William M. Steedly

Two-dimensional Prony modeling and parameter estimation

A new method for estimating the two-dimensional (2D) exponential modes and amplitude coefficients in a Prony model is presented. This method involves two parts, each utilizing a 1D singular value decomposition-based technique, and is capable of locating frequencies anywhere in the 2D frequency plane. Simulations are shown which demonstrate the performance of the algorithm. >

The Cramer-Rao bound for pole and amplitude coefficient estimates of damped exponential signals in noise

A complete Cramer-Rao bound (CRB) derivation is provided for the case in which signals consist of arbitrary exponential terms in noise. Expressions for the CRBs of the parameters of a damped exponential model with one set of poles and multiple sets of amplitude coefficients are derived. CRBs for the poles and amplitude coefficients are derived in terms of rectangular and polar coordinate parameters. For rectangular parameters it is shown that CRBs for the real and imaginary parts of poles and amplitude coefficients are equal and uncorrelated. In polar coordinates, the angle and magnitude CRBs are also uncorrelated. Furthermore, the CRBs of the pole angles and relative magnitudes are equal and are logarithmically symmetric about the unit circle. >

Statistical analysis of TLS-based Prony techniques

Abstract We present an analysis of parameter variance statistics for the TLS-Prony method applied to damped exponential signals. We derive the covariance matrix of the estimated parameters for this method. The parameters include the magnitudes and angles of the poles, and the magnitudes and angles of the amplitude coefficients. We verify the theoretical results using Monte-Carlo simulations studies. We also compare the variance results to the corresponding Cramer-Rao bounds for several cases.

A modified TLS-Prony method using data decimation

The paper introduces a modified TLS-Prony method that incorporates data decimation. The use of data decimation results in the reduction in the computational complexity because one high-order estimation is replaced by several low-order estimations. The authors present an analysis of pole variance statistics for this modified TLS-Prony method. This analysis provides a quantitative comparison of the parameter estimation accuracy as a function of decimation factors. The authors show that by using decimation, one can obtain comparable statistical performance results at a fraction of the computational cost, when compared with the conventional TLS-Prony algorithm. >

The Cramer-Rao bound for pole and amplitude estimates of damped exponential signals in noise

Expressions are derived for the Cramer-Rao bounds (CRBs) of the parameters of an exponential model with one set of poles and multiple sets of amplitude coefficients. The poles of this model may lie anywhere in the complex plane. The CRB for pole angle is log-symmetric about the unit circle with minimum on the unit circle, while the CRB for pole magnitude has its minimum inside the unit circle for finite-length datasets and is not symmetric. Simulation results show that error-standard-deviation ellipses about poles turn out to be circular. The CRBs for estimates of the amplitude coefficients of real and imaginary parts are also available.<<ETX>>

Practical comparison of adaptive filter algorithms

Linear filters can be designed to pass signals of interest and suppress undesired signal components. Wiener [1942] originated work to determine conditions for an optimal linear filter. The present paper reviews the problem of optimally reconstructing one signal as a filtered version of a second signal. This problem has applications in noise reduction, echo or interference cancellation from a signal of interest, system modeling, and equalization. Also included is an overview of methods to implement optimal, adaptive linear filters. The focus of the paper is on contrasting two methods for the particular problem of restoring speech signals in loud audio backgrounds. The discussion includes consideration of the many problems encountered in applications of adaptive processing. Trade-offs include sacrificing steady-state MSE for adaptation rate, controlling errors introduced by round-off selecting filter order, and operation count (complexity).<<ETX>>

Full-polarization two-dimensional Prony modeling with application to radar target identification

A new two-dimensional (2-D) technique is developed to estimate the polarimetric characteristics of scattering centers that exist on radar targets. This technique uses a 2-D damped exponential model to approximate the scattering from radar targets. The validity of this model is investigated relative to the scattering characteristics that exist on the targets of interest. Simulations are shown which validate the technique.

Evaluation of single- and full-polarization two-dimensional Prony techniques applied to radar data

The recently developed 2-D TLS-Prony technique is applied to a single and full-polarization synthetically generated radar data set. The radar target analyzed is a generic aircraft consisting of a fuselage, wing, stabilizer, and tail. The 2-D TLS-Prony technique is a parametric estimation technique that models the radar return frequency domain data (multiple angle, multiple frequency data, e.g., SAR/ISAR) using damped exponentials. The techniques ability to accurately model and characterize the target are investigated. Scattering center location and characterization are accomplished by the technique. Issues such as model order selection, bandwidth requirements, and modeling error are examined for both single and full polarization data sets.

Statistical analysis of SVD-based Prony techniques

The authors present an analysis of parameter variance statistics for the SVD-Prony method applied to damped exponential signals. The covariance matrix of the estimated parameters for this method is derived. The parameters include the magnitudes and angles of the poles, and the magnitudes and angles of the amplitude coefficients. The theoretical results are verified using Monte Carlo simulation studies. The variance results are compared to the corresponding Cramer-Rao bounds for several cases.<<ETX>>

High resolution exponential modeling of fully polarized radar returns

A method for modeling radar target scattering data for the purpose of automatic target recognition is considered. The approach is to estimate a time-domain feature vector which describes the target. The target is characterized by a set of scattering centers. Using the motion of a transient polarization response, scattering centers are estimated along with their polarization. An exponential model for the fully polarized radar return and estimation algorithm are presented