A mean-square 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 non-Gaussian, dynamical systems and is more general than the previous bounds in the literature. The case of singular conditional distribution of the one-step-ahe...

Let X = (X1, ..., X ˆ n) be a random sample from distribution fθ. Let θ = δ(X) be an estimator of θ. Let T (X) be a su cient statistic for θ. As we have seen already, MSE provides one way to compare the quality of di erent estimators. In particular, estimators with smaller MSE are said to be more e cient. On the other hand, once we know T (X), we can discard X. How do these concepts relate to e...

OF THESIS Submitted in Partial Fulfillment of the Requirements for the Degree of Master of Science Optical Science and Engineering The University of New Mexico Albuquerque, New Mexico May, 2007

In most situations the best estimator of a function of the parameter exists, but sometimes it has a complex form and we cannot compute its variance explicitly. Therefore, a lower bound for the variance of an estimator is one of the fundamentals in the estimation theory, because it gives us an idea about the accuracy of an estimator. It is well-known in statistical inference that the Cram&eac...

A solution of the Bayesian recursive relations by the particle filter approach is treated. The stress is laid on the sample size setting as the main user design problem. The Cramér-Rao bound was chosen as a tool for setting the sample size for the three basic types of the state estimation, for filtering, prediction and smoothing. The mean square error matrices of particle filter state estimates...

In an orthogonal-frequency-division multiplex (OFDM) system, the problem of sampling clock synchronization and channel estimation is analyzed. In such systems, when the number of sub-carriers is large, a sampling clock frequency mismatch between the transmitter and the receiver dramatically degrades the performance. Obviously, the channel-impulse response is unknown at the receiver and also nee...

An accurate frequency estimator for real sinusoid based on Discrete Fourier Transform (DFT) is proposed. The proposed the interpolation of maximum DFT spectral line and two Discrete-Time (DTFT) lines can operate with both rectangular window sidelobe decay (MSD) window. In coarse estimation step, MSD used. According to value estimate, negative component removed. fine utilized achieve Cramer–Rao ...