Results 1  10
of
32
Relative Location Estimation in Wireless Sensor Networks
, 2003
"... Selfconfig uration in wireless sensor networks is ag eneral class of estimation problems which we study via the CramerRao bound (CRB).Specifically, we consider sensor location estimation when sensors measure received sig]P strengI (RSS) or timeofarrival (TOA) between themselves and neig boring s ..."
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Cited by 193 (16 self)
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Selfconfig uration in wireless sensor networks is ag eneral class of estimation problems which we study via the CramerRao bound (CRB).Specifically, we consider sensor location estimation when sensors measure received sig]P strengI (RSS) or timeofarrival (TOA) between themselves and neig boring sensors.A small fraction of sensors in the network have known location while the remaining locations must be estimated.We derive CRBs and maximumlikelihood estimators (MLEs) under Gaussian and log normal models for the TOA and RSS measurements, respectively.An extensive TOA and RSS measurement campaig in an indoor o#ce area illustrates MLE performance.Finally, relative location estimation alg orithms are implemented in a wireless sensor network testbed and deployed in indoor and outdoor environments.The measurements and testbed experiments demonstrate 1 m RMS location errorsusing TOA, and 1 m to 2 m RMS location errors using RSS. Index Terms sensor position location estimation, radio channel measurement, sig nal streng h, timeofarrival, wireless sensor network testbed, selfconfig uration, CramerRao bound I.
Regularization for uniform spatial resolution properties in penalizedlikelihood image reconstruction
 IEEE Tr. Med. Im
, 2000
"... Traditional spaceinvariant regularization methods in tomographic image reconstruction using penalizedlikelihood estimators produce images with nonuniform spatial resolution properties. The local point spread functions that quantify the smoothing properties of such estimators are spacevariant, as ..."
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Cited by 40 (20 self)
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Traditional spaceinvariant regularization methods in tomographic image reconstruction using penalizedlikelihood estimators produce images with nonuniform spatial resolution properties. The local point spread functions that quantify the smoothing properties of such estimators are spacevariant, asymmetric, and objectdependent even for spaceinvariant imaging systems. We propose a new quadratic regularization scheme for tomographic imaging systems that yields increased spatial uniformity and is motivated by the leastsquares tting of a parameterized local impulse response to a desired global response. We have developed computationally e cient methods for PET systems with shiftinvariant geometric responses. We demonstrate the increased spatial uniformity of this new method versus conventional quadratic regularization schemes in simulated PET thorax scans.
A Theoretical Study of the Contrast Recovery and Variance of MAP Reconstructions From PET Data
 IEEE Trans. Med. Imag
, 1999
"... We examine the spatial resolution and variance properties of PET images reconstructed using maximum a posteriori (MAP) or penalizedlikelihood methods. Resolution is characterized by the contrast recovery coefficient (CRC) of the local impulse response. Simplified approximate expressions are derived ..."
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Cited by 31 (4 self)
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We examine the spatial resolution and variance properties of PET images reconstructed using maximum a posteriori (MAP) or penalizedlikelihood methods. Resolution is characterized by the contrast recovery coefficient (CRC) of the local impulse response. Simplified approximate expressions are derived for the local impulse response CRCs and variances for each voxel. Using these results we propose a practical scheme for selecting spatially variant smoothing parameters to optimize lesion detectability through maximization of the local CRCtonoise ratio in the reconstructed image. I. INTRODUCTION PET image reconstruction algorithms based on maximum likelihood (ML) or maximum a posteriori (MAP) principles can produce improved spatial resolution and noise properties in comparison to conventional filtered backprojection (FBP) methods. It is often important to be able to quantify this improvement in terms of the resolution (or bias) and variance of the resulting images. These measures can be...
New Statistical Models for RandomsPrecorrected PET Scans
 in Information Processing in Medical
, 2001
"... PET measurements are usually precorrected for accidental coincidence events by realtime subtraction of the delayed window coincidences. Randoms subtraction compensates in mean for accidental coincidences but destroys the Poisson statistics. We propose and analyze two new approximations to the exa ..."
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Cited by 20 (16 self)
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PET measurements are usually precorrected for accidental coincidence events by realtime subtraction of the delayed window coincidences. Randoms subtraction compensates in mean for accidental coincidences but destroys the Poisson statistics. We propose and analyze two new approximations to the exact loglikelihood of the precorrected measurements, one based on a "shifted Poisson" model, the other based on saddlepoint approximations to the measurement probability mass function (pmf). The methods apply to both emission and transmission tomography; however in this paper we focus on transmission tomography. We compare the new models to conventional dataweighted least squares (WLS) and conventional maximum likelihood (based on the ordinary Poisson (OP) model) using simulations and analytic approximations. The results demonstrate that the proposed methods avoid the systematic bias of the WLS method, and lead to significantly lower variance than the conventional OP method. The saddlepoint method provides a more accurate approximation to the exact loglikelihood than the WLS, OP and shifted Poisson alternatives.
Resolution properties of regularized image reconstruction methods
 of EECS, Univ. of Michigan, Ann Arbor, MI
, 1995
"... This paper examines the spatial resolution properties of penalizedlikelihood image reconstruction methods by analyzing the local impulse response. The analysis shows that standard regularization penalties induce spacevariant local impulse response functions, even for spaceinvariant tomographic s ..."
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Cited by 18 (12 self)
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This paper examines the spatial resolution properties of penalizedlikelihood image reconstruction methods by analyzing the local impulse response. The analysis shows that standard regularization penalties induce spacevariant local impulse response functions, even for spaceinvariant tomographic systems. Paradoxically, for emission image reconstruction the local resolution is generally poorest in highcount regions. We show that the linearized local impulse response induced by quadratic roughness penalties depends on the object only through its projections. This analysis leads naturally to a modified regularization penalty that yields reconstructed images with nearly uniform resolution. The modified penalty also provides a very practical method for choosing the regularization parameter to obtain a specified resolution in images reconstructed by penalizedlikelihood methods.
Minimum variance in biased estimation: Bounds and asymptotically optimal estimators
 IEEE Trans. Signal Processing
, 2004
"... Abstract—We develop a uniform Cramér–Rao lower bound (UCRLB) on the total variance of any estimator of an unknown vector of parameters, with bias gradient matrix whose norm is bounded by a constant. We consider both the Frobenius norm and the spectral norm of the bias gradient matrix, leading to two ..."
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Cited by 12 (7 self)
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Abstract—We develop a uniform Cramér–Rao lower bound (UCRLB) on the total variance of any estimator of an unknown vector of parameters, with bias gradient matrix whose norm is bounded by a constant. We consider both the Frobenius norm and the spectral norm of the bias gradient matrix, leading to two corresponding lower bounds. We then develop optimal estimators that achieve these lower bounds. In the case in which the measurements are related to the unknown parameters through a linear Gaussian model, Tikhonov regularization is shown to achieve the UCRLB when the Frobenius norm is considered, and the shrunken estimator is shown to achieve the UCRLB when the spectral norm is considered. For more general models, the penalized maximum likelihood (PML) estimator with a suitable penalizing function is shown to asymptotically achieve the UCRLB. To establish the asymptotic optimality of the PML estimator, we first develop the asymptotic mean and variance of the PML estimator for any choice of penalizing function satisfying certain regularity constraints and then derive a general condition on the penalizing function under which the resulting PML estimator asymptotically achieves the UCRLB. This then implies that from all linear and nonlinear estimators with bias gradient whose norm is bounded by a constant, the proposed PML estimator asymptotically results in the smallest possible variance. Index Terms—Asymptotic optimality, biased estimation, bias gradient norm, Cramér–Rao lower bound, penalized maximum likelihood, Tikhonov regularization.
Uniformly Improving the CramérRao Bound and MaximumLikelihood Estimation
"... Abstract — An important aspect of estimation theory is characterizing the best achievable performance in a given estimation problem, as well as determining estimators that achieve the optimal performance. The traditional CramérRao type bounds provide benchmarks on the variance of any estimator of a ..."
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Cited by 7 (4 self)
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Abstract — An important aspect of estimation theory is characterizing the best achievable performance in a given estimation problem, as well as determining estimators that achieve the optimal performance. The traditional CramérRao type bounds provide benchmarks on the variance of any estimator of a deterministic parameter vector under suitable regularity conditions, while requiring apriori specification of a desired bias gradient. In applications, it is often not clear how to choose the required bias. A direct measure of the estimation error that takes both the variance and the bias into account is the meansquared error (MSE), which is the sum of the variance and the squarednorm of the bias. Here, we develop bounds on the MSE in estimating a deterministic parameter vector x0 over all bias vectors that are linear in x0, which includes the traditional unbiased estimation as a special case. In some settings, it is possible to minimize the MSE over all linear bias vectors. More generally, direct minimization is not possible since the optimal solution depends on the unknown x0. Nonetheless, we show that in many cases we can find bias vectors that result in an MSE bound that is smaller than the CRLB for all values of x0. Furthermore, we explicitly construct estimators that achieve these bounds in cases where an efficient estimator exists, by performing a simple linear transformation on the standard maximum likelihood (ML) estimator. This leads to estimators that result in a smaller MSE than the ML estimator for all possible values of x0. I.
Location estimation accuracy in wireless sensor networks
 In Asilomar Conf. on Signals and Systems
, 2002
"... The peertopeer nature of a wireless sensor network presents the opportunity for accurate and lowconfiguration sensor location estimation. Range measurements are made between pairs of sensors, reyardless of their a priori coordinate howledge. This paper quantifies via the CramerRao Bound (CRB) vav ..."
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Cited by 5 (1 self)
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The peertopeer nature of a wireless sensor network presents the opportunity for accurate and lowconfiguration sensor location estimation. Range measurements are made between pairs of sensors, reyardless of their a priori coordinate howledge. This paper quantifies via the CramerRao Bound (CRB) vaviance limits on location estimators which use measured timeofarrival (TOA) or received signal strength (RSS). An eztensiue campaign memures TOA and RSS in a &device multipointtomultipoint indoor network for input into "'mumlikelihood estimators (MZEs) of location. RMS location errors of 1.2 and 2.2 m are demonstrated usiny TOA and RSS, respectively. 1
A lower bound on the Bayesian MSE based on the optimal bias function
 IEEE Transactions on Information Theory
, 2009
"... Abstract—A lower bound on the minimum meansquared error (MSE) in a Bayesian estimation problem is proposed in this paper. This bound utilizes a wellknown connection to the deterministic estimation setting. Using the prior distribution, the bias function which minimizes the Cramér–Rao bound can be ..."
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Cited by 5 (0 self)
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Abstract—A lower bound on the minimum meansquared error (MSE) in a Bayesian estimation problem is proposed in this paper. This bound utilizes a wellknown connection to the deterministic estimation setting. Using the prior distribution, the bias function which minimizes the Cramér–Rao bound can be determined, resulting in a lower bound on the Bayesian MSE. The bound is developed for the general case of a vector parameter with an arbitrary probability distribution, and is shown to be asymptotically tight in both the high and low signaltonoise ratio (SNR) regimes. A numerical study demonstrates several cases in which the proposed technique is both simpler to compute and tighter than alternative methods. Index Terms—Bayesian bounds, Bayesian estimation, minimum meansquared error (MSE) estimation, optimal bias, performance
Empirical Evaluation of the Limits on Localization Using Signal Strength
, 2009
"... This work investigates the lower bounds of wireless localization accuracy using signal strength on commodity hardware. Our work relies on tracedriven analysis using an extensive indoor experimental infrastructure. First, we report the best experimental accuracy, twice the best prior reported accur ..."
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Cited by 4 (2 self)
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This work investigates the lower bounds of wireless localization accuracy using signal strength on commodity hardware. Our work relies on tracedriven analysis using an extensive indoor experimental infrastructure. First, we report the best experimental accuracy, twice the best prior reported accuracy for any localization system. We experimentally show that adding more and more resources (e.g., training points or landmarks) beyond a certain limit, can degrade the localization performance for laterationbased algorithms, and that it could only be improved further by “cleaning ” the data. However, matching algorithms are more robust to poor quality RSS measurements. We next compare with a theoretical lower bound using standard Cramér Rao Bound (CRB) analysis for unbiased estimators, which is frequently used to provide bounds on localization precision. Because many localization algorithms are based on different mathematical foundations, we apply a diverse set of existing algorithms to our packet traces and found that the variance of the localization errors from these algorithms are smaller than the variance bound established by the CRB. Finally, we found that there exists a wide discrepancy from what freespace models predict in the signal to distance function even in an environment with limited shadowing and multipath, thereby imposing a fundamental limit on the achievable localization accuracy indoors.