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Article

Cascaded Detection Method for Ship Targets Using High-Frequency Surface Wave Radar in the Time–Frequency Domain

1
College of Information Science and Engineering, Henan University of Technology, Zhengzhou 450001, China
2
School of Electronic Information, Wuhan University, Wuhan 430072, China
3
Yangtze Delta Region Institute, University of Electronic Science and Technology of China, Huzhou 313001, China
4
Institute for Complexity Science, Henan University of Technology, Zhengzhou 450001, China
5
Electrical and Computer Engineering, Memorial University of Newfoundland, St. John’s, NL A1B 3X5, Canada
*
Author to whom correspondence should be addressed.
Remote Sens. 2025, 17(15), 2580; https://doi.org/10.3390/rs17152580
Submission received: 18 June 2025 / Revised: 22 July 2025 / Accepted: 23 July 2025 / Published: 24 July 2025

Abstract

Compact high-frequency surface wave radars (HFSWRs) utilize miniaturized antennas, resulting in lower antenna gain and a reduced signal-to-noise ratio (SNR) for target echoes. Due to noise interference, ship echoes in the noise region often fall below the detection threshold, leading to missed detections. To address this issue, this paper proposes a cascaded detection method in the time–frequency (TF) domain to improve ship detection performance under such conditions. First, TF features are extracted from TF representations of ship and noise signals. Supervised machine learning algorithms are then employed to distinguish targets from noise, reducing false alarms. Next, a non-constant false alarm rate (CFAR) threshold is computed based on the noise mean, standard deviation, and an adjustment factor to improve detection robustness. Experiments show that the classification accuracy between the ship and noise signals exceeds 99%, and the proposed method significantly outperforms the conventional CFAR and TF-domain CFAR in terms of detection performance.

Graphical Abstract

1. Introduction

Over-the-horizon detection (OTH) of maritime targets holds significant value in both civilian and military domains, including maritime sovereignty protection, navigation, anti-smuggling, and long-range early warning [1,2]. HFSWR enables OTH detection by exploiting the diffraction characteristics of 3–30 MHz electromagnetic waves propagating along the sea surface, facilitating over-the-horizon detection of the observation area and continuous monitoring of soft targets (wind, waves, and currents) and hard targets (ships and low-altitude aircraft) within the ocean’s exclusive economic zone. Based on the type of receiving antenna, HFSWR can be classified into the compact [3] and array types [4]. The compact type uses monopole cross-loop antennas, which require less space and are easier to install and maintain. However, limited by the size of the antenna aperture, its beam is relatively wide, and the received echo gain is low, leading to a weak SNR of echo from ships on the sea surface. Additionally, affected by factors such as background noise, sea clutter, and radar cross section (RCS) fluctuations, the echo signals of ship targets are unstable and observability is low, posing significant challenges for ship target detection in complex marine environments [5,6].
Based on the statistical model of sea clutter, the CFAR method can adaptively adjust the detection threshold according to changes in clutter power to maintain a stable false alarm rate and has been widely used in radar systems. By estimating the mean of reference cell samples on both sides of the target, Finn et al. proposed a cell-averaging (CA) target detection algorithm [7]. Under homogeneous clutter, the detection performance of CA-CFAR is optimal. In the presence of sharp sea clutter or interferences, CA-CFAR can result in excessive false alarms. In multi-target environments, its detection performance degrades significantly, leading to the target-masking phenomenon. To reduce false alarms caused by noise and edge interference, Hansen proposed the Greatest of CFAR (GO)-CFAR [8]. To address performance degradation in multi-target scenarios, Trunk proposed the Smallest of (SO)-CFAR [9]. By sorting the reference cell samples and selecting a specific ranked sample as the estimate of clutter power level, Rohling proposed the Ordered Statistics (OS)-CFAR [10]. This method outperforms mean-based CFAR algorithms in detecting multi-targets. Based on the idea of ordered statistics, subsequent researchers estimated the background clutter power intensity by optimizing the reference sample selection strategy and proposed improved methods such as Censored Mean Level Detector (CMLD)-CFAR [11], Trimmed-Mean (TM)-CFAR [12], and Switching (S)-CFAR [13,14].
In practical environments, clutter and interference distributions are non-homogeneous and vary over time. The radar target detector needs to select an appropriate decision strategy based on the changes in the detection background. For non-uniform detection backgrounds, some adaptive selection CFAR detectors have been developed. For example, Ensemble (E)-CFAR [15] combines methods such as CA, GO, SO, TM, and Geometric Mean (GM) to form a detection statistic. Variability Index (VI)-CFAR [16] adaptively selects CA-CFAR, GO-CFAR, and SO-CFAR for target detection based on the mean ratio of clutter samples within the preceding and following reference windows. To enhance target detection performance in non-homogeneous environments, CFAR detectors tailored for non-homogeneous clutter and multi-target environments have been proposed, such as Test Inclusive (TI)-CFAR, (First-order Difference) FOD-CFAR, and Second-order Difference (SOD)-CFAR [17,18,19], utilizing the statistical characteristics of clutter samples within a sliding window. In the presence of exponential noise, Weinberg proposed an interference target control method in sliding window detection using a Bayesian approach [20]. Based on the Bayesian theory, Zhu applied Weinberg’s method to VI-CFAR and proposed a Bayesian Variability Index (BVI)-CFAR method [21]. This method improves the anti-interference ability of VI-CFAR in a multitarget environment by background region segmentation, evaluating clutter power level, and optimizing the selection strategy of a regional interference control model. This method, like [20], is mainly applied to radar target detection under the background of exponential noise. In practical environments, the background of radar target detection may change over time, and this method may become ineffective. Subsequently, based on the Weibull clutter distribution model, Zhu proposed a Bayesian CFAR detector via interference control [22]. Simulation results demonstrate that this detector can predict and compensate for interference within the reference cells, enhancing the anti-interference ability of the traditional detector in heterogeneous environments. In practical detection environments, it is difficult to predict the number of interfering targets and the parameters of the probability density distribution of sea clutter in advance. Therefore, traditional CFAR is easily affected by strong clutter, interference, and noise within the reference cells, leading to missed detection of radar targets and poor detection performance. When detecting ship targets using traditional CFAR, it is based on the “point target” assumption. However, when a ship maneuvers or is affected by noise and sea clutter interference, its Doppler spectrum tends to broaden and split, thereby violating the “point target” assumption and leading to an increased false alarm rate. On the TF plane, the ship target no longer appears as a “point target” but rather as a “line target”, which is more robust to the limitations of the point target assumption. Regardless of whether the target is weak, multiple, non-stationary, or located near clutter, ship echoes consistently manifest as intermittent or continuous “line targets” in TF images. Therefore, detecting ship targets based on the TF ridge of radar echo signals offers an effective and reliable approach.
High-frequency (HF) radar target detection in the range Doppler (RD) map and transform domain has received significant attention in recent years. Lei et al. utilized the Short Time Fourier Transform (STFT) and image region growing segmentation method to detect maneuvering targets and zero-frequency clutter edge targets in skywave OTH high-frequency radar [23]. However, the STFT suffers poor TF energy concentration, resulting in blurred TF ridges, making it difficult to accurately extract target signals in the presence of strong clutter. Jangal et al. applied wavelet decomposition and reconstruction to filter out sea clutter and land clutter signals in RD maps, subsequently obtaining point target signals through image binarization [24]. In practical applications, however, the choice of wavelet basis function and decomposition scale significantly affects the detection results, often causing target signals to be misidentified as noise and removed. Grosdidier et al. proposed using a morphological component analysis to separate target components in RD maps. Simulation experiments have demonstrated that this method shows promising potential and outperforms traditional GOCA-CFAR. The challenge lies in selecting appropriate dictionaries to represent Bragg peaks and target signals, as the first-order sea clutter region is not strictly linear, and the ship target signal is not an ideal point target [25,26], resulting in unstable detection performance. Li et al. improved Jangal’s method by using a peak signal-to-noise ratio-based algorithm to automatically determine the optimal scale of discrete wavelet transform (DWT) and enhanced the target signal using a fuzzy set-based method and adaptive threshold segmentation of the reconstructed RD map to extract target signals [27]. The method outperforms Jangal’s in detection performance [24], although a target SNR as high as 20–40 dB is required for clutter edge detection. This is mainly because clutter edge targets are easily treated as background noise during binarization processing. Building on the work of Jangal and Li, Lu et al. [28] applied a principal component analysis (PCA) to radar coherent channel echo signals, followed by wavelet decomposition and reconstruction to suppress sea clutter signals. As a result, the SNR of ship targets can be improved by more than 10 dB, significantly enhancing the detection performance of weak targets.
The time–frequency analysis (TFA) method represents a one-dimensional (1D) radar echo signal as a two-dimensional (2D) TF image, while transforming the point target signal in the RD map into a line target signal. Based on the energy distribution of the target signal on the TF plane, image processing methods can be employed to extract and detect the ship target signal. Cai et al. [29] successfully separated non-stationary target signals using synchronous extraction transform (SET) and image binarization methods. Experimental results demonstrated that this method outperformed traditional CFAR methods in detecting weak and non-stationary targets. However, a drawback of this approach is that its detection performance is significantly influenced by image segmentation thresholds, leading to high false alarm rates in ship detection under complex clutter and interference backgrounds. Yang et al. proposed a joint detection method that combines TFA and CFAR in the TF domain, termed as the time–frequency binary integration CFAR (TF-BI-CFAR) method. This method uses the ratio between the peak and mean values of the projection curve to determine the extraction boundary of the TF ridge during the preprocessing stage. Due to the fixed ratio threshold, when multiple TF ridges have similar frequencies, they are easily mistaken for a single ridge, potentially leading to missed detections of multiple target signals with close frequencies [30]. Subsequently, based on the TF domain sea clutter distribution model, Yang et al. proposed a fixed-threshold TF CFAR method that improved the detection performance of ship target signals in non-uniform sea clutter environments. However, the target detection threshold is fixed and cannot be adaptively adjusted according to the power levels of noise, interference, and clutter in different scenarios. The anti-interference capability and robustness of this method require further improvement [31]. Qu et al. proposed an RD domain virtual aperture expansion method that overcomes the physical aperture limitation of shipborne HFSWRs through RD processing and motion phase compensation. This method significantly enhances the direction-of-arrival estimation performance of single and multiple targets in strong clutter environments, addressing the limitations of traditional time domain approaches in practical applications [32]. Subsequently, Qu et al. proposed an RD Domain Spatio-Temporal Data Block Extrapolation method (RDSDBE) [33], which constructs spatio-temporal data blocks via time domain segmentation and extrapolates virtual array elements. This method resolves the failure of traditional aperture expansion techniques in shipborne HFSWR under strong clutter, significantly improving multi-target DOA estimation performance while being compatible with continuous platform motion, providing new insights for maneuvering detection of shipborne HFSWR.
To enhance the detection performance of HFSWR for ship targets, this paper proposes a cascaded TF domain detection method. In target detection, the proposed method first extracts TF features from the set of TF ridges associated with the noise region. With the aid of AIS information, labels for both noise and target signals are obtained. Subsequently, supervised machine learning techniques are applied to classify the TF ridges in the noise region, enabling the removal of noise-related TF ridges and mitigating the impact of noise on subsequent constant false alarm rate (CFAR) decisions. This results in a cascaded detection framework in the TF domain, where noise reduction is performed prior to detection, thereby significantly enhancing the performance of ship target detection in noisy environments.

2. Methods

2.1. Theoretical Foundations

Due to the Heisenberg uncertainty principle, the short time Fourier transform (STFT) exhibits limited TF energy concentration, resulting in blurred TF ridges. However, it remains advantageous due to its computational simplicity and immunity to cross-term interference. The synchrosqueezed transform (SST) is a postprocessing technique derived from STFT, was originally introduced by Daubechies through wavelet-based analysis [34]. Synchrosqueezing works by reassigning dispersed TF coefficients to their corresponding instantaneous frequency positions. Let the STFT of the target echo signal s(t) be S T F T ( t , ω ) ; then, the SST is defined as
S S T ( t , η ) = + S T F T ( t , ω ) δ ( η ω ^ ( t , ω ) ) d ω ,
δ η - ω ^ t , ω denotes the synchrosqueezing operator, which yields sharper TF ridges than those produced by conventional STFT. Figure 1 illustrates the TF ridge of a simulated target at a Doppler frequency of −0.22 Hz in the presence of Gaussian noise. The simulation parameters are set as follows: the radar operates at a frequency of 13.15 MHz, with a frequency sweep bandwidth of 60 kHz and a sweep period of 0.54 s. Within each sweep cycle, 256 samples are collected, and a total of 256 frequency sweeps are performed. The target is initialized at a range of 50 km with a radial velocity of −2.5 m/s. As shown in Figure 1b, the SST-based TF ridge is sharper, with significantly better energy concentration compared to the STFT-based ridge in Figure 1a. This sharpness and concentration make SST more conducive to the extraction and detection of radar target signals.
During the coherent integration time (CIT), the Doppler frequency and energy distribution of a target’s TF ridge evolve gradually or abruptly, forming a signal sequence that can be treated as a time series. Accordingly, TF feature extraction begins with analyzing the amplitude information of the ridge, followed by computing time domain feature values. Let the extracted TF ridge be denoted as Ridge(i), where i ∈ [1, 256] indicates the index of each sampling point. The following describes the detailed process of TF ridge feature extraction.
(1)
Mean absolute value: in radar target detection, the average amplitude of the echo signal serves as a primary indicator of target signal strength.
M A V = 1 N i = 1 N R i d g e ( i ) ,
N is the length of the TF ridge, which is equal to 256.
(2)
Aspect ratio: due to fluctuations in the ship’s RCS and observation angle, the TF ridge may appear continuous or intermittent. Additionally, differing radial velocities between the ship and noise cause their energy distributions to occupy separate Doppler frequency bands on the TF plane. Accordingly, the TF ridge aspect ratio is defined to capture this distinguishing characteristic. Let N denote the length of the extracted TF ridge, and W represent the number of Doppler distribution units. The TF ridge aspect ratio can then be expressed as
R N W = N W ,
(3)
Kurtosis: kurtosis characterizes the sharpness of the data distribution along the TF ridge [35]. For a normal distribution, the kurtosis value is equal to 3. A high kurtosis indicates a peaked distribution, while a low kurtosis suggests a flatter profile.
T k u r t o s i s = 1 N i = 1 N ( R i d g e ( i ) m T ) 4 σ T 4 ,
In Equation (4), mT represents the mean of Ridge(i), and σT represents the standard deviation of Ridge(i).
(4)
Skewness: skewness quantifies the asymmetry of the TF ridge amplitude distribution [36], and its calculation formula is as follows.
T s k e n e s s = 1 N i = 1 N ( R i d g e ( i ) m T ) 3 σ T 3 ,
(5)
Variance: variance reflects the degree of signal energy dispersion, providing a means to distinguish target, clutter, and noise, as shown in the following equation.
V A R = 1 N 1 i = 1 N ( R i d g e ( i ) m T ) 2 ,
(6)
Average amplitude change: the average amplitude change is computed as the mean of adjacent-point amplitude differences along the TF ridge, reflecting signal complexity.
A A C = 1 N 1 i = 1 N 1 R i d g e ( i + 1 ) R i d g e ( i ) ,
(7)
Peak factor: the peak factor, defined as the ratio of the peak amplitude to the RMS value, indicates the presence of impulsive components in the signal. The calculation formula is as follows:
P F = max ( R i d g e ( i ) ) 1 N i = 1 N R i d g e ( i ) ,
max(·) represents taking the maximum value.
(8)
Ratio of standard deviations after bisection: the standard deviation of the entire TF ridge, denoted as std1, is first computed. The ridge is then bisected, and the standard deviation of one half, denoted as std2, is calculated. The ratio of the standard deviations is as follows:
R s t d = s t d 1 s t d 2 ,
(9)
Ratio of bisected means: the TF ridge coefficients are split into two groups based on the global mean. The means of the upper and lower subsets are denoted as m22 and m21, respectively. The ratio between the two is as follows:
R m e a n = m 22 m 21 ,
(10)
Absolute standard deviation of the difference: this metric resembles the root mean square but is derived from the standard deviation of differences between adjacent TF amplitudes. Its calculation formula is as follows:
D a s d = 1 N 1 i = 1 N 1 ( R i d g e ( i + 1 ) R i d g e ( i ) ) 2 ,
(11)
Integral ratio: the integral value represents the total energy of the TF ridge. The integral ratio compares this energy to that of the surrounding TF region, excluding the ridge. The formula is as follows:
I R = i = 1 N R i d g e ( i ) t = 0 N 2 f = 0 F 2 S ( t , f ) ,
In Equation (12), t represents the duration of the TF ridge, and F represents the set of Doppler bins in the TF region. In the TF plane, noise exhibits a short duration and weak energy distribution, appearing scattered. However, the target signal can be approximated as a single-frequency signal with high TF concentration. Assuming that the TF region where the TF ridge of the target signal is located is represented by S(t, f), the TF amplitude distribution within this region can reflect the energy concentration of the TF ridge. Next, TF features are extracted from the TF region where the TF ridge is located.
(12)
Maximum kurtosis: kurtosis, which represents the normalized fourth-order central moment, characterizes the amplitude distribution within the TF region that encompasses the ridge [37]. It is commonly employed to determine whether a random variable follows a normal distribution.
K m = t = 0 N 1 f = 0 F 1 S ( t , f ) 4 t = 0 N 1 f = 0 F 1 S ( t , f ) 2 2 ,
(13)
Renyi entropy: Renyi entropy generalizes Shannon entropy and quantifies the TF energy concentration of the target signal for a given order α [38]. The value of Rα indicates the quality of TF concentration: a smaller Rα suggests better TF concentration, while a larger Rα indicates poorer TF concentration, with α set to 2 in this case.
R α = 1 1 α log 2 t = 0 N 1 f = 0 F 1 S ( t , f ) α ,    ( α 2 ) ,
(14)
Normalized third-order Renyi entropy [39].
R α = 1 1 α log 2 t = 0 N 1 f = 0 F 1 S ( t , f ) α ,    ( α 2 ) ,
(15)
Gradient: in the TF domain, the radar echo is represented as a 2D image, denoted as z = S(t, f). Assuming that z has continuous first-order partial derivatives within S, the gradient at each point (t, f) can be calculated using the following formula.
g r a d z = S t i + S f j ,
The gradient of each pixel is calculated and accumulated sequentially, and the average gradient feature is obtained by averaging.
(16)
Image entropy: image entropy quantifies signal uncertainty, with higher entropy indicating greater randomness or complexity in the TF image. The formula for calculating image entropy is as follows.
H = k = 1 K p k log 2 p k ,
In Equation (17), k represents the grayscale level, ranging from 0 to 255, with K = 255, and pk denotes the probability of pixels at that level.

2.2. TF Ridge Extraction Method

Applying the SST to the measured radar data, the TF image is as shown in Figure 2b. Figure 2a displays the corresponding RD spectrum. In the TF image, the target ridge line exhibits a longer duration and high energy concentration, while the noise signal changes irregularly and has a shorter duration and weaker energy. These characteristics allow for the classification of radar target and noise signals. When extracting the TF ridge, the TF image is first binarized, as shown in Figure 2c. Image binarization is performed using the triangle threshold method [40], which constructs a triangle on the histogram to determine the threshold by finding the point of maximum distance. This method is particularly effective for processing images with unimodal histograms. The pixels of the binarized image are then accumulated along the time axis, producing a cumulative curve of TF image pixels, where suspected target signals form peaks. Although some noise has been removed as background pixels during the binarization process, residual interference and clutter may still superimpose on the target signal, generating disordered false peaks. Therefore, the boundaries for TF ridge extraction are determined by the projection area where the peaks are located, enhancing the anti-interference ability of target signal extraction. The projection curve is processed using a moving average filter with a window width of 64 to obtain a segmentation threshold curve, which provides the boundary values of the peak projection area, as shown in Figure 2d. Using this moving average threshold to determine the boundaries for TF ridge extraction can reduce false alarms caused by other pseudo-peaks formed by noise, interference, and clutter. It can also eliminate peak projection areas that are smaller than the moving average threshold, further lowering false alarms. To extract complete TF ridges, a maximum value search is employed to identify the single TF ridge with the highest energy within the segmented boundaries, as shown in Figure 2e.

2.3. Cascade Detection Method

Using AIS information, parameters such as the ship’s identification number, longitude, latitude, ground track, and ground speed can be obtained for ships navigating at sea. By mapping this geographic data onto the radar RD map through coordinate transformation, the result shown in Figure 3a is obtained. Through a statistical analysis of ship information received by the AIS, it was observed that some ship targets fall within the noise region, as shown in Figure 3a. Therefore, based on the distribution characteristics of AIS ships, the TF image is divided into noise and non-noise regions, as shown in Figure 3b. Since zero frequency typically represents stationary objects, such as island and buildings, TF ridges at zero-frequency positions are excluded when detecting targets in non-noise regions. Based on the Doppler frequency distribution range of AIS ship targets, it is inevitable that ship targets will fall on the edges of the positive and negative first-order peaks or be completely submerged within them. During preprocessing, the positive and negative first-order peak regions are treated as target regions for TF ridge extraction to facilitate subsequent target detection.
As illustrated in Figure 4, the proposed method consists of three main stages: preprocessing, denoising, and non-CFAR detection. The preprocessing step includes TF representation, binarization, and TF ridge extraction. The binarized image accumulates pixels along the time axis to form a projection curve, followed by the application of a sliding average threshold to the projection curve for TF ridge extraction. Subsequently, the TF ridge extracted from noise regions is subjected to binary classification to obtain the target signal TF ridge. Finally, non-CFAR detection is performed on the TF ridges extracted from non-noise regions and the classified target TF ridges. If the average energy of the TF ridge under test is greater than or equal to the detection threshold, the detection result is “true”, denoted as “H1”; otherwise, the detection result is “false”, denoted as “H0”.
In the TF image, the statistical characteristics of noise fluctuate over time, and the standard deviation also varies accordingly. By setting the threshold as w*σ, an adaptive threshold that changes with noise can be determined, ensuring strong anti-interference capability of the radar detector. The non-CFAR detection method for radar targets in the TF domain primarily calculates the detection threshold T using the mean u and standard deviation σ of the TF image noise, along with the adjustment factor w, as shown in the following equation.
T = u + ω σ ,
During detection, if the average energy of the TF ridge is greater than or equal to the decision threshold T, the ridge is considered a “true” target; otherwise, it is considered a “false” target. Figure 5 shows the variation of radar target detection thresholds calculated from measured radar data across different radar scans and range bins. In a sequence of 60 radar scans, the overall trend of the target detection threshold initially increases and then decreases as the range bin increases, as shown in Figure 5a. Due to the influence of noise or interference, the detection threshold fluctuates between range bins, as depicted in Figure 5b, indicating that the non-CFAR detection method proposed in this paper can adaptively adjust the detection threshold according to changes in background noise or interference power intensity, demonstrating strong anti-interference capabilities.

3. Results

The radar data used in this study is sourced from the Ocean State Measuring and Analyzing Radar (OSMAR)-SD (S stands for Small, Smart, and Super, and D stands for Digital), developed by Wuhan University [41]. The radar is located in Dongshan, Fujian Province, China, and collected synchronous AIS and radar data for three months from September to November 2015. Target detection is conducted on the radar data from the first 30 range bins (i.e., 75 Km). The operating parameters of the radar are shown in Table 1.

3.1. Denoising

A training sample set was constructed using radar echo and AIS data. The radar echo data selected for this experiment was from 22 September 2015. After preprocessing the radar echo data to obtain TF ridges, AIS target matching was performed. The successfully matched TF ridges in the noise region were considered as target samples and labeled as ‘+1’, while the remaining TF ridges in the noise region were treated as noise samples and labeled as ‘−1’. The matching criteria are that the absolute value of the distance error between the radar target and the AIS target is less than or equal to one range bin, and the absolute value of the velocity error is less than or equal to four Doppler bins. Through data sample collection over a one-day period, a total of 22,000 samples are obtained, including 12,000 positive samples (target samples) and 10,000 negative samples (noise samples).
Before applying machine learning algorithms for target and noise classification, the distribution of their TF features should be examined, as shown in Figure 6. In terms of feature separability, Feature 4 (skewness feature) is distinctly separated from Feature 10 and Feature 15, as shown in Figure 6a,b. Feature 15 (gradient feature) shows slightly weaker separation from Feature 16 and Feature 3, with a very small overlapping area, as shown in Figure 6c,d. According to the principles of machine learning for target classification, greater feature separability leads to higher classification accuracy. Based on the TF feature separability shown in Figure 4, it can be concluded that the extracted TF features can effectively distinguish between the target and noise signals in the noise region.
After constructing the sample set, model training is performed using Support Vector Machine (SVM) [42], Decision Tree (43) [43], K-Nearest Neighbor (KNN) [44], and Neural Network (NN) [45] classifiers, with a 5-fold cross-validation. The primary reason for having more target samples than noise samples during training is to enhance the model’s sensitivity to target features. The confusion matrix for the prediction results of target and noise samples is shown in Figure 7. According to the confusion matrix validation results, the classification accuracy of target TF ridges and noise TF ridges in the noise region reaches over 99%, approaching 100%. Based on the extracted TF features and supervised classifiers, effective noise reduction effects are achieved in HFSWR target detection.
Using the data from 22 September 2015 for model training, the trained model was subsequently applied to radar echo data from different dates, with the denoising effects presented in Table 2. The experimental results indicate that using TF features for denoising effectively improve the matching rate of detected targets, thereby enhancing the probability of radar target detection. After denoising, the matching rate can be improved by over 1% compared to before denoising, and the number of detected targets is reduced by more than 20,000 with almost no loss in the number of matched targets. The matching rate, defined as the ratio of the number of targets matched with AIS to the number of detected targets, indirectly verifies the effectiveness of the method.

3.2. Non-CFAR Detection

3.2.1. Ship Target Detection in Noise Regions

Figure 8 presents an example of target detection in the noise region, where the target has an SNR of 3.49 dB and is located at the 25th range bin, equivalent to 62.5 km, with a Doppler frequency of 0.67 Hz, corresponding to a radial velocity of approximately 7.75 m/s. The traditional CFAR method based on sliding windows is affected by the samples from the left and right reference cells, leading to an elevated detection threshold and, consequently, missing the ship target. The TF-based method extends the point target in the Doppler spectrum to a line target, allowing for the observation of the dynamic range of time and velocity changes of the ship target, as shown in Figure 8d,e. The Doppler region where the ship target may be located is identified through projection and a moving average threshold. Subsequently, all potential TF ridge samples in this range bin are extracted through a maximum value search. The TF ridge samples located in the noise region are classified using a machine learning algorithm to obtain candidate target TF ridges. Finally, a non-CFAR detector is designed based on the mean and standard deviation of the noise in Figure 8e to make decisions on the candidate target TF ridges, successfully detecting the target. Experimental results demonstrate that using a machine learning classification method combined with a non-CFAR detector on the TF image is not limited by the inhomogeneous noise variations present in traditional sliding window methods, thus helping to improve the detection probability of ship targets.

3.2.2. Statistical Analysis of Target Detection in Noise Regions

The detection on the TF image is divided into noise and non-noise regions. In the noise region, target detection involves using TF features and classifiers for denoising, followed by non-CFAR decision-making. Since the number of detected targets varies with different false alarm rates and detection thresholds, a comparison is made of the number of detected targets in the noise region and the number of AIS-matched targets when the number of detected targets is equal to 40,000.
The target detection range in the noise regions spans from −0.9529 Hz to −0.6427 Hz and from 0.6427 Hz to 0.9529. As shown in Table 3, the traditional sliding window CFAR method achieves a target matching rate of no more than 1.5%. Among the TF detection methods, the TF-BI-CFAR has a matching rate of 7.32%, while the TF-Non-CFAR cascaded detection method achieves 36.2%, significantly outperforming TF-BI-CFAR and other sliding window CFAR detection methods. This indicates that utilizing TF features for noise reduction can effectively decrease the occurrence of false alarms and improve radar target detection probability. The primary reason for the low target matching rate of traditional sliding window CFAR methods in noise regions is the influence of noise and interference signals within the reference window, which elevates the detection threshold and results in a lower target matching rate.

3.2.3. SNR Distribution of Matching Target in Noise Regions

When the number of detected targets is 40,000, a statistical analysis of the SNR of matched targets in noise area is conducted. As shown in Figure 9, the SNR of matched targets for traditional CFAR is above 0 dB, and the number of matched targets is lower than that of TF-Non-CFAR. Table 4 presents a comparison of the number of matched targets between TF-Non-CFAR and traditional CFAR across different SNR ranges. Below 10 dB, the number of matched targets for TF-Non-CFAR is more than twice that of traditional CFAR, and above 10 dB, it is more than 1.6 times that of traditional CFAR. This sufficiently demonstrates that TF-Non-CFAR outperforms traditional CFAR in detecting weak targets.
To further verify the effectiveness of the proposed method, the performance of TF-Non-CFAR and TF-BI-CFAR in detecting targets in noise areas is compared. The number of detected targets for both methods is 40,000. The number of detected and matched targets in the noise area are summarized in Table 5. TF-Non-CFAR outperforms TF-BI-CFAR in noise regions primarily due to the noise reduction achieved by leveraging TF features and machine learning models. By classifying noise and target signals based on the extracted TF ridges in noise regions, the number of noise signals is significantly reduced. After applying non-CFAR decision-making, the matching rate is at least 6.3% higher than that of TF-BI-CFAR. As shown in Figure 10, the target matching rate of TF-Non-CFAR in noise areas is at least twice that of TF-BI-CFAR, reaching up to five times higher on October 6. These results demonstrate that the cascaded TF-Non-CFAR detection method significantly improves HFSWR’s ship target detection performance in noise areas.

3.3. Statistical Analysis of Matching Targets

Under the same number of detection targets, Figure 11a–d presents the matching rate distribution of the TF methods and the traditional CFAR methods over a four-day detection period. Within the range of 20,000 to 70,000 detection targets, the radar target matching rates of both the TF methods and the traditional CFAR methods gradually decrease as the number of detection targets increases. Among them, the matching rate of the TF methods is significantly higher than that of the traditional CFAR methods, indicating superior detection performance. The matching rates of traditional CFAR methods are not significantly different, with BVI-CFAR and TM-CFAR having slightly higher matching rates than other CFAR methods. However, there is no substantial difference in detection performance overall, indirectly indicating that traditional CFAR methods have a lower detection probability and higher false alarm rates when detecting HFSWR ship targets. Among TF methods, TF-Non-CFAR has a matching rate that is 1% to 4% higher than TF-BI-CFAR, indicating that machine learning-based noise reduction further enhances the detection performance of TF methods for HFSWR ship targets. This can effectively improve the detection probability of HFSWR ship targets and reduce false alarms.

4. Discussion

To analyze the effect of the parameter w on the radar detection probability (Pd) and false alarm probability (Pfa), Figure 12 displays the distribution curves of Pd and Pfa for various values of w. In this context, Pd is defined as the ratio of detected targets matched with AIS data to the total number of detected targets, whereas Pfa is defined as the ratio of detected targets not matched with AIS data to the total number of detected targets. As shown in Figure 12, increasing w leads to a higher Pd, although the rate of increase gradually diminishes and tends to stabilize; similarly, Pfa decreases with increasing w and also tends to stabilize. As w increases, the detection threshold rises, resulting in a reduced number of detected targets. Therefore, to detect as many weak target signals as possible, a lower value of w should be selected. Conversely, to improve the Pd, w should be increased. The appropriate w value needs to be selected based on the actual situation.
Figure 13a,b shows the variation in target matching rate under different noise intensities. The overall trend of noise intensity first increases and then decreases, with local fluctuations of varying degrees, reflecting the time-varying nature of the actual detection environment. Figure 13c presents the distribution curves of matching rates under different w values. When w is fixed and noise power varies, the detection threshold adjusts accordingly, thereby maintaining the detector’s anti-interference capability and robustness. When noise power is fixed, as w increases, the detection threshold will increase, enhancing the radar’s target detection performance but reducing its ability to detect weak targets.
By utilizing prior AIS ship Doppler frequency distribution data, the TF image of an echo signal is segmented into noise and non-noise regions. This paper employs artificial experience to design HFSWR ship target TF features for training a model that classifies noise and ship target. The extracted TF features effectively capture differences in morphology, energy, and other distributions between noise and ship targets, achieving nearly 100% classification accuracy and demonstrating substantial noise reduction. However, due to the limitation of machine learning in nonlinear modeling, the noise reduction model shows relatively poor classification capability for ship targets outside the noise area, specifically in the sea clutter region. This is primarily because, in the sea clutter region, ship target signals are mixed with sea clutter, which hinders the extraction of effective features needed to distinguish between sea clutter and ship targets, leading to poor classification outcomes. Focusing on the characteristics of HFSWR echo signals, future research will explore the use of generative adversarial networks [46], diffusion models [47] to distinguish target signals from sea clutter, thereby addressing the limitation of insufficient real training samples.

5. Conclusions

This study proposes a cascaded detection method for ship targets using HFSWR in the TF domain. By utilizing prior AIS ship data and SST technology, a TF domain dataset of radar ship targets is constructed. Based on the differences in morphology and energy characteristics between noise and ship targets in the TF image, the TF domain features from the noise regions of radar echo signals are extracted. A machine learning-based model is then developed to denoise ship targets within noise regions. Subsequently, a non-CFAR detection method for ship targets in the TF domain is introduced, utilizing the mean, standard deviation, and standard deviation adjustment factor of the noise regions. Experimental results demonstrate that the proposed two-stage cascade detection method, comprising noise reduction followed by decision-making, outperforms traditional sliding window-based CFAR methods. Moreover, the machine learning-based noise reduction significantly improves the detection performance of TF methods for HFSWR ship targets, especially enhancing HFSWR’s ability to detect ship targets within noise regions.

Author Contributions

Conceptualization, H.Z. and Y.T.; methodology, Z.Y.; formal analysis, B.Z.; data curation, H.Z. and Y.T.; writing—original draft preparation, Z.Y.; writing—review and editing, G.L. and W.H.; supervision, P.L. and Y.Q.; funding acquisition, Z.Y. All authors have read and agreed to the published version of the manuscript.

Funding

This research was funded by the National Natural Science Foundation of China, grant number 62401199, and the Open Project of the Institute for Complexity Science, Henan University of Technology, grants CSKFJJ-2024-24 and CSKFJJ-2025-45. The research was also funded by the High-level Talent Program of the Henan University of Technology, grant number 2022BS045.

Data Availability Statement

For the results and data generated during this study, please contact the corresponding author.

Acknowledgments

The authors thank the anonymous reviewers for carefully reading our manuscript and for their comments and suggestions.

Conflicts of Interest

The authors declare no conflicts of interest.

Abbreviations

The following abbreviations are used in this manuscript:
HFSWRHigh-Frequency Surface Wave Radar
SNRSignal to Noise
TFTime–Frequency
CFARConstant False Alarm Rate
RCSRadar Cross Section
CACell Averaging
GOGreatest of
SOSmallest of
OSOrdered Statistics
CMLDCensored Mean Level Detector
TMTrimmed-Mean
S-CFARSwitching-CFAR
E-CFAREnsemble-CFAR
GMGeometric Mean
VIVariability Index
TITest Inclusive
FODFirst-Order Difference
SODSecond-Order Difference
BVIBayesian Variability Index
HFHigh Frequency
RDRange Doppler
STFTShort Time Fourier transform
DWTDiscrete Wavelet Transform
PCAPrincipal Component Analysis
TFATime–Frequency Analysis
1DOne-Dimensional
2DTwo-Dimensional
SETSynchronous Extraction Transform
TF-BI-CFARTime–Frequency Binary Integration-CFAR
SSTSynchrosqueezed Transform
CITCoherent Integration Time
AISAutomatic Identification System
TF-Non-CFARTime–Frequency Non-CFAR
OSMAROcean State Measuring and Analyzing Radar
SDS stands for Small, Smart, and Super, and D stands for Digital
KNNK-Nearest Neighbor
DTDecision Tree
SVMSupport Vector Machine
NNNeural Network
PdDetection Probability
PfaFalse Alarm Probability

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Figure 1. TF ridge of simulation target. (a) STFT; (b) SST.
Figure 1. TF ridge of simulation target. (a) STFT; (b) SST.
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Figure 2. TF ridge extraction process: (a) power spectrum; (b) TF image; (c) binary image; (d) projection curve; (e) extracted TF ridge.
Figure 2. TF ridge extraction process: (a) power spectrum; (b) TF image; (c) binary image; (d) projection curve; (e) extracted TF ridge.
Remotesensing 17 02580 g002aRemotesensing 17 02580 g002b
Figure 3. AIS target distribution and noise region division. (a) AIS target; (b) noise area division.
Figure 3. AIS target distribution and noise region division. (a) AIS target; (b) noise area division.
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Figure 4. Diagram of ship target cascaded detection in time–frequency domain for HFSWR.
Figure 4. Diagram of ship target cascaded detection in time–frequency domain for HFSWR.
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Figure 5. Distribution of detection thresholds when w = 1. (a) Distribution curves of detection thresholds at different range bins for consecutive radar scans; (b) distribution curve of detection thresholds for the first 30 range bins of a single radar scan.
Figure 5. Distribution of detection thresholds when w = 1. (a) Distribution curves of detection thresholds at different range bins for consecutive radar scans; (b) distribution curve of detection thresholds for the first 30 range bins of a single radar scan.
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Figure 6. Distribution of TF features of target and noise samples: (a) feature 4 and feature 10; (b) feature 4 and feature 15; (c) feature 15 and feature 16; (d) feature 15 and feature 3.
Figure 6. Distribution of TF features of target and noise samples: (a) feature 4 and feature 10; (b) feature 4 and feature 15; (c) feature 15 and feature 16; (d) feature 15 and feature 3.
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Figure 7. Validation results of confusion matrices. (a) KNN; (b) DT; (c) SVM; (d) NN.
Figure 7. Validation results of confusion matrices. (a) KNN; (b) DT; (c) SVM; (d) NN.
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Figure 8. Target detection in noise region. (a) RD map; (b) RD spectrum; (c) projection curve; (d) extraction of TF ridge samples; (e) target detection.
Figure 8. Target detection in noise region. (a) RD map; (b) RD spectrum; (c) projection curve; (d) extraction of TF ridge samples; (e) target detection.
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Figure 9. SNR distribution of matched targets in noise regions: (a) 22 September; (b) 25 September; (c) 6 October; (d) 15 November.
Figure 9. SNR distribution of matched targets in noise regions: (a) 22 September; (b) 25 September; (c) 6 October; (d) 15 November.
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Figure 10. Target matching rate in noise areas.
Figure 10. Target matching rate in noise areas.
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Figure 11. Distribution of matching rates for the same number of detection targets over a four-day period: (a) 22 September; (b) 25 September; (c) 6 October; (d) 15 November.
Figure 11. Distribution of matching rates for the same number of detection targets over a four-day period: (a) 22 September; (b) 25 September; (c) 6 October; (d) 15 November.
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Figure 12. Distribution curves of Pd and Pfa under different w values.
Figure 12. Distribution curves of Pd and Pfa under different w values.
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Figure 13. Distribution of target matching rates under different noise intensities. (a) Distribution curves of noise power at different range bins for consecutive radar scans; (b) distribution curve of noise power for the first 30 range bins of a single radar scan; (c) distribution curve of target matching rates under different w values.
Figure 13. Distribution of target matching rates under different noise intensities. (a) Distribution curves of noise power at different range bins for consecutive radar scans; (b) distribution curve of noise power for the first 30 range bins of a single radar scan; (c) distribution curve of target matching rates under different w values.
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Table 1. HFSWR parameters.
Table 1. HFSWR parameters.
ParameterValue
Carrier frequency (MHz)13.15
Sweep band (kHz)60
Range resolution (km)2.5
Velocity resolution (m/s)0.0825
Receive antennaCross-Loop/Monopole
Sweep cycle (s)0.54
Coherent integration time (CIT) (s)138.24
Table 2. Comparison of detection results with and without denoising.
Table 2. Comparison of detection results with and without denoising.
MethodDateDetected NumberMatched NumberMatching Rate (%)
Without denoising22 September145,21715,89310.94
6 October156,17113,7128.78
15 November156,33216,45410.52
Denoising22 September139,36215,81411.34
6 October139,52013,6759.80
15 November139,55616,40511.75
Table 3. Performance of different detectors for ship target detection in noise regions.
Table 3. Performance of different detectors for ship target detection in noise regions.
MethodDetected Number
of Noise Region
Matched Number
of Noise Region
Matching Rate (%)
CA-CFAR98561231.24
OS-CFAR90231021.13
TM-CFAR93281131.21
CMLD-CFAR92651231.32
VI-CFAR96531241.28
FOD-CFAR8741790.90
SOD-CFAR10,3441051.01
BVI-CFAR93031141.22
TF-BI-CFAR45743357.32
TF-Non-CFAR74326936.20
Table 4. Number of matched targets in different SNR ranges.
Table 4. Number of matched targets in different SNR ranges.
SNRDateCFARTF-Non-CFAR
<10 dB22 September37107
25 September37350
6 October1478
15 November3788
≥10 dB22 September76124
25 September49192
6 October43128
15 November28158
Table 5. Number of matched targets in noise regions with the same number of detection targets over four days.
Table 5. Number of matched targets in noise regions with the same number of detection targets over four days.
MethodDateDetected Number
of Noise Region
Matched Number
of Noise Region
Matching Rate (%)
TF-BI-CFAR22 September45743357.32
25 September60362934.85
6 October39461914.84
15 November36612526.88
TF-Non-CFAR22 September74326936.20
25 September247927811.21
6 October64715724.26
15 November77820326.09
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MDPI and ACS Style

Yang, Z.; Zhou, H.; Tian, Y.; Liu, G.; Zhang, B.; Qin, Y.; Li, P.; Huang, W. Cascaded Detection Method for Ship Targets Using High-Frequency Surface Wave Radar in the Time–Frequency Domain. Remote Sens. 2025, 17, 2580. https://doi.org/10.3390/rs17152580

AMA Style

Yang Z, Zhou H, Tian Y, Liu G, Zhang B, Qin Y, Li P, Huang W. Cascaded Detection Method for Ship Targets Using High-Frequency Surface Wave Radar in the Time–Frequency Domain. Remote Sensing. 2025; 17(15):2580. https://doi.org/10.3390/rs17152580

Chicago/Turabian Style

Yang, Zhiqing, Hao Zhou, Yingwei Tian, Gan Liu, Bing Zhang, Yao Qin, Peng Li, and Weimin Huang. 2025. "Cascaded Detection Method for Ship Targets Using High-Frequency Surface Wave Radar in the Time–Frequency Domain" Remote Sensing 17, no. 15: 2580. https://doi.org/10.3390/rs17152580

APA Style

Yang, Z., Zhou, H., Tian, Y., Liu, G., Zhang, B., Qin, Y., Li, P., & Huang, W. (2025). Cascaded Detection Method for Ship Targets Using High-Frequency Surface Wave Radar in the Time–Frequency Domain. Remote Sensing, 17(15), 2580. https://doi.org/10.3390/rs17152580

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