Application of the Fornasini-Marchesini first model to data collected on a complex target model

This work describes the computation of scatterers that lay on the body of a real target which are depicted in radar images. A novelty of the approach is the target echoes collected by the radar are formulated into the first Fornasini-Marchesini (F-M) state space model [1] to compute poles that give rise to the scatterer locations in the two-dimensional (2-D) space. Singular value decomposition carried out on the data provides state matrices that capture the dynamics of the target. Furthermore, eigenvalues computed from the state transition matrices provide range and cross-range locations of the scatterers that exhibit the target silhouette in 2-D space. The maximum likelihood function is formulated with the state matrices to obtain an iterative expression for the Fisher information matrix (FIM) from which posterior Cramer-Rao bounds associated with the various scatterers are derived. Effectiveness of the 2-D state-space technique is tested on static range data collected on a complex conical target model; its accuracy to extract target length is judged and compared with the physical measurements. Validity of the proposed 2-D state-space technique and the Cramer-Rao bounds are demonstrated through data collected on the target model.