Parameter Estimation for Chirp Signals with Deterministic Time-Varying Amplitude. Estimation de Signaux Chirp à Amplitude Variant dans le Temps

Parameter Estimation for Chirp Signals with Deterministic Time-Varying Amplitude

Estimation de Signaux Chirp à Amplitude Variant dans le Temps

François Vincent Olivier Besson 

ENSICA, Département Avionique et Systèmes, 1 Place Émile Blouin, 31056 Toulouse.

Page: 
165-174
|
Received: 
9 February 1999
| |
Accepted: 
N/A
| | Citation

OPEN ACCESS

Abstract: 

We consider the problem of estimating the parameters of chirp signals with deterministic time-varying amplitude . A method which is computationally simpler than the Maximum Likelihood estimator is proposed . It invokes the extended invariance principle to split the minimization problem and to decouple estimation of the phase parameters from that of the amplitude parameters . In a first step, using a less detailed model for the signal, a simple scheme for estimating the phase parameters is presented. Then, amplitude parameters are obtained from least-squares minimization techniques. The overall procedure provides asymptotically efficient estimates. Numerical simulations attest to the validity of the theoretical analysis. 

Résumé 

Nous traitons dans cet article de l'estimation de signaux chirp dont l'amplitude, déterministe, varie dans le temps. Nous proposons une alternative à l'estimateur du Maximum de Vraisemblance qui est plus simple d'un point de vue calculatoire . Pour ceci, nous utilisons le principe d'invariance étendu qui permet de scinder le problème de minimisation et de découpler l'estimation des paramètres de phase de celle des paramètres d'amplitude . Dans un premier temps, en utilisant un modèle moins détaillé pour le signal, c'est-à-dire en considérant que tous les échantillons de l'amplitude sont à estimer, on obtient de manière simple les paramètres de phase. Les paramètres d'amplitude sont ensuite estimés par une technique des moindres carrés. La procédure permet d'obtenir des estimateurs asymptotiquement efficaces. Des simulations numériques viennent valider l'étude théorique. 

Keywords: 

Chirp signals, time-varying amplitude, maximum likelihood estimation, extended invariance principle.

Mots clés 

Amplitude variant dans le temps, maximum de vraisemblance, principe d'invariance étendu.

1. Introduction et Position du Problème
2. Modèle du Signal et Principe D'invariance Étendu
3. Estimation
4. Exemples Numériques
5. Conclusions
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