1. Introduction
High-frequency surface wave radar (HFSWR) has the advantages of long detection range, real-time, and continuous operation in all weathers compared with microwave radar [
1,
2], and has been used in most coastal countries for sustained observations of the ocean surface. Thus far, there are more than 400 HF radar stations around the world for ocean observations [
3,
4]. By processing the echo data, HFSWRs are used to serve various societal applications such as ocean current and wave monitoring [
5], oil spill pollution trajectory forecasting [
6], and tsunami warning [
7,
8], and so on. At the same time, it also plays an important role in ship detection for monitoring the 200-nautical-mile exclusive economic zone. It should be noted that the maximum radar detection range depends on its frequency, bandwidth, and power. With a typical bandwidth of 100 kHz, an operating frequency of 8 MHz, and 30 watts of transmitting power, the WEllen RAdar (WERA) achieves ship detection ranges up to 200 km [
9]. With a frequency of 4.55 MHz, a bandwidth of 25 kHz, and an average radiated power of 40 watts, a long-range SeaSonde high-frequency radar can “see” ships to a range of approximately 120 km [
10]. According to the antenna type, HFSWR can be classified into two main families [
11]. One class is the phased array system. An example of a phased array system is the WERA with a linear receiving antenna array developed by the University of Hamburg [
12,
13]. WERA was designed to allow for a wide range of working frequencies, spatial resolutions, and antenna configurations. In addition to measuring ocean currents and wave mapping, WERA can also be used for ship target detection and tracking [
14,
15]. The other class is the crossed-loop/monopole (CLM) antenna system [
3]. These radar systems mostly consist of the SeaSonde radar system developed by Coastal Ocean Dynamics Applications Radar (CODAR) Ocean Sensors, Ltd. [
16,
17]. SeaSonde radars are also used to detect and track ships entering and leaving ports, which achieves multi-use of HF radar [
18,
19]. Now, real-time vessel detections for the approaches to New York Harbor and the Delaware Bay are provided by SeaSonde radar systems. These detections are supplied to the Naval Research Lab’s (NRL) Open Mongoose data fusion engine where they are turned into vessel tracks using a combination of data from different sensors [
20]. Another example is the Ocean State Monitoring and Analyzing Radar (OSMAR) developed by Wuhan University, which is available in both a phased array [
21] and compact CLM system [
22]. The advantage of a compact CLM radar system is that it can save valuable coastal resources and facilitate installation and maintenance, but its small antenna aperture also means a low spatial gain, which makes the target echoes become more easily submerged by the sea clutter. Meanwhile, the CLM antenna may be distorted due to the surrounding obstacles within a distance of 1–2 wavelengths from the antenna [
23]. The surrounding objects may introduce an error of up to 10°–15° to the estimation of the direction of arrival (DOA) [
23]. Therefore, for the compact HF radar systems deployed to detect ship targets, some cooperative or non-cooperative signal sources are usually used to calibrate the measured CLM antenna pattern [
24,
25]. As we know, the ship detection threshold depends on the target radar cross section (RCS). In the HF band, the ship RCS fluctuates within a confined range with radar wavelength [
26,
27]. Emery et al. [
28] found that the ships’ radial velocities and spectral amplitudes can vary significantly as they move within the radar coverage area, and that larger ships are likely to provide stronger backscatter. Small ships tend to have lower RCS since the height of a ship has an important significance on the ship’s RCS [
29]. Echoes from small ships are often masked by those from other large ships. Therefore, HFSWR ship detection is a challenging problem.
According to the Bragg scattering mechanism, the first-order echoes appear as two strong spectral peaks symmetrically located on both sides of the zero Doppler frequency, while the surrounding second-order spectral components are lower than their first-order counterparts [
30,
31]. When the radial velocities of the target and the Bragg wave are approximately the same, the target echo usually falls into the Bragg region so that target masking occurs. In addition, when multiple targets of different sizes at the same distance and direction from the radar have similar radial velocities, the Doppler spectral peaks of large targets tend to mask those of small targets, which can also cause the missed detection of small targets. The detection of small ships is more challenging, and it depends on many factors such as radar frequency, integration time, target cross section, and sea state conditions. The clutter level can be reduced by lowering the radar operating frequency [
32,
33]. A higher bandwidth and antenna directivity are recommended to reduce the clutter area. A different length of echo data will result in a different signal-to-noise ratio (SNR) of the target and the corresponding detection threshold is also different. Roarty et al. [
34] analyzed the relationship between detection threshold and data length, and they found that a coherent integration time (CIT) of 1–2 min had the highest detection probability. Compared with large targets, small targets with a low RCS are more difficult to be detected. The constant false alarm rate (CFAR) algorithm [
35,
36] has been widely used for radar target detection. For the case of a homogeneous environment, a cell average CFAR (CA-CFAR) [
37] is optimal for target detection. However, a homogeneous sea environment is rarely seen in reality. To address the non-homogeneous environments, the smallest of CFAR (SO-CFAR) [
38] and the greatest of CFAR (GO-CFAR) [
39] were proposed, but the performance of these two detectors drops significantly for targets in the clutter-edge and multi-target scenario, respectively. The ordered statistics CFAR (OS-CFAR) [
40] and its variants such as automatic censored mean level CFAR (ACMLD-CFAR) [
41], generalized OS-CFAR (GOS-CFAR) [
42], and so on were developed, and this type of CFAR processor exhibits a good performance in multi-target and clutter transition situations. The limitation of these methods is that they make assumptions about the nature or composition of the background, but once the assumptions are not valid, as in a real fluctuating environment, their performance drops dramatically. The trimmed-mean CFAR [
43] and the variably trimmed-mean CFAR [
44] are other types of CFAR detectors, which have a robust performance in a non-homogeneous environment but suffer performance losses in a homogeneous case. In addition, it is difficult to apply a single CFAR detector to work satisfactorily in both homogeneous and non-homogeneous environments, which may occur alternately in practice. To address this problem, composite CFAR detectors were developed for accommodating a variety of environments. For example, the adaptive order statistic (AOS) CFAR [
45] and the selection and estimation (SE) test processor [
46], and variability index CFAR (VI-CFAR) [
47] have the ability to select the appropriate CFAR detector for the current operational environment. The VI-CFAR detector consists of three CFAR detectors: CA-CFAR, GO-CFAR, and SO-CFAR. It selects the most appropriate of these by utilizing the variability index (VI) and mean ratio (MR) statistics. However, the performance of VI-CFAR degrades severely if there are interfering targets distributed on either side of the test cell. Recently, for the scenario with multi-target and targets at the clutter edge, several new CFAR detectors such as cell under test inclusive CFAR [
48], first-order difference CFAR (FOD-CFAR) [
49], and second-order difference CFAR (SOD-CFAR) [
50,
51] have been developed. When the statistical distribution characteristics of the clutter do not satisfy the hypothesized distribution, the above CFAR detectors may fail. For SOD-CFAR, the number of interfering targets is estimated based on the minimum of the second-order difference of the ordered samples in the reference window. By using the Shapiro–Wilk (S–W) test [
52,
53] method, SOD-CFAR implements the uniformity test on the remaining samples after removing interfering targets. However, the S–W test assumes a Gaussian distribution, and it is not suitable for cases with a uniform distribution [
54]. In other words, when the distribution characteristic of the clutter located in reference units is not Gaussian, the SOD-CFAR detector may not work. In practical application, the target number and distribution property of reference units are often unknown. Therefore, the decision threshold of the cell under test (CUT) could be easily raised by interference, clutter, and other larger ship targets located in the reference units. As a result, these CFAR detectors generally have a poor detection performance when the target appears at the Bragg peaks’ edge or for cases with multiple targets. To address this problem, the time–frequency constant false alarm rate (TF-CFAR) method is proposed, which can directly extract target ridges and will not be significantly affected by sea clutter and other ship’s signals.
TF representation [
55,
56,
57,
58] provides an effective way to analyze multi-component signals and has been applied in radar target detection [
59,
60,
61]. Panagopoulos and Soraghan [
62] presented a method for weak target detection by X-band radar using a set of three signal processing techniques (i.e., signal averaging, time–frequency representation, and morphological filtering) to suppress unwanted sea clutter radar echo. However, sea echoes of an X-band radar are quite different from those of an HF radar in terms of time–frequency characteristics [
59,
63], which limits the application of the method in [
62] to only X-band radar. Moreover, it may be inaccurate if the target detection in the TF plane is only based on the duration of TF ridges because such a duration is sometimes shorter than that of sea clutter and interference. For targets at the HFSWR clutter edge, Stankovic et al. proposed a decomposition method based on S transform [
64] to separate a target signal from heavy sea clutter. When the target signal approaches the first-order sea clutter in the TF plane, it is very difficult to distinguish the target and clutter decomposition components [
65], thus, the S method will fail. To overcome the above disadvantages, Zuo et al. [
66] proposed a method based on TF iteration decomposition to detect slow-moving weak targets in sea clutter. Two criteria, i.e., signal duration and time–frequency concentration, are applied to determine the presence of weak target signal components, but they may also be easily affected by sea clutter and interference. In addition, the number of iterations needs to be adjusted manually to obtain the best detection performance for weak targets. Besides the above methods, the combination of TF representation and image segmentation has also been studied and applied in HF radar target detection. Li et al. used discrete wavelet transform to reconstruct ship target signals from the range-Doppler (RD) image contaminated by sea clutter [
67]. After the removal of sea clutter and interference, the Ostu algorithm [
68] is used for the adaptive segmentation of the RD grayscale images and identification of ship targets. Likewise, the detection threshold also needs to be adjusted adaptively according to clutter intensity, and weak target components may be easily mistaken as background noise. Cai et al. used synchro-extracting transform (SET) to represent radar signals and the Ostu algorithm to extract the TF ridges of ships [
69]. Although their method detected weak ship signals successfully, its disadvantages remain the same as [
68]. For HFSWR, Yang et al. [
70] proposed a TF domain binary integration method to improve the detection of weak target signals, and they reported that the combination of CFAR and TF-CFAR can lead to a further improvement. Although the time–frequency binary integration CFAR (TF-BI-CFAR) in [
70] improves the performance of weak targets’ detection, the method still suffers from the masking problem due to strong clutter and large targets, so that the detection performance in the scenarios of multi-target and clutter edge is poor. Later, Yang et al. [
71] found that the log-normal distribution was optimal to model sea clutter in the TF domain, and with this model they achieved a better performance for weak and non-stationary target detection than other conventional CFAR detectors.
The above target detection methods involving the TF domain analysis mainly focus on signal representations or weak signal detection, and have not given enough consideration to the case of multi-target and targets at the Bragg edge, where target masking often happens. In this paper, a TF-CFAR method is developed to improve the performance of clutter-edge targets and multi-target detection. Multi-synchrosqueezing transform (MSST) [
72] is used to represent the radar signal in a TF image and the Hessian matrix is adopted to identify TF ridge candidates. Whether a single TF ridge belongs to a ship or not is determined by a detection threshold. Before target detection, the relationship between the detection threshold and the false alarm probability (
Pfa) is calculated by fitting a probability distribution model of sea clutter. The advantage of combining MSST and the Hessian matrix is that the TF ridges of multi-targets can be separated easily. The detection of TF ridges without using reference units can avoid targets from being missed in strong clutter and multi-target scenarios. To validate the proposed method, a dataset collected by the Ocean State Monitoring and Analyzing Radar, type SD (OSMAR-SD) on 5 October 2015 is used along with the ship records from an automatic identification system (AIS) as the ground truth. Results show that the method proposed in this paper outperforms the conventional CFAR and TF-BI-CFAR methods for HFSWR.
The remaining sections of this paper are organized as follows.
Section 2 describes the target signal representation, extraction, and detection in the TF domain. Experimental results are illustrated in
Section 3.
Section 4 gives some discussions.
Section 5 contains a brief conclusion.