*C. Track termination*

A maintained track will be terminated if one of the following conditions occurs:


#### **3. Experiment Results**

To test the target detection and tracking performance of a bistatic compact HFSWR and verify the effectiveness and applicability of the proposed target tracking method, vessel detection and tracking experiments were conducted using field data simultaneously collected by a newly developed T/R-R compact HFSWR system, as shown in Figure 2, in operation at North China Sea from 9:57 a.m. to 13:42 p.m. on 30 April 2019. The monostatic T/R radar is located at Weihai (122.07◦E, 37.54◦N), while the other independent receiving station is deployed at Yantai (121.49◦E, 37.45◦N). The baseline distance *L* is 52 km, and *ϕ* is 10.35◦ for this configuration.

**Figure 2.** Transmitting antenna and one receiving antenna array of the developed T/R-R compact HFSWR system. (**a**) Transmitting antenna installed at Weihai radar station. (**b**) One receiving antenna array.

The compact HFSWR system used a solid-state transmitter with a maximum peak power of 2 kW and linear frequency modulated interrupting continuous wave (FMICW) as its transmitted waveform. A 10-meter-high omnidirectional log-periodic antenna, as shown in Figure 2a, was used to transmit electromagnetic waves with a working frequency of 4.7 MHz. Two similar linear receiving antenna arrays with an antenna element height of 4 meters were placed along the coast at Weihai and Yantai, respectively. Here, only the photo of the receiving antenna array at the Yantai station is shown in Figure 2b. Each receiving antenna array consists of eight active whip antenna units with an inter-element distance of 15 m. Thus, the aperture size of each receiving array is 105 m. The maximum detection range is designed as 100 km. As for vessel detection, the coherent integration time is set to be 262.144 s. A moving slide window method with a window length of 266.144 s is used to produce the detection data. The window slides forward with a step of 60 s, thus the data rate is 1 frame/min. The two radars are synchronized using a GPS time reference. Simultaneous automatic identification system (AIS) data were used as ground truth for comparisons and evaluations [39].

From the data collected by the bistatic compact HFSWR at Yantai, the range sum *R* and the azimuth *θ<sup>R</sup>* of the detected targets were estimated, then their ranges *RR* were calculated from Equation (2) and the measured state vectors [*R<sup>m</sup> <sup>R</sup> <sup>θ</sup><sup>m</sup> <sup>R</sup> <sup>v</sup><sup>m</sup> dR*] can be obtained. Then the proposed target tracking method was applied to the target detection data to obtain the bistatic target tracks. The target tracking method proposed in [11] was applied to the target plot data sequence measured by the monostatic HFSWR at Weihai to produce the monostatic target tracks. The threshold parameters involved in the tracking algorithm were determined via trial-and-error and they are summarized as follows:


From the obtained tracking results, three typical targets are selected for analysis, as shown in Figure 3.

**Figure 3.** Tracking results of three typical targets. The blue and green dots indicate the location of the monostatic HFSWR at Weihai and the bistatic HFSWR at Yantai, respectively. The black angular sector illustrates the detection region of the monostatic HFSWR at Weihai. The three targets are marked as '1', '2', and '3' and named as target 1, target 2, and target 3, respectively. The tracks in blue, green, and black represent the tracking results from the monostatic radar, bistatic radar, and matched AIS, respectively. The red dot indicates the first plot of a track.

In Figure 3, the blue and green dots indicate the location of the monostatic HFSWR at Weihai and the bistatic HFSWR at Yantai, respectively. The black angular sector illustrates the detection region of the monostatic HFSWR at Weihai. The three targets are marked as '1', '2', and '3' and named as target 1, target 2, and target 3, respectively. The tracks in blue, green, and black represent the tracking results from the monostatic radar, bistatic radar, and matched AIS, respectively. The red dot indicates the first plot of a track. It is shown that target 1 is captured by both the monostatic and bistatic radars simultaneously, target 2 is tracked by the monostatic radar only, and target 3 is only detected by the bistatic radar. The general information of these three targets reported by AIS are listed in Table 1, and their photos are shown in Figure 4.


**Table 1.** General information for three targets.

(**c**)

**Figure 4.** Photos of three targets considered in this paper. (**a**) Target 1—HUI RONG, the photo is from the website: www.yantaiport.com.cn. (**b**) Target 2—MARAN HELEN, the photo is from: www.marinetraffic.com. (**c**) Target 3—ZHONGTIEBOHAI 1 HAO, the photo is from: image.baidu.com.

The tracking results of these three targets are analyzed and compared in detail as follows. (1) Target tracks obtained by both the monostatic and bistatic radars.

As shown in Figure 3, target 1 moves nearly along the bistatic bisector direction of the bistatic

radar at Yantai, its velocities have significant projection components in the radial direction of the monostatic radar at Weihai. Thus, it is captured by both radars. The tracks in longitudes and latitudes of target 1 are shown in Figure 5.

**Figure 5.** Comparison between radar tracks and automatic identification system (AIS) track of target 1.

It can be seen from Figure 5 that the obtained tracks from both the bistatic radar and monostatic radar are broken into two track segments. The four track segments are marked as '1', '2', '3', and '4', whose durations were 10:38–11:32 a.m. for track segment 1 with 54 plots, 11:13–11:44 a.m. for track segment 2 with 32 plots, 11:37 a.m.–12:16 p.m. for track segment 3 with 40 plots, and 11:54 a.m.–12:37 p.m. for track segment 4 with 44 plots. The duration for the matched AIS track was from 10:38 a.m. to 12:37 p.m. with 120 plots. It is shown that these four track segments together cover the entire AIS track.

In order to quantitatively evaluate the tracking performance, the positions provided by the AIS track in longitudes and latitudes, as well as the velocities, were projected onto the coordinates of the monostatic radar at Weihai and bistatic radar at Yantai, respectively, to obtain the corresponding range data, azimuth data, and Doppler velocity data sequences. The root-mean-square error (RMSE) and statistical error distribution criteria were used for accuracy evaluation.

The range data, azimuth data, and Doppler velocity data sequences corresponding to the four track segments are compared with those obtained by the AIS track projections, the results are shown in Figure 6. Figure 6a,c,e illustrate the range, azimuth, and Doppler velocity comparison results of the monostatic radar, respectively. The corresponding comparison results of the bistatic radar are shown in Figure 6b,d,f, respectively. The Sample number denotes the sequence number of a plot in a track.

As the monostatic radar at Weihai and bistatic radar at Yantai measure targets under different coordinates, the scales of their kinematic parameters are different. According to the velocities reported by AIS, target 1 moves at a nearly constant velocity during the observation period. However, the instability of the instantaneously measured course results in fluctuations in radial velocity projections. It can be observed that the range data, azimuth data, and Doppler velocity data sequences obtained from track segment 1 and track segment 3 of the monostatic compact HFSWR are in good agreement with those of the AIS results, the corresponding RMSEs are 1.24 km, 1.18◦, and 1.3 km/h, respectively. By contrast, the range and azimuth data sequences obtained from track segment 2 and track segment 4 of the bistatic compact HFSWR agree well with those of the AIS results, with a relatively larger RMSEs of 3.6 km and 1.94◦, respectively. It is worth noting that the agreement between the bistatic Doppler velocity data sequences and the projected results of AIS is fairly good, with a RMSE of 0.55 km/h. For clarity, the results are listed in Table 2.

**Figure 6.** Kinematic parameter comparisons for target 1. (**a**) Range comparison for monostatic radar. (**b**) Range comparison for bistatic radar. (**c**) Azimuth comparison for monostatic radar. (**d**) Azimuth comparison for bistatic radar. (**e**) Doppler velocity comparison for monostatic radar. (**f**) Doppler velocity comparison for bistatic radar.

**Table 2.** Root-mean-square error (RMSE) of range, azimuth and Doppler velocity for target 1.


The error distributions of the range, azimuth, and Doppler velocity data sequences of target 1 for both monostatic and bistatic HFSWR are illustrated in Figure 7 for more detailed analysis.

**Figure 7.** Kinematic parameter error distributions for target 1. (**a**) Range error distribution for monostatic radar. (**b**) Range error distribution for bistatic radar. (**c**) Azimuth error distribution for monostatic radar. (**d**) Azimuth error distribution for bistatic radar. (**e**) Doppler velocity error distribution for monostatic radar. (**f**) Doppler velocity error distribution for bistatic radar.

It can be seen from Figure 7 that the majority of range error, azimuth error, and Doppler velocity error for monostatic HFSWR are less than 1.5 km, 2◦, and 1 km/h, respectively, while those for bistatic HFSWR are less than 4 km, 3◦, and 1 km/h, respectively.

The above results indicate that the monostatic radar achieves better tracking accuracy than that of the bistatic radar for target 1. However, the RMSE of the Doppler velocity from bistatic HFSWR is lower than that of monostatic HFSWR. The azimuth estimation results from both monostatic radar and bistatic radar display some random fluctuations due to the coarse azimuth resolution caused by reduced aperture size. It is worth mentioning that the range accuracy is different for monostatic radar and bistatic radar. The range resolution of the CORMS is designed to be 2.5 km. The range accuracy of the monostatic radar is much higher than this value as reported in [11], while the range accuracy of the bistatic radar is worse than this design value because the calculated ranges are affected by error in

azimuth estimations.

It can also be observed that the three kinematic parameters between track segment 1 and track segment 3, as well as between track segment 2 and track segment 4 are consistent. The track fragmentation is probably due to the missed detections at some sampling time, which may be caused by the weak returned echos due to the relatively smaller ship size, or sea clutter interference, etc. Combining the simultaneous target detections of a monostatic and bistatic radar, the overlapped discontinuous track segments belonging to the same target can be bridged together to obtain a longer track. Thus, there is a potential for this radar configuration to maintain better track consistence.

(2) Target tracks obtained only by the monostatic radar.

As a Doppler radar, HFSWR favors detecting targets that have significant velocity projection components along its radial directions. The track of target 2 can only be produced from the monostatic radar data as it sails nearly along the tangent direction of the isorange ellipse of the bistatic radar. The obtained two track segments, marked as '1' and '2', and the matched AIS track are illustrated in Figure 8. The durations of these two track segments are 11:52 a.m.–12:28 p.m. for track segment 1 with 37 plots, 12:40–1:33 p.m. for track segment 2 with 54 plots. The duration for the matched AIS track is from 11:52 a.m. to 1:33 p.m. with 102 plots.

**Figure 8.** Track comparison between monostatic radar and AIS of target 2.

The comparisons of the corresponding range data, azimuth data, and Doppler velocity data sequences are shown in Figure 9. It is observed that both the range data and Doppler velocity data sequences agree well with those of the AIS projection results with RMSEs of 1.37 km, and 0.36 km/h, respectively, which are similar to the results obtained by the monostatic radar for target 1. However, the accuracy of the azimuth data sequence is a little worse with an RMSE of 2.66◦ due to the target's longer distance from the radar site, which leads to large target position deviations from its true trajectory. It can be seen from Figure 9c that the Doppler velocity changes from positive values to negative ones, and then becomes positive again around the 40th plots. This is because that target 2 moves nearly along the tangent direction of the Weihai radar. At some locations, its Doppler velocity becomes nearly zero and thus it is difficult to be detected. The missed detections may lead to the track fragmentation. However, the tracking algorithm adopted here has not been considered such situations.

**Figure 9.** Kinematic parameter comparisons for target 2. (**a**) Range comparison for monostatic radar. (**b**) Azimuth comparison for monostatic radar. (**c**) Doppler velocity comparison for monostatic radar.

The error distributions of the range, azimuth, and Doppler velocity data sequences of target 2 for monostatic HFSWR are illustrated in Figure 10 for more detailed analysis.

It can be seen from Figure 10 that the majority of range error, azimuth error, and Doppler velocity error for monostatic HFSWR are less than 1.5 km, 4◦, and 0.6 km/h, respectively.

**Figure 10.** Kinematic parameter error distributions for target 2. (**a**) Range error distribution. (**b**) Azimuth error distribution. (**c**) Doppler velocity error distribution.

(3) Target track obtained only by the bistatic radar.

It can be seen from Figure 3 that target 3 goes beyond the maximum detection range of 100 km of the monostatic radar at Weihai. Fortunately, it is still within the detection range of the bistatic radar at Yantai. Thus, it is only captured by the bistatic radar. From this perspective, the coverage area of the monostatic radar is expanded. The obtained track, as well as its matched AIS track, whose duration are from 10:11 a.m. to 11:08 a.m. with 58 plots, are shown in Figure 11. It is observed that the track obtained by the bistatic radar deviates from its true trajectory but shows a similar course with that of AIS.

**Figure 11.** Track comparison between bistatic radar and AIS of target 3.

The kinematic comparisons of the corresponding range data, azimuth data, and Doppler velocity data sequences are shown in Figure 12.

**Figure 12.** Kinematic parameter comparisons for target 3. (**a**) Range comparison for bistatic radar. (**b**) Azimuth comparison for bistatic radar. (**c**) Doppler velocity comparison for bistatic radar.

Compared with the results provided by AIS, it can be noted that the range errors are nearly constant for all the plots with an RMSE of 3.7 km and a standard deviation of 0.3 km. The azimuth data of AIS keep nearly constant, while the azimuth data sequence of the bistatic radar presents fluctuations with an RMSE of 2.3◦ and a maximum deviation of 4.58◦. The RMSE of Doppler velocity is 0.55 km/h and the maximum deviation is 1.05 km/h, indicating again that a bistatic HFSWR can measure the Doppler velocity of a target with high accuracy.

The error distributions of the range, azimuth, and Doppler velocity data sequences of target 3 for bistatic HFSWR are illustrated in Figure 13 for more detailed analysis.

**Figure 13.** Kinematic parameter error distributions for target 3. (**a**) Range error distribution. (**b**) Azimuth error distribution. (**c**) Doppler velocity error distribution.

It can be seen from Figure 13 that the majority of range error, azimuth error, and Doppler velocity error for monostatic HFSWR are less than 4 km, 3◦, and 1 km/h, respectively.
