25 June 1999 Detection and estimation of general frequency-modulated signals using reversible jump MCMC methods
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Abstract
General frequency modulated signals can be used to characterize many vibrations in dynamic environments, with applications to engine monitoring and sonar. Most work in to parameter estimation of such signals assumes knowledge of the number of carrier frequencies present in the signal. In this paper, we make no such assumption, and use Bayesian techniques to address jointly the problem of model selection and parameter estimation. Following the work of Andrieu and Doucet, who addressed the problem of joint Bayesian model selection and parameter estimation for non-modulated sinusoids in white Gaussian noise, a posterior distribution for the parameter and model order is obtained. This distribution is to o complicated to evaluate analytically, so we use a reversible jump Markov chain Monte Carlo algorithm to draw samples for the distribution. Some simulated examples are presented to illustrate the algorithm's performance.
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Keith D. Copsey, Neil J. Gordon, Alan Marrs, "Detection and estimation of general frequency-modulated signals using reversible jump MCMC methods", Proc. SPIE 3816, Mathematical Modeling, Bayesian Estimation, and Inverse Problems, (25 June 1999); doi: 10.1117/12.351318; https://doi.org/10.1117/12.351318
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KEYWORDS
Modulation

Statistical analysis

Monte Carlo methods

Computer simulations

Fourier transforms

Signal to noise ratio

Statistical modeling

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