# Study on Active Tracking of Underwater Acoustic Target Based on Deep Convolution Neural Network
## 3 Simulation and Verification of Real World Signal  
### Setting of Simulation Signal  
We use the bright spot echo model [27] to construct the echo signal of the active sonar, and preprocess the echo signal to generate a data set of the simulated target. The bright spot echo model is often used in the simulation of active sonar echo signals [28], which saves time and improves efficiency in technical verification. The transmitted signal will echo when it encounters the target. According to the target bright spot model theory, in the case of high frequency, the echo of a complex target is  
Figure 10: Time-frequency image of the signal to be identified, based on the Kalman filtering and calculating the filtered target state. formed by the superposition of several wavelets. Each wavelet can be regarded as a wave emitted from a certain scattering point, and this scattering point is a bright spot. It can be a real bright spot or an equivalent bright spot. The echo signal of a single bright spot target can be expressed as  
\[H\Big{(}\overset{\rightharpoonup}{r},w\Big{)}=A\Big{(}\overset{\rightharpoonup}{r},w \Big{)}\text{e}^{\text{i}(w\tau+\varphi)} \tag{18}\]  
In Formula (18), \(A\Big{(}\overset{\rightharpoonup}{r},w\Big{)}\) is the target scattering intensity factor, which is related to frequency, and narrowband signals can take the center frequency value. \(\tau\) is the delay factor that determined by the sound path \(\zeta\) of the equivalent echo center point relative to a reference point. \(\tau=2\zeta/c\), \(c\) is the sound speed. \(\varphi\) is the phase factor, which is the phase jump generated when the echo is formed. The underwater complex target echo can be regarded as the result of the superposition of several independent bright spot signals. When the number of target bright spot echoes is \(N\), the LFM signal is used as the transmit signal, and the total target echo signal \(S(t)\) after superposition can be expressed as,  
\[H\Big{(}\overset{\rightharpoonup}{r},w\Big{)}=\sum_{n=1}^{N}A_{n}\Big{(} \overset{\rightharpoonup}{r},w\Big{)}\text{e}^{\text{i}(w\tau_{n}+\varphi_{n})} \tag{19}\]  
The echo of the simulated target is composed of a set of three different parameters, \(A_{n},\tau_{n},\varphi_{n}(n=1\ldots N)\). The echo signal received by the receiving array of the active sonar, in addition to the echo and environmental noise reflected by the target, will also receive the scattered waves generated by the random scatterers in the ocean to the emitted acoustic signal and the seabed reverberation. In the simulation of this article, we ignored these effects. Therefore, when the signal is used as the transmission signal, the time-domain form of the target echo signal received by a single array element can be expressed as,  
\[S(t)=\sum_{i=1}^{P}A_{i}s(t-\tau_{i})\text{e}^{-\text{i}\varphi_{i}} \tag{20}\]  
Then the signal matrix received by the array with the number of elements \(M\) is  
\[Y(t)=[S_{1}(t),S_{2}(t),\ldots,S_{M}(t)] \tag{21}\]  
In the simulation experiment, we set up a simulated underwater acoustic environment and set Gaussian white noise as the background noise of the marine environment. Active sonar can only work normally and recognize the target when the difference between the received signal level and the background interference level is greater than or equal to the detection threshold of the device. In this article, we set the active sonar transmitting transducer and the receiving array at the same place, and the environmental noise is isotropic background interference. The SNR of the active sonar received signal is,  
\[DT=SL-2 TL+TS-(NL-DI) \tag{22}\]  
In Formula (22), \(SL\) is the emission sound source level, \(TL\) is the transmission loss from the transmitter to the target, \(TS\) is the target intensity of the target, the receiving directivity index of the receiving array is \(DI\), the detection threshold of the sonar processing device is \(DT\), the background interference is environmental noise, and its sound level is \(NL\) within the working bandwidth of the device.