2.1. Main functions

The primary function of the ECDIS is to contribute to safe navigation. More detailed functions given in the requirements are related mostly to navigational charts. According to these, the ECDIS should:

• • Be capable of displaying all chart information necessary for safe and efficient navigation;

• • Facilitate simple and reliable updating of the ENC;

• • Reduce the navigational workload in comparison to using a paper chart;

• • Provide appropriate alarms or indications with respect to the information displayed or malfunction of the equipment.

Display of the ENC should follow IMO and International Hydrographic Organization (IHO) standards. From the anti-collision point of view, it is important that requirements for displaying other navigational information are also given. These also include radar and AIS data.

2.2. Display of target data

Although the ECDIS is focused on presenting chart information, display of other navigational information for enhancing navigational safety is also allowed. The most important data included in the Resolution are radar and AIS data. According to IMO (2006), these data can be transferred from systems that are compliant with suitable IMO standards and added to the display. However, they should not degrade SENC information (standardised database with chart information) and should be clearly distinguishable from it. The possibility of removing radar/AIS data by a single operator action, if needed, should be ensured. No further requirements are stated.

Radar information transferred to the ECDIS can include both radar image and/or tracked target information. It is crucial that the added navigational information should use a common reference system with the SENC. The radar image and the position from the position sensor should both be adjusted automatically for antenna offset from the conning position.

It can be noticed while analysing the requirements for the ECDIS that they focus mostly on chart display. AIS and radar are only mentioned in reference to other IMO documents such as those of the International Electrotechnical Commission (IEC, 2008). In fact, the concept of integration presented in IEC (2008) assumes only target association and selection of one of the targets: radar or AIS. It can be seen that no advanced fusion algorithms are needed to fulfil these requirements, except harmonized criteria for the association. Nevertheless, presentation of integrated radar–AIS information on the ECDIS screen is commonly used and plays an important role in modern navigation.

4.1. Problems of association

Differences between tracking radar and AIS concepts cause tracks to be received from both systems, which, although describing the same target, are of a different nature. Therefore, it is not a trivial problem to properly associate radar and AIS tracks. The following main problems in the association process can be identified (Stateczny and Kazimierski, Reference Stateczny, Kazimierski and Rohling2013):

• • Lack of time synchronisation between measurements in both systems;

• • Various time intervals of measurements;

• • Different speeds and courses (dualism);

• • Lack of identification of radar targets;

• • Large differences in position accuracies;

• • Target representation – size of radar echo in relation to point AIS targets.

Most of these problems can be solved using methods presented in the literature (e.g. Kazimierski, Reference Kazimierski and Rohling2013), and their description is beyond the scope of this paper. However, it is worth mentioning that the values used for track fusion are already an approximation of data and not real measurements. Many of the problems are caused by inaccuracies in the radar target tracking methods briefly presented above.

In Kazimierski (Reference Kazimierski and Rohling2013), a three-step algorithm was proposed for radar–AIS data association. In this approach, three association criteria were proposed:

• • Position;

• • Movement vector;

• • History.

The first one is the most natural; however, it might happen that there is more than one target in the vicinity, so it is good to also check target movement. In addition, it may be necessary to confirm the association tendency in a period of time, thus, the criterion of history is also used.

The idea of association is to create a gate around the target data. The crucial task is then to determine a proper size of this gate. It has to be small enough to avoid false association, but large enough to include system errors. It can be said that a distance of three to four cables should be enough for position correlation (Stateczny and Kazimierski, Reference Stateczny, Kazimierski and Rohling2013), and the movement vector gate can be established based on IMO accuracy requirements for radar tracking.

4.2. Track fusion algorithms

When the tracks are received and associated, a process of track fusion begins. It is assumed that the state vector and covariance are known from both systems (radar and AIS) and that they describe the same target. Various algorithms for track fusion are presented in the literature (e.g. Gan and Harris, Reference Gan and Harris2001; Yang et al., Reference Yang, Cheng, Wei and Lu2006; Hill et al., Reference Hill, Sabol, Alfriend and Alfriend2010). From these, the most popular appear to be

• • Simple fusion;

• • With the use of cross-covariance.

In the simple fusion algorithm presented in, for example, Matzka and Altendorfer (Reference Matzka and Altendorfer2008) or Liggins et al. (Reference Liggins, Llinas and Hall2009), the fusion is a weighted average of elementary estimates (x), where the weights are computed directly from the covariance (P). For radar–AIS tracking of one target, the fusion equation has the form:

(1)$$x = \left( {P_r ^{ - 1} + P_a ^{ - 1}} \right)^{ - 1} \left( {P_r ^{ - 1} x_r + P_a ^{ - 1} x_a} \right),$$

with an error covariance matrix of the form

(2)$$P = \left( {P_r ^{ - 1} + P_a ^{ - 1}} \right)^{ - 1}. $$

The case of calculating fusion with cross-covariance is more complicated, and in a classical form, it requires more information from elementary filters. According to Matzka and Altendorfer (Reference Matzka and Altendorfer2008), the fusion for two sensors can be calculated as follows:

(3)$$x = x_a + W\left( {x_r - x_a} \right)$$

Where

(4)$$W = \left( {P_a -P_{ar}} \right)U_{ar} ^{ - 1} $$

(5)$$U_{ar} = P_a + P_r - P_{ar} -P_{ar} ^{ - 1} $$

and P _ar is the cross-covariance matrix, calculated recursively with the use of the Kalman Filter matrices of elementary filters. Such a solution is useless if only the estimated value and its covariance are known and no more details about elementary filters are given. This is a situation similar to the one in the ECDIS, where no information about tracking filters is transmitted, only the values. This situation also can happen if methods other than the Kalman Filter are used, such as the previously mentioned neural method. Thus, a method of approximation of the cross-covariance matrix by the Hadamard product of input matrices was proposed by Matzka and Altendorfer (Reference Matzka and Altendorfer2008):

(6)$$P_{ar} = \rho \left( {P_a \bullet P_r} \right)^{1/2} $$

where ρ is an effective correlation coefficient, determined empirically. In this research, a value of 0·4 is adopted, following Kazimierski and Stateczny (Reference Kazimierski and Stateczny2011).

An interesting approach, often used in the literature, is to fuse even more than two sensors using the Probabilistic Data Association Filter (PDAF) method and its mutations and developments. The filter is described thoroughly in Liggins et al. (Reference Liggins, Llinas and Hall2009) and its implementation can be found in Kwiatkowski et al. (Reference Kwiatkowski, Popik, Buszka, Wawruch, Weintrit and Neumann2011).

5.1. Research concept

The research focused on analysis of methods and variance matrices. Three stages of the research were proposed:

• • Comparison of fusion algorithms;

• • Comparison of variation matrices;

• • Length of sliding window analysis.

The state vector was formulated as:

(7)$$x = \left[ {BE, D, COG, SOG} \right]^T $$

where BE is the true bearing to the target (angle between north and the line connecting the ship to the target, in degrees), D is the distance from the ship to the target (in nautical miles), COG is the course over the ground of the target (in degrees), SOG is the speed over ground of the target (in knots). After the association process, both vectors were synchronized and COG and SOG were known for both sensors.

All the values in the state vector were treated as independent measurements. Thus, the variance matrices in the first stage had the form of a diagonal matrix:

(8)$$P = diag\left( {{\sigma _{BE} }^2, {\sigma _D} ^2, {\sigma _{COG}} ^2, {\sigma _{SOG} }^2} \right)$$

For the radar, particular values were taken, following IMO requirements:

(9)$$P_r = diag\left( {\it 4, 2500, 25, 0\!\cdot\!25} \right)$$

For the AIS target, particular values were taken based on the so-called relative accuracy:

(10)$$P_a = diag\left( {\it 0\!\cdot\!04, 225, 9, 0\!\cdot\!0001} \right).$$

5.2. Research scenario

The research was performed in prepared software in VisualBasic.Net. The software allows implementation of any fusion method and easy adjustment of its parameters. Data for the scenarios can be simulated, imported off-line from files or received on-line via serial ports. In the research, the data were imported from previously recorded files.

Data for the research were recorded on research-school ship Nawigator XXI in the southern Baltic Sea. NMEA strings from tracking radar and from AIS were recorded and then played back in the software. The scenario presented in this paper included radar and AIS observation of ferry Wolin with a Length Over All (LOA) of 189 m and GT of almost 23 000 tonnes. Two hours of observation were recorded, with the Nawigator XXI remaining stationary. The trace of the target received from the AIS is presented in Figure 2.

Figure 2. Trace of AIS target in the experiment, relative to own ship position.

Analysis of the influence of the length of sliding window was carried out in the third stage of the research.

6.1. Comparison of fusion algorithms

In this stage, fusion using two methods – simple fusion and cross-covariance – was examined. The variance matrix was stated based on IMO requirements as in Equations (9) and (10). A comparison of course estimation is presented in Figure 3.

Figure 3. Comparison of course estimated with different fusion methods.

During analysis of Figure 3, it can be noticed that the estimated fusion is much closer to the AIS data, as these data are much more accurate. The graph is also more smoothed than the radar graph. However, both fusions deviate slightly towards the radar course, thus following its values. This observation confirms that both fusion methods are performing the task according to assumptions. It can also be noticed that the cross-covariance method relies more on the covariance matrix, because this fusion is closer to AIS data.

6.2. Comparison of variances

In the second stage of the research, the influence of the covariance matrix values was examined. Apart from those stated in Equation (8), a modification of the covariance matrices was proposed. The values in the state vector were treated as samples of the variable measurements. Thus, sample variances for the set of values over a sliding window were proposed as items in the covariance matrices:

(11)$$P_v = diag \left( {var\left( {BE_{k - l} {:} BE_k} \right), var\left( {D_{k - l} {:}D_k} \right), var\left( {COG_{k - l} {:}COG_k} \right), var\left( {SOG_{k - l} {:}SOG_k} \right)} \right) $$

where l is the length of the sliding window. To retain the influence of sensor accuracy, the covariance matrix used in this stage of research was a Hadamard product of Equations (8) and (10), resulting in the matrix:

(12)$$\eqalign{P = & diag \bigg( \sigma_{BE}^{2\ast} var\bigg( BE_{k - l} \colon BE_k \bigg) \comma \sigma_D^{2\ast} var\bigg(D_{k - l} \colon D_k \bigg)\comma \sigma_{COG}^{2\ast} var\bigg(COG_{k - l} \colon COG_k \bigg)\comma \cr & \quad \sigma_{SOG}^{2\ast} var\bigg(SOG_{k - l} \colon SOG_k \bigg) \bigg)}$$

The results are shown in Figure 4. The covariance matrix, based on dynamic measurements of variance is called ‘sample variance’ in the figure, and it is also examined, as well as the covariance matrix based on accuracies. In Figure 4, the graph labelled ‘accuracies’ is the same as in the case of Figure 3, and the line labelled ‘sample variance’ shows the case where simple fusion is used but a covariance matrix is calculated according to Equation (12), and the length of the sliding window is set to ten. It can be noticed that fusion in this case is more subjected to AIS as the more accurate sensor. At the beginning, when the radar values are significantly varying, fusion is almost equal to AIS, but when the AIS data begin to vary, the fusion deviates into radar, yet remaining more smoothed, almost like AIS data. This interesting feature might be used for detecting temporary errors of any sensor. However, the problem of manoeuvres might occur. For better analysis of this issue, another research step is proposed, in which the influence of the length of the window is analysed.

Figure 4. Comparison of course estimated with different variances for simple fusion.

6.3. Length of sliding window analysis

In this stage, the research focused on analysing the influence of the size of the sliding window. Simple fusion is used with a covariance matrix based on sample variance and the sliding window length varies. Four values were used: 2, 5, 10 and 20, and the results are presented in Figure 5. The graph shows the difference between the AIS course and the fusion/ radar course.

Figure 5. Comparison of course differences for different sliding window lengths.

Based on Figure 5, it can be noticed that the most different from the AIS is the radar, and that all the fusion values are relatively close to the AIS values. However, it may be observed that for smaller values, the line for fusion becomes closer to the radar line. It can be thus concluded that the shorter the single window is, the more fusion is sensitive to changes. For very small values, e.g. 2, fusion jumps rapidly. On the other hand, for values of more than 20, the fusion results are almost the same as for the AIS, and the influence of the radar is minimised. It can be assumed that the optimal length of the sliding window is somewhere between 10 and 20.