**1. Introduction**

The atmospheric duct is an abnormal phenomenon in the tropospheric atmosphere that includes evaporation, surface, and elevated ducts. Ducting occurs when a radio ray originating at the Earth's surface is sufficiently refracted so that it is either bent back toward the Earth's surface or travels in a path parallel to the Earth's surface. These types have different causes. Evaporation duct is caused by water surface evaporation, and it mainly appears over the ocean, with an occurrence of over 85% [1]. Surface and elevated ducts (low-altitude atmospheric ducts) are mainly caused by weather phenomena, such as radiation-inversion, sinking-inversion, and advection-inversion. The occurrence of offshore low-altitude atmospheric ducts is 20–60% [2]. The atmospheric duct has an important impact on radio wave propagation. Figure 1 illustrates the comparison of the distribution of electromagnetic wave propagation loss in a standard atmosphere and surface ducts. From the diagram, when the surface duct appears, the distribution of electromagnetic wave propagation loss changes significantly. Electromagnetic waves can propagate beyond the visualrangewithsmallpropagationloss,aneventcalledtheover-the-horizonphenomenon.

The atmospheric duct will cause the radar system to produce the detection blind area, the clutter echo enhancement, the target-positioning error increase, and other adverse effects, thereby affecting its performance [3]. Therefore, it is important to obtain the atmospheric duct parameters when evaluating the radar performance.

The acquisition methods of atmospheric duct parameters include direct detection and remote-sensing inversion. The direct detection method uses radiosondes or rocketsondes

**Citation:** Han, J.; Wu, J.; Zhang, L.; Wang, H.; Zhu, Q.; Zhang, C.; Zhao, H.; Zhang, S. A Classifying-Inversion Method of Offshore Atmospheric Duct Parameters Using AIS Data Based on Artificial Intelligence. *Remote Sens.* **2022**, *14*, 3197. https:// doi.org/10.3390/rs14133197

Academic Editor: MichaelJ. Newchurch

Received: 28 May 2022 Accepted: 30 June 2022 Published: 3 July 2022

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to measure the atmospheric duct parameters, though it is expensive and difficult to operate. However, remote-sensing inversion has a high spatial-temporal resolution and has gained grea<sup>t</sup> attention recently. Ground-based Global Navigation Satellite System (GNSS) occultation signal is one of the signal sources used for atmospheric remote-sensing [4,5]. Zuffada [6] realized that the use of ground-based occultation signal bending angles laid a theoretical foundation for the inversion of the atmospheric duct. Wang [7] proposed a method of retrieving atmospheric duct parameters using a ground-based GNSS occultation signal and carried out experimental verification. Due to the fixed number of GNSS, the number of occultation events received every day was limited (about 100 times) [7], which leads to atmospheric ducts often being missed.

**Figure 1.** Distribution diagram of radio wave propagation loss.

AIS system is a navigation aid system applied in maritime safety and communication between ships and shore, and between ships [8,9]. The International Maritime Organization stipulates that AIS systems should be installed on all international sailing ships of 300 tons and above, and all non-international sailing ships of 500 gross tons and above. Therefore, in offshore waters, there is a large amount of widely-distributed AIS information. E.R. Bruin [10] analyzed the influence of different atmospheric duct environments on AIS signals. Atmospheric ducts can increase the propagation distance of AIS signals. Zhang [11] discussed the propagation characteristics of AIS signals in different atmospheric duct environments and demonstrated that the low-altitude atmospheric duct (especially the surface duct) had a significant influence on AIS signals at sea. From previous observations, the AIS signal is affected by the atmospheric duct in the process of propagation and can be used to invert atmospheric duct parameters.

The inversion algorithm is an important aspect in the field of atmospheric duct remote sensing. The common inversion algorithm used for remote-sensing of atmospheric ducts was the global optimization algorithm, such as the genetic algorithm and particle swarm optimization [12]. Gerstoft [12] proposed a method for inverting atmospheric duct parameters using sea surface echo from the genetic algorithm called refraction-from-cluster (RFC) technology. In 2007, Yardim [13] proposed a GA-MC hybrid algorithm, which can ensure the inversion accuracy and improve the inversion speed. With the development of artificial intelligence technology, the deep-learning theory has been applied to the inversion of atmospheric duct parameters. Guo [14] outlined a method of inverting atmospheric duct parameters using deep-learning network and sea clutter that greatly improved the inversion speed of atmospheric duct parameters. Han [15] illustrated a method to predict the height of the evaporation duct using a recurrent neural network. Hilesit [16] demonstrated a method to characterize the parameters of the evaporation duct in the ocean boundary layer based on an artificial neural network. Han [17] outlined a cooperative inversion model of atmospheric duct parameters using ground-based GNSS occultation signals and a deep-learning network and established a weight loss function construction

method. Tepecik [18] demonstrated an atmospheric duct inversion method using a genetic algorithm and deep learning.

Wang [7] and Gerstoft [12] adopted a one-step inversion strategy and only one model is established to judge the type of atmospheric duct and invert the parameters of atmospheric duct. Hilaire [19] showed a two-step inversion strategy: the classification of atmospheric duct types, and the inversion of atmospheric duct parameters. This effectively improved the inversion accuracy of atmospheric duct parameters.

From previous findings, we adopted a classifying-inversion model of atmospheric duct parameters based on AIS signals including two parts: classification of duct type and inversion of duct parameters. Before the inversion of atmospheric duct parameters, the types of atmospheric ducts were classified and judged. This model has higher inversion accuracy than that of the traditional method.

The content of this manuscript is arranged as follows: In Section 2, using the AIS signal simulation algorithm and data of the AIS signal power, we deduced the influence of different atmospheric duct types on AIS signal power distribution. Section 3 introduces the modeling methods of the classifying-inversion model, including the modeling methods of the atmospheric duct classification model and duct parameters inversion model. Section 4 illustrates the analysis of test results. The conclusions are presented in Section 5.

### **2. The Effect of the Atmospheric Duct on the AIS Signal**

The atmospheric duct includes evaporation, surface, and elevated ducts. We focused on the effect of elevated and surface ducts on AIS signals as the evaporation duct has almost no influence on AIS signals [20]. In this part, AIS power simulation and measurement data were used to analyze the effect of different atmospheric duct types on AIS signals, necessary for modeling the atmospheric duct classifying-inversion model.
