Bayesian Detection and Estimation of Noisy Sinusoids with Reversible Jump Simulated Annealing

This paper presents a novel algorithm that combines a global nonlinear optimization routine based on the Bayesian Inference Reversible Jump Markov Chain Monte Carlo (BI-RJMCMC) method under various proposal distributions with Simulated Annealing (SA). It performs a global search in the joint space of the parameters and number of parameters, thereby surmounting the problem of local minima and converging to the modes of the full posterior distribution efficiently. Finally, the algorithm is used for detecting the number of sinusoids and estimating their parameters from corrupted data. The results of all the simulations support the effectiveness and reliability of the algorithm.