Exact and closed-form CRLBS for high-order kinematic parameters estimation using LFM coherent pulse train

In radar signal processing, the detection and parameter estimation of high-speed maneuvering targets, which often utilize a coherent pulse train signal with linear frequency modulation, have been receiving increasing attention. Fundamentally and significantly, the Cramer-Rao lower bound (CRLB), as a cornerstone for evaluating the estimation performance of high-order kinematic parameters, has been derived and investigated here. In this paper, a 2-D echo signal model expressed in the fast-frequency and slow-time domains is adopted. The scaled orthogonal Legendre polynomials are deliberately introduced to solve the inverse problem of the Fisher information matrix, and then, a linear mapping relationship between different polynomial parameters can be used to obtain the analytical CRLB expressions. The main contributions included are: 1) the CRLBs, which are exact and closed form, have been extended to arbitrary motion model orders and reference time instants; 2) the influences of the motion model order, the reference time instant, as well as the radar parameters on the CRLBs are exploited comprehensively; and 3) some specific cases, including four low-order motion models and two preferred reference times, are also presented to better demonstrate the CRLB performance relationships. It highlights the fact that the reference time instant corresponding to the middle of the pulse train is a reasonable and compromised choice for parameter estimation, although it is not necessarily optimal for the kinematic parameters of all models and orders. The above research results are illustrated with numerical simulations and further verified using the maximum likelihood estimation method combined with Monte Carlo experiments.