航空重力傅里叶基追踪低通滤波方法研究

航空重力测量受到各种各样的高频噪声干扰，因此，低通滤波是提取重力信号的重要环节，其关键在于设计性能优越的低通滤波器.目前航空重力测量中常用FIR（Finite Impulse Response）低通滤波方法存在明显的滤波边缘效应，导致不得不舍弃边缘部分数据.针对这一问题，本文引入一种可以有效抑制边缘效应的新方法——傅里叶基追踪低通滤波方法（Fourier Basis Pursuit Low Pass Filter，FBPLPF）.该方法通过基追踪准则，选择全局优化，采用凸优化中的内点算法，将低频信号挤压在低频上，实现低频信号与高频信号的有效分离，能够有效减少有限时间序列造成的谱污染和谱泄漏.最后利用仿真实验和实测数据对该方法进行了验证，均方根误差（RMS）东西测线为0.7×10^-5 m·s^-2，南北测线为1.4×10^-5 m·s^-2，与FIR低通滤波方法舍弃边缘数据后统计的均方根误差相当.表明该方法可以不舍弃或者舍弃少量边缘数据，提高航空重力数据的利用率.

Research on the Fourier basis pursuit low pass filter for airborne gravity

There are various high frequency noises in the airborne gravimetry; therefore low pass filtering is an important part of airborne gravity signal extraction, and the most important step is to design a low pass filter with better performance. The finite impulse response low-pass filter is commonly used in the airborne gravity data processing, but the result of this method has obvious edge effect that leads to data rejection at both ends. In order to solve the problem, this paper introduced a method called Fourier basis pursuit low pass filter which can effectively suppress the edge effect. Using basis pursuit through global optimization and the so-called interior point algorithm, this method can effectively squeeze low frequency signals in low frequencies, thus separating low frequency and high frequency signals, and reducing spectral smearing and leakage caused by the finite size of the time series. This method is verified by simulation data and measured data. The root mean square errors of the east-west survey lines and the north-south survey lines are 0.7×10^-5 m·s^-2 and 1.4×10^-5 m·s^-2, respectively, which is equivalent to FIR low-pass filter method after abandoning edge data. Our results show that this method cannot abandon edge data or abandon a small amount of edge data, and thus greatly improve the utilization of the airborne gravity data.