arXiv subjects

Petre Stoica

Publications and source records attributed to Petre Stoica.

44 records · Page 3Linked to original sources

arXiv2016

Pearson information-based lower bound on Fisher information

The Fisher information matrix (FIM) plays an important role in the analysis of parameter inference and system design problems. In a number of cases, however, the statistical data distribution and its associated information matrix are either unknown or intractable. For this reason, it is of interest to develop useful lower bounds on the FIM. In this lecture note, we derive such a bound based on moment constraints. We call this bound the Pearson information matrix (PIM) and relate it to properties of a misspecified data distribution. Finally, we show that the inverse PIM coincides with the asymptotic covariance matrix of the optimally weighted generalized method of moments.

math.ST↗

arXiv2016

Scalable and Passive Wireless Network Clock Synchronization

Clock synchronization is ubiquitous in wireless systems for communication, sensing and control. In this paper we design a scalable system in which an indefinite number of passively receiving wireless units can synchronize to a single master clock at the level of discrete clock ticks. Accurate synchronization requires an estimate of the node positions. If such information is available the framework developed here takes position uncertainties into account. In the absence of such information we propose a mechanism which enables simultaneous synchronization and positioning. Furthermore we derive the Cramer-Rao bounds for the system which show that it enables synchronization accuracy at sub-nanosecond levels. Finally, we develop and evaluate an online estimation method which is statistically efficient.

cs.NI↗

arXiv2016

Vandermonde Decomposition of Multilevel Toeplitz Matrices with Application to Multidimensional Super-Resolution

The Vandermonde decomposition of Toeplitz matrices, discovered by Carathéodory and Fejér in the 1910s and rediscovered by Pisarenko in the 1970s, forms the basis of modern subspace methods for 1D frequency estimation. Many related numerical tools have also been developed for multidimensional (MD), especially 2D, frequency estimation; however, a fundamental question has remained unresolved as to whether an analog of the Vandermonde decomposition holds for multilevel Toeplitz matrices in the MD case. In this paper, an affirmative answer to this question and a constructive method for finding the decomposition are provided when the matrix rank is lower than the dimension of each Toeplitz block. A numerical method for searching for a decomposition is also proposed when the matrix rank is higher. The new results are applied to studying MD frequency estimation within the recent super-resolution framework. A precise formulation of the atomic $\ell_0$ norm is derived using the Vandermonde decomposition. Practical algorithms for frequency estimation are proposed based on relaxation techniques. Extensive numerical simulations are provided to demonstrate the effectiveness of these algorithms compared to the existing atomic norm and subspace methods.

cs.IT↗

arXiv2015

Cramer-Rao bound analog of Bayes rule

In this lecture note, we show a general property of the Cramer-Rao bound (CRB) that quantifies the interdependencies between the parameters in a vector. The presented result is valid for more general models than the additive noise model and also generalizes previous results to vector parameters. The CRB analog to Bayes' rule will be illustrated via two examples.

math.ST↗

arXiv2015

Online Hyperparameter-Free Sparse Estimation Method

In this paper we derive an online estimator for sparse parameter vectors which, unlike the LASSO approach, does not require the tuning of any hyperparameters. The algorithm is based on a covariance matching approach and is equivalent to a weighted version of the square-root LASSO. The computational complexity of the estimator is of the same order as that of the online versions of regularized least-squares (RLS) and LASSO. We provide a numerical comparison with feasible and infeasible implementations of the LASSO and RLS to illustrate the advantage of the proposed online hyperparameter-free estimator.

math.ST↗

arXiv2014

Weighted SPICE: A Unifying Approach for Hyperparameter-Free Sparse Estimation

In this paper we present the SPICE approach for sparse parameter estimation in a framework that unifies it with other hyperparameter-free methods, namely LIKES, SLIM and IAA. Specifically, we show how the latter methods can be interpreted as variants of an adaptively reweighted SPICE method. Furthermore, we establish a connection between SPICE and the l1-penalized LAD estimator as well as the square-root LASSO method. We evaluate the four methods mentioned above in a generic sparse regression problem and in an array processing application.

math.ST↗

arXiv2014

A Recursive Method for Enumeration of Costas Arrays

In this paper, we propose a recursive method for finding Costas arrays that relies on a particular formation of Costas arrays from similar patterns of smaller size. By using such an idea, the proposed algorithm is able to dramatically reduce the computational burden (when compared to the exhaustive search), and at the same time, still can find all possible Costas arrays of given size. Similar to exhaustive search, the proposed method can be conveniently implemented in parallel computing. The efficiency of the method is discussed based on theoretical and numerical results.

cs.IT↗

arXiv2013

Designing Unimodular Codes via Quadratic Optimization is not Always Hard

The NP-hard problem of optimizing a quadratic form over the unimodular vector set arises in radar code design scenarios as well as other active sensing and communication applications. To tackle this problem (which we call unimodular quadratic programming (UQP)), several computational approaches are devised and studied. A specialized local optimization scheme for UQP is introduced and shown to yield superior results compared to general local optimization methods. Furthermore, a \textbf{m}onotonically \textbf{er}ror-bound \textbf{i}mproving \textbf{t}echnique (MERIT) is proposed to obtain the global optimum or a local optimum of UQP with good sub-optimality guarantees. The provided sub-optimality guarantees are case-dependent and generally outperform the $π/4$ approximation guarantee of semi-definite relaxation. Several numerical examples are presented to illustrate the performance of the proposed method. The examples show that for cases including several matrix structures used in radar code design, MERIT can solve UQP efficiently in the sense of sub-optimality guarantee and computational time.

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