*2.2. AIS Signal Power Simulation*

The AIS signal power calculation formula is shown in Equation (5):

$$P = P\_t + G\_t + G\_r - L\_1 - L \tag{5}$$

where *Pt* is the transmission power of the AIS system, which is 41 dBm. *Gt* is the transmit antenna gain, *Gr* is the receiving antenna gain, *L* is the propagation loss of AIS in an atmospheric environment, and *L*1 is the cable transmission loss of AIS receiving equipment.

The propagation loss of the AIS signal in an atmospheric environment was obtained using the parabolic equation method [23]. Parabolic equations are divided into the narrowangle parabolic equation and wide-angle parabolic equation. We employed the narrowangle parabolic equation, suitable for the calculation of radio wave propagation with an elevation angle of less than 10 degrees. The expression of the narrow-angle parabolic equation is shown in Equation (6).

$$\frac{\partial^2 u(\mathbf{x}, z)}{\partial z^2} + 2ik \frac{\partial u(\mathbf{x}, z)}{\partial \mathbf{x}} + k^2 (n^2(\mathbf{x}, z) - 1)u(\mathbf{x}, z) = 0 \tag{6}$$

where *<sup>u</sup>*(*<sup>x</sup>*, *z*) is the component of the electric or magnetic field, *k*0 is the wave number, and *<sup>n</sup>*(*<sup>x</sup>*, *z*) is the atmospheric refractive index at different distances and heights. The Split-Step Fourier Transform (SSFT) method is the main method for solving parabolic equations [24]. The SSFT solution of the narrow-angle parabolic equation is shown in Equation (7) [23].

$$u(x+\Delta x, z) = e^{\frac{ik(w^2-1)\Delta x}{2}} \Im^{-1} \left\{ e^{\frac{-i\pi^2 p^2 \Delta x}{2k}} \Im u(x, z) \right\} \tag{7}$$

where *αe* is the radius of the Earth, *p* is the transform domain variable, and −<sup>1</sup> are Fourier transform and inverse transform respectively. The equation of AIS signal path propagation loss obtained from Equation (8) is:

$$L = 20 \text{lg}f + 10 \text{lg}r - 20 \text{lg}|u(x, z)| - 27.6\tag{8}$$

where *L* is propagation loss, *f* is AIS signal frequency, and *r* is the propagation distance.

### *2.3. AIS Signal Receiving Test*

In June 2020, the China Research Institute of Radiowave Propagation carried out an AIS signal receiving test in the coastal area of Nantong, China. AIS signal-receiving equipment are often used to receive AIS signals in coastal areas and to collect meteorological sounding data in the test area. The sounding data were obtained twice a day at 08:00 and 20:00 Beijing time respectively. The test area is shown in Figure 3. Parameters of AIS signal-receiving equipment are shown in Table 1.

**Figure 3.** AIS signal receiving test position.

**Table 1.** Parameters of AIS signal-receiving equipment.


We selected three typical atmospheric environments: no atmospheric duct, surface duct, and elevated duct. The corresponding atmospheric duct profile is illustrated in Figure 4.

AIS signal data were selected at the same time as sounding data, and the signal position and power distribution are shown in Figure 5. The x-axis is the longitude direction distance, the y-axis is the latitude direction distance, and the AIS signal-receiving equipment is located at point 0 of the y-axis. When there is no atmospheric duct, the AIS signal is distributed within 100 km as seen in Figure 5. When the surface duct appeared, the maximum distance of the AIS signal was over 500 km, and the signal power was strong. The signal power beyond 100 km was about −80 dBm. When the elevated duct appeared, the AIS signal was distributed within 200 km, and the signal power was weak (about −100 dBm).

Using sounding data and Equation (5), the AIS signal power variation with distance was determined in three atmospheric environments and was compared with the actual received AIS signal power, as shown in Figure 6. The red dotted line shows the sensitivity of AIS signal-receiving equipment (−112 dBm); the solid green line is the simulated AIS signal power variation curve with distance; the blue points are the distribution of measured AIS signal power with distance. Figure 6 illustrates that the AIS simulation results are in good agreemen<sup>t</sup> with the measured data, thereby revealing the effectiveness of the AIS signal power simulation algorithm used in our study.

**Figure 4.** Atmospheric duct profile calculated by sounding data.

**Figure 5.** AIS signal distribution in different atmospheric ducts.

**Figure 6.** Comparison between simulated AIS signal power and measured AIS signal power.

From the above analysis, we observed obvious differences in AIS signal distribution in different atmospheric environments, mainly as follows:


These show that AIS signals can be used to invert atmospheric ducts, and the types of atmospheric ducts can be distinguished since surface and elevated duct have different influences on AIS.

### **3. Modeling of Duct Parameters Classifying-Inversion Model**

In this section, we introduced two artificial intelligence methods: genetic algorithm (GA) and DNN, as well as the modeling process of the classifying-inversion model of atmospheric duct parameters using AIS data.

### *3.1. Artificial Intelligence Method for Atmospheric Duct Inversion*

From previous studies, the main artificial intelligence methods used for atmospheric duct parameter inversion were GA and DNN. DNN is a deep learning network structure. GA is designed according to the evolution law of organisms in nature, and the optimal solution is searched by simulating the natural evolution process. In this algorithm, the problem-solving process is transformed into the evolutionary process of biological chromosome genes through mathematical means and computer simulation. GA has been widely used in combinatorial optimization, machine-learning, signal processing, adaptive control,

and artificial life [25]. GA consists of three steps: selection, crossover, and mutation. The GA flow chart is shown in Figure 7.

### **Figure 7.** GA flow chart.

DNN is composed of input, hidden, and output layers. The hidden layer can have multiple layers that enhance the expression ability of DNN. The neurons in the output layer have multiple outputs that flexibly apply to classification regression, dimensionality reduction, and clustering. The schematic diagram of DNN is shown in Figure 8. The DNN layer is fully connected with the other layers, and any neuron in the *i* layer must be connected with a neuron in the *i* + 1 layer.

**Figure 8.** The schematic diagram of DNN.

### *3.2. Classifying-Inversion Flow of Atmospheric Duct*

In this study, we employed the idea of "classification before inversion" for atmospheric duct parameters inversion. The first step was to establish a classification model of atmospheric duct, use the received AIS signal to judge the occurrence of atmospheric ducts, and distinguish the types of atmospheric duct occurrence. Secondly, the surface duct parameter inversion model and the elevated duct parameter inversion model were established respectively. The flow chart of atmospheric duct Classifying-inversion model is shown in Figure 9.

**Figure 9.** Flow chart of atmospheric duct Classifying-inversion model.

The atmospheric duct classification model adopted DNN, and the atmospheric duct parameters inversion model adopted GA and DNN respectively, and two classifyinginversion models were established as Model-1 and Model-2. In addition, we used GA to establish the traditional atmospheric duct inversion model (Model-3) and compared it with the aforementioned models. The model information is illustrated in Table 2.

**Table 2.** The model information.

