An improved semisoft threshold algorithm and its evaluation for denoising random walk in GNSS time series

Abstract

全球导航卫星定位系统在卫星定轨和信号质量等方面存在的差异性,造成GNSS时间序列中的随机漫步噪声十分复杂,已经成为制约GNSS技术在高精度变形监测行业领域深入应用的瓶颈。本文针对具有量级小、频率低、敏感性差等复杂特征的随机漫步噪声,提出了一种改进的半软阈值算法,通过引入可变因子形成了统一的半软阈值函数体系,提高了常规半软阈值对随机漫步噪声的适应性。为了验证和评估改进半软阈值算法的效果,利用MATLAB平台仿真生成有线性趋势项、年周期项和随机漫步噪声的GNSS时间序列,共1700个历元。结果表明,改进的半软阈值法较经典方法在信噪比和均方根误差上表现出更加优良的性能。自相关分析的评估结果表明,改进方法所消除的噪声与随机漫步噪声在形态特征上具有高度的一致性。谱指数分析评估结果,进一步从定量角度验证了改进方法对随机漫步噪声的特有适用性。 The differences in the satellite orbit and signal quality of global navigation satellite positioning system, resulting in the complexity of random walk noise in GNSS time series, has become a bottleneck problem in applying GNSS technology to the high precision deformation monitoring industry. For the complex characteristics of random walk noise, small magnitude, low frequency and low sensitivity, an improved semisoft threshold algorithm is presented. Then it forms a unified system of semisoft threshold function, so as to improve the adaptability of conventional semisoft threshold for random walk noise. In order to verify and evaluate the effect of improved semisoft threshold algorithm, MATLAB platform is used to generate a linear trend, periodic and random walk noise of the GNSS time series, a total of 1700 epochs. The results show that the improved semisoft threshold method is better than the classical method, and has better performance in the SNR and root mean square error. The evaluation results show that the morphological character has been performanced high consistency between the noise reduced by improved method with random walk noise. Further from the view of quantitative point, the evaluation results of spectral index analysis verify the applicability of the improved method for random walk noise.