Generalized conditionnal maximum likelihood estimators in the large sample regime
Abstract
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 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 where several independent observations of the same individual signals are available, which are allowed to perform a Gaussian random walk between observations. In the proposed generalized CSM, the parameters are connected with both the expectation value and the covariance matrix, which is a significant change in comparison with the usual CSM. Even if the batch form of the associated generalized conditional maximum likelihood estimators (GCMLEs) can be easily exhibited, it becomes uncom-putable as the number of observations increases. As a main contribution , we introduce a recursive form of GCMLEs which allows to explore, by Monte-Carlo simulations, their asymptotic performance in terms of mean-squared error. We exhibit non consistent GMLEs when the number of observations tends to infinity, which highlights the consequence of combining (even slightly) dependent observations .
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