Data Fusion Performance of HFSWR Systems for Ship ...

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Data Fusion Performance of HFSWR Systems for Ship Traffic Monitoring Salvatore Maresca, Paolo Braca, Jochen Horstmann Centre for Maritime Research and Experimentation, viale San Bartolomeo 400, 19100, La Spezia, Italy Email: {maresca, braca, horstmann}@cmre.nato.int

Abstract—In Maritime Situational Awareness (MSA), lowpower High-Frequency Surface-Wave (HFSW) radars fit the role of long-range early-warning tools by virtue of their over-thehorizon (OTH) coverage. Unfortunately these sensors, developed mainly for ocean remote sensing applications, exhibit poor range and azimuth resolution, high non-linearity and significant false alarm rate due to clutter and interference. For these reasons, the Joint Probabilistic Data Association (JPDA) logic, followed by the Unscented Kalman Filter (UKF), is proposed. Then, to exploit two simultaneously operating HFSW radars with overlapping fields of view, a track-to-track association and fusion (T2T-A/F) logic is applied. The capabilities of the JPDA-UKF tracking algorithm in combination with the T2T-A/F strategy are evaluated using a set of purpose-defined performance metrics, such as the time-on-target (ToT), the false alarm rate (FAR) and the root mean square error (RMSE). Special attention is paid to the comparison of the JPDA-UKF with the 3D (rangeazimuth-doppler) Ordered Statistics Constant False Alarm Rate (OS-CFAR) detection algorithm. A procedure based on track length modelling for the analysis of true and false tracks is presented as well. Single-sensor and multi-sensor tracking performances are investigated using real data collected during the NATO Battlespace Preparation 2009 (BP09) HF-radar experiment, which took place between May and December 2009 in the Mediterranean Sea. Ship reports from the Automatic Identification System (AIS) are used as ground truth information. Preliminary results are reported and discussed. Keywords—high-frequency surface wave (HFSW) radar, real data, sea clutter, target detection, target tracking, data fusion.

I. I NTRODUCTION ARITIME surveillance is a requirement for a number of national and international communities, in terms of both law enforcement, search and rescue, environmental protection and resource management. Research activities are pursued to develop reliable and cost-effective systems, built on existing sensors and processing techniques or on completely new solutions. In such a context, low-power HFSW radars, typically exploited for ocean remote sensing applications, and, in particular, surface currents, wind and wave measurements, may provide an additional low-cost source of data for maritime surveillance. Their OTH coverage capability, together with a continuous-time mode of operation makes them also suited for the purpose of ship detection and tracking. The Wellen Radar (WERA), developed at the University of Hamburg (Germany), is one such system [1]. Unfortunately, HFSWradars suffer from poor azimuth resolution, high non-linearity

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and significant false-alarm rate. It is worth noting that the underlying physics which regulate the signal transmission in the HF-band are quite different from the common microwave region. An overview of the main theoretical elements for modeling the backscatter signal can be found in [2]. These issues have been partially solved by a simple MultiTarget Tracking (MTT) algorithm, i.e. a Nearest Neighbor (NN) data association rule with an α − β − γ filter [3]. Reports from the AIS systems on-board of ships have been used as ground-truth data for ship classification and for assessing single-sensor tracking performance [3]–[5]. Unfortunately, the NN data association rule becomes a bottleneck of any MTT system, as soon as it is required to act in medium-level clutter environments. Many approaches exist that overcome the NN data association rule, both enumerative and non-enumerative [6], [7]. Enumerative approaches require the explicit definition of the data association hypotheses. Among these, we have the Multi-Hypothesis Tracking (MHT), the JPDA, the 0 − 1 integer programming and assignment algorithms. Non-enumerative state estimation approaches include Probabilistic MHT (PMHT), the Symmetric Measurement Equation (SME), event-averaged mean field, and Markov random field methods. Among non-enumerative approaches we can find also the Random Finite Set (RFS) theory. Moreover, recent advances in this area have led to the so-called Probability Hypothesis Density (PHD) filter, which uses Gaussian mixtures and particle approach. Promising results have been obtained in comparison with the conventional MHT method. An overview of the RFS methodology and PHD filtering is given in [8]. A further problem in radar target tracking applications arises when the state and measurement update equations are nonlinearly related, e.g. when target motion is modeled in Cartesian coordinates, while measurements are available in the sensor coordinates [9], [10]. In the majority of the cases, the motion of large vessels following commercial ship routes can be described with the nearly constant velocity (NCV) model [11]. On the other hand, HFSW systems, which can be a particular kind of Doppler radar, provide range-rate measurements. Two possible solutions are commonly used in MTT problems: tracking in mixed coordinates and tracking in Cartesian coordinates. The former approach is based on the Extended Kalman Filter (EKF), which can suffer from high non-linearity and lead to the rapid divergence of the filter itself. In the second approach, measurements in sensor coordinates, are converted in Cartesian coordinates. The converted measure-

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ment error covariance can be quite large for far-range targets, which is the case of HFSW radars. The UKF addresses the flaws of the EKF by using a deterministic sampling approach [12]. The state distribution is a Gaussian random vector, whose posterior mean and covariance are accurately estimated using a minimal set of carefully chosen sigma points. In order to improve the MTT performance, the JPDA logic followed by the UKF, namely JPDA-UKF, was proposed in [13]. See [11], [12], [14] for further information about the algorithms. In Multi-Sensor MTT (MS-MTT) systems, measurements from several sensors are combined to obtain a more complete picture of the surveyed region. Three main types of architecture, namely, centralized, distributed and decentralized, are commonly used in MS-MTT applications [6], [8], [11]. In centralized architectures, several sensors monitor the region of interest and only one fusion center (FC) gathers and process all acquired measurements and update the tracks. In distributed architectures, there are several fusion centers: one of them is the central, while the remaining ones are local FCs. In this kind of architecture, each FC can be considered as a combination of a local and a central fusion center. Each FC is connected with several sensors and the measurements they report are used to update the track state inside the FC. Furthermore, each fusion center perfoms also track-to-track fusion whenever it receives additional information from its neighboring FCs. Usually, the algorithms developed for distributed architectures can be used also with decentralized architectures [6], [11]. In the case of HFSW radars, the first problem is the azimuth resolution at long distances (i.e. cross-range resolution increases with range). Other problems concern the Doppler shifts, addressed in [15], and the RCS of the targets. Since ship detection is here implemented in the frequency domain, missed detections may happen when the vessel velocity vector leads to a return in proximity of the Bragg scattering region (i.e. first-order resonant scattering by ocean waves). Separated acquisition geometries allow to measure different radial velocity components. Aspect diversity can also reduce RCS variability due to target orientation, from head-on to broadside [5]. For these reasons, a track-to-track association and fusion (T2T-A/F) logic, see [6], was presented in [16]. In order to consider the pros and cons of the fusion strategy, only qualitatively addressed in [13] and [16], the T2T-A/F system is compared with the two standalone-operating HFSW radar systems. The JPDA-UKF and T2T-A/F output tracks are labelled as true or false if they are successfully associated to the AIS reports or not, respectively. Also true and false detections generated by the 3D-OS-CFAR algorithm are taken into account. The capabilities of the proposed algorithms are evaluated using a set of ad hoc performance metrics, such as the time-ontarget, the false alarm rate, the root mean square error and the track fragmentation (TF). A procedure based on track length modelling for the analysis of true and false tracks is presented as well. The paper is organized as follows. In Section II, both the AIS and HF data formats, the association procedure and the performance metrics are presented. Experimental results are shown and discussed in Section III, while conclusions and guidelines for future work are provided in Section IV.

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P ERFORMANCE A SSESSMENT

Under some assumptions, both static and kinematic AIS information can be used as ground-truth data for ship detection, tracking and data fusion performance assessment. First, ships equipped with AIS transponders are assumed to be the only ones present in the surveyed region and their identifiers, namely the Maritime Mobile Service Identity (MMSI), are unique. Second, the information transmitted by ships are reliable and not corrupted by any errors (intentional or unintentional). Third, since AIS reports are linearly interpolated on the HFSW-radar timestamps, the new data vectors are assumed true. Both tracks and detections are labelled as true or false if they are successfully associated to the AIS reports or not, respectively. Finally, a set of performance metrics is proposed to investigate both true and false tracks. A. HFSW radar and AIS data AIS ground-truth data: Ships exceeding a certain gross tonnage and belonging to given categories are required to repeatedly broadcast their position and other navigation information, as stated by the International Maritime Organization (IMO) in the Safety Of Life At Sea (SOLAS) convention [17]. These reports contain both dynamic (e.g. latitude, longitude, course-over-ground (COG), speed-over-ground (SOG), time) and static (e.g. type, dimensions) information. In this paper the AIS dataset represents the set of the target state vectors: X , {X n }n∈N ,

(1)

where N is the number of ships reporting their static and kinematic information in the recording interval. Kinematic reports are then linearly interpolated on the HFSW-radar timestamps. In order to cope with possible unwanted artifacts after this pre-processing phase, we define a flag index: ( 1, ∆Tl ≤ ∆Tmax l In = (2) 0, otherwise where l = 1, . . . , Ln −1 represents the time tl at which the nth ship transmits its position, Ln is the length of the AIS message from ship n and ∆Tl = tl − tl−1 is the time interleaved from the last position report at time tl−1 . The parameter ∆Tmax represents the maximum acceptable time from the last report. In this phase longitude, latitude, COG and SOG information are converted to obtain the current Cartesian data vector. Each AIS data vector X is then linearly interpolated on the radar ¯ the ground-truth dataset. timestamps tk to obtain X, HFSW radar detection and track data: Detection and track files (i.e. the outputs of the OS-CFAR, JPDA-UKF and T2Tˆ k and represent the available A/F filters) are denoted with X state estimates at time k: ˆ k , {ˆ X xm k }m∈Mk , where Mk is the number of track contacts at time k.

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B. Track validation procedure

metric can be evaluated as:

The association procedure, performed on each daily dataset, consists of four main steps: ˆk 1) For each k ∈ K, associate the active track contacts X from the T2T-A/F system to the available ground-truth ¯ k, data X 2) retrieve the entire daily tracks from the set of survived IDs, and 3) retrieve the parents IDs, i.e. the track IDs from the two JPDA-UKF outputs which were fed to the T2T fusion algorithm. 4) Do as step 2) for the parents IDs. In the case of detection files, only step 1) is performed. Each ¯ k at time k, with n ∈ Nk , is associated AIS contact x ¯nk ∈ X ˆ to a single track contact x ˆm k ∈ X k , with m ∈ Mk . The association is carried out by searching the nearest among all ˜ k ≤ Mk HFSW radar contacts falling inside a 3D the M (i.e. range, azimuth, range-rate) validation gate centered on the AIS contact, as follows: ¯nk ) : d(ˆ xm ¯nk ) = minj∈M˜ k {d(ˆ xjk , x ¯nk )}, (ˆ xm k →x k ,x

(4)

˜ k . The distance d(ˆ where j = 0, . . . , M xjk , x ¯nk ) is evaluated from the Cartesian coordinates of the state vectors x ˆjk and x ¯nk . n If the current x ¯k AIS state vector has a validated track contact x ˆm k , we define this occurency as a correct detection, otherwise it is a missed detection. All the other contacts, which are not validated, are defined as false alarms. C. Performance Metrics 1) Time-on-target: The ToT is defined as the percentage of time during which the tracker follows the whole interpolated ship route. It is evaluated for each available cooperative vessel and then averaged over all the ships. This operation is performed for each of the days in the recording interval, as follows: D N 1 X 1 X ˆln T oT , (5) D Nd n=1 ¯ln d=1 where Nd is the number of ships on day d, while ¯ln and ˆln are the true (i.e. from the interpolated AIS) and estimated (i.e. from the radar) track lengths for ship n, respectively. For brevity, the dependency of¯ln and ˆln from d has been omitted. The ToT can be evaluated at the varying of both kinematic (i.e. range, azimuth, range-rate) and static (i.e. size) information. In this case, ¯ln represents a fraction of the track falling in the specific range, azimuth or range-rate interval. 2) False alarm rate: The false alarm rate (FAR), is defined as the number of false tracks contacts, normalized by the recording interval and the area of the surveyed region. As well known, the FAR is strongly related to the ToT and, statistically, to an increase of the probability of detection corresponds an increase of the probability of false alarm. With false alarm we define each single contact belonging to a false track. This

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D Md ˆli 1 XX , F AR , D A · ∆T i=1

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where ˆli is the length of the ith false track, Md0 is the number of false tracks on day d, A is the area of the surveyed region [m2 ] and ∆T is the daily record length [s]. Like the ToT, it is evaluated in the specific range, azimuth or range rate interval. On these, FAR values are normalized first such that their weighted sum provides the total FAR per unit of time and area for that day. 3) Tracking error: The error committed by the tracking algorithms is evaluated in terms of RMSE for different kinematic parameters, both Cartesian and polar, (e.g. position, velocity and range, azimuth, range-rate). 4) Track fragmentation: The track fragmentation is quantitatively given by the ToT and the number of sub-tracks associated with the same target. In an ideal system, we would like to have a ToT of 100% with just a single track. Unfortunately, the event in which the tracking algorithm is able to follow a given target along its whole route is very rare. Despite the algorithm adopted, this becomes dramatically true for low-power HFSW radars, not developed for traffic surveillance purposes. This means that along a single ship route we can observe different sub-tracks, composing the overall ship picture. As easily understandable, this number mainly depends on different aspects: the detection and tracking algorithms, the target size, its relative geometry to the sensor and sea clutter. III. E XPERIMENTAL R ESULTS Two Wellen Radar (WERA) systems were deployed on the Italian coast of the Ligurian Sea (Mediterranean Sea), one on Palmaria Island (44◦ 20 3000 N, 9◦ 500 3600 E) and the other one at San Rossore Park (43◦ 400 5300 N, 10◦ 160 5200 E). Both WERA radars were transmitting at about 12.5 MHz with approximately 32 W and operated on a continuous basis, trasmitting linear frequency-modulated continuous-wave (LFMCW) chirps. The two systems used the same operating frequency, with orthogonal modulating waveforms. Range resolution was 1.5 km (with bandwidth 100 kHz). The angles w.r.t. North of the two array installations were φ1 = 296.2◦ and φ2 = 12.0◦ , respectively. The azimuth information was extracted via beamforming of the received data, using an Hamming window. Target detection was performed in the FFT domain by a 3D (azimuth-range-Doppler) OS-CFAR algorithm [3]. CPIs were made of 512 samples, with an overlap of 75%. Therefore, radar timestamps occurred every 33.28 s. Further information about WERA and its on-site setup can be found in [1]. More information about the experiment can be found in [13], [16]. The proposed algorithms are tested on a 25-day dataset collected between May 8th and June 4th , with the exception of three days (i.e. May 20th , 21st and 27th ). Only the track contacts falling inside the common region have been taken into account, mainly because the overlap region allows to consider the same vessel tracks and to have the possibility of data fusion.

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A. Analysis of true tracks

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The average number of AIS-carrying vessels varied from a minimum of 59 on May 18th , to a maximum of 91 on May 26th . Fig. 1 depicts the true active tracks on May 12nd and is displayed as follows. The output tracks from T2T-A/F algorithm (blue) are shown w.r.t. the AIS ship routes (black) in the fusion region. Output tracks from the two JPDA-UKFs of Palmaria (green) and San Rossore (red) are reported as well. There is a quite good agreement with the ground-truth data, i.e. the AIS ship routes, but, unfortunately, the tracking capabilities of the three systems significantly degrade after 100 km distance and at the edges of the 120◦ area covered by each sensor.

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Fig. 1. True active HFSW radar tracks and AIS data in the fusion region on May 12nd , 2009. Interpolated AIS data (black), Palmaria JPDA-UKF (green), San Rossore JPDA-UKF (red), T2T-A/F (blue).

A typical ship route is the one crossed by the ship with MMSI 218033000, and shown in Fig. 2. In this case, the T2TA/F system is able to successfully track the target for almost the whole trajectory. 1) Time-on-target analysis: The ToT, averaged over 25 days, is presented in Fig. 3 at 10 km range intervals. No AIS reports were available in the first 10 km from San Rossore (b). The peak ToT values at Palmaria are in the range of 10 − 50 km, where they are about 65−77% for the JPDA-UKF (green) and about 41−55% for the OS-CFAR algorithm (red), see Fig. 3(a). The T2T fusion strategy (blue) grants about 80 − 90% in the same interval, but rapidly falls below 50% over 70 − 80 km. For San Rossore, the peak value is 55% in the same interval, for both the JPDA-UKF and the OS-CFAR algorithms, while the data fusion allows to achieve a final value of about 79%, see Fig. 3(b). This means that the gain of the T2T-A/F system w.r.t. San Rossore is more significant than w.r.t. Palmaria. A possible reason can be found in the geometry of the ship routes w.r.t. the sensors positions. The ToT versus range-rate is depicted in Fig. 4, showing an almost uniform behaviour for the tracking algorithms. Concerning the JPDA-UKF in combination with the T2T-

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Fig. 2. Typical commercial ship route: cargo ship Finlandia (MMSI 218033000) crossing the fusion region on May 12nd , 2009. AIS trajectory (black), T2T-A/F (blue), Palmaria (green), San Rossore (red).

A/F strategy, Palmaria (a) exhibits a larger ToT than San Rossore (b), with a maximum value of about 62% against about 45%. Interestingly, the OS-CFAR ship detection preformances degrade with increasing radial speed (in modulus) for Palmaria and slightly less for San Rossore. This is in good agreement also with Fig. 3(a), where the JPDA-UKF was shown to outperform the OS-CFAR algorithm in the first 80 km. The analysis of Fig. 4 reveals that this improvement mainly concerns large radial speeds. In fact, the tracking capability significantly degrades for those radial speeds corresponding to the first-order Bragg scattering contributions from the sea surface (e.g. for a carrier frequency of 12.50 MHz, these are about ±4.32 m/s). The aspect diversity, exploited by the trackfusion strategy, allows to fix this issue and the notches are less significant, especially for the T2T-A/F at San Rossore, as shown in Fig. 4(b). In Fig. 5, the ToT estimates are shown for the vessel with MMSI 218033000. In each bar, the number of subtracks is depicted in white. The comparison demonstrates that the T2TA/F strategy overcomes the single JPDA-UKFs, as it was shown also in Fig. 2. This improvement manifests both in terms of ToT and track fragmentation. 2) Tracking error analysis: The RMSE is computed for both the position and velocity components of the state vector . Results are shown in Fig. 6, in sub-figures (a) and (b) respectively. Curves are estimated averaging only the subtracks of the T2T-A/F system obtained from the fusion of the tracks at the two sensors. Results are considered only for tracks shorter than 100 samples. Let us consider the RMSE of the position estimate, as depicted in Fig. 6(a). The error is about 0.6−1.0 km (green and red lines), for both Palmaria and San Rossore. As expected, the error of the two standalone systems are close, while the T2T-A/F system (blue) provides an RMSE significantly below the two JPDA-UKFs, about 200 − 300 m on average. Further

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Fig. 3. Estimated ToT percent versus range [km], w.r.t. Palmaria (a) and San Rossore sites (b): T2T-A/F (blue), JPDA-UKF (green), OS-CFAR (red).

Fig. 4. Estimated ToT percent versus range-rate [m/s], w.r.t. Palmaria (a) and San Rossore sites (b): T2T-A/F (blue), JPDA-UKF (green), OS-CFAR (red). 100 90 80 70 60 ToT %

information about the placement of the AIS transponder (i.e. from-bow and from-port distances) have not been considered, even if not negligible for the size of the ships involved. We simply assumed that the corrections were null on average. The RMSE of the velocity estimate is presented in Fig. 6(b). Significant differences arise not only from the mean error level, but also from the analysis of the transitory error, almost eliminated by the T2T fusion algorithm (blue). When one of the two sensors loses its track, the other one most likely is able to follow it, thus reducing track fragmentation. This fact can be observed in figure 7, which depicts the error on the position (a) and velocity (b) estimates for ship 218033000. Let us consider the T2T-A/F output (blue). All the transitory phases are almost eliminated, in agreement to what shown also in Fig. 6. When T2T fusion is effectively performed, the final track estimate is significantly better, in terms of both ToT, estimate accuracy and track fragmentation. However, this occurs at the cost of an increase of the FAR, as it will be shown in Sec. III-B1. 3) Track fragmentation analysis: For each day we evaluated the mean and standard deviation of the number of sub-tracks that compose the final track estimate. Results are summarized in Table I for only five days (i.e. May 10 − 14).

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Fig. 5. Estimated ToT for ship with MMSI 218033000, on May 12nd , 2009: T2T-A/F (blue), JPDA-UKF (green), OS-CFAR (red).

It can be observed that San Rossore exhibits a significant track-fragmentation issue, see columns 2 and 4. In fact, both the mean and standard deviation can be compared to the values

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Fig. 6. RMSE of the position (a) and velocity (b) state vector components: T2T-A/F (blue), Palmaria (green), San Rossore (red).

Fig. 7. Ship route, position and velocity errors for ship with MMSI 218033000 on May 12th , 2009: AIS (black), Palmaria JPDA-UKF (green), San Rossore JPDA-UKF (red), T2T-A/F (blue).

obtained at Palmaria. However, the same conclusion cannot be made in terms of ToT. The values show that the JPDA-UKF at Palmaria performs better than the JPDA-UKF at San Rossore, see columns 3 and 5. These results can be explained by a more favourable ship-sensor relative geometry. Interestingly, the T2T-A/F algorithm performs better than the two trackers, but remaining closer to the JPDA-UKF at Palmaria in terms of ToT, see column 7. Track fragmentation statistics slightly increase, see column 6. The reason of this can be found in the OR fusion strategy implemented. In conclusion, results shown in Table I can be seen as a further proof of our analysis, i.e. the T2T-A/F system seems to rely more on Palmaria than on San Rossore. B. Analysis of false tracks False tracks recorded on May 12nd are shown in Fig. 8. What can immediately be seen is the significant number of active false tracks, i.e. having a good time-coherency but no associated AIS report. Some of them closely follow the ship routes we observed during the analysis of the true tracks, see Fig. 1. Moreover, most of them, especially those at far distance,

Date 10/05 11/05 12/05 13/05 14/05

TABLE I.

Palmaria (µ; σ) (3.7; 1.8) (3.9; 2.5) (3.9; 2.8) (3.8; 2.2) (3.3; 2.1)

ToT 29 32 27 29 22

San Rossore (µ; σ) T oT (3.6; 2.0) 18 (3.8; 2.4) 19 (3.6; 2.3) 19 (3.3; 2.1) 17 (3.3; 2.0) 20

Fusion (µ; σ) T oT (4.2; 2.7) 35 (4.3; 2.7) 37 (4.7; 3.2) 36 (4.3; 2.5) 33 (4.4; 2.8) 32

T RACK FRAGMENTATION STATISTICS AND AVERAGE THE RECORDING INTERVAL M AY 10 − 14, 2009.

T OT IN

exhibit a peculiar fragmented behaviour. This fragmentation, already observed during the analysis of the true tracks, is overcome by the T2T-A/F algorithm. In addition, a significant amount of false tracks crowds the sea in front of the coasts of Tuscany (Italy). It is possible that in the surveyed area a number of ships are not carrying any AIS transponder (e.g. fishing boats, military vessels), can be out the BS line-of-sight, can be AIS-carrying ships outside the validation gate or, in the worst hypothesis, not cooperative. 1) False alarm rate: False alarm rate is evaluated versus range, as shown in Fig. 9, in sub-figures (a) and (b) for Pal-

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Fig. 8. False active tracks in the fusion region on May 12nd , 2009: Palmaria (green), San Rossore (red), T2T-A/F (blue).

maria and San Rossore respectively. As expected, the tracking algorithm significantly reduces the number of false alarms and cancels most of clutter-originated ones, cfr. green (JPDA-UKF) and red (OS-CFAR) lines in both sub-figures. It is interesting to observe that most of the false contacts accumulate in the first 60 km from both radars, in agreement to what shown also in Fig. 8. The T2T-A/F strategy (blue) tends to increase the number of false alarms compared to the standalone trackers. Again, this fact can be explained by the OR fusion strategy implemented [16]. However, an increase of the FAR brings also an increase of the ToT and viceversa, as pointed out in Sec. III-A1. The estimated FAR curves versus range-rate are shown in Fig. 10, in sub-figures (a) and (b) for Palmaria and San Rossore respectively. A relevant amout of false contacts is produced by sea clutter, not perfectly filtered out by the detection algorithm (red line). On the contrary, the tracking algorithms prune most of these returns and false track contacts accumulate suspiciously between the Bragg velocities, where most of the vessels were observed. Unfortunately, we cannot say anything else about them. In fact, we assumed that no other ships were present in the surveyed region, except those carrying the AIStransponder. C. Overview on track length modelling Track length can be seen as a sort of survival time of the ship route. This term is used in the automatic controls theory, for describing the time-before-failure of the machines. Usually this time is modelled with a Weibull distribution. With f (l; λ, k) we define the probability density function of track length l: k −(l/λ)k ·e · u (l) , (7) λ where k > 0 and λ > 0 are the shape and scale parameters of the distribution and u (.) is the unit step function. In this paper, f (l; λ, k) =

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(b) FAR vs range w.r.t. San Rossore. Fig. 9. Estimated FAR versus range [km], w.r.t. Palmaria (a) and San Rossore sites (b): T2T-A/F (blue), JPDA-UKF (green), OS-CFAR (red).

we propose a model for track length which is a mixture of two Weibull distributions. The first one accounts for short tracks (i.e. from targets moving tangentially or in proximity of the first-order Bragg scattering and having a high fragmentation rate, or just with a poor relative Radar Cross Section). The second one accounts for long tracks (i.e. the tracks generated from targets exploiting a good geometry radial speed-RCS). The mixture can be rewritten as: f (l; λ, k) = p · f1 (l1 ; λ1 , k1 ) + (1 − p) · f2 (l2 ; λ2 , k2 ) , (8) where f1 (l1 ; λ1 , k1 ) and f2 (l2 ; λ2 , k2 ) are two Weibull distributions and p is the mixing probability. In the first part of this analysis, true tracks are analysed and their density parameters evaluated according to the following steps: 1) Extract the number N1 of sub-tracks longer than a given length lmax . 2) Extract all the other sub-tracks, i.e. N2 satisfying N = N1 + N2 , where N is the total number of tracks we considered. 3) Model the overall track-length distribution as mixture of two Weibull distributions, using p0 = N1 /(N1 +

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IV. C ONCLUSIONS In this paper, results of the experiment on HFSW radars have been presented and discussed. A procedure for track validation and the definition of metrics for performance assessment have been proposed. The T2T fusion strategy has demonstrated its effectiveness w.r.t. the single-sensor JPDAUKFs, in terms of increased ToT and accuracy, but at the cost of a slightly increase of the track fragmentation and FAR. The tracking algorithms have been also compared with the OS-CFAR detector to show the significant reduction of the false alarms. A basic track length model has been applied to both true and false tracks, in order to extract possible common features. Research in this direction is currently ongoing.

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(b) FAR vs range-rate w.r.t. San Rossore. Fig. 10. Estimated FAR versus range-rate [m/s], w.r.t. Palmaria (a) and San Rossore sites (b): T2T-A/F (blue), JPDA-UKF (green), OS-CFAR (red).

N2 ) and 1 − p0 = N2 /(N1 + N2 ) as starting mixing probabilities for maximum likelihood estimation of the five parameters. As said, this model is intended to provide a preliminary matching of the distribution of the tracks, by accounting for long radially-moving tracks and short fragmented tracks. This fact leads us to the second part of the analysis. If we assume that longer false tracks (i.e. for which l > 50 samples) are most-likely generated by real targets, we can model them with the same Weibull distribution used for the true tracks. The same can be done also for shorter tracks. Unfortunately, among them we can find also both homogeneous clutter-originated tracks and non-homogeneous clutteroriginated tracks (i.e. those generated by land scattering). For this reason, we cannot make any further division, unless to separate one-by-one all the suspect tracks. Concluding, the modelling of false tracks follows the steps addressed for the true tracks, assuming the same distribution for the longer tracks. The second distribution instead models both short ship tracks, and clutter-originated tracks. Research in this sense is currently ongoing.

[6] [7] [8] [9]

[10]

[11] [12] [13]

[14]

[15]

[16]

[17]

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