Results 1  10
of
21
Performance Bounds for Estimating Vector Systems
 IEEE Transactions on Signal Processing
, 2000
"... We propose a unified framework for the analysis of estimators of geometrical vector quantities and vector systems through a collection of performance measures. Unlike standard performance indicators, these measures have intuitive geometrical and physical interpretations, are independent of the coord ..."
Abstract

Cited by 13 (3 self)
 Add to MetaCart
We propose a unified framework for the analysis of estimators of geometrical vector quantities and vector systems through a collection of performance measures. Unlike standard performance indicators, these measures have intuitive geometrical and physical interpretations, are independent of the coordinate reference frame, and are applicable to arbitrary parameterizations of the unknown vector or system of vectors. For each measure, we derive both finitesample and asymptotic lower bounds that hold for large classes of estimators and serve as benchmarks for the assessment of estimation algorithms. Like the performance measures themselves, these bounds are independent of the reference coordinate frame, and we discuss their use as system design criteria. I. INTRODUCTION T HE NEED TO estimate threedimensional (3D) geometrical vector quantities and systems of vectors occurs in a number of classes of problems, e.g., direction estimation, constant velocity trajectory estimation, orientat...
Conditional Maximum Likelihood Timing Recovery: Estimators and Bounds
 IEEE Trans. on Signal Processing
, 2001
"... This paper is concerned with the derivation of new estimators and performance bounds for the problem of timing estimation of (linearly) digitally modulated signals. The conditional maximum likelihood (CML) method is adopted, in contrast to the classical lowSNR unconditional ML (UML) formulation tha ..."
Abstract

Cited by 12 (2 self)
 Add to MetaCart
This paper is concerned with the derivation of new estimators and performance bounds for the problem of timing estimation of (linearly) digitally modulated signals. The conditional maximum likelihood (CML) method is adopted, in contrast to the classical lowSNR unconditional ML (UML) formulation that is systematically applied in the literature for the derivation of nondataaided (NDA) timingerrordetectors (TEDs). A new CMLTED is derived and proved to be selfnoise free, in contrast to the conventional lowSNRUML TED. In addition, the paper provides a derivation of the conditional CramrRao Bound (CRB ), which is higher (less optimistic) than the modified CRB (MCRB) [which is only reached by decisiondirected (DD) methods]. It is shown that the CRB is a lower bound on the asymptotic statistical accuracy of the set of consistent estimators that are quadratic with respect to the received signal. Although the obtained bound is not general, it applies to most NDA synchronizers proposed in the literature. A closedform expression of the conditional CRB is obtained, and numerical results confirm that the CML TED attains the new bound for moderate to high .
Objective Functions For Ocean Acoustic Inversion Derived By Likelihood Methods
 J. Comp. Acoust
, 2000
"... this paper a class of objective functions derived from an assumption of additive Gaussian errors by use of maximum likelihood principles is presented. Under these assumptions the likelihood functions L and objective functions # are related: L(m)=kexp  #(m) T (1.1) where T is a scaling par ..."
Abstract

Cited by 10 (8 self)
 Add to MetaCart
this paper a class of objective functions derived from an assumption of additive Gaussian errors by use of maximum likelihood principles is presented. Under these assumptions the likelihood functions L and objective functions # are related: L(m)=kexp  #(m) T (1.1) where T is a scaling parameter 46 and k is a normalization factor. The form in Eq. (1.1) is also related to the scaling of the objective functions in simulated annealing and genetic algorithms. m is the unknown parameters, these are any parameters used by an oceanacoustic forward model, as geoacoustic, source and receiver parameters. 7 Good values of these parameters are found through optimization using exhaustive search, simulated annealing or 259 July 5, 2000 15:24 WSPC/130JCA 00023 260 C. F. Mecklenbrauker & P. Gerstoft genetic algorithms. The forward models, the objective functions and the search methods are conveniently combined in one program package SAGA. 8 The assumptions leading to these objective functions are thus clear. As they are derived from maximum likelihood principles the resulting estimators have good properties. They are consistent, asymptotically Gaussian distributed, and asymptotically e#cient. Thus, they converge to the true value for a large number of data samples: The bias disappears asymptotically and the variance of the estimator approaches zero. Moreover, no other biasfree estimator exists with a smaller variance in the limit for a large number of data samples. The CramerRao Bound is asymptotically tight. This means that no other ambiguity surface has stronger curvature at its peak if the peak is located at the true parameter. In that sense, it is the peakiest surface. However, the CramerRao Bound is only a local measure, it provides no information abo...
Wideband Source Localization Using a Distributed Acoustic VectorSensor Array
 IEEE Trans. Sig. Proc
, 2003
"... Abstract—We derive fast wideband algorithms, based on measurements of the acoustic intensity, for determining the bearings of a target using an acoustic vector sensor (AVS) situated in free space or on a reflecting boundary. We also obtain a lower bound on the meansquare angular error (MSAE) of suc ..."
Abstract

Cited by 8 (0 self)
 Add to MetaCart
Abstract—We derive fast wideband algorithms, based on measurements of the acoustic intensity, for determining the bearings of a target using an acoustic vector sensor (AVS) situated in free space or on a reflecting boundary. We also obtain a lower bound on the meansquare angular error (MSAE) of such estimates. We then develop general closedform weighted leastsquares (WLS) and reweighted leastsquares algorithms that compute the threedimensional (3D) location of a target whose bearing to a number of dispersed locations has been measured. We devise a scheme for adaptively choosing the weights for the WLS routine when measures of accuracy for the bearing estimates, such as the lower bound on the MSAE, are available. In addition, a measure of the potential estimation accuracy of a distributed system is developed based on a twostage application of the Cramér–Rao bound. These 3D results are quite independent of how bearing estimates are obtained. Naturally, the two parts of the paper are tied together by examining how well distributed arrays of AVSs located on the ground, seabed, and in free space can determine the 3D position of a target The results are relevant to the localization of underwater and airborne sources using freely drifting, moored, or ground sensors. Numerical simulations illustrate the effectiveness of our estimators and the new potential performance measure. I.
Effects of MultipathInduced Angular Spread on Direction of Arrival Estimators in Array Signal Processing
"... We consider the effects of multipath on three array signal processing algorithms for direction of arrival (DOA) estimation. We adopt a model in which the source signals impinge on an array of sensors over a spread of angles. Such a scenario arises in mobile telecommunications, where the angular spre ..."
Abstract

Cited by 5 (2 self)
 Add to MetaCart
We consider the effects of multipath on three array signal processing algorithms for direction of arrival (DOA) estimation. We adopt a model in which the source signals impinge on an array of sensors over a spread of angles. Such a scenario arises in mobile telecommunications, where the angular spread is caused by multipath from a large number of scatterers local to each source. We analyze the effect of this angular spread on the DOA estimates obtained from MUSIC, ESPRIT, and weighted subspace fitting (WSF). We develop analytical expressions for the bias of the DOA estimates, and discuss variance properties, for small source spread angles. We compare the various techniques, and validate the analysis with simulation results.
On the high SNR conditional maximumlikelihood estimator full statistical characterization
 IEEE Trans. Signal Processing
, 2006
"... In the field of asymptotic performance characterization of Conditional Maximum Likelihood (CML) estimator, asymptotic generally refers to either the number of samples or the Signal to Noise Ratio (SNR) value. The first case has been already fully characterized although the second case has been only ..."
Abstract

Cited by 3 (0 self)
 Add to MetaCart
In the field of asymptotic performance characterization of Conditional Maximum Likelihood (CML) estimator, asymptotic generally refers to either the number of samples or the Signal to Noise Ratio (SNR) value. The first case has been already fully characterized although the second case has been only partially investigated. Therefore, this correspondence aims to provide a sound proof of a result, i.e. asymptotic (in SNR) Gaussianity and efficiency of the CML estimator in the multiple parameters case, generally regarded as trivial but not so far demonstrated. Index Terms Maximum Likelihood, statistical efficiency, high Signal to Noise Ratio, array processing.
Non efficiency and non Gaussianity of a maximum likelihood estimator at high signal to noise ratio and finite number of samples
 in Proc. IEEE Int. Conf. Acoust., Speech, Signal Processing
, 2004
"... In estimation theory, the asymptotic efficiency of the Maximum Likelihood (ML) method for independent identically distributed observations and when the number T of observations tends to infinity is a well known result. In some scenarii, the number of snapshots may be small making this result unappli ..."
Abstract

Cited by 3 (3 self)
 Add to MetaCart
In estimation theory, the asymptotic efficiency of the Maximum Likelihood (ML) method for independent identically distributed observations and when the number T of observations tends to infinity is a well known result. In some scenarii, the number of snapshots may be small making this result unapplicable. In the array processing framework, for Gaussian emitted signals, we fill this lack at high Signal to Noise Ratio (SNR). In this situation, we show that the ML estimation is asymptotically (with respect to SNR) non efficient and non Gaussian. 1.
Minimum Mean Square Distance Estimation of a Subspace IRIT/ENSEEIHT, 2011 [Online]. Available: http://dobigeon.perso.enseeiht.fr/app_MMSD.html
"... Abstract—We consider the problem of subspace estimation in a Bayesian setting. Since we are operating in the Grassmann manifold, the usual approach which consists of minimizing the mean square error (MSE) between the true subspace U and its estimate ^U may not be adequate as the MSE is not the natur ..."
Abstract

Cited by 3 (3 self)
 Add to MetaCart
Abstract—We consider the problem of subspace estimation in a Bayesian setting. Since we are operating in the Grassmann manifold, the usual approach which consists of minimizing the mean square error (MSE) between the true subspace U and its estimate ^U may not be adequate as the MSE is not the natural metric in the Grassmann manifold GN;p, i.e., the set of pdimensional subspaces in N. As an alternative, we propose to carry out subspace estimation by minimizing the mean square distance between U and its estimate, where the considered distance is a natural metric in the Grassmann manifold, viz. the distance between the projection matrices. We show that the resulting estimator is no longer the posterior mean of U but entails computing the principal eigenvectors of the posterior mean of UU T. Derivation of the minimum mean square distance (MMSD) estimator is carried out in a few illustrative
Secondorder parameter estimation
 IEEE Trans. on Signal Processing
, 2005
"... Abstract—This work provides a general framework for the design of secondorder blind estimators without adopting any approximation about the observation statistics or the a priori distribution of the parameters. The proposed solution is obtained minimizing the estimator variance subject to some cons ..."
Abstract

Cited by 2 (1 self)
 Add to MetaCart
Abstract—This work provides a general framework for the design of secondorder blind estimators without adopting any approximation about the observation statistics or the a priori distribution of the parameters. The proposed solution is obtained minimizing the estimator variance subject to some constraints on the estimator bias. The resulting optimal estimator is found to depend on the observation fourthorder moments that can be calculated analytically from the known signal model. Unfortunately, in most cases, the performance of this estimator is severely limited by the residual bias inherent to nonlinear estimation problems. To overcome this limitation, the secondorder minimum variance unbiased estimator is deduced from the general solution by assuming accurate prior information on the vector of parameters. This smallerror approximation is adopted to design iterative estimators or trackers. It is shown that the associated variance constitutes the lower bound for the variance of any unbiased estimator based on the sample covariance matrix. The paper formulation is then applied to track the angleofarrival (AoA) of multiple digitallymodulated sources by means of a uniform linear array. The optimal secondorder tracker is compared with the classical maximum likelihood (ML) blind methods that are shown to be quadratic in the observed data as well. Simulations have confirmed that the discrete nature of the transmitted symbols can be exploited to improve considerably the discrimination of near sources in mediumtohigh SNR scenarios. Index Terms—Blind estimation, directionofarrival, estimation bounds, nondataaided, secondorder techniques, tracking. I.
1 Conditional and Unconditional CramérRao Bounds for NearField Source Localization
"... Nearfield source localization problem by a passive antenna array makes the assumption that the timevarying sources are located near the antenna. In this context, the farfield assumption (i.e. planar wavefront) is, of course, no longer valid and one has to consider a more complicated model paramet ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
Nearfield source localization problem by a passive antenna array makes the assumption that the timevarying sources are located near the antenna. In this context, the farfield assumption (i.e. planar wavefront) is, of course, no longer valid and one has to consider a more complicated model parameterized by the bearing (as in the farfield case) and by the distance, named range, between the source and a reference coordinate system. One can find a plethora of estimation schemes in the literature, but their ultimate performance in terms of Mean Square Error (MSE) have not been fully investigated. To characterize these performance, the CramérRao Bound (CRB) is a popular mathematical tool in signal processing. The main cause for this is that the MSE of several highresolution direction of arrival algorithms are known to achieve the CRB under quite general/weak conditions. In this correspondence, we derive and analyze the socalled conditional and unconditional CRBs for a single timevarying nearfield source. In each case, we obtain non matrix closedform expressions. Our approach has two advantages: (i) due to the fact that one has to inverse the Fisher information matrix, the computational cost for a large number of snapshots (in the case of the conditional CRB) and/or for a large number of sensors (in the case of the unconditional CRB), of a matrixbased CRB can be high while our approach is low and (ii) some useful information can be deduced from the behavior of the bound. In particular, an explicit relationship between the conditional and the unconditional CRBs is provided and one shows that closer is the source from the array and/or higher is the signal carrier frequency, better is the range estimation.