1,589 research outputs found

    On the Existence of an MVU Estimator for Target Localization with Censored, Noise Free Binary Detectors

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    The problem of target localization with censored noise free binary detectors is considered. In this setting only the detecting sensors report their locations to the fusion center. It is proven that if the radius of detection is not known to the fusion center, a minimum variance unbiased (MVU) estimator does not exist. Also it is shown that when the radius is known the center of mass of the possible target region is the MVU estimator. In addition, a sub-optimum estimator is introduced whose performance is close to the MVU estimator but is preferred computationally. Furthermore, minimal sufficient statistics have been provided, both when the detection radius is known and when it is not. Simulations confirmed that the derived MVU estimator outperforms several heuristic location estimators.Comment: 25 pages, 9 figure

    Space Time MUSIC: Consistent Signal Subspace Estimation for Wide-band Sensor Arrays

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    Wide-band Direction of Arrival (DOA) estimation with sensor arrays is an essential task in sonar, radar, acoustics, biomedical and multimedia applications. Many state of the art wide-band DOA estimators coherently process frequency binned array outputs by approximate Maximum Likelihood, Weighted Subspace Fitting or focusing techniques. This paper shows that bin signals obtained by filter-bank approaches do not obey the finite rank narrow-band array model, because spectral leakage and the change of the array response with frequency within the bin create \emph{ghost sources} dependent on the particular realization of the source process. Therefore, existing DOA estimators based on binning cannot claim consistency even with the perfect knowledge of the array response. In this work, a more realistic array model with a finite length of the sensor impulse responses is assumed, which still has finite rank under a space-time formulation. It is shown that signal subspaces at arbitrary frequencies can be consistently recovered under mild conditions by applying MUSIC-type (ST-MUSIC) estimators to the dominant eigenvectors of the wide-band space-time sensor cross-correlation matrix. A novel Maximum Likelihood based ST-MUSIC subspace estimate is developed in order to recover consistency. The number of sources active at each frequency are estimated by Information Theoretic Criteria. The sample ST-MUSIC subspaces can be fed to any subspace fitting DOA estimator at single or multiple frequencies. Simulations confirm that the new technique clearly outperforms binning approaches at sufficiently high signal to noise ratio, when model mismatches exceed the noise floor.Comment: 15 pages, 10 figures. Accepted in a revised form by the IEEE Trans. on Signal Processing on 12 February 1918. @IEEE201

    MIMO Radar Target Localization and Performance Evaluation under SIRP Clutter

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    Multiple-input multiple-output (MIMO) radar has become a thriving subject of research during the past decades. In the MIMO radar context, it is sometimes more accurate to model the radar clutter as a non-Gaussian process, more specifically, by using the spherically invariant random process (SIRP) model. In this paper, we focus on the estimation and performance analysis of the angular spacing between two targets for the MIMO radar under the SIRP clutter. First, we propose an iterative maximum likelihood as well as an iterative maximum a posteriori estimator, for the target's spacing parameter estimation in the SIRP clutter context. Then we derive and compare various Cram\'er-Rao-like bounds (CRLBs) for performance assessment. Finally, we address the problem of target resolvability by using the concept of angular resolution limit (ARL), and derive an analytical, closed-form expression of the ARL based on Smith's criterion, between two closely spaced targets in a MIMO radar context under SIRP clutter. For this aim we also obtain the non-matrix, closed-form expressions for each of the CRLBs. Finally, we provide numerical simulations to assess the performance of the proposed algorithms, the validity of the derived ARL expression, and to reveal the ARL's insightful properties.Comment: 34 pages, 12 figure

    Generalized robust shrinkage estimator and its application to STAP detection problem

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    Recently, in the context of covariance matrix estimation, in order to improve as well as to regularize the performance of the Tyler's estimator [1] also called the Fixed-Point Estimator (FPE) [2], a "shrinkage" fixed-point estimator has been introduced in [3]. First, this work extends the results of [3,4] by giving the general solution of the "shrinkage" fixed-point algorithm. Secondly, by analyzing this solution, called the generalized robust shrinkage estimator, we prove that this solution converges to a unique solution when the shrinkage parameter β\beta (losing factor) tends to 0. This solution is exactly the FPE with the trace of its inverse equal to the dimension of the problem. This general result allows one to give another interpretation of the FPE and more generally, on the Maximum Likelihood approach for covariance matrix estimation when constraints are added. Then, some simulations illustrate our theoretical results as well as the way to choose an optimal shrinkage factor. Finally, this work is applied to a Space-Time Adaptive Processing (STAP) detection problem on real STAP data

    Target Localization and Tracking in Wireless Sensor Networks

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    This thesis addresses the target localization problem in wireless sensor networks (WSNs) by employing statistical modeling and convex relaxation techniques. The first and the second part of the thesis focus on received signal strength (RSS)- and RSS-angle of arrival (AoA)-based target localization problem, respectively. Both non-cooperative and cooperative WSNs are investigated and various settings of the localization problem are of interest (e.g. known and unknown target transmit power, perfectly and imperfectly known path loss exponent). For all cases, maximum likelihood (ML) estimation problem is first formulated. The general idea is to tightly approximate the ML estimator by another one whose global solution is a close representation of the ML solution, but is easily obtained due to greater smoothness of the derived objective function. By applying certain relaxations, the solution to the derived estimator is readily obtained through general-purpose solvers. Both centralized (assumes existence of a central node that collects all measurements and carries out all necessary processing for network mapping) and distributed (each target determines its own location by iteratively solving a local representation of the derived estimator) algorithms are described. More specifically, in the case of centralized RSS-based localization, second-order cone programming (SOCP) and semidefinite programming (SDP) estimators are derived by applying SOCP and SDP relaxation techniques in non-cooperative and cooperative WSNs, respectively. It is also shown that the derived SOCP estimator can be extended for distributed implementation in cooperative WSNs. In the second part of the thesis, derivation procedure of a weighted least squares (WLS) estimator by converting the centralized non-cooperative RSS-AoA localization problem into a generalized trust region sub-problem (GTRS) framework, and an SDP estimator by applying SDP relaxations to the centralized cooperative RSS-AoA localization problem are described. Furthermore, a distributed SOCP estimator is developed, and an extension of the centralized WLS estimator for non-cooperative WSNs to distributed conduction in cooperative WSNs is also presented. The third part of the thesis is committed to RSS-AoA-based target tracking problem. Both cases of target tracking with fixed/static anchors and mobile sensors are investigated. First, the non-linear measurement model is linearized by applying Cartesian to polar coordinates conversion. Prior information extracted from target transition model is then added to the derived model, and by following maximum a posteriori (MAP) criterion, a MAP algorithm is developed. Similarly, by taking advantage of the derived model and the prior knowledge, Kalman filter (KF) algorithm is designed. Moreover, by allowing sensor mobility, a simple navigation routine for sensors’ movement management is described, which significantly enhances the estimation accuracy of the presented algorithms even for a reduced number of sensors. The described algorithms are assessed and validated through simulation results and real indoor measurements

    Estimation of a kk-monotone density: limit distribution theory and the spline connection

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    We study the asymptotic behavior of the Maximum Likelihood and Least Squares Estimators of a kk-monotone density g0g_0 at a fixed point x0x_0 when k>2k>2. We find that the jjth derivative of the estimators at x0x_0 converges at the rate n−(k−j)/(2k+1)n^{-(k-j)/(2k+1)} for j=0,...,k−1j=0,...,k-1. The limiting distribution depends on an almost surely uniquely defined stochastic process HkH_k that stays above (below) the kk-fold integral of Brownian motion plus a deterministic drift when kk is even (odd). Both the MLE and LSE are known to be splines of degree k−1k-1 with simple knots. Establishing the order of the random gap τn+−τn−\tau_n^+-\tau_n^-, where τn±\tau_n^{\pm} denote two successive knots, is a key ingredient of the proof of the main results. We show that this ``gap problem'' can be solved if a conjecture about the upper bound on the error in a particular Hermite interpolation via odd-degree splines holds.Comment: Published in at http://dx.doi.org/10.1214/009053607000000262 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org
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