**4. Test and Analysis**

*4.1. Dataset*

Three types of data were used for DNN modeling: AIS signal power data, atmospheric duct parameters data, and type data. Among them, AIS signal power data and type data were used to establish the atmospheric duct classification model. AIS signal power data and atmospheric duct parameters data were used to establish the inversion model of atmospheric duct parameters.

The data were mainly obtained from (1) AIS data receiving test introduced in Section 2.3, including the measured AIS power and atmospheric duct parameters calculated using sounding data; (2) simulation data, including the simulation data of atmospheric duct parameters and AIS power. The sample size was about 5900 groups; 800 groups of no atmospheric duct data, 1300 groups of surface duct data, and 3800 groups of elevated duct data.

We divided the dataset into training, verification, and test sets, among which the training set accounted for 80%, the verification set for 17.5%, and the test set for 2.5%.

### *4.2. Comparison of Atmospheric Duct Classification Results*

The accuracy of the atmospheric duct classification model was compared using the test set data, and the results are shown in Figure 10. In Figure 10, the red asterisk indicated the type of atmospheric duct in the test set (0 indicates no duct; 1 indicates a surface duct; 2 indicates elevated duct), and the blue circle indicated the prediction result of the model. The prediction accuracy of the classification model attained 97%.

**Figure 10.** Comparison of atmospheric duct classification results.

From Figure 10, the classification of the surface duct was correct, because when the surface duct appeared, AIS signal power increased. The wrong samples mainly occurred when there was either no duct or an elevated duct. When the elevated duct strength was relatively small, it exerted little influence on the AIS signal, similar to that without an atmospheric duct.

### *4.3. Comparison of Inversion Results of Surface Duct Parameters*

We selected three surface duct samples and used Model-1, Model-2, and Model-3 to invert the surface duct parameters. The inversion results are shown in Table 5. The bold figures in the table are the inversion results with the smallest error from the true value.

From Table 5, the inversion results of the atmospheric duct inversion models (Model-1 and Model-2) established using the classifying-inversion idea proposed in our study are much closer to the true values than those of the traditional inversion model (Model-3). Especially for Sample 1 and Sample 2, the inversion results of the traditional model are quite different from the true values.


**Table 5.** Inversion results of surface duct parameters.

The bold are the closest to the true value

### *4.4. Comparison of Inversion Results of Elevated Duct Parameters*

We selected three elevated duct samples and used Model-1, Model-2, and Model-3 to invert the parameters. The inversion results are shown in Table 6. The bold part in the table is the inversion result with the smallest error from the true value.


**Table 6.** Inversion results of elevated duct parameters.

The bold are the closest to the true value

Table 6 illustrates that the inversion results of the traditional method (Model-3) have a big deviation from the true value, similar to the surface duct inversion result. In the model established in this paper, the error between the result of Model-1 inversion and the real value was smaller. For example, consider Sample 2 with a comparison diagram of the atmospheric duct profile illustrated in Figure 11. The red line is the true value calculated by sounding data, the blue line is the inversion result by Model-1, and the green line is the inversion result by Model-2. Model-1 inversion of atmospheric duct layer height was consistent with the true value, while Model-2 inversion of atmospheric duct layer height was lower than the true value.

Figure 12 is a comparison diagram of AIS signal power. The black asterisks are the measured AIS signals' power, the red line is the AIS signal power distribution determined from the sounding data, the blue line is the AIS signal power distribution obtained using Model-1 inversion results, and the green line is the AIS signal power distribution determined using Model-2 inversion results. We observed that the AIS signal power distribution obtained using Model-1 was closer to the actual AIS signal power distribution than Model-2 in the range of 80–200 km (the range affected by atmospheric ducts).

**Figure 11.** Comparison of atmospheric duct profiles.

**Figure 12.** Comparison diagram of AIS signal power.
