1,589 research outputs found
On the Existence of an MVU Estimator for Target Localization with Censored, Noise Free Binary Detectors
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
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
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
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 (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
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 -monotone density: limit distribution theory and the spline connection
We study the asymptotic behavior of the Maximum Likelihood and Least Squares
Estimators of a -monotone density at a fixed point when .
We find that the th derivative of the estimators at converges at the
rate for . The limiting distribution depends
on an almost surely uniquely defined stochastic process that stays above
(below) the -fold integral of Brownian motion plus a deterministic drift
when is even (odd). Both the MLE and LSE are known to be splines of degree
with simple knots. Establishing the order of the random gap
, where 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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