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.

滚动角速率对于弹丸的制导和控制至关重要。然而弹丸的高速旋转给横滚角速率的直接测量带来了严峻的挑战。然而，径向磁力计信号被高速旋转调制，因此可以通过提取径向磁力计信号的瞬时频率来实现滚动角速率。本研究的目的是找出一种精确的瞬时频率提取方法，以获得准确的滚动角速率。为了达到这个目标，本文提出了一种改进的样条核chirplet变换（MSCT）算法。由于径向磁强计信号的非线性调频特性，现有文献中的时频分析方法无法在时频平面上获得极好的能量集中，从而导致瞬时频率提取精度很差。然而，MSCT 可以通过在原始样条核核 chirplet 变换的基础上用 Chirp Z 变换算子代替短时傅里叶变换算子来克服能量集中不良的问题。Chirp Z变换的引入可以提高变换核的构造精度。由于变换核的构造精度决定了时频分布的集中度，因此MSCT可以获得更精确的瞬时频率。MSCT的性能通过一系列数值模拟、高速转盘实验和实际飞行测试来评估。