Rational invariant subspace approximations with applications

Includes bibliographical references.Subspace methods such as MUSIC, Minimum Norm, and ESPRIT have gained considerable attention due to their superior performance in sinusoidal and direction-of-arrival (DOA) estimation, but they are also known to be of high computational cost. In this paper, new fast algorithms for approximating signal and noise subspaces and that do not require exact eigendecomposition are presented. These algorithms approximate the required subspace using rational and power-like methods applied to the direct data or the sample covariance matrix. Several ESPRIT- as well as MUSIC-type methods are developed based on these approximations. A substantial computational saving can be gained comparing with those associated with the eigendecomposition-based methods. These methods are demonstrated to have performance comparable to that of MUSIC yet will require fewer computation to obtain the signal subspace matrix

The theory of linear prediction

Linear prediction theory has had a profound impact in the field of digital signal processing. Although the theory dates back to the early 1940s, its influence can still be seen in applications today. The theory is based on very elegant mathematics and leads to many beautiful insights into statistical signal processing. Although prediction is only a part of the more general topics of linear estimation, filtering, and smoothing, this book focuses on linear prediction. This has enabled detailed discussion of a number of issues that are normally not found in texts. For example, the theory of vector linear prediction is explained in considerable detail and so is the theory of line spectral processes. This focus and its small size make the book different from many excellent texts which cover the topic, including a few that are actually dedicated to linear prediction. There are several examples and computer-based demonstrations of the theory. Applications are mentioned wherever appropriate, but the focus is not on the detailed development of these applications. The writing style is meant to be suitable for self-study as well as for classroom use at the senior and first-year graduate levels. The text is self-contained for readers with introductory exposure to signal processing, random processes, and the theory of matrices, and a historical perspective and detailed outline are given in the first chapter

New Methods for MLE of Toeplitz Structured Covariance Matrices with Applications to RADAR Problems

This work considers Maximum Likelihood Estimation (MLE) of a Toeplitz structured covariance matrix. In this regard, an equivalent reformulation of the MLE problem is introduced and two iterative algorithms are proposed for the optimization of the equivalent statistical learning framework. Both the strategies are based on the Majorization Minimization (MM) paradigm and hence enjoy nice properties such as monotonicity and ensured convergence to a stationary point of the equivalent MLE problem. The proposed framework is also extended to deal with MLE of other practically relevant covariance structures, namely, the banded Toeplitz, block Toeplitz, and Toeplitz-block-Toeplitz. Through numerical simulations, it is shown that the new methods provide excellent performance levels in terms of both mean square estimation error (which is very close to the benchmark Cram\'er-Rao Bound (CRB)) and signal-to-interference-plus-noise ratio, especially in comparison with state of the art strategies.Comment: submitted to IEEE Transactions on Signal Processing. arXiv admin note: substantial text overlap with arXiv:2110.1217

Estimation of the coherence time of stochastic oscillations from modest samples

‘Quasi-periodic’ or ‘solar-like’ oscillations can be described by three parameters – a characteristic frequency, a coherence time (or ‘quality factor’) and the variance of the random driving process. This paper is concerned with the estimation of these quantities, particularly the coherence time, from modest sample sizes (observations covering of the order of a hundred or fewer oscillation periods). Under these circumstances, finite sample properties of the periodogram (bias and covariance) formally invalidate the commonly used maximum-likelihood procedure. It is shown that it none the less gives reasonable results, although an appropriate covariance matrix should be used for the standard errors of the estimates. Tailoring the frequency interval used, and oversampling the periodogram, can substantially improve parameter estimation. Maximum-likelihood estimation in the time-domain has simpler statistical properties, and generally performs better for the parameter values considered in this paper. The effects of added measurement errors are also studied. An example analysis of pulsating star data is given.Web of Scienc

Resolvability of objects from the standpoint of statistical parameter estimation

Radiance estimation and object resolvability by statistical parameter analysis of aperture fiel

Feature Extraction for Music Information Retrieval

Copyright c © 2009 Jesper Højvang Jensen, except where otherwise stated