Figure 1.
(a) Range-Doppler image of real X-band RC F-SAR data. The clutter with a bandwidth of around 800 Hz and a ship appearing at −500 Hz are clearly visible. (b) Normalized image. (c) Clustered detections with their centroids and bounding boxes at azimuth times t = 15 s, t = 20 s and t = 30 s, respectively. (d) Target trajectory obtained from a tracking algorithm (orange) and cluster centroids (blue).
Figure 1.
(a) Range-Doppler image of real X-band RC F-SAR data. The clutter with a bandwidth of around 800 Hz and a ship appearing at −500 Hz are clearly visible. (b) Normalized image. (c) Clustered detections with their centroids and bounding boxes at azimuth times t = 15 s, t = 20 s and t = 30 s, respectively. (d) Target trajectory obtained from a tracking algorithm (orange) and cluster centroids (blue).
Figure 2.
Illustration of the average Doppler spectrum of a range-Doppler image containing clutter and ship targets (a) before and (b) after normalization over Doppler. The red curve in (a) is the average Doppler profile estimated without considering the targets. The green line in (b) is the detection threshold computed based on clutter plus noise level.
Figure 2.
Illustration of the average Doppler spectrum of a range-Doppler image containing clutter and ship targets (a) before and (b) after normalization over Doppler. The red curve in (a) is the average Doppler profile estimated without considering the targets. The green line in (b) is the detection threshold computed based on clutter plus noise level.
Figure 3.
Clutter Doppler centroid map computed by using the measured aircraft Euler angles for a circular flight carried out with F-SAR (details about the flight are given in
Section 6).
Figure 3.
Clutter Doppler centroid map computed by using the measured aircraft Euler angles for a circular flight carried out with F-SAR (details about the flight are given in
Section 6).
Figure 4.
Block diagram of the proposed algorithm which uses RC airborne radar data as input. The individual blocks and processing steps are numbered from 1 to 17 and are discussed in detail in the text.
Figure 4.
Block diagram of the proposed algorithm which uses RC airborne radar data as input. The individual blocks and processing steps are numbered from 1 to 17 and are discussed in detail in the text.
Figure 5.
Patch of HH polarization X-band F-SAR data containing a ship target (at a range of approx. 7570 m). For visualization purposes, the data were normalized to the maximum power.
Figure 5.
Patch of HH polarization X-band F-SAR data containing a ship target (at a range of approx. 7570 m). For visualization purposes, the data were normalized to the maximum power.
Figure 6.
Logarithmic plot of the PDFs of the ocean only (red) and ocean with a ship signal (blue) are shown. For visualization purposes, the intensity axis is truncated as the maximum intensity due to the ship is around 600.
Figure 6.
Logarithmic plot of the PDFs of the ocean only (red) and ocean with a ship signal (blue) are shown. For visualization purposes, the intensity axis is truncated as the maximum intensity due to the ship is around 600.
Figure 7.
Amplitude over range profile of the sea backscatter in HH, VV and HV polarization channels of RC F-SAR X-band radar data.
Figure 7.
Amplitude over range profile of the sea backscatter in HH, VV and HV polarization channels of RC F-SAR X-band radar data.
Figure 8.
Average amplitude range profile with range dependent pre-detection thresholds. A high target peak (=ship) is present at a range of approximately 7500 m. The effectiveness of the MAD based pre-detection is evaluated in three different zones; near (red), mid (green) and far range (blue). Details are shown in
Figure 9.
Figure 8.
Average amplitude range profile with range dependent pre-detection thresholds. A high target peak (=ship) is present at a range of approximately 7500 m. The effectiveness of the MAD based pre-detection is evaluated in three different zones; near (red), mid (green) and far range (blue). Details are shown in
Figure 9.
Figure 9.
Details of the pre-detection thresholds computed for different factors in (a) near (b) mid and (c) far ranges.
Figure 9.
Details of the pre-detection thresholds computed for different factors in (a) near (b) mid and (c) far ranges.
Figure 10.
RC F-SAR X-band HH polarized radar data acquired during a linear flight track. Ship signal is indicated in the figure.
Figure 10.
RC F-SAR X-band HH polarized radar data acquired during a linear flight track. Ship signal is indicated in the figure.
Figure 11.
Binary detection map after applying the proposed pre-detection algorithm. The pre-detected ship signal (left) as well as spiky clutter peaks can clearly be seen.
Figure 11.
Binary detection map after applying the proposed pre-detection algorithm. The pre-detected ship signal (left) as well as spiky clutter peaks can clearly be seen.
Figure 12.
Ratio of the false alarm rates over range for X-band HH (top), VV (middle) and HV (bottom) polarization before (blue) and after pre-detection and target cancellation (red). Note that a ship target is present at around 42° incidence angle.
Figure 12.
Ratio of the false alarm rates over range for X-band HH (top), VV (middle) and HV (bottom) polarization before (blue) and after pre-detection and target cancellation (red). Note that a ship target is present at around 42° incidence angle.
Figure 13.
Doppler centroid map estimated from (a) linearly and (b) circularly acquired F-SAR L-band HH polarized RC data. The ship histories in both (a,b) can be clearly seen. (c,d) Doppler centroid maps re-estimated after cancelling the potential targets using the proposed pre-detection algorithm.
Figure 13.
Doppler centroid map estimated from (a) linearly and (b) circularly acquired F-SAR L-band HH polarized RC data. The ship histories in both (a,b) can be clearly seen. (c,d) Doppler centroid maps re-estimated after cancelling the potential targets using the proposed pre-detection algorithm.
Figure 14.
(
a) RC radar data, (
b) Google Earth image and (
c) Pauli image corresponding to
Figure 13a. Sandbanks can be clearly observed in the Google Earth image. The bright spots in the Pauli image are strong scatterers, e.g., buoys or ships.
Figure 14.
(
a) RC radar data, (
b) Google Earth image and (
c) Pauli image corresponding to
Figure 13a. Sandbanks can be clearly observed in the Google Earth image. The bright spots in the Pauli image are strong scatterers, e.g., buoys or ships.
Figure 15.
Range-Doppler image of a target free image patch (a) before and (b) after clutter normalization. The normalized average power profiles of (a,b) are shown in (c).
Figure 15.
Range-Doppler image of a target free image patch (a) before and (b) after clutter normalization. The normalized average power profiles of (a,b) are shown in (c).
Figure 16.
Data containing a ship target: (a) range-Doppler image before clutter normalization, (b) average Doppler spectrum estimated without using pre-detection for removing the target from (a,c) normalized image after using the average Doppler spectrum from (b,d) target free estimation of average power spectrum after using pre-detection algorithm, (e) normalized image after using (d).
Figure 16.
Data containing a ship target: (a) range-Doppler image before clutter normalization, (b) average Doppler spectrum estimated without using pre-detection for removing the target from (a,c) normalized image after using the average Doppler spectrum from (b,d) target free estimation of average power spectrum after using pre-detection algorithm, (e) normalized image after using (d).
Figure 17.
Estimated texture parameter of the K-distribution along (a,c) range and (b,d) azimuth using data acquired during a linear and circular flight.
Figure 17.
Estimated texture parameter of the K-distribution along (a,c) range and (b,d) azimuth using data acquired during a linear and circular flight.
Figure 18.
Binary detection map based on the K-distribution obtained from the same RC F-SAR X-band HH polarized data shown in
Figure 10. The detected ship signal (left) and high sea clutter spikes can be clearly observed.
Figure 18.
Binary detection map based on the K-distribution obtained from the same RC F-SAR X-band HH polarized data shown in
Figure 10. The detected ship signal (left) and high sea clutter spikes can be clearly observed.
Figure 19.
Binary detection map in range-Doppler domain using (a) K-distribution and (b) K-Rayleigh distribution. The thresholds estimated in both the cases are shown on the top right. The X-band HH F-SAR data were used as an input. The detection maps were generated using 128 azimuth and 512 range samples, the desired false alarm rate was set to .
Figure 19.
Binary detection map in range-Doppler domain using (a) K-distribution and (b) K-Rayleigh distribution. The thresholds estimated in both the cases are shown on the top right. The X-band HH F-SAR data were used as an input. The detection maps were generated using 128 azimuth and 512 range samples, the desired false alarm rate was set to .
Figure 20.
(
a) Range-Doppler image showing the total range of the complete scene and 128 Doppler bins respectively (cf. black box in
Figure 4 bottom right). The ship signal is highlighted by the red box. (
b) Scaled detail of the red box from (
a); (
c) the clustered ship signal with its centroid and the bounding box. The ship pixels shown in this example were detected using the K-distribution.
Figure 20.
(
a) Range-Doppler image showing the total range of the complete scene and 128 Doppler bins respectively (cf. black box in
Figure 4 bottom right). The ship signal is highlighted by the red box. (
b) Scaled detail of the red box from (
a); (
c) the clustered ship signal with its centroid and the bounding box. The ship pixels shown in this example were detected using the K-distribution.
Figure 21.
Flight tracks flown during the two-day North Sea campaign (top: day 1; bottom: day 2).
Figure 21.
Flight tracks flown during the two-day North Sea campaign (top: day 1; bottom: day 2).
Figure 22.
Simultaneously acquired fully polarimetric X- and L-band data of the region around Cuxhaven and the corresponding AIS data.
Figure 22.
Simultaneously acquired fully polarimetric X- and L-band data of the region around Cuxhaven and the corresponding AIS data.
Figure 23.
(a) Google Earth image showing a part of the test site. The region within the white box marks the area where the data were acquired during (b) a linear and (c) a circular F-SAR flight track. The red and yellow ellipses in (b,c) are the 3 dB antenna footprints of the X- and L-band antenna, respectively.
Figure 23.
(a) Google Earth image showing a part of the test site. The region within the white box marks the area where the data were acquired during (b) a linear and (c) a circular F-SAR flight track. The red and yellow ellipses in (b,c) are the 3 dB antenna footprints of the X- and L-band antenna, respectively.
Figure 24.
Logarithmic PDFs of different distribution functions plotted for (
a) near (
b) mid and (
c) far range using the data acquired during the linear flight track (cf.
Figure 23b). The estimated parameters corresponding to different distribution functions are shown in the legends of the plots, apart from the 3MD model since it has 8 unknowns.
Figure 24.
Logarithmic PDFs of different distribution functions plotted for (
a) near (
b) mid and (
c) far range using the data acquired during the linear flight track (cf.
Figure 23b). The estimated parameters corresponding to different distribution functions are shown in the legends of the plots, apart from the 3MD model since it has 8 unknowns.
Figure 25.
Logarithmic PDFs of different distribution functions plotted for (
a) near (
b) mid and (
c) far range using data acquired during the circular flight track (cf.
Figure 23c). The estimated parameters corresponding to different distribution functions are shown in the legends of the plots.
Figure 25.
Logarithmic PDFs of different distribution functions plotted for (
a) near (
b) mid and (
c) far range using data acquired during the circular flight track (cf.
Figure 23c). The estimated parameters corresponding to different distribution functions are shown in the legends of the plots.
Figure 26.
Average Doppler spectrum of the linearly acquired data estimated in near, mid and far range. The ambiguities cause a variation in the average power in the noise region of the spectrum.
Figure 26.
Average Doppler spectrum of the linearly acquired data estimated in near, mid and far range. The ambiguities cause a variation in the average power in the noise region of the spectrum.
Figure 27.
Logarithmic CCDFs of different distribution functions plotted for (
a) near (
b) mid and (
c) far range. These plots are generated from the same data used for generating the plots shown in
Figure 24.
Figure 27.
Logarithmic CCDFs of different distribution functions plotted for (
a) near (
b) mid and (
c) far range. These plots are generated from the same data used for generating the plots shown in
Figure 24.
Figure 28.
Logarithmic CCDFs of different distribution functions plotted for (
a) near (
b) mid and (
c) far range. These plots are generated from the same data used for generating the plots shown in
Figure 25.
Figure 28.
Logarithmic CCDFs of different distribution functions plotted for (
a) near (
b) mid and (
c) far range. These plots are generated from the same data used for generating the plots shown in
Figure 25.
Figure 29.
(a) Linearly acquired real single-channel HH polarized RC X-band radar data. (b) Corresponding binary detection map shown in time-domain after applying CFAR based ship detection in range–Doppler domain. K-Rayleigh distribution function was used in the near and mid ranges, and the 3MD model was used in the far range of the data. The desired false alarm rate was set to . The detected ship signal is clearly visible in the RC data and in the detection map.
Figure 29.
(a) Linearly acquired real single-channel HH polarized RC X-band radar data. (b) Corresponding binary detection map shown in time-domain after applying CFAR based ship detection in range–Doppler domain. K-Rayleigh distribution function was used in the near and mid ranges, and the 3MD model was used in the far range of the data. The desired false alarm rate was set to . The detected ship signal is clearly visible in the RC data and in the detection map.
Figure 30.
(a) Circularly acquired real single-channel HH polarized RC X-band radar data. (b) Corresponding binary detection map shown in time-domain after applying CFAR based ship detection in range–Doppler domain. K-Rayleigh distribution was used in the near and mid ranges, and the 3MD model was used in the far range of the data. The desired false alarm rate was set to . The detections marked by the red circles are due to the interfering signals from a ground surveillance radar located close to the test site (for visualization purposes not all of the interfering signals are marked).
Figure 30.
(a) Circularly acquired real single-channel HH polarized RC X-band radar data. (b) Corresponding binary detection map shown in time-domain after applying CFAR based ship detection in range–Doppler domain. K-Rayleigh distribution was used in the near and mid ranges, and the 3MD model was used in the far range of the data. The desired false alarm rate was set to . The detections marked by the red circles are due to the interfering signals from a ground surveillance radar located close to the test site (for visualization purposes not all of the interfering signals are marked).
Figure 31.
(a) Circularly acquired real single-channel HH polarized RC L-band radar data. (b) Binary detection map shown in time-domain after applying CFAR based ship detection in range–Doppler domain. K-Rayleigh distribution was used in the near and mid ranges, and the 3MD model was used in the far range of the data. The desired false alarm rate was set to . The detections marked by the red circles are due to the interfering signals from a ground surveillance radar located close to the test site (for visualization purposes not all of the interfering signals are marked).
Figure 31.
(a) Circularly acquired real single-channel HH polarized RC L-band radar data. (b) Binary detection map shown in time-domain after applying CFAR based ship detection in range–Doppler domain. K-Rayleigh distribution was used in the near and mid ranges, and the 3MD model was used in the far range of the data. The desired false alarm rate was set to . The detections marked by the red circles are due to the interfering signals from a ground surveillance radar located close to the test site (for visualization purposes not all of the interfering signals are marked).
Figure 32.
RC F-SAR X-band VV polarized radar data with a ship moving at (a) 45°, (b) 90° and (c) 0° w.r.t the flight track. The detection results corresponding to (a–c) are shown in (d–f) respectively. Only the K-Rayleigh distribution was used for detection because the maximum incidence angle in the data is below 50°. The desired false alarm rate was set to .
Figure 32.
RC F-SAR X-band VV polarized radar data with a ship moving at (a) 45°, (b) 90° and (c) 0° w.r.t the flight track. The detection results corresponding to (a–c) are shown in (d–f) respectively. Only the K-Rayleigh distribution was used for detection because the maximum incidence angle in the data is below 50°. The desired false alarm rate was set to .
Table 1.
Measured target SCNR before and after clutter normalization.
Table 1.
Measured target SCNR before and after clutter normalization.
Range-Doppler Image | Target SCNR [dB] |
---|
Before normalization (Figure 16a) | 24.02 |
After normalization but without pre-detection (Figure 16c) | 14.20 |
After normalization with pre-detection and target cancellation (Figure 16e) | 23.08 |
Table 2.
Radar system and acquisition geometry parameters for the linear and circular flight.
Table 2.
Radar system and acquisition geometry parameters for the linear and circular flight.
Acquisition Parameters | Linear | Circular |
---|
Average platform velocity [m/s] | 91.4 | 83.55 |
Platform altitude above ground [m] | 5638 | 5637 |
Total observation time along azimuth [s] | 90 | 400 |
Number of SAR image(s) used | 1 | 1 |
Azimuth spacing [m] | 0.038 | 0.034 |
Chirp bandwidth [MHz] for X- and L-band | 384, 150 |
Incidence angle range [°] | 15–60 |
Radar wavelength [m] for X- and L-band | 0.0306, 0.226 |
Pulse repetition frequency [Hz] | 2403.85 |
Total number of range samples | 17,723 |
Ground swath [km] | 8 |
Range Resolution [m] for X- and L-band | 0.39, 1.0 |
Range sample spacing [m] for X- and L-band | 0.3, 0.6 |
Azimuth antenna length [m] for X- and L-band | 0.3 m (Transmit), 0.2 m (Receive) (X-band) |
0.3 m (Transmit), 0.3 m (Receive) (L-band) |
Geographical coordinates | Shown in Figure 23a |
Table 3.
Estimated threshold errors for different clutter models for linearly acquired F-SAR data.
Table 3.
Estimated threshold errors for different clutter models for linearly acquired F-SAR data.
Clutter Models | Near Range | Mid-Range | Far Range |
---|
CCDF |
---|
| | | |
---|
K-NLLSQ | 3.97 | 8.01 | −10.34 | −2.16 |
K-Vstat | 2.41 | 6.89 | - |
K-Xstat | 3.23 | 7.61 | - |
Chi-square | 6.98 | 8.87 | −10.34 | −4.98 |
3MD | 5.62 | 8.27 | −10.34 | −5.17 |
K-Rayleigh | −5.79 | −0.26 | - |
Table 4.
Estimated threshold error for different clutter models for circularly acquired F-SAR data.
Table 4.
Estimated threshold error for different clutter models for circularly acquired F-SAR data.
Clutter Models | Near Range | Mid-Range | Far Range |
---|
CCDF |
---|
| | |
---|
K-NLLSQ | 6.89 | 6.02 | −5.86 |
K-Vstat | 5.19 | 4.60 | - |
K-Xstat | 6.19 | 5.49 | - |
Chi-square | 9.70 | 7.73 | −11.65 |
3MD | 8.94 | 6.94 | −10.86 |
K-Rayleigh | −6.68 | 2.27 | - |
Table 5.
False alarm rate errors for linearly acquired data. The values in the table are the ratio between the estimated actual false alarm rate and the set false alarm rate of .
Table 5.
False alarm rate errors for linearly acquired data. The values in the table are the ratio between the estimated actual false alarm rate and the set false alarm rate of .
Distribution Functions | Near Range | Mid-Range | Far Range |
---|
K-NLLSQ | 80.5 | 112.1 | 3.08 |
K-Vstat | 35.1 | 57.1 | - |
K-Xstat | 56.9 | 86.8 | - |
Chi-square | 277.4 | 242.9 | 2.43 |
3MD | 149.2 | 135.9 | 1.56 |
K-Rayleigh | 1.31 | 1.68 | - |
Table 6.
False alarm rate errors for circularly acquired data. The values in the table are the ratio between the estimated actual false alarm rate and the set false alarm rate of .
Table 6.
False alarm rate errors for circularly acquired data. The values in the table are the ratio between the estimated actual false alarm rate and the set false alarm rate of .
Distribution Functions | Near Range | Mid-Range | Far Range |
---|
K-NLLSQ | 63.3 | 74.6 | 12.2 |
K-Vstat | 30.6 | 38.9 | - |
K-Xstat | 46.9 | 55.9 | - |
Chi-square | 422.4 | 234.9 | 9.43 |
3MD | 257.9 | 154.7 | 7.73 |
K-Rayleigh | 2.03 | 2.08 | - |