Irregular Micromotion Period Measurement: Reentry Boosters as a Case Study

This work introduces the concept of irregular micromotion for the first time and proposes the first effective irregular micro-Doppler (m-D) period measurement using short-time similarity statistics and a Transformer-based neural network. The m-D period is one of the most important m-D features because it not only quantitatively depicts space targets’ motion patterns, but also serves as a prior basis for measuring many other parameters. In order to demonstrate the irregular m-D phenomenon, a dynamic model of reentry rocket boosters is built using the theory of viscous flow around a slender body, and analysis of reentry booster under radar observation is carried out using electromagnetic calculation simulation. The proposed m-D period estimator utilizes a typical two-stage processing method, including a nonstationary signal processing technique and transformer-based network. In the first stage, a short-time similarity matrix maps an explicit correlation characteristic of the periodic pattern of irregular micromotion echo and is used as the input of the neural network. In the second stage, a neural network consisting of two separate period and periodicity predictors is proposed to accurately estimate the time-varying period of irregular micromotions. The short-time similarity matrix functions as a bottleneck bridging traditional nonstationary periodic modulated signal processing and flourishing deep learning-based feature representation, and helps predict the nonlinearly time-varying period out of short-time similarity matrices, triggering a breakthrough on traditional echo period estimation methods. By separating the two Transformers in the predictors and adding the loss of repetition count of irregular micromotions into the loss function, our method achieves a 23.3% decrease in period mean absolute error (MAE) and a 36.4% decrease in count MAE compared to the baseline. The performance of the network under different signal-to-noise ratios (SNRs) is also analyzed. Imaging experiments in the inverse-Radon (iRadon) domain using an estimated m-D period as prior are also carried out to show the necessity of the proposed method. This work has expanded m-D-based studies to a larger area with time-varying parameters, and thus, it is worth augmentations.