## 2 System Model
### Estimation of FSO PE with BIGRU-Attention Model  
#### 2.4.1 Estimating FSO-PE Using BiGRU-Attention Model  
The collimation requirements for airborne communication terminals are higher, with the increase in airborne laser communication distance. Large \(s_{1}\) can lead to large deviations from the laser beam. The application of the BiGRU-Attention neural network model in an FSO system can effectively solve the problem of light PE caused by UAV jitter. \(y_{FSO}\), PE, and outage probability are entered into the neural model as parameters corresponding to \(x_{1},\ x_{2}\) and \(x_{3}\), respectively.  
After the BiGRU-Attention layer, the BiGRU model extracts time-varying information for \(y_{FSO}\), PE, and outage probability. The attention mechanism assigns different attention weights to the three sequence parameters. Different weights can distinguish the importance level of different parameters and improve the accuracy of classification, hence effectively solving the problem in FSO.  
The BiGRU-Attention model is a bidirectional recursive neural model that simultaneously reads inputs from both ends of the \(y_{FSO}\), PE, and interrupts probability parameter time series. The \(y_{FSO}\) parameter is the optical signal power of the PD, which represents the signal quality of the free-space optical communication system. This parameter is obtained from the PD measurement on the relay node R. The PE parameter is the angle error between the beam at the transmitter and the receiver. This parameter can be measured by sensors on both the sending and receiving ends. The outage probability is estimated by calculating the number of interruptions in the free-space optical communication link in a certain period. BiGRU-Attention processes all three sequence parameters as inputs.  
The BiGRU-Attention model runs on the relay node R. Through a bidirectional mechanism, BiGRU-Attention can capture input parameter information and help extract the features of the entire parameter sequence. According to the bidirectional mechanism characteristics of BiGRU-Attention, it operates in the signal processing unit of the relay node. The signal processing unit of the relay node is connected to each module to obtain the measurement signal \(y_{FSO}\) of the photodetector, the error data PE pointing to the sensor, and the outage probability of the statistical unit. The signal processing unit has the function of processing time series signals and can run the BiGRU-Attention model. It connects to the three data sources mentioned above to obtain feature vectors.  
After obtaining the results of BiGRU-Attention, the signal processing unit can output the control signal, adjust the beam direction of the transmitter, and complete error correction. This can maximize the effectiveness of the network. This effectively solves the problem of PE in FSO communication systems. The attention mechanism network selects the most critical part of \(y_{FSO}\), PE and outage probability parameter time series by learning the attention distribution. This distribution indicates that the network should enhance the critical parameter feature information while decoding.  
The BiGRU-Attention model proposed in this paper enters the network through the input and output signals \(y_{FSO}\), PE and outage probability as parameters. The BiGRU network learns the parameter time series information. The attention network then emphasizes the importance of key parameter features. Finally, the BiGRU-Attention model effectively solves the pointing error problem in the FSO system.