On separating the information of slow-mode angular motion of projectile

The information on angular motion of projectile can be expressed by the Amplitude Modulation (AM) index of radar echo. In order to separate the information of slow-mode angular motion, a method based on Empirical Mode Decomposition (EMD) is proposed. Three issues are discussed in this article. First, the angular motion of projectile is approximated as a fast-mode circle superposing over that of the slow-mode according to the theory of exterior ballistics. Next, the characteristics of AM index that can represent the angular motion are discussed. Considering the effects of Discrete Fourier Transform (DFT) and the interference of noise, the index of AM is modeled as nonstationary time series in which the slow fluctuation corresponds to the slow-mode circular motion. Then an EMD-based separating method is suggested to obtain the index of the slow-mode motion. It includes two steps. The first step is to divide the index into a series of Intrinsic Mode Functions (IMFs) and the residual item. The second step is to reconstruct the index of the slow-mode motion with the components of the lower frequency IMFs and the residual by utilizing the prior knowledge about the difference in the periods. Compared with theoretical value and the result of stationary wavelet transform, as well as the in-flight experiment, the results show the validity and effectiveness.