In continuation to an earlier work, we further develop bounds on the mean-squared error (MSE) when estimating a deterministic parameter vector 0 in a given estimation problem, as well as estimators that achieve the optimal performance. The traditional Cramér–Rao (CR) type bounds provide benchmarks on the variance of any estimator of 0 under suitable regularity conditions, while requiring a prio...

Noise-compensated autoregressive (AR) analysis is a problem insufficiently explored with regard to the accuracy of the estimate. This paper studies comprehensively the lower limit of the estimation variance, presenting the asymptotic Cramér– Rao bound (CRB) for Gaussian processes and additive Gaussian noise. This novel result is obtained by using a frequency-domain perspective of the problem as...

LINKÖPING Technical reports from the Automatic Control group in Linkk oping are available as UNIX-compressed Postscript les by anonymous ftp at the address 130.236.20.24

Analytical expressions are derived for the CramérRao (CR) lower bound on the variance of frequency estimates for the two-signal time-series data models consisting of either one real sinusoid or two complex sinusoids in white Gaussian noise. The expressions give the bound in terms of the signal-tonoise ratio (SNR), the number N of data samples, and a function dependent on the frequency separatio...

The harmonic model sampled on a P -dimensional grid contaminated by an additive white Gaussian noise has attracted considerable attention with a variety of applications. This model has a natural interpretation in a P -order tensorial framework and an important question is to evaluate the theoretical lowest variance on the model parameter (angular-frequency, real amplitude and initial phase) est...

Despite of the increased interest in independent component analysis (ICA) during the past two decades, a simple closed form expression of the Cramér–Rao bound (CRB) for the demixing matrix estimation has not been established in the open literature. In the present paper we fill this gap by deriving a simple closedform expression for the CRB of the demixing matrix directly from its definition. A ...

Sampling a finite stream of filtered pulses violates the bandlimited assumption of the Nyquist-Shannon sampling theory. However, recent low rate sampling schemes have shown that these sparse signals can be sampled with perfect reconstruction at their rate of innovation. To reach this goal in the presence of noise, an estimation procedure is needed to estimate the time-delay and the amplitudes o...

Unbiased Cramér-Rao lower bound (CRB) theory can be used to calculate lower bounds to the variances of unbiased estimates of a set of parameters given only the probability density function of a random vector conditioned on the true parameter values. However, when the estimated parameter values are required to satisfy inequality constraints such as positivity, the resulting estimator is typicall...