  We address the problem of structured covariance matrix estimation for radar
space-time adaptive processing (STAP). A priori knowledge of the interference
environment has been exploited in many previous works to enable accurate
estimators even when training is not generous. Specifically, recent work has
shown that employing practical constraints such as the rank of clutter subspace
and the condition number of disturbance covariance leads to powerful estimators
that have closed form solutions. While rank and the condition number are very
effective constraints, often practical non-idealities makes it difficult for
them to be known precisely using physical models. Therefore, we propose a
robust covariance estimation method for radar STAP via an expected likelihood
(EL) approach. We analyze covariance estimation algorithms under three cases of
imperfect constraints: 1) a rank constraint, 2) both rank and noise power
constraints, and 3) condition number constraint. In each case, we formulate
precise constraint determination as an optimization problem using the EL
criterion. For each of the three cases, we derive new analytical results which
allow for computationally efficient, practical ways of setting these
constraints. In particular, we prove formally that both the rank and condition
number as determined by the EL criterion are unique. Through experimental
results from a simulation model and the KASSPER data set, we show the estimator
with optimal constraints obtained by the EL approach outperforms state of the
art alternatives.
