Generalized Conditional Maximum Likelihood Estimators in the Large Sample Regime

In modern array processing or spectral analysis, mostly two different signal models are considered: the conditional signal model (CSM) and the unconditional signal model. The discussed signal models are Gaussian and the signal sources parameters are connected either with the expectation value in the conditional case or with the covariance matrix in the unconditional one. We focus on the CSM resulting from several observations of partially coherent signal sources whose amplitudes undergo a Gaussian random walk between observations. In the proposed generalized CSM, the signal sources parameters become connected with both the expectation value and the covariance matrix. Even though an analytical expression of the associated generalized conditional maximum likelihood estimators (GCM-LEs) can be easily exhibited, it does not allow computation of GCMLEs in the large sample regime. As a main contribution, we introduce a recursive form of the GCMLEs which allows their computation whatever the number of observations combined. This recursive form paves the way to assess the effect of partially coherent amplitudes on GCMLEs mean-squared error in the large sample regime. Interestingly, we exhibit non consistent GMLEs in the large sample regime.