Joint mean and COvariance Matching Estimation Techniques: MCOMET

The EXtended Invariance Principle (EXIP) has been recently applied to the structured covariance estimation of a zero mean Gaussian vector [1–2]: the resulting method was named COMET (COvariance Matching Estimation Techniques) [3]. We present in this paper an asymptotically efficient Approximate Maximum Likelihood Method for the joint estimation of the structured mean and covariance of a Gaussian vector. We call the obtained criterion MCOMET (Mean and COvariance Matching Estimation Techniques). It is shown to be separable with respect to mean and covariance parameters and composed of the COMET criterion and a new additional term MMET. Moreover this criterion can be optimized in a computationally efficient way through the use of embedded estimators. It is finally applied to array processing problems.