Adaptive Radar Detection in Heterogeneous Clutter Plus Thermal Noise via the Expectation-Maximization Algorithm.

This paper addresses adaptive radar detection of $N$ pulses coherently backscattered by a prospective target in heterogeneous disturbance. As customary $K \geq N$ range cells adjacent to the one under test are used for estimation purposes. The disturbance in each range cell is described by a non-Gaussian model based on a mixture of $L < K$ Gaussian distributions. Gaussian components are characterized by an unknown low-rank matrix plus thermal noise with unknown power level. We first derive a detector inspired by the generalized likelihood ratio test that adaptively estimates the statistical properties of the disturbance from the observed data. To overcome the intractability of the involved maximum-likelihood estimation problem, a suitable approximate strategy based on the expectation-maximization algorithm is developed. This also allows us to classify the cell under test by selecting the “maximum a posteriori Gaussian distribution” for the disturbance (under both hypotheses). Accordingly, a likelihood ratio test is also proposed. An extensive performance analysis, conducted on synthetic data as well as on two different experimental datasets (PhaseOne and IPIX for land and sea radar returns, respectively), shows that the proposed approaches outperform state-of-the-art competitors in terms of both detection capabilities and false alarms control.