A novel approach to time-varying spectral probability estimation

A robust method of spectral estimation is examined which uses a decision-directed empirical Bayes receiver to estimate the time-varying a priori probability of signal occurrence in a given bin of the FFT of a signal. The a priori probability of spectral content for each bin is modeled as a finite-state Markov chain and an exact, recursive, nonlinear least squares estimator is employed to estimate the current state of the Markov process, and consequently the marginal probability for each of the bins. A generalized Bayes likelihood ratio test (GLRT) is used as the detector which feeds decisions to the state estimator. The estimate of the states is used along with a Markov probability vector to generate estimates of the a priori probability for use in the GLRT. Receiver operating characteristic curves are generated to illustrate algorithm performance.