Bayesian detection and estimation of cisoids in colored noise

The problem of estimating the number of cisoids in colored noise is addressed. It is assumed that the noise can be modeled by an autoregression whose order has also to be estimated. A new criterion is proposed for estimating the number of cisoids and the autoregressive model order, as well as a new algorithm for estimating the cisoidal frequencies. In the derivation, a Bayesian methodology and subspace decomposition are employed. The proposed criterion significantly outperforms the popular MDL and AIC as applied in a paper by Nagesha and Kay. In addition, an algorithm that reduces the computational complexity of the solution is developed, computer simulations that demonstrate the performance of the criterion are included.