Related papers: An Uncertainty Principle for Estimates of Floquet …
We compute a variance lower bound for unbiased estimators in specified statistical models. The construction of the bound is related to the original Cram\'er-Rao bound, although it does not require the differentiability of the model.…
The Cram\'er-Rao bound serves as a crucial lower limit for the mean squared error of an estimator in frequentist parameter estimation. Paradoxically, it requires highly accurate prior knowledge of the estimated parameter for constructing…
We derive lower bounds on the variance of estimators in quantum metrology by choosing test observables that define constraints on the unbiasedness of the estimator. The quantum bounds are obtained by analytical optimization over all…
The classical Cram\'er-Rao inequality gives a lower bound for the variance of a unbiased estimator of an unknown parameter, in some statistical model of a random process. In this note we rewrite the statment and proof of the bound using…
Bounding the optimal precision in parameter estimation tasks is of central importance for technological applications. In the regime of a small number of measurements, or that of low signal-to-noise ratios, the meaning of common frequentist…
The estimation of the frequencies of multiple superimposed exponentials in noise is an important research problem due to its various applications from engineering to chemistry. In this paper, we propose an efficient and accurate algorithm…
We revisit the problem of computing submatrices of the Cram\'er-Rao bound (CRB), which lower bounds the variance of any unbiased estimator of a vector parameter $\vth$. We explore iterative methods that avoid direct inversion of the Fisher…
We propose a statistical framework for the problem of parameter estimation from a noisy optomechanical system. The Cram\'er-Rao lower bound on the estimation errors in the long-time limit is derived and compared with the errors of…
Many results in the quantum metrology literature use the Cram\'er-Rao bound and the Fisher information to compare different quantum estimation strategies. However, there are several assumptions that go into the construction of these tools,…
We study the effects of intrinsic noise on chemical reaction systems, which in the deterministic limit approach a limit cycle in an oscillatory manner. Previous studies of systems with an oscillatory approach to a fixed point have shown…
Using differential geometry, I derive a form of the Bayesian Cram\'er-Rao bound that remains invariant under reparametrization. With the invariant formulation at hand, I find the optimal and naturally invariant bound among the Gill-Levit…
We investigate the problem of estimating simultaneously multiple parameters encoded in the shape of the modes on which the light is expanded. For this, we generalize the mode-encoded parameter estimation theory as introduced in Ref.[1] to a…
Floquet multipliers (characteristic multipliers) play significant role in the stability of the periodic equations. Based on the iterative method, we provide a unified algorithm to compute the Floquet multipliers (characteristic multipliers)…
We develop a parametric high-resolution method for the estimation of the frequency nodes of linear combinations of complex exponentials with exponential damping. We use Kronecker's theorem to formulate the associated nonlinear least squares…
We seek to characterize the estimation performance of a sensor network where the individual sensors exhibit the phenomenon of drift, i.e., a gradual change of the bias. Though estimation in the presence of random errors has been extensively…
This paper studies distance estimation for diffusive molecular communication. The Cramer-Rao lower bound on the variance of the distance estimation error is derived. The lower bound is derived for a physically unbounded environment with…
Cooperative diversity systems are wireless communication systems designed to exploit cooperation among users to mitigate the effects of multipath fading. In fairly general conditions, it has been shown that these systems can achieve the…
Frequentist and Bayesian phase estimation strategies lead to conceptually different results on the state of knowledge about the true value of the phase shift. We compare the two frameworks and their sensitivity bounds to the estimation of…
Forced oscillations threaten the reliability of widearea power systems, and different approaches to estimate forced oscillation have been explored over the past several years. Though these efforts provide powerful tools to estimate a forced…
In quantum computation, amplitude estimation is a fundamental subroutine that is utilized in various quantum algorithms. A general important task of such estimation problems is to characterize the estimation lower bound, which is referred…