Roll angular rate extraction based on modified spline-kernelled chirplet transform

Abstract

The roll angular rate is much crucial for the guidance and control of the projectile. Yet the high-speed rotation of the projectile brings severe challenges to the direct measurement of the roll angular rate. Nevertheless, the radial magnetometer signal is modulated by the high-speed rotation, thus the roll angular rate can be achieved by extracting the instantaneous frequency of the radial magnetometer signal. The objective of this study is to find out a precise instantaneous frequency extraction method to obtain an accurate roll angular rate. To reach this goal, a modified spline-kernelled chirplet transform (MSCT) algorithm is proposed in this paper. Due to the nonlinear frequency modulation characteristics of the radial magnetometer signal, the existing time-frequency analysis methods in literature cannot obtain an excellent energy concentration in the time-frequency plane, thereby leading to a terrible instantaneous frequency extraction accuracy. However, the MSCT can overcome the problem of bad energy concentration by replacing the short-time Fourier transform operator with the Chirp Z-transform operator based on the original spline-kernelled chirplet transform. The introduction of Chirp Z-transform can improve the construction accuracy of the transform kernel. Since the construction accuracy of the transform kernel determines the concentration of time-frequency distribution, the MSCT can obtain a more precise instantaneous frequency. The performance of the MSCT was evaluated by a series of numerical simulations, high-speed turntable experiments, and real flight tests. The evaluation results show that the MSCT has an excellent ability to process the nonlinear frequency modulation signal, and can accurately extract the roll angular rate for the high spinning projectiles.