Chinghui J. Ying

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. >

A combined order selection and parameter estimation algorithm for undamped exponentials

We propose an approximate maximum likelihood parameter estimation algorithm, combined with a model order estimator for superimposed undamped exponentials in noise. The algorithm combines the robustness of Fourier-based estimators and the high-resolution capabilities of parametric methods. We use a combination of a Wald (1945) statistic and a MAP test for order selection and initialize an iterative maximum likelihood descent algorithm recursively based on estimates at higher candidate model orders. Experiments using simulated data and synthetic radar data demonstrate improved performance over MDL, MAP, and AIC in places of practical interest.

On Model Order Determination For Complex Exponential Signals: Performance Of An FFT-initialized ML Algorithm

We present an algorithm for model order determination and simultaneous maximum likelihood parameter estimation for complex exponential signal modeling. The algorithm exploits initial nonparametric (i.e., FFT) frequency location estimates and Cram&-Rru, Bound (CRB) resolution limits to significantly reduce the search space for the correct model order and parameter estimates. The algorithm initially overestimates the model order. After iterative minimization to obtain maximum likelihood (ML) parameter estimates for that order, a post-processing step eliminates the extraneous sinusoidal modes using CFU3 resolution limits and statistical detection tests. Because the algorithm searches on only a limited set of model orders and parameter regions, it is computationally tractable even for large data lengths and model orders. In this paper we analyze the performance of the algorithm and compare with other existing approaches.

Complex SAR phase history modeling using two-dimensional parametric estimation techniques

Using a point scatterer assumption, high-frequency SAR phase histories can be modeled as a sum of 2D complex exponentials in additive noise. This paper summarizes our SAR signal modeling experience using the XPatch simulated scattering data. We apply several 2D parametric estimation techniques including 2D TLS-Prony, MEMP, 2D IQML, and 2D CLEAN to estimate the complex exponential model parameters. From the estimation results, we discuss the engineering trade-offs among memory requirement, computation requirement, and estimation accuracy.

Minimum variance linear estimation of amplitudes for exponential signal models

This article presents the minimum variance consistent linear estimator for amplitude parameters in exponential signal models. A simple heuristic algorithm is presented to compute the weighting matrix that minimizes error variance; the resulting weighted least squares estimator accounts for the statistics of pole estimation errors. Additionally, analysis of binary diagonal weighting matrices demonstrates that for unweighted least-squares, the amplitude variance is reduced by truncating the Vandermonde system of equations.

Model order selection for summation models

In this paper, we propose two model order selection procedures for a class of summation models. We exploit the special structure in the class of candidate models to provide a data dependent zipper bound on the model order. The proposed upper bound is also a consistent estimator of model order. Further, minimum descriptive length, AIC and maximum apriori when accompanied with the data dependent prior exhibit an improved rate of convergence to their asymptotic behaviour and an improved detection rate for finite SNR and finite data lengths. Asymptotic properties of the maximum likelihood parameters are used to derive the proposed methods. All simulations use the complex undamped exponential model.

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>>

On Model Order Determination of Complex Exponential Signals

Abstract We present an algorithm for model order determination and corresponding maximum likelihood parameter estimation for complex exponential signal modeling. The algorithm exploits initial nonparametric frequency location estimates to significantly reduce the search space for the correct model order and parameter estimates. An FFT is used to obtain initial frequency region estimates. An initial overdetermined model order and initial frequency estimates are obtained using the CRB resolution limit and the FFT peaks. After iterative minimization, a post-processing step eliminates the extraneous sinusoidal modes using CRB resolution limits arii statistical detection tests. Because the algorithm searches on only a limited set of model orders and parameter regions, it is computationally tractable even for large data lengths and model orders. Simulations are provided to illustrate the performance of the proposed algorithm.

Statistical analysis of true and extraneous mode estimates for the TLS-Prony algorithm

The authors present a statistical analysis of the poles and amplitude coefficients estimated using a total least squares (TLS)-Prony method where signals consist of arbitrary damped exponential terms in noise. Both the true and extraneous modes are considered in the analysis. The derivation for this procedure is based on a first order perturbation analysis; thus the analysis assumes high SNR. The complete covariance matrix for the estimated pole and amplitude coefficient parameters is derived. The statistics of the mode energies for both the true and extraneous modes are developed. To first order the distributions of the true mode energies are well approximated by Gaussian distributions, and the energies of the extraneous modes are central chi /sup 2/ distributed. The theory was verified with Monte-Carlo simulations.<<ETX>>