This paper proposes a heuristic singular spectrum analysis (SSA) approach to extract signals from suspended sediment concentration (SSC) time series contaminated by multiplicative noise, in which multiplicative noise is converted to approximate additive noise by multiplying with the signal estimate of the time series. Therefore both the signal and noise components need to be recursively estimated. Since the converted additive noise is heterogeneous, a weight factor is introduced according to the variance of additive noise. The proposed heuristic SSA approach is employed to process the SSC series in San Francisco Bay compared to the traditional SSA and homomorphic log-transformation SSA approach. By using our heuristic SSA approach, the first 10 principal components derived can capture 96.49% of the total variance with the fitting error of 6.17 mg/L, better than those derived by traditional SSA approach and homomorphic log-transformation SSA approach that catch 88.97% and 87.35% of the total variance with the fitting errors of 14.47 mg/L and 15.03 mg/L, respectively. Therefore, our heuristic SSA approach can extract more signals than traditional SSA and homomorphic log-transformation SSA approach. Furthermore, the results from the simulation cases show that all the mean root mean squared errors and mean absolute errors derived by our heuristic SSA are smaller than the traditional and homomorphic log-transformation SSA, which indicate that the extracted signals by heuristic SSA approach are much closer to the real signals than those by the other two approaches. Therefore it can be conclude that our heuristic SSA approach performs better in extracting signals from SSC time series contaminated with multiplicative noise.

中文翻译：

---

乘性噪声污染的悬浮泥沙浓度时间序列的启发式奇异谱分析方法

本文提出了一种启发式奇异频谱分析（SSA）方法，从受乘性噪声污染的悬浮泥沙浓度（SSC）时间序列中提取信号，其中乘以时间序列的信号估计值，将乘性噪声转换为近似加性噪声。因此，信号和噪声分量都需要递归估计。由于转换后的加性噪声​​是异质的，因此根据加性噪声的方差引入加权因子。与传统的SSA和同态对数转换SSA方法相比，所提出的启发式SSA方法用于处理旧金山湾的SSC系列。通过使用我们的启发式SSA方法，派生的前10个主成分可以捕获96.49％的总方差，而拟合误差为6。17 mg / L，优于传统SSA方法和同态对数变换SSA方法衍生的那些，分别捕获了总方差的88.97％和87.35％，拟合误差分别为14.47 mg / L和15.03 mg / L。因此，与传统的SSA和同态对数变换SSA方法相比，我们的启发式SSA方法可以提取更多的信号。此外，仿真案例的结果表明，我们的启发式SSA得出的所有均方根均方根误差和平均绝对误差均小于传统的同态对数变换SSA，这表明启发式SSA方法提取的信号非常多。比其他两种方法更接近真实信号。