# Maritime Over the Horizon Sensor Integration:
## 4 Track Modeling Process  
Since EEZ monitoring is our goal, vessels which are the most interesting to us are vessels used for the transportation of goods, such as various types of cargo vessels and tankers. The typical characteristics of these vessels are:  
* Most are very large and their length is often more than 100 m, while their displacement is usually more than 50,000 DWTs. * The top speed seldom exceeds 25 knots, while the usual cruising speed ranges from 10 to 20 knots (sometimes even less than that). * Most of the time they are traveling along a straight line, and when they make turns they do so slowly and in a wide arc. It is clear that the vessels of our interest are easy to track. On the other hand, before the vessels can be tracked at all, the radar tracks need to be fused into fusion tracks. Since the positions of two radar tracks originating from the same vessel may differ significantly, while the actual vessel's position is often somewhere between them, the fusion algorithm is based on the MMSE approach. Furthermore, in order to favor a radar track whose position best matches the actual vessel's position, the weighting factor is introduced into the fused track position calculations. This weighting factor is called the _confidence level (CL)_, and it represents the reliability of radar data and takes values ranging between 0 and 1. The confidence level for each radar track is calculated with the following equation:  
\[CL=\frac{CL_{smr}+CL_{mg}+CL_{c}}{3} \tag{1}\]  
Figure 3: 2 of the data fusion algorithm. where \(CL_{SNR}\) represents the confidence level based on the signal to noise ratio of the target's detection and is calculated in the following manner:  
\[CL_{SNR}=\left\{ \begin{array}{cc}\frac{(SNR-10)}{50},\ SNR<60\ dB\\ 1,\ SNR>60\ dB\end{array} \right. \tag{2}\]  
It is worth noting that target will not be detected by a radar if its SNR is below 10 dB, while all of the targets with an \(SNR\) greater than 60 dB are considered stable. \(CL_{ang}\) represents the confidence level based on the relative angle between the target and the radar, and its values are stored in a table. \(CL_{c}\) represents the confidence level based on the consistency of the radar tracking, and it is calculated in the following manner:  
\[CL_{C}=0.05+\left\{ \begin{array}{cc}0.05,\ \text{until it reaches 1, if the track data are based on detection}\\ -0.1,\ \text{until it reaches 0, if the track data are based on prediction}\end{array} \right. \tag{3}\]  
At the end, the fused track (vessel) parameters (geographical latitude and longitude) are calculated as follows:  
\[Lat_{o}=\frac{\Sigma_{i=1}^{n}CL_{i}\cdot Lat_{o}(i)}{\Sigma_{j=1}^{n}CL_{j}}, \tag{4}\]  
\[Long_{o}=\frac{\Sigma_{i=1}^{n}CL_{i}\cdot Long_{o}(i)}{\Sigma_{j=1}^{n}CL_{j }}, \tag{5}\]  
where \(CL_{i}\), \(Lat_{o}(i)\) and \(Long_{o}(i)\) are the confidence level, latitude and longitude, respectively, reported by the \(ith\) radar; and \(n\) is the number of radars detecting the target, i.e., the total number of radar tracks that are needed to be fused into a single fused track. With the radar tracks fused into fused tracks, predictions for their next occurrences need to be made. Since the real vessel is traveling in a straight line most of the time, while radar detections and thus radar tracks \"fall\" around that line, we decided to keep the tracking process as simple as possible and rely on the algorithm based on a linear regression [26]. In particular, due to its robustness and good tolerance to outliers, the Thiel-Sen Estimator [27; 28] is used during the prediction calculations, in the following manner.