A Hybrid Empirical–Neural Model for HFSWR False Alarm Reduction Caused by Meteo-Tsunami-Like Phenomena

Abstract

The meteo-tsunami as an atmospheric phenomenon is still being researched, and its effects beyond physical ones (destruction if they hit the shore) are yet to be fully classified. One such effect is an increase in false alarm occurrence in high frequency surface wave radar (HFSWR) systems used for vessel traffic surveillance and control. Unfortunately, this effect is characterized by high-dimensional and highly nonlinear functional dependencies that cannot be described by closed-form mathematical equations. Since an artificial neural network is a highly parallelized distributed architecture with a fast flow of signals from input to output designed not to execute a predefined set of commands, but to “learn” dependencies during the training process and to apply that knowledge to solve unknown, but similar problems, it is a natural solution to the presented problem. Hybrid empirical–neural model-based probabilistic neural networks (PNN) used in this research proved to be quite capable of recognizing when an increase in false alarms can be expected based on the monitoring of atmospheric conditions in the HFSWR network coverage area and to eliminate them from the system, thus increasing the safety and security of all the actors in maritime traffic.

1. Introduction

Over-The-Horizon Radars based on Surface Waves in HF band (also known as High Frequency Surface Wave Radars—HFSWRs) are well known sensors used in oceanography [1,2,3,4]. They have the unique ability to provide constant data regarding sea waves’ height and direction [5], currents [6] and winds [7], at very long ranges, even in harsh environments (although it might affect nominal performances of the system). This makes them a sensor of choice for marine disaster warning [8]. Moreover, production and operating costs of HFSWRs are considerably lower than other sensors which can cover large areas beyond the horizon, namely dedicated oceanographic satellites [9,10].

The aforementioned benefits caught the attention of those interested in maritime surveillance and control of large water areas, namely Exclusive Economic Zones (EEZ). So, various parties across the globe started with the development and deployment of HFSWRs dedicated to maritime surveillance [11,12,13,14,15].

On the other hand, no system has only benefits with no drawbacks. A major drawback of HFSWRs is grater susceptibility to environmental noise, compared to microwave sensors, which are less dependent on environmental noise. Environmental noise dependance on geographical region of the World is summarized in [16]. The noise in the HF spectrum is the strongest in equatorial regions of the World and its effects on HFSWRs are discussed in [17]. Furthermore, HFSWRs are quite large systems requiring a land area which may spread several hundreds of meters directly on the shore, which brings challenges caused by coastal erosion [18]. Additionally, many equatorial regions are suffering from underdeveloped infrastructure, so there is a major concern about how to deliver data from HFSWRs to the control centers. One possible solution is via satellite network, where each HFSWR represents a sensor in the IoT service [19].

At the end, the sea itself or more precisely the sea state [20,21] and other meteorological factors represent major factors which may severely limit the effectiveness of HFSWRs. In this article, some meteorological events and their effects on HFSWR performance will be discussed, with an emphasis on the phenomenon called meteo-tsunami [22,23] and phenomena related to it. These phenomena and their influence on HFSWR are characterized by high-dimensional and highly nonlinear functional dependencies that cannot be described by closed-form mathematical equations and moreover are not yet fully known.

One of the approaches that can be used to solve such problems, where there is available data but insufficient explicit modeling knowledge, are artificial neural networks. Artificial neural networks are highly parallelized, and have a distributed architecture composed of tightly coupled small processing units—neurons [24,25,26]. They mimic the functions of human brains, and their architecture allows them to execute known functional dependencies, but rather than learning them explicitly, it maps them based on a set of solved examples. After the successful completion of the learning process, the artificial neural network can provide solutions not only for the solved examples presented to it during training, but also for the examples that were not present during training. This ability allows artificial neural networks to model problems whose physical nature is not yet sufficiently known. One of these scenarios is the abovementioned problem of the dependence of the number of false HFSWR targets on the physical parameters describing strong atmospheric disturbances in the coverage area. The rest of the paper is organized as follows, in Section 2, various meteorological situations occurring at sea and the shore as well as their influence on the HFSWRs are discussed. In Section 3, a description of observed phenomena is given together with mechanisms which lead to their occurrence and the influence they have on HFSWRs. Section 4 proposes a solution, i.e., a hybrid empirical–neural model for false alarm reduction caused by phenomena similar to the meteo-tsunami, and detailed performance analysis is presented. The work is concluded in Section 5.

2. Analysis of HFSWR Network Performance in Various Meteorological Conditions

In this chapter, the HFSWR sensor network in meteorological conditions specific to the Gulf of Guinea will be analyzed. These meteorological conditions could be classified as follows:

• Clear weather, without or with light winds, both at the HFSWR sites and on the open sea, the so-called “Calm Sea”;
• Clear weather at the HFSWR sites, but with strong winds on the open sea;
• Stormy weather (heavy rain and wind) at the HFSWR sites, which partially covers the radar observation zone;
• Severe meteorological disturbances that create conditions similar to meteo-tsunamis, and meteo-tsunamis.

It should be noted that the HFSWR network covers an area of over 100,000 square kilometers, with the HFSWR sites being separated by almost 100 km. So, it is almost impossible to have identical meteorological conditions simultaneously over the entire area. In practice, it most often happens that a combination of the abovementioned meteorological conditions occurs in the observation zone.

2.1. HFSWR Performances in the Event of “Calm Sea”

These atmospheric conditions are characterized by clear and sunny weather, with low wind intensity. The effects that such weather conditions have on the operation of HFSWRs are practically negligible. The main reason lies in the fact that the weak wind, which characterizes such weather conditions, has very little effect on the sea surface by creating waves of low height. In such conditions, the sea state does not exceed 3 on the Douglas scale [27], and according to [28], there is no difficulty in wave propagation over the sea surface. Moreover, propagation may be slightly better in the case of a sea state between 1 and 3 than in the case of sea state 01. Of course, this improvement in the conditions for surface wave propagation is negligible and in practice it is assumed that surface wave propagation in sea states from 0 to 3 is practically constant.

The range-Doppler Map (RD Map) produced during the HFSWR signal processing shows that Bragg lines can be detected up to 300 km (Figure 1), i.e., oceanographic data can be collected to a distance of almost 300 km.

As for vessel detection, it is possible at ranges even beyond the nominal range of the radar2. Figure 2 shows one such example.

Finally, clear weather does not cause any difficulties in the operation of satellite links3 and there are no problems with communication between HFSWRs and the command center. So, data from HFSWRs will arrive on time and without delays to the command center.

2.2. HFSWR Performances Conditions When There Is a Strong Wind on the Open Sea, While the Weather Is Clear at the HFSWR Sites

Figure 3 shows a satellite image of a storm that affected part of the HFSWR network coverage area.

As can be seen from Figure 3, the storm did not affect the coast itself, but it did affect most of the HFSWR coverage area and caused an increase in wave height at sea. Under storm conditions, the sea surface becomes rough and irregular, which interferes with the propagation of surface radio waves that HFSWR relies on. This reduces how far the radar signal can travel, leading to a shorter detection range. On RD maps, this effect appears as shorter Bragg lines and increased background clutter, as can be seen from Figure 4.

Comparing Figure 4 and Figure 1, it can be seen that the length of the Bragg lines has decreased from almost 300 km to barely 210 km. The decrease in the oceanographic performance of the HFSWR leads to a decrease in vessel detection capabilities as well. Figure 5 shows the detection capabilities of the HFSWR network under the conditions described above.

In these meteorological conditions, the vessel detection capabilities of HFSWR are reduced to a range of about 150 km. Since the target whose data is shown in Figure 5 is at the edge of the current operational capabilities, the detections from which the track is created are not consistent and do not appear in every integration period, so the track is maintained on predictions, both those obtained during the process of target tracking by a single radar and during multiple radar data fusions. Please note that the detection files from the HFSWR are transferred to the command center at regular intervals, since there is no storm above the HFSWR sites.

It should be emphasized that in these environmental conditions, the number of false alarms detected by HFSWRs increase, but the majority can be successfully eliminated at the level of the algorithm for tracking a single radar. Although they are not present in Figure 5, this might be more of an exception than a rule.

2.3. Storm at HFSWR Sites, Which Partially Affects the Coverage Area

Figure 6 shows a satellite image of a storm that affected the HFSWR sites themselves, and to a lesser extent spread to the coverage area.

The storm affected the very coast where the HFSWR were installed, but most of the HFSWR coverage area was not affected. In such weather conditions, the range of the HFSWR will be reduced due to the increase in propagation losses, but this reduction is not as drastic as in the example in Section 2.2. On RD maps, this is also manifested as a reduced length of Bragg lines and an increase in background clutter, as can be seen from Figure 7.

Comparing Figure 7 and Figure 1, it can be seen that the length of the Bragg lines decreased from almost 300 km to about 250 km, but the decrease is not as drastic as in Figure 4 (210 km). Moreover, there is significantly less background noise compared to Figure 4. Naturally, decrease in oceanographic performance led to the decrease in vessel detection capabilities, compared to the case presented in Section 2.1. Figure 8 shows the detection capabilities of the HFSWR network in the conditions described above.

Figure 8 shows that the range of the HFSWRs is reduced to about 180 km. Since the target whose data is shown in Figure 8 is at the edge of the detection range, the detections from which the track is created are not consistent and do not appear in every integration period, so the track is maintained based on predictions.

It should be emphasized here that the detection files from the HFSWRs are not received at regular intervals, because satellite communication is very difficult due to heavy rain at the HFSWR sites. This adds another layer of complexity to the whole situation.

3. Meteo-Tsunamis and Their Effects on HFSWR Vessel Detection

3.1. A Short Explanation of Meteo-Tsunami Phenomenon

The phenomenon called “meteo-tsunami” is a special type of tsunami wave, caused by the activity of atmospheric phenomena, and unlike all other tsunamis, it does not move radially from the place of origin, but exclusively in the direction of the movement of the meteorological phenomenon that caused it. Meteorological tsunamis (or meteo-tsunamis) are always local events and can become energetic only due to multiple resonances, such as Proudman’s or Greenspan’s [22,30]. These waves are mainly associated with atmospheric gravity waves, pressure surges, the passage of atmospheric fronts, etc., which usually create barotropic sea waves in the open ocean and amplify them near the coast using special resonant mechanisms. With a sudden increase in air pressure, the sea level falls, and the sea surface reacts to this by creating waves. If the speed of the storm front along the coast is almost the same as the speed of the sea waves, the wave height can grow as if the wave is being driven by a pressure disturbance, since the sea surface is “pressed” multiple times.

A wave generated by storm fronts can grow via the above mechanism.

While everyday wind generated waves have a wavelength of up to 150 m and a relative height of 2 to 3 m, a tsunami in the deep ocean has a wavelength of about 200 km. Due to the huge wavelength, the wave can be shorter than 0.5 m. Therefore, a tsunami is difficult to detect in deep water, while a ship can pass over it without noticing it [31].

As a tsunami approaches the coast, the water becomes shallower, the wave compresses, and its speed decreases. Its wavelength decreases to less than 20 km, while its height increases enormously, creating a highly visible wave. It is to be expected that the tsunami will become more obvious with increasing wave height as the water depth decreases. It is important to emphasize that a meteo-tsunami can also form in shallower waters and then spread in the direction of deep waters. In this case, the wave is visible practically immediately after formation, and after moving into deep waters, its height decreases. It is important to note that regardless of the direction of spread of a meteo-tsunami, it is always caused by meteorological phenomena and cannot be sustained without them. In other words, after the cessation of the phenomenon that caused it, a meteo-tsunami is sustained by inertia for a short period of time, after which it disappears completely.

Some recent events illustrating these mechanisms are presented below.

On 1 November 2022, a sequence of low-pressure systems and embedded convective lines over the southwest UK/English Channel generated a meteo-tsunami recorded at multiple Class-A tide gauges (Port Isaac, St Mary’s, Newlyn, Plymouth, Totnes), with minute-scale (2–120 min) oscillations and wave heights up to ~0.3 m, superposed on storm-surge conditions [32]. On 19–20 June 2024, a sequence of rissagas struck the Balearic Islands; AEMET reported oscillations up to ~1.4 m at Ciutadella on 19 June, with local flooding reported around the harbor and at Puerto Alcúdia [33].

In the western Mediterranean, Spain’s meteorological service AEMET issued meteo-tsunami alerts for Menorca on 18 May 2025 and again on 23 July 2025, warning of rapid harbor-level oscillations (locally up to ~0.7 m) and strong currents consistent with resonant amplification in semi-enclosed basins [34].

3.2. Example of HFSWR Network Operation in Conditions of Severe Meteorological Phenomena Similar to Meteo-Tsunamis

In addition to causing great material damage and even loss of life, meteo-tsunamis and similar phenomena can cause a number of other problems. One of these problems is the occurrence of a large number of false alarms in marine monitoring systems based on HFSWRs. During the propagation of sea waves caused by a meteo-tsunami, or a similar phenomenon, multiple waves appear, which in some areas may have a height significantly different from the surrounding waves. These higher waves, from the perspective of the HFSWR, represent point reflectors, which move at speeds comparable to the speeds of vessels, and cannot be eliminated at all in the process of primary radar processing. This leads to an increase in the number of false alarms generated by the HFSWR. To make matters worse, since the wavelengths of these waves over the continental plate may be smaller than the radar resolution cell, it follows that the radar generates false plots that move at real speeds and are within the expected radius of the tracking algorithm. It is clear that the data association procedure within the tracking algorithm will recognize these plots as real targets and form tracks based on them. The end result can be seen in Figure 9.

From Figure 9, a large number of false tracks are clearly visible, which cannot be integrated with any automatic identification system (AIS)4 data, because they do not actually exist. Such an increase in the number of unidentified vessels can easily cause an alarm in the command center and trigger urgent action by the authorities.

3.3. Mechanism of Meteo-Tsunami Occurrence in Gulf of Guinea

The occurrence and intensity of meteo-tsunami-like waves over time are influenced by changes in the physical state of the atmosphere in the observed area. In order to demonstrate the connection between the change in the physical state of the atmosphere and the emergence, change in intensity and disappearance of waves that cause the detection of false targets in a certain time period, Figure 10, Figure 11, Figure 12 and Figure 13 show the changes in atmospheric temperature, wind gust speed and the number of false HFSWR targets, obtained by real-time measurements during the days in which the meteo-tsunami-like phenomena occurred. The temperature and wind gust speed measurements were carried out at a hydrometeorological station in the HFSWR network area of the Gulf of Guinea.

The measured data shown in Figure 10, Figure 11, Figure 12 and Figure 13 show that the dependence of the change in the number of false targets on the change in the physical parameters of the atmosphere is very complex and cannot be simply expressed analytically. However, a rough analysis of the measured data allows us to observe the following approximate regularities:

• Before the formation of the waves, there is a sudden drop in air temperature of 4 to 7 °C.
• Before the formation of the first waves, at the same time as the sudden change in air temperature, there is a sudden increase in wind speed from approximately 15–20 km/h to 50–60 or even more km/h.
• The development of the situation on the sea surface, as well as the increase in wave height, which is manifested by the appearance and gradual growth of the number of false HFSWR targets, begins with a time delay of about 30 min. This latency is explained by the inertia of the sea water mass and the need for the wind to transfer sufficient kinetic energy to the sea waves to reach the critical height required to generate false reflections.
• After reaching its maximum, the change in the number of false HFSWR targets approximately follows the trend of the change in wind gusts. At the same time, the air temperature increases towards the value before the meteo-tsunami like phenomenon occurrence.
• False targets disappear approximately when the wind calms down, and the wind gusts drop below 15–20 km/h and the air temperature increases by approximately 3 to 4 °C

In order to remove these non-existent vessel tracks and prevent false alarms, in the next chapter an empirical–neural model will be proposed that correctly recognizes these false tracks as products of phenomena similar to meteo-tsunamis and removes them from the system.

4. A Hybrid Empirical–Neural Model for False Alarm Reduction

The main task of the hybrid empirical–neural model for the reduction in false alarms is a real-time estimation of the number of false targets detected by the HFSWR based on the values of the physical parameters describing strong atmospheric disturbances, and to eliminate such targets from further tracking. The currently achieved version of the model presented in this paper takes into account the following parameters: air temperature (T), wind speed (v) and time of day (t). The model consists of three components:

• False Target Number Module Activation Function (FTN_MAF) module with artificial neural networks;
• Algorithm for updating the list of HFSWR targets to be deleted; and
• Process that performs the analysis and tracking of targets with the recording and further manipulation of targets that do not have confirmation from AIS.

Figure 14 shows the architecture of the hybrid empirical–neural model for the reduction in false alarms.

4.1. FTN_MAF Module

The main purpose of the FTN_MAF module with artificial neural networks, based on the real-time values of air temperature (T) and wind speed (v) obtained from the meteorological data acquisition subsystem connected to the HFSWR sensor-network meteorological station, and the time of day (t) obtained from the system clock, is to perform the following two key tasks:

• Detecting the meteorological condition immediately before the onset of an atmospheric disturbance and the time when such a condition occurs and when the appearance of false HFSWR targets caused by high sea waves is expected, as well as detecting the condition and time when the disturbance is over and when the appearance of false targets is no longer expected. This task is represented by the Module Activation Function (MAF) which has two states encoded by a high and low signal level. This function is in the period between the two abovementioned states at a high signal level, and at a low signal level outside of that time period. A high level of the MAF signal indicates to the process in the command center that is responsible for monitoring HFSWR targets that an atmospheric disturbance, similar to a meteo-tsunami, is in progress and that during that period, it must switch to a special operating mode that involves the detection and elimination of false HFSWR targets caused by high sea waves.
• The estimation of the number of false HFSWR targets caused by high sea waves in real time. This number of false targets is represented via the discrete False Target Number (FTN) output of the module.

The architecture of the FTN_MAF module is shown in Figure 15.

This module consists of two submodules: the MAF submodule and the FTN submodule. The MAF submodule is responsible for performing the first of the two tasks mentioned above, and it controls the MAF module output, while the FTN submodule is responsible for performing the second task and it controls the FTN module output. Both submodules use a separate trained artificial neural network of the same type to perform their task. The type of network used is PNN (Probabilistic Neural Network).

4.1.1. PNN (Probabilistic Neural Network)

The architecture of the Probabilistic Neural Network (PNN) [35,36,37] is shown in Figure 16. It consists of an input layer, a hidden layer, a class layer, and an output (decision) layer. The task of this neural network is to classify a signal sample represented by the vector of input variables x = [x₁, x₂, …, x_N] where N denotes the number of input variables, and to determine to which class the sample belongs among a predefined set of classes S = {1, 2, …, S}, where S is the total number of sample classes. The PNN performs a mapping of a set of input signal samples X = {x₁, x₂, …, x_P}, where P is the total number of samples, into a discrete set of class labels.

$$s=f_{PNN}\left(\mathbf{x}\right),\mathbf{x}\in \left\{{\mathbf{x}}_1,{\mathbf{x}}_2,\dots ,{\mathbf{x}}_P\right\},s\in \left\{1,2,\dots ,S\right\}$$

(1)

The input layer acts as a buffer that distributes the components of the input vector x to every neuron in the hidden layer.

The hidden layer contains the main information about the classes. Neurons in the hidden layer are grouped so that each class s (where s = 1, 2, …, S) has its own group of neurons. The number of neurons in each group Hₛ is determined during the training process and equals the number of training samples belonging to class s. The activation function of neurons in the hidden layer belonging to class s is Gaussian, so that their outputs are given by

$$h_i^{\left(s\right)}\left(\mathbf{x}\right)={\displaystyle \frac{1}{{\left(2\pi \right)}^{\frac{N}{2}}{\sigma }_d^N}}·e^{-{\displaystyle \frac{‖\mathbf{x}-{\mathbf{w}}_i^{\left(s\right)}‖}{2{\sigma }_d^2}}}$$

(2)

where the vector w_i^(s) of dimension N represents the weight vector (center of the activation function) of the i-th neuron in class s, and σ_d denotes the spread parameter (standard deviation) of the activation function.

The neurons in the class layer estimate the probability that a sample x belongs to class s. Each group of neurons of class s in the hidden layer corresponds to one neuron in the class layer. The output of the s-th neuron represents the estimated probability

$$p_s\left(\mathbf{x}\right)={\displaystyle \frac{1}{{\left(2\pi \right)}^{\frac{N}{2}}{\sigma }_d^N}}·{\displaystyle \frac{1}{H_s}}{\sum }_{i=1}^{H_s}{e}^{-{\displaystyle \frac{‖\mathbf{x}-{\mathbf{w}}_i^{\left(s\right)}‖}{2{\sigma }_d^2}}},s=1,2,\dots ,S$$

(3)

which is obtained using Parzen’s window technique [35].

The output (decision) layer contains a single neuron that determines the final class of the input sample according to Bayes’ decision rule [35,36]

$$s=\arg \underset{s}{\max } p_s\left(\mathbf{x}\right)$$

(4)

i.e., the sample is classified into the class with the highest estimated probability.

The internal representation of the Gaussian function and the spread parameter (denoted as σ) in the MATLAB 2023b [38] environment assumes that the value of the Gaussian function equal to one half of its maximum is reached for input values of ±σ. Therefore, the spread parameter σ used for creating a PNN in MATLAB is scaled with respect to the theoretical standard deviation σ_D according to $\sigma =\sqrt{-2\mathrm{l}\mathrm{n}\left(0.5\right)}·{\sigma }_D\approx 1.1774·{\sigma }_D$.

During network training, the number of neurons in the hidden and class layers is defined, and the weight vectors of the hidden neurons are set so that the network correctly classifies all samples from the training set. The spread parameter σ is not determined during training; it is predefined and strongly affects the generalization ability of the PNN. By repeating the training for different values of σ (typically in the range [0, 2]) and monitoring the root mean square error (RMSE) during testing on an independent dataset, the optimal spread parameter value can be selected to minimize the output error and maximize the generalization capability of the network.

4.1.2. MAF Submodule

The MAF submodule manages the Module Activation Function (MAF) signal, which in real time carries information about the time at which a state of strong atmospheric disturbances occurs in the HFSWR network coverage area, and when this state ceases. This submodule contains the following components:

• Differential block;
• PNN_MAF artificial neural network; and
• MAF generator.

The differential block has the task of determining in real time the increments of the air temperature and wind speed values between two time points whose time distance is equal to the data acquisition interval t_CLK (the period of the acquisition subsystem clock signal).

$$\begin{array}{c}\Delta T=T\left(t\right)-T\left(t-t_{CLK}\right)\\ \Delta v=v\left(t\right)-v\left(t-t_{CLK}\right)\end{array}$$

(5)

To calculate these increments, this block uses an input data buffer with a time shift (shift register—SR) in accordance with the clock t_CLK.

The PNN_MAF artificial neural network has the task of monitoring in real time the change in air temperature and wind speed in the observation zone of the HFSWR network and detecting the time of occurrence of strong atmospheric disturbances that can lead to a significant increase in false alarms in the HFSWR system. This network fully follows the classical PNN architecture presented in [35], with the input variable vector in this particular case being

x = [ΔT Δv t],

(6)

while the TRS output has two classes TRS = {1, 2}, where class 1 represents a low-level signal (inactive signal), while class 2 represents a high-level signal (trigger signal) that announces the occurrence of false alarms. This practically means that the PNN_MAF network performs the mapping

$$TRS=f_{PNN\text{\_}AFM}\left(\Delta T,\Delta v,t\right),\hspace{1em}TRS\in \left\{1,2\right\}$$

(7)

The MAF generator, upon receiving the trigger signal from the PNN_MAF network, raises the MAF signal to a high (active) level, which signals to the other parts of the monitoring system that a condition close to a meteo-tsunami is in progress and that during that period the system must switch to a special operating mode that involves the detection and elimination of false HFSWR targets caused by sea waves. This generator keeps the MAF signal at a high level until the fulfillment of the following condition. In the currently available version of the proposed model, the average wind speed and the average number of detected false targets in the last hour are checked, and if the condition where the average wind speed drops below 15 km/h and the average number of detected false targets drops below 1 is satisfied, than the MAF signal returns to a low (inactive) level.

4.1.3. FTN Submodule

The FTN submodule has the task of estimating the number of false targets caused by a meteorological phenomenon in the HFSWR network coverage zone, based on the air temperature and wind speed values which are read in real time from the meteorological station, as well as the current time. This submodule contains the following components:

• PNN_FTN artificial neural network; and
• SF (Smoothing Function) correction block.

The PNN_FTN artificial neural network has the task of estimating the number of false targets in the HFSWR system originating from abnormal sea waves in real time, by monitoring the air temperature and wind speed values in the HFSWR network coverage area. This network fully follows the PNN architecture presented in 4.1.1, except that the input vector in this particular case is

x = [T v t],

(8)

while the output s has S = MAX_FTN+1 classes S = {1, 2, …, MAX_FTN+1}, where the variable MAX_FTN represents the maximum number of false targets that the system can detect. This is because class 1 represents the situation when there is no false target, class 2 represents the situation when there is one false target, class 3 represents the situation when there are 2 false targets, and so on. This practically means that the PNN_FTN network performs the following mapping:

$$s=f_{PNN\_FTN}\left(T,v,t\right),s\in \left\{1,2,\dots ,MAX\_FTN+1\right\}$$

(9)

The SF (Smoothing Function) correction block has the task of mitigating and smoothing out large oscillations in the output of the PNN_FTN artificial neural network that can occur in the event of a misclassification of the input sample. This block takes into account the current value of the output of the PNN_FTN artificial neural network s(t), as well as the buffered values of the output of that network s(t − t_CLK) and s(t − 2t_CLK) at times t − t_CLK and t − 2t_CLK, respectively, to form a final estimate of the number of false HFSWR targets (FTN) at time t in the following way

$$\begin{array}{c}\mathrm{if}\hspace{0.33em}\left(s\left(t\right)>2s\left(t-t_{CLK}\right)\hspace{0.33em}\mathrm{or}\hspace{0.33em}s\left(t\right)<round\left(0.5s\left(t-t_{CLK}\right)\right)\right)\hspace{0.33em}\mathrm{and}\hspace{0.33em}abs\left(s\left(t\right)-s\left(t-t_{CLK}\right)\right)>1\hspace{0.33em}\\ \mathrm{t}\mathrm{h}\mathrm{e}\mathrm{n}FTN={\displaystyle \frac{s\left(t\right)+s\left(t-t_{CLK}\right)+s\left(t-2t_{CLK}\right)}{3}}\\ \end{array}$$

(10)

4.2. Algorithm for Updating the List of Targets That Need to Be Deleted

According to the proposed model, the process executed in the HFSWR network command center which performs HFSWR target tracking is upgraded with a special operating mode that includes additional functionalities related to the elimination of false HFSWR targets caused by strong atmospheric disturbances from further tracking, thereby significantly reducing false alarms in the system. The transition to the special operating mode is controlled by the MAF signal. Raising the MAF signal from a low to a high level indicates that the HFSWR target tracking process should transition to a special operating mode that should be maintained as long as this signal is at a high level. The transition of the MAF signal from a high to a low level indicates that the process should return to normal operating mode. During the special operating mode, the HFSWR target tracking process uses an algorithm to update the list of HFSWR targets to be deleted from the system in order to make a final decision on which targets should be deleted from the system and thus eliminate false alarms caused by the influence of strong atmospheric disturbances. The algorithm for updating the list of HFSWR targets to be deleted from the system in the operating mode that processes the occurrence of waves, like a meteorological tsunami, is shown in Figure 17. In each processing cycle, before executing the algorithm, the tracking process forms a preliminary list of targets—candidates for deletion from the system, which is composed of targets that do not have AIS confirmation and forwards it to the algorithm for processing.

Upon acceptance of the preliminary list, the HFSWR target list update algorithm records the list length L, i.e., the number of targets on the list that are candidates for deletion from the system, and compares this value with the estimated number of false targets FTN due to the action of meteo-tsunami-like waves, which it receives from the FTN_MAF module in each processing cycle. If the estimated number of false targets is greater than or equal to the length of the preliminary list (FTN ≥ L), then it can be argued with high probability that all targets in the list of candidates for deletion are in fact false targets originating from meteo-tsunami-like waves. In this case, all targets remain in the deletion list, confirming their deletion from the tracking system.

In the case where the estimated number of false targets is less than the length of the preliminary list (FTN < L), then it can be argued with high probability that in the candidate list for deletion from the system, there are approximately FTN false targets originating from the effects of a meteo-tsunami-like wave and approximately L-FTN targets that may or may not be false, but do not originate from the effects of a meteo-tsunami-like wave and should be excluded from the deletion list that is returned to the target tracking process. By excluding these targets from the deletion list, they are left in the system for further monitoring and resolution of their final status. Overall, in accordance with the selected triage criterion in the deletion list, FTN targets should be selected to remain on the list, thereby confirming their deletion from the system, and other L-FTN targets should be excluded from the deletion list, thus leaving them in the system for further monitoring. The mentioned triage criterion used in the currently achieved version of the proposed model is based on empirical experience gained during the operational usage of the HFSWR network, which relates to false targets caused by the action of weather-tsunami-like waves. This experience can be expressed through the following facts:

• False targets caused by weather-tsunami-like waves in the majority of cases have a course belonging to the range 120–240°. This is because tsunami-like waves, observed so far, move from the shore towards the open sea.
• If the time of the first target appearance is considered, newer targets not confirmed by AIS are more likely to be false targets caused by waves like a meteo-tsunami than older ones, because older ones are more likely to have appeared before the occurrence of the atmospheric phenomenon causing the waves.

In accordance with the above facts, the triage criterion used in the proposed model is given as follows:

• In the list of targets of the candidate for deletion, find all targets whose course belongs to the range 120–240°. These are TOS (Towards Open Sea) targets and let there be a total of K of them.
• If K = FTN, then TOS targets should be left on the target deletion list, and the rest should be removed from the deletion list.
• If K < FTN, then TOS targets and the latest FTN—K targets should be left on the target deletion list and the rest should be removed from the deletion list.
• If K > FTN, then the latest FTN from the TOS shall remain on the target deletion list, and the rest should be removed from the deletion list.

4.3. Development and Field Results

The development and testing of the prototype of this module was carried out in the MATLAB development environment. For its development and testing, the following data are used:

• Data on the change in air temperature and wind gust speed in real time, which were obtained from the hydrometeorological station of the OTH sensor network on days when a strong atmospheric disturbance occurred.
• Data on the change in the number of false targets in real time on the same days, which were obtained at the network command center.

4.3.1. Development and Testing of FTN Submodule

The key activity in the development of this submodule is the training and testing of the PNN_FTN neural network, which is presented in Section 4.1.2. In accordance with Equation (5), a training set was selected for training the PNN_FTN network, whose samples are of the format {[T v t], s}, s{1,2, … MAX_FTN+1} and which is formed by the union of all samples obtained from measurements on days 2, 3 and 4 (Figure 11, Figure 12 and Figure 13). Since measurements were performed on each day in the period from 5 to 15 h with a data acquisition period of 10 min, which is 61 samples per day, the total number of training samples was 3 * 61 = 183. To test the trained PNN_FTN network, a set of 61 samples of the same format as the training set were used, obtained by measurements under the same conditions on day 1, and which were not used during network training. Before starting the network training process, the MATLAB development environment independently determines the maximum number of classes into which the input samples are mapped based on the training samples. Accordingly, when training the PNN_FTN neural network, the maximum number of classes was 11, which allowed the detection of a maximum of 10 false HFSWR targets (MAX_FTN = 10).

The PNN_FTN neural network was trained with different values of the spread parameter [0.1–1.9] for each training session. After completing one training session, the training quality and the degree of generalization achieved by the trained network were quantified by testing it on the test set and calculating the root mean square error of the network output (RMSE_{PNN_FTN}) according to the expression:

$$RMS{E}_{PNN\text{\_}FTN}=\sqrt{{\displaystyle \frac{1}{Tu}}{\displaystyle \sum _{i=1}^{Tu}{(s_i^{(t)}-{\widehat{s}}_i^{(t)})}^2}}$$

(11)

where s_i^(t) represents the estimated number of false targets that the neural network gives at its output, while ${\widehat{s}}_i^{(t)}$ represents the desired output of the neural network (the exact value of the number of false targets) when the combination of input variables of the ith sample [T v t]i^(t) is present at the input. For the test set T1 consisting of samples obtained by measurements on day 1, the number of samples is Tu = 61.

Table 1. Dependence of the root mean square error of testing (RMSE_PNN__FTN) of the PNN_FTN neural network expressed in the number of targets on the selected value of the training spread parameter (σ) on test set T1.

σ	0.1	0.2	0.3	0.4	0.5	0.6	0.7	0.8	0.9	1.0
RMSEPNN_FTN	1.463	1.463	1.463	1.463	1.463	1.439	1.439	1.383	1.376	1.376
σ	1.1	1.2	1.3	1.4	1.5	1.6	1.7	1.8	1.9
RMSEPNN_FTN	1.376	1.376	1.376	1.351	1.351	1.351	1.351	1.351	1.357

shows the dependence of the mean square error of the PNN_FTN neural network (RMSE_{PNN_FTN}) on the selected value of the spread parameter (σ). From the group of trained networks that showed the smallest value of the mean square error of testing (RMSE_{PNN_FTN} = 1.351) for the realization of the FTN submodule, the PNN_FTN network trained at the value of the spread parameter σ = 1.5 was selected.

After installing the trained network in the FTN submodule, the FTN output of this submodule was tested on the same test set and the mean square error of the submodule output (RMSE_FTN) was calculated using

$$RMS{E}_{FTN}=\sqrt{{\displaystyle \frac{1}{Tu}}{\sum }_{i=1}^{Tu}({FTN}_i^{\left(t\right)}-tar{FTN}_i^{\left(t\right)}{)}^2}$$

(12)

where FTN_i^(t) represents the estimated number of false targets that the FTN submodule gives at its output after applying the smoothing function of the SF correction block to the output of the PNN_FTN neural network, while tarFTN_i^(t) represents the desired output of the FTN submodule (the exact value of the number of false targets). The root mean square error of the FTN output of this submodule was RMSE_FTN = 0.724, which indicates that by softening and smoothing the sudden jumps of the PNN_FTN neural network output by applying function (6), the error in estimating the number of false HFSWR targets was reduced.

Figure 18 shows a comparison of the output of the PNN_FTN neural network (s) (PNN network without SF correction block) and the output of the FTN submodule (FTN) (PNN network with correction block) with reference (correct) values on the test set whose samples belong to the set of measured results that were not used during training (day 1). It can be seen that the corrected output of the PNN_FTN neural network, which also represents the output of the entire FTN submodule (FTN), is closer to the reference values than the raw uncorrected output of the PNN_FTN neural network (s), which justifies the introduction of the SF correction block. It can also be seen that there is relatively good agreement of the output of the entire FTN submodule with the reference values, which justifies the use of the proposed PNN architecture and the FTN submodule architecture in the process of estimating the number of false targets in the HFSWR sensor network.

In order to compare the performance of the PNN_FTN neural network and the FTN submodule in predicting the number of false targets on a set of samples that were not used during training and on a set of samples that were used in the training process, the original testing set containing samples that were not used in the training process was replaced with a set containing samples obtained from measurements on day 3 (T3-Day 3, Figure 12) and that were used in the training process, and the network and submodule were retested. Due to the complexity of the analysis of the results and taking into account the practically unchanged behavior of the key parameters of interest for days 2–4, one day (day 3) was selected for conducting a detailed analysis. The comparative testing results are shown in

Table 2. Comparative presentation of the results of testing the PNN_FTN neural network (σ = 1.5) and FTN submodule on test sets T1-Day 1 and T3-Day 3.

Test Set	T1—Day 1	T3—Day 3
PNN_FTN: RMSEPNN_FTN	1.351	1.293
FTN submodule PNN_FTN + SF correction block: RMSEFTN	0.724	1.241

.

By analyzing the test results in Table 2, it can be seen that in both test sets, correcting the output of the PNN_FTN with the SF block gives better results in estimating the number of false targets than if this network were used alone, which justifies the use of the SF block in the FTN submodule, with this improvement being more pronounced on the test set T1-Day 1 than on the test set T3-Day 3.

Figure 19 shows a comparison of the output of the PNN_FTN (s) (PNN network without SF correction block) and the output of the FTN submodule (FTN) (PNN network with correction block) with reference (correct) values on the test set whose samples belong to the set of measured results used during training (T3-Day 3). It can be seen that the output of the PNN_FTN neural network (s) as well as the output of the FTN submodule (FTN) are close to the reference values, but that the coincidence of their estimated number of false targets with the reference values is not ideal, as would be expected at first, given that the samples from the test were used during training. The test can show that on the test set T3-Day 3, the matching of the PNN_FTN neural network output with the reference values would be ideal at values of the parameter spread of 0.530 and lower (the mean square error would be 0), but the testing results on the test set that did not contain the samples used in the training process, i.e., on the set T1-Day 1 (the mean square error would be 1.414 and higher), would deteriorate, which would mean that the generalization ability of the network would deteriorate. Insisting on too good a match of the neural network output with the reference values on the samples used during the network training can lead to the effect of overtraining the network, which reduces the generalization ability of the network, and this is not desired.

4.3.2. Development and Testing of MAF Submodule

The MAF submodule was developed in the MATLAB development environment. The key activity in the development of this submodule is the training and testing of the PNN_MAF neural network, which is presented in Section 4.1.2. In order to train this network, it was necessary to generate the desired trigger signals (TRS signals) that the PNN_MAF neural network should generate at its output after successful training, depending on the values of the samples fed to its input. The trained PNN_MAF neural network has the task of recognizing atmospheric conditions that lead to the occurrence of meteo-tsunami-like waves and to signal the occurrence of such conditions in real time with a trigger signal (a low-high-low signal level sequence where the high level lasts very briefly). Accordingly, by analyzing the measured data for days 1, 2, 3 and 4 (Figure 10, Figure 11, Figure 12 and Figure 13) and monitoring the temporal changes in air temperature and wind gusts in these data, the desired trigger signals for these days were generated and used in the training and testing processes of the PNN_MAF neural network (Figure 20, Figure 21, Figure 22 and Figure 23). When generating trigger signals, a low signal level was represented by the intensity “0” while a high level was represented by the intensity “10”.

In accordance with expression (3), a training set and a test set were formed for training and testing the PNN_MAF network, the samples of which are of the format {[ΔT Δv t], TRS}, TRS ∈ {1,2}. The values of the air temperature increase ΔT and the wind gust increase Δv were obtained by processing the measured data for air temperature (T) and wind gust (v) using a differential block. The values of the trigger signal class TRS were obtained by sampling the trigger signals from Figure 10, Figure 11, Figure 12 and Figure 13 with the same sampling step as for temperature and wind gust sampling, and if the sample had a low level (“0”) it belonged to class 1, and if it had a high level (“10”) it belonged to class 2.

The appearance of the desired (reference) trigger signal (TRS) that was used during the testing of the PNN_AFM neural network, generated based on the air temperature and wind gust values measured during day 1, is shown in the below figure.

For training the PNN_MAF network, a set was formed by processing the measured data for air temperature and wind gusts, and sampling the desired trigger signal for days 2, 3 and 4 (Figure 21, Figure 22 and Figure 23). Since measurements were performed on each day in the period from 5 to 15 h with a data acquisition period of 10 min, which is 61 samples per day, and since the sampling of the desired trigger signal was also with the same time step, the total number of samples for training was 3 × 61=183. For testing the PNN_MAF network, a set was formed by processing the measured data for air temperature and wind gusts and sampling the desired trigger signal for day 1 (Figure 19). Based on the above analysis of the sampling method, since it is only one day, the total number of samples for testing was 61. Also, based on the selection of samples, it can be seen that the test samples were not used in the training process of the neural network.

The training of the PNN_MAF neural network was performed at different values of the spread parameter from the range [0.1–1.9] for each training session. After completing one training session, the quantification of the quality of the training and the degree of generalization achieved by the trained network was performed by testing it on the test set and calculating the root mean square error of the network output (RMSE_{PNN_MAF}) according to the following expression:

$$RMS{E}_{PNN\_MAF}=\sqrt{{\displaystyle \frac{1}{Tu}}{\sum }_{i=1}^{Tu}({TRS}_i^{\left(t\right)}-{tarTRS^}_i^{\left(t\right)}{)}^2}$$

(13)

where TRS_i^(t) represents the value of the trigger signal level that the neural network provides at its output, while tarTRS_i^(t) represents the desired output of the neural network (the desired trigger signal level that the neural network should generate at its output) when the combination of input variables of the i-th sample [ΔT Δv t]_i^(t) is supplied to its input. For the test set Tdif₁—Day1 consisting of samples obtained by processing the measured data belonging to day 1 using the differential block, the number of samples is Tu = 61.

Table 3. Dependence of the root mean square error of testing (RMSE_{PNN_MAF}) of the PNN_MAF neural network expressed in the TRS signal level of the range [0, 10] on the selected value of the training parameter spread (σ) on the test set Tdif₁-Day 1.

σ	0.1	0.2	0.3	0.4	0.5	0.6	0.7	0.8	0.9	1.0
RMSEPNN_MAF	1.280	1.280	0	0	0	0	0	0	0	0
σ	1.1	1.2	1.3	1.4	1.5	1.6	1.7	1.8	1.9
RMSEPNN_MAF	0	0	0	0	0	0	0	0	0

shows the dependence of the mean square error of testing the PNN_MAF neural network (RMSE_{PNN_MAF}) on the selected value of the spread of the training parameter (σ). It can be seen that for a value of the spread parameter equal to 0.3 or greater, the value of the mean square error of testing is equal to 0 (RMSE_{PNN_MAF} = 0). This means that for these values of the spread parameter, the PNN_MAF neural network performs an ideal (infallible) classification of samples from the test set. From the group of trained networks that showed ideal classification, the PNN_MAF network trained at the spread parameter value σ = 1 was selected for the realization of the MAF submodule. This is explained by the fact that spread parameter values close to unity in most cases of classification problems have the potential to provide good generalization capabilities of the PNN neural network.

In order to compare the performance of the PNN_MAF neural network in generating a trigger signal on a set of samples that were not used during training and on a set of samples that were used in the training process, the original testing set containing samples that were not used in the training process was replaced with a set containing samples obtained by processing the measured results related to day 3 (Tdif₃-Day 3, Figure 22) and that were used in the training process, and the network was retested. The mean square error of the PNN_MAF neural network testing in this case was equal to zero, which means that the selected value of the spread parameter before training the network σ = 1, ensured that this network also showed ideal classification on the samples that were used during training the network.

Figure 24 shows a comparison of the output of the PNN_MAF neural network (TRS) with the reference trigger signal obtained by simulation on the test set whose samples were not used during network training (Tdif₁—Day1). Figure 25 shows a comparison of the output of the same network with the reference trigger signal obtained by simulation on the test set whose samples were used in network training (Tdif₃—Day3). In both cases, an ideal agreement of the output trigger signal with the reference one can be observed, which justifies the use of the differential block and the proposed PNN architecture in the process of generating the trigger signal.

The output from the PNN_MAF neural network (TRS) is fed to the input of the MAF generator, which is also implemented in the MATLAB development environment. As already explained in Section 4.1.1, the MAF generator, immediately upon identification of the “low level—high level—low level” sequence of the trigger signal sent by the PNN_MAF network, raises its MAF output (MAF signal) from low (“0”) to high (active) level (“5”), which signals to the other parts of the tracking system that a meteorological tsunami-like phenomenon is in progress and that during that period it must switch to a special operating mode that involves the detection and elimination of false HFSWR targets caused by high sea waves. This generator keeps the MAF signal at a high level until the conditions indicating that the meteo-tsunami has ceased are met, which is, as far as the currently achieved and implemented version of the proposed model is concerned, that the value of the average wind gust speed is less than 15 km/h and that detected false targets in the last hour is less than 1. Based on the conditions for the end of the atmospheric phenomenon, the fulfillment of which is checked by the average number of the MAF generator, it is clear that it was necessary to feed the BLC output of the BLC submodule to the MAF generator so that it would have information about the current estimate of the number of false targets in the OTH sensor network surveillance area at any moment. In accordance with the previously mentioned MAF generator architecture and the above-described method of its implementation, Figure 26 shows the temporal change in the MAF signal, which is one of the outputs of the BLC_MAF module and is sent to the process that analyzes and tracks HFSWR targets. This display was obtained by simulation on the test set Tdif₁—Day1, whose samples were not used in the training of the PNN_MAF neural network, and is given in parallel with the change in air temperature, wind gusts and the estimated number of false HFSWR targets on day 1. Figure 27 shows the temporal change in the MAF signal obtained by simulation on the test set Tdif₃—Day3, whose samples were used in the training of the PNN_MAF neural network, and is given in parallel with the change in air temperature, wind gusts and the estimated number of false OTH targets on day 3. Analyzing the time course of the MAF signal in both testing cases, it can be seen that the time period of its high (active) level (beginning of the period, duration of the period and end of the period) very well represents the time period of the presence of a meteorological tsunami-like phenomenon that causes the reading of false HFSWR targets and thus reliably switches the process that deals with the tracking of HFSWR targets to a special operating mode. This confirms that the choice of the FTN_MAF module architecture for the implementation of the prototype of the hybrid empirical–neural model for the reduction in false alarms was good.

5. Conclusions

Analyzing the presented results of the application of the hybrid empirical–neural model for the reduction in false alarms, it can be said that this model represents an effective alternative approach for solving the problem of false alarms because it offers a solution to this problem with a relatively small expenditure of hardware and software resources and the avoidance of complex mathematical calculations. This is because this model combines the existing empirical experience in tracking targets with HFSWR with the main advantages of using artificial neural networks. These advantages primarily relate to the ability of artificial neural networks to model problems whose physical nature is not yet sufficiently known (which is the case here) as well as the relative ease of developing and implementing appropriate neural structures into the model. By training PNN-type neural networks using measured values of meteorological parameters that characterize strong atmospheric disturbances (atmospheric temperature, wind gust speed, current weather), a prototype of the FTN-MAF module was developed, which is an integral part of the hybrid empirical–neural model. The results of testing the prototype of this module on measured values show that this module has the ability to estimate in real time, based on the values of the abovementioned meteorological parameters, while avoiding complex mathematical calculations, the beginning and end of atmospheric disturbances that cause the appearance of false HFSWR targets, as well as to estimate at any time, during the duration of these disturbances, the total number of false targets that should be eliminated from further monitoring. Since the training and testing of the artificial neural networks of the FTN-MAF module was performed on a relatively small number of training and testing samples, it cannot be considered that the required degree of generalization of the neural networks of this module has been achieved, which will guarantee its reliable operation in a real environment, so the implementation and operational use of the proposed model will have to wait for the acquisition of a larger set of samples that will more completely represent the problem being modeled. However, the presented results obtained by the prototype justify the use of artificial neural networks in solving the problem of recognizing and eliminating false HFSWR targets. They also show that the proposed model architecture has great potential to train its neural networks on a larger number of samples to obtain a model that is ready for implementation in the existing HFSWR sensor system and operational use, and that artificial neural networks of the PNN type can be a good choice in the efficient realization and implementation of the proposed model.