Pseudo-Maximum Likelihood Estimation of ballistic missile precession frequency

Abstract

In order to estimate a ballistic missile precession frequency, which is an important feature parameter in ballistic target recognition, we firstly establish the dynamic Radar Cross Section (RCS) signal model for a conical ballistic missile warhead with precession motion. Scintillation which is an important factor that cannot be ignored in radar measurement is taken into account in the model establishment, and modeled either as a log-normal or chi-square multiplicative noise. The distribution of obtained RCS signal is non-Gaussian and cannot be obtained in closed-form. Hence, the exact Maximum Likelihood Estimation (MLE) of the pertinent parameter, the missile precession frequency, is untractable. In the paper, we propose three pseudo-MLE approaches to estimate the parameter of missile precession frequency. The first approach ignores the multiplicative noise in the measured RCS. The second approach ignores the additive noise (i.e., assuming the infinite signal-to-noise ratio (SNR)). The third approach enforces a Gaussian distribution on both additive and multiplicative noise components. The Cramér–Rao lower bound (CRLB) corresponding to the maximum SNR scenario is derived. Simulations indicate that accounting for the multiplicative noise in the estimation significantly improves estimation performance, and also show the validation and robustness of the proposed methods.