A new kernel-based approach for spectral estimation

Abstract: The paper addresses the problem to estimate the power spectral density of an ARMA zero mean Gaussian process. We propose a kernel based maximum entropy spectral estimator. The latter searches the optimal spectrum over a class of high order autoregressive models while the penalty term induced by the kernel matrix promotes regularity and exponential decay to zero of the impulse response of the corresponding one-step ahead predictor. Moreover, the proposed method also provides a minimum phase spectral factor of the process. Numerical experiments showed the effectiveness of the proposed method.