Deterministic ML estimation for unknown numbers of signals

The knowledge about the number of signals plays a crucial role in array processing. The performance of most direction finding algorithms relies strongly on a correctly specified number of signals. When the number of signals is unknown, conventional approaches apply information theoretic criteria or multiple tests to estimate the number of signals and parameters of interest simultaneously. These methods usually compute ML estimates for a hierarchy of nested models. The total computational complexity is significantly higher than the standard ML procedure. In this contribution, we develop a novel ML approach that computes ML estimates only for the maximal hypothesized number of signals. Furthermore, we introduce a multiple hypothesis test to identify relevant components that are associated with the true DOA parameters. Numerical experiments show that the proposed method provides comparable estimation accuracy as the standard ML method does.