Bayesian detection and MMSE frequency estimation of sinusoidal signals via adaptive importance sampling

A novel solution for the problem of detecting the number of complex exponentials embedded in Gaussian noise and estimating their frequencies is proposed. In contrast to standard techniques, the marginalized posterior density is utilized to evaluate a model selection criterion and compute the MMSE estimates. To compute the required integrals, a numerically efficient procedure, termed adaptive importance sampling (AIS), is introduced. This procedure can naturally handle parameter constraints and, it greatly improves convergence as compared to standard Monte Carlo approaches. Our method has the benefit of not only out-performing the standard techniques, but it also sidesteps the pitfalls associated with multidimensional optimization.