold or the noise covariance on the resolution threshold a comparison is made between the resolution thresholds of the music algorithm for uniformly polarized arrays and the proposed algorithm for diversely polarized arrays

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

a modified music algorithm for direction of arrival estimation in the presence of antenna array manifold mismatch we introduce a modified multiple signal classification music algorithm to estimate the directions of arrival doas of multiple radio frequency signals we specifically consider an antenna array with an imperfectly calibrated array response the modified music algorithm estimates the doa of each signal individually after attempting to null the other signals that are present we compare the new approach to the conventional music algorithm in simulations and show that the new approach leads to improved performance the new approach converges quickly and produces doa estimates with smaller mean error and standard deviation than music over a range of incident signal separations we recommend our approach for systems with challenging antenna placements a time varying host platform and limited processing capabilities

exact test size and power of a gaussian error linear model for an internal pilot study wittes and brittain recommended using an internal pilot study to adjust sample size the approach involves five steps in testing a general linear hypothesis for a general linear univariate model with gaussian errors first specify the design hypothesis desired test size power a smallest clinically meaningful effect and a speculated error variance second conduct a power analysis to choose provisionally a planned sample size third collect a specified proportion of the planned sample as the internal pilot sample and estimate the variance but do not test the hypothesis fourth update the power analysis with the variance estimate to adjust the total sample size fifth finish the study and test the hypothesis with all data we describe methods for computing exact test size and power under this scenario our analytic results agree with simulations of wittes and brittain furthermore our exact results apply to any general linear univariate model with fixed predictors which is much more general than the two sample t test considered by wittes and brittain in addition our results allow for examination of the impact on test size of internal pilot studies for more complicated designs in the framework of the general linear model we examine the impact of i small samples ii allowing the planned sample size to decrease iii the choice of internal pilot sample size and iv the maximum allowable size of the second sample all affect test size power and expected total sample size we present a number of examples including one that uses an internal pilot study in a three group analysis of variance

joint channel and carrier offset estimation in cdma communications this paper addresses the problem of cdma multiuser detection in the presence of unknown multipath channels and residual carriers an analytic algorithm that provides closed form channel and carrier offset estimates is proposed the algorithm first converts the multiuser estimation problem into single user problems and then analytically solves the resulting nonlinear multivariate optimization problems using a polynomial matrix projection property the performance of the proposed algorithm is investigated through first order perturbation analysis we also calculate the cramer rao bound crb to illustrate the efficiency of the new algorithm the analyzes are supported by computer simulations

perturbation analysis of subspace based methods in estimating a damped complex exponential we present a study of mode variance statistics for three svd based estimation methods in the case of a single mode damped exponential the methods considered are namely kumaresan tufts matrix pencil and kung s direct data approximation through first order perturbation analysis we derive closed form expressions of the variance of the complex mode frequency and damping factor estimates these expressions are used to compare the different methods and to determine the optimal prediction order for matrix pencil and direct data approximation methods application to the undamped case shows the coherence of the results with those already stated in the literature it is also found that the variances converge linearly towards the cramer rao bound finally the theoretical results are verified using monte carlo simulations

internal pilot studies i type i error rate of the naive t test when sample size is recalculated using unblinded interim data use of the usual t test at the end of a study may lead to an elevated type i error rate this paper describes a numerical quadrature investigation to calculate the true probability of rejection as a function of the time of the recalculation the magnitude of the detectable treatment effect and the ratio of the guessed to the true variance we consider both restricted designs those that require final sample size at least as large as the originally calculated size and unrestricted designs those that permit smaller final sample sizes than originally calculated our results indicate that the bias in the type i error rate is often negligible especially in restricted designs some sets of parameters however induce non trivial bias in the unrestricted design