A Global Convergence Analysis of the Pavon–Ferrante Algorithm for Spectral Estimation
نویسنده
چکیده
In this paper, we provide a detailed analysis of the global convergence properties of an extensively studied and extremely effective fixed-point algorithm for the Kullback–Leibler approximation of spectral densities, proposed by Pavon and Ferrante in [1]. Our main result states that the algorithm globally converges to one of its fixed points. Index Terms Approximation of spectral densities, spectral estimation, generalized moment problems, Kullback– Leibler divergence, fixed-point iteration, convergence analysis.
منابع مشابه
On the well-posedness of multivariate spectrum approximation and convergence of high-resolution spectral estimators
In this paper, we establish the well-posedness of the generalized moment problems recently studied by Byrnes-Georgiou-Lindquist and coworkers, and by Ferrante-Pavon-Ramponi. We then apply these continuity results to prove almost sure convergence of a sequence of high-resolution spectral estimators indexed by the sample size. ∗Partially supported by the Ministry of Education, University, and Res...
متن کاملOn the Geometry of Maximum Entropy Problems
We show that a simple geometric result suffices to derive the form of the optimal solution in a large class of finiteand infinite-dimensional maximum entropy problems concerning probability distributions, spectral densities, and covariance matrices. These include Burg’s spectral estimation method and Dempster’s covariance completion, as well as various recent generalizations of the above. We th...
متن کاملHellinger Versus Kullback-Leibler Multivariable Spectrum Approximation
In this paper, we study a matricial version of a generalized moment problem with degree constraint. We introduce a new metric on multivariable spectral densities induced by the family of their spectral factors, which, in the scalar case, reduces to the Hellinger distance. We solve the corresponding constrained optimization problem via duality theory. A highly nontrivial existence theorem for th...
متن کاملHarmonics Estimation in Power Systems using a Fast Hybrid Algorithm
In this paper a novel hybrid algorithm for harmonics estimation in power systems is proposed. The estimation of the harmonic components is a nonlinear problem due to the nonlinearity of phase of sinusoids in distorted waveforms. Most researchers implemented nonlinear methods to extract the harmonic parameters. However, nonlinear methods for amplitude estimation increase time of convergence. Hen...
متن کاملConvergence analysis of spectral Tau method for fractional Riccati differential equations
In this paper, a spectral Tau method for solving fractional Riccati differential equations is considered. This technique describes converting of a given fractional Riccati differential equation to a system of nonlinear algebraic equations by using some simple matrices. We use fractional derivatives in the Caputo form. Convergence analysis of the proposed method is given an...
متن کامل