Partitioning of radar signals in stationary and ground moving targets by use of low-rank and compressed sensing methods

The aim of this thesis is to develop an approach which evades the most fundamental short coming of space-time adaptive processing (STAP): its need for training data. STAP is the state-of-the-art approach for conducting ground moving target indication (GMTI). Among other things, an extensive amount of research was conducted in the recent decades to reduce its computational complexity or the required amount of training data. However, non has been done to avoid it completely. In doing so and using measurement data from the current cell under test (CUT) alone, most short comings can be avoided as there are: clutter residuals from not sufficiently suppressed clutter contributions and target masking or self-nulling. This is advantageous in case of heterogeneous busy environments e. g. urban areas. This work presents the first approach to do so for which compressive sensing (CS) and affine rank minimization (ARM) techniques are used. By exploiting the correlated nature of GMTI clutter signals a low rank matrix can be formed from the measurement matrix corresponding to the CUT. This is done by focusing the clutter ridge in the angle-Doppler domain a. k. a. radar scene. Moving targets sparsely present in the radar scene are invariant with respect to the focus operation i. e. they remain sparse. The focused radar scene therefore renders to be the sum of a low rank and a sparse matrix which can be separated by use of an compressed robust principal component analysis (CRPCA) approach. The aim after separation is the low rank matrix to contain all clutter contributions and the sparse matrix to hold all moving targets. As a prerequisite for this to work, however, the so called rank sparsity incoherence condition must be met. Among other things this means that the low rank matrix must not contain spiky entries. This is not fulfilled as the clutter ridge by its very nature is spiky. To mitigate this issue a model based projection filter is applied onto the measurement data as a preconditioning step. The required parameters of the model projection filter are estimated during the clutter focused operation. Depending on the quality of the estimated parameters, all clutter energy is suppressed in the preconditioning step resulting the low rank matrix to be empty. In case the preconditioning step is not able to suppress all clutter contributions, the clutter residuals are usually of non spiky nature allowing to apply the aforementioned CRPCA separation. In summary, this is a three step approach for which an auto-clutter focus (ACF) algorithm, a model based projection filter, and an CRPCA based separation model are presented in this work. With them it is possible to separate strictly static from moving targets. As such effects like internal clutter motion are not covered and are subject to future research. The approach is evaluated thoroughly by use of a simulation model. As mentioned before this work is based on CS and ARM techniques. Most standard methods from the literature, however, do not consider the practical needs of radar signal processing e. g. they suffer from restrictions to real numbers, slow convergence rate, low reconstruction performance, or knowledge of unknown parameters like the precise number of sparse entries or the exact rank of a low rank matrix. Therefore, various CS and ARM algorithms are combined and extended in this work to comprise a set of high performative CS, ARM, and CRPCA algorithms which do not suffer the aforementioned restrictions. In summary, the work presented here represents a completely new approach to solving the GMTI problem. Nevertheless, as GMTI renders to be a complex task further research is needed with regard to a practical application.