During pulsar navigation, the high-frequency noise carried by the pulsar profile signal reduces the accuracy of the pulse TOA (Time of Arrival) estimation. At present, the main method to remove signal noise by using wavelet transform is to redesign the function of the threshold and level of wavelet transform. However, the signal-to-noise ratio and other indicators of the filtered signal need to be further optimised, so a more appropriate wavelet basis needs to be designed. This paper proposes a wavelet basis design method based on frequency domain analysis to improve the denoising effect of pulsar signals. This method first analyses the pulsar contour signal in the frequency domain and then designs a Crab pulsar wavelet basis (CPn, where n represents the wavelet basis length) based on its frequency domain characteristics. In order to improve the real-time performance of the algorithm, a wavelet lifting scheme is implemented. Through simulation, this method analyses the pulsar contour signal data at home and abroad. Results show the signal-to-noise ratio can be increased by 4 dB, the mean square error is reduced by 61% and the peak error is reduced by 45%. Therefore, this method has better filtering effect.

中文翻译：

---

基于脉冲星信号的小波基频域设计方法

在脉冲星导航过程中，脉冲星轮廓信号携带的高频噪声降低了脉冲TOA（到达时间）估计的准确性。目前，利用小波变换去除信号噪声的主要方法是重新设计小波变换的阈值和电平函数。但滤波后信号的信噪比等指标需要进一步优化，因此需要设计更合适的小波基。本文提出了一种基于频域分析的小波基设计方法，以提高脉冲星信号的去噪效果。该方法首先在频域分析脉冲星轮廓信号，然后根据其频域特性设计Crab脉冲星小波基（CPn，n代表小波基长）。为了提高算法的实时性，实现了小波提升方案。该方法通过仿真分析国内外脉冲星轮廓信号数据。结果表明，信噪比可提高4 dB，均方误差降低61%，峰值误差降低45%。因此，该方法具有较好的过滤效果。