# PMT Fluorescence Signal Denoising Processing Based on Wavelet Transform and BP Neural Network
## 4 Temperature Drift of PMT
### Data Processing  
In the selection of algorithms, the commonly used Empirical Mode Decomposition (EMD) algorithm is first considered. However, the EMD algorithm still has many shortcomings in practical calculation and application, including mode mixing, endpoint effects, and screening iteration stopping standards. Among them, when there are intermittent phenomena caused by abnormal events (such as intermittent signals, pulse interference, and noise) in the signal, the decomposition results of EMD will exhibit mode aliasing. The occurrence of mode aliasing not only leads to false time-frequency distribution but also causes IMF to lose its physical meaning. The widely used Kalman Filter (KF) [35] is an earlier time-domain denoising algorithm, mainly applied in fields such as communication, navigation, sensor networks, etc., but it can only be applied to linear systems. The later proposed Extended Kalman Filter (EKF) has theoretical limitations that cannot be overcome by themselves, such as low first-order linearization approximation accuracy, the need to calculate Jacobian matrices, and the requirement for continuous differentiability of nonlinear functions. Secondly, EKF is sensitive to the selection of initial estimation and process noise. When there are complex situations such as model mismatch, measurement interference, measurement loss, measurement delay, or state mutation in the system, EKF filtering accuracy is poor, and numerical stability is poor. Although Particle Filters (PFs) are also suitable for nonlinear and non-Gaussian systems, their computational cost is high and increases with the increase in state dimensions. At the same time, a large number of particles are required to calculate the posterior distribution, and in high-dimensional state spaces, PF are more susceptible to problems such as insufficient sample size and particle degradation, leading to unstable estimation results. The limitation of its high computational complexity is also not suitable for long-term operation on platforms with limited computing and storage performance, such as embedded systems. The characteristic of an ELMAN neural network [36] is that the output of the hidden layer is delayed and stored by the receiving layer, which makes it sensitive to historical state data. The addition of internal feedback network enhances the network's ability to process dynamic information, thereby achieving the goal of dynamic modeling. In addition,  
Figure 11: Comparison of AD values before and after weighting. ELMAN neural networks can approximate any nonlinear mapping with arbitrary accuracy, without considering the specific form of external noise on the system. If the input and output data of the system are correct, the system can be modeled. However, due to the fact that the learning process of ELMAN neural networks is based on gradient descent, this may result in the network only being able to find local optimal solutions and unable to find global optimal solutions. BP neural networks [37; 38] are suitable for solving problems that traditional algorithms or computational methods find difficult to solve. A BP neural network is a mature nonlinear mapping method for solving real-world problems. In addition, it has the ability to classify any complex pattern and can solve XOR problems that simple sensors cannot solve. A BP neural network does not require mathematical relationships to determine the mapping relationship between input and output. It only imports input and output data into the training set, trains itself, finds exercises between the input and output, establishes a model, and finally imports input values into the model to obtain the latest expected output values. The transmission process of the BP neural network consists of two parts, namely forward transmission and backward transmission. In the forward transmission process, data are processed layer by layer from the entry layer to the hidden layer and, then, transferred to the output layer.