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Standard CramerRao bound CramerRao bound with nuisance parameter Bayesian CramerRao bound Other bounds
"... We assume y(n) = a(n)e2ipif0n + b(n), n = 0,...,N − 1 with y(n) : the received signal a(n) : a zeromean random process or a timevarying amplitude. b(n) : circular white Gaussian stationary additive noise. Goal: Estimating the frequency f0 in multiplicative and additive noise ..."
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We assume y(n) = a(n)e2ipif0n + b(n), n = 0,...,N − 1 with y(n) : the received signal a(n) : a zeromean random process or a timevarying amplitude. b(n) : circular white Gaussian stationary additive noise. Goal: Estimating the frequency f0 in multiplicative and additive noise
Blind Signal Separation: Statistical Principles
, 2003
"... Blind signal separation (BSS) and independent component analysis (ICA) are emerging techniques of array processing and data analysis, aiming at recovering unobserved signals or `sources' from observed mixtures (typically, the output of an array of sensors), exploiting only the assumption of mut ..."
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Cited by 522 (4 self)
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Blind signal separation (BSS) and independent component analysis (ICA) are emerging techniques of array processing and data analysis, aiming at recovering unobserved signals or `sources' from observed mixtures (typically, the output of an array of sensors), exploiting only the assumption
Rethinking biased estimation: Improving maximum likelihood and the CramérRao bound
 TRENDS IN SIGNAL PROCESS
, 2007
"... One of the prime goals of statistical estimation theory is the development of performance bounds when estimating parameters of interest in a given model, as well as constructing estimators that achieve these limits. When the parameters to be estimated are deterministic, a popular approach is to boun ..."
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Cited by 21 (12 self)
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the unbiased Cramér–Rao bound (CRB) for all values of the unknowns. We then present a general framework for constructing biased estimators with smaller MSE than the standard maximumlikelihood (ML) approach, regardless of the true unknown values. Specializing the results to the linear Gaussian model, we derive
Limited information estimators and exogeneity tests for simultaneous probit models
, 1988
"... A twostep maximum likelihood procedure is proposed for estimating simultaneous probit models and is compared to alternative limited information estimators. Conditions under which each estimator attains the CramerRao lower bound are obtained. Simple tests for exogeneity based on the new twostep es ..."
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Cited by 459 (0 self)
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A twostep maximum likelihood procedure is proposed for estimating simultaneous probit models and is compared to alternative limited information estimators. Conditions under which each estimator attains the CramerRao lower bound are obtained. Simple tests for exogeneity based on the new two
Posterior CramérRao bounds for discretetime nonlinear filtering
 IEEE Trans. Signal Processing
, 1998
"... Abstract—A meansquare error lower bound for the discretetime nonlinear filtering problem is derived based on the Van Trees (posterior) version of the Cramér–Rao inequality. This lower bound is applicable to multidimensional nonlinear, possibly nonGaussian, dynamical systems and is more general tha ..."
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Cited by 178 (4 self)
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Abstract—A meansquare error lower bound for the discretetime nonlinear filtering problem is derived based on the Van Trees (posterior) version of the Cramér–Rao inequality. This lower bound is applicable to multidimensional nonlinear, possibly nonGaussian, dynamical systems and is more general
Research Article An MLBased Estimate and the CramerRao Bound for DataAided Channel Estimation in KSPOFDM
"... We consider the CramerRao bound (CRB) for dataaided channel estimation for OFDM with known symbol padding (KSPOFDM). The pilot symbols used to estimate the channel are positioned not only in the guard interval but also on some of the OFDM carriers, in order to improve the estimation accuracy for ..."
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We consider the CramerRao bound (CRB) for dataaided channel estimation for OFDM with known symbol padding (KSPOFDM). The pilot symbols used to estimate the channel are positioned not only in the guard interval but also on some of the OFDM carriers, in order to improve the estimation accuracy
Practical automotive applications of CramérRao bound analysis
 in Proc. IEEE Intelligent Vehicles symposium
"... Abstract — The CramérRao lower bound places a bound, in a mean squared sense, on the performance of all unbiased estimators. In this paper, as a base for discussion, we provide a straight forward derivation of such bounds for estimators of mobile node positions, operating on observations of distanc ..."
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Cited by 2 (1 self)
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Abstract — The CramérRao lower bound places a bound, in a mean squared sense, on the performance of all unbiased estimators. In this paper, as a base for discussion, we provide a straight forward derivation of such bounds for estimators of mobile node positions, operating on observations
CramérRao Lower Bounds for LowRank Decomposition of Multidimensional Arrays
 IEEE Trans. on Signal Processing
, 2001
"... Unlike lowrank matrix decomposition, which is generically nonunique for rank greater than one, lowrank threeand higher dimensional array decomposition is unique, provided that the array rank is lower than a certain bound, and the correct number of components (equal to array rank) is sought in the ..."
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Cited by 32 (5 self)
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in the decomposition. Parallel factor (PARAFAC) analysis is a common name for lowrank decomposition of higher dimensional arrays. This paper develops CramrRao Bound (CRB) results for lowrank decomposition of three and fourdimensional (3D and 4D) arrays, illustrates the behavior of the resulting bounds
The true CramerRao Bound for Timing . . .
"... This contribution derives the CramerRao bound (CRB) related to the estimation of the time delay of a linearly modulated bandpass signal with unknown carrier phase and frequency. We consider the following two scenarios: (i) joint estimation of the time delay, the carrier phase and the carrier frequ ..."
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This contribution derives the CramerRao bound (CRB) related to the estimation of the time delay of a linearly modulated bandpass signal with unknown carrier phase and frequency. We consider the following two scenarios: (i) joint estimation of the time delay, the carrier phase and the carrier
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