Simulated annealing: theory and applications
Simulated annealing: theory and applications
Numerical recipes in FORTRAN (2nd ed.): the art of scientific computing
Numerical recipes in FORTRAN (2nd ed.): the art of scientific computing
Fundamentals of statistical signal processing: estimation theory
Fundamentals of statistical signal processing: estimation theory
On the computation of discrete Legendre polynomial coefficients
Multidimensional Systems and Signal Processing
On an ambiguity in the definition of the amplitude and phase of a signal
Signal Processing
Simulated annealing algorithms for continuous global optimization: convergence conditions
Journal of Optimization Theory and Applications
IEEE Transactions on Signal Processing
Joint Bayesian model selection and estimation of noisy sinusoidsvia reversible jump MCMC
IEEE Transactions on Signal Processing
Analysis and synthesis of multicomponent signals using positivetime-frequency distributions
IEEE Transactions on Signal Processing
On polynomial phase signals with time-varying amplitudes
IEEE Transactions on Signal Processing
A New Flexible Approach to Estimate the IA and IF of Nonstationary Signals of Long-Time Duration
IEEE Transactions on Signal Processing - Part II
Energy separation in signal modulations with application to speechanalysis
IEEE Transactions on Signal Processing
Product high-order ambiguity function for multicomponentpolynomial-phase signal modeling
IEEE Transactions on Signal Processing
Maximum likelihood parameter estimation of superimposed chirpsusing Monte Carlo importance sampling
IEEE Transactions on Signal Processing
A fast algorithm for estimating the parameters of a quadratic FM signal
IEEE Transactions on Signal Processing
Estimation of amplitude and phase parameters of multicomponentsignals
IEEE Transactions on Signal Processing
Simulated annealing: Practice versus theory
Mathematical and Computer Modelling: An International Journal
Single tone parameter estimation from discrete-time observations
IEEE Transactions on Information Theory
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We consider the modeling of non-stationary discrete signals whose amplitude and frequency are assumed to be nonlinearly modulated over very short-time duration. We investigate the case where both instantaneous amplitude (IA) and instantaneous frequency (IF) can be approximated by orthonormal polynomials. Previous works dealing with polynomial approximations refer to orthonormal bases built from a discretization of continuous-time orthonormal polynomials. As this leads to a loss of the orthonormal property, we propose to use discrete orthonormal polynomial bases: the discrete orthonormal Legendre polynomials and a discrete base we have derived using Gram-Schmidt procedure. We show that in the context of short-time signals the use of these discrete bases leads to a significant improvement in the estimation accuracy. We manage the model parameter estimation by applying two approaches. The first is maximization of the likelihood function. This function being highly nonlinear, we propose to apply a stochastic optimization technique based on the simulated annealing algorithm. The problem can also be considered as a Bayesian estimation which leads us to apply another stochastic technique based on Monte Carlo Markov Chains. We propose to use a Metropolis Hastings (MH) algorithm. Both approaches need an algorithm parameter tuning that we discuss according our application context. Monte Carlo simulations show that the results obtained are close to the Cramer-Rao bounds we have derived. We show that the first approach is less biased than the second one. We also compared our results with the higher ambiguity function-based method. The methods proposed outperform this method at low signal to noise ratios (SNR) in terms of estimation accuracy and robustness. Both proposed approaches are of a great utility when scenarios in which signals having a small sample size are non-stationary at low SNRs. They provide accurate system descriptions which are achieved with only a reduced number of basis functions.