Abstract

What are the main findings?

A multi-feature detection method based on trajectory prediction integration is proposed for airborne elevation-scanning radar ship target detection to realize multi-scan feature accumulation.

Validated with C-band dual-polarization airborne elevation-scanning radar real data, the method outperforms conventional single-frame three-feature detection and other existing scanning algorithms.

What are the implications of the main findings?

The method addresses the low signal-to-clutter ratio and strong spatio-temporal non-stationarity of sea clutter that plague airborne elevation-scanning radar detection, making up for the defects of existing scanning algorithms.

Measured data show that VH polarization outperforms VV polarization in detection, beam position affects performance, and refining beam position segmentation of continuous-scan radar can further improve detection, guiding radar parameter configuration.

In order to address the challenges faced by airborne scanning radars in detecting maritime ship targets, such as low signal-to-clutter ratios and the strong spatio-temporal non-stationarity of sea clutter, this paper proposes a multi-feature detection method based on trajectory prediction integration. First, the Margenau–Hill Spectrogram (MHS) is employed for time–frequency analysis and uniformization processing. The extraction of features is conducted across three dimensions: energy intensity, spatial clustering, and distributional disorder. The metrics employed in this study include ridge integral (RI), maximum size of connected regions (MS), and scanning slice time–frequency entropy (SSTFE). Feature normalization is achieved via reference units to eliminate dynamic range variations. Secondly, a trajectory prediction matrix is constructed to correlate target cross-scan distance variations. When combined with a scan weight matrix that dynamically adjusts multi-frame contributions, this approach enables effective accumulation of target features across multiple scans. Finally, the greedy convex hull algorithm is used to complete target detection with a controllable false alarm rate. The validation process employs real-world data from a C-band dual-polarization airborne scanning radar. The findings indicate a 36.11% enhancement in the number of successful detections in comparison to the conventional single-frame three-feature detection method. Among the extant scanning algorithms, this approach evinces optimal feature space separability and detection performance, thus offering a novel pathway for maritime target detection using airborne scanning radars.

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1. Introduction

The vastness of the ocean makes the radar swath width critically important for detecting maritime vessels. To overcome the limitations of existing radar swath width imaging modes, airborne radars employ a continuous scan mode in the elevation direction, increasing detection swath width by reducing resolution.

When operating in scanning mode, airborne radar is incapable of simultaneously optimizing scanning efficiency and observation time. The number of pulses accumulated by each beam position per scan is limited, resulting in a low target-to-clutter ratio. Concurrently, large-incidence scanning detection has been shown to exacerbate the complexity and variability of non-stationary, non-uniform, and non-Gaussian sea clutter. Consequently, conventional statistical modeling approaches that rely on analyzing the clutter echo distribution become difficult to implement. Space-Time Adaptive Processing (STAP) imposes elevated demands on hardware, including multi-channel capabilities [1], thereby prompting apply feature detection methods to airborne radar data. Radar feature detection methods extract physically meaningful and separable features across multiple domains, including time [2], frequency [3], time–frequency [4], polarization [5], and Fractional Fourier Transform (FRFT) [6] and so on [7]. For one-dimensional features, the detection thresholds are determined via probability density integration or Monte Carlo methods [8]. In the case of multidimensional statistical measures, one approach involves the utilization of convex hull learning [9], concave hull learning [10], and Support Vector Machines (SVM) [2] to determine the decision space. Reference [11] extracted three polarization features via Van Zyl decomposition, built a detector with fast convex hull learning, and verified full-polarization features’ excellent performance in detecting sea clutter weak maritime targets. Reference [12] proposed a weighted biased soft-margin SVM algorithm with multi-features, constructed a classifier with a controllable false alarm rate, and proved its superior detection performance for sea-surface small targets in sea clutter. Reference [13] proposed a fast feature-fusion-based detector, realized feature normalization and optimal fusion with threshold decision, and confirmed that it is faster than decision-SVM-based detectors. An alternative approach utilizes supervised neural networks to map multidimensional detection metrics [14,15]. Reference [16] proposed a marine dual-channel convolutional neural network with a false-alarm-controllable classifier, fusing time–frequency and amplitude features via a dual-channel convolutional neural network (CNN), and exhibiting better performance than a single-channel CNN for marine targets. Reference [17] proposed an adaptive maritime target detection (AMTD) framework based on active self-learning (SL), which senses environment shifts and updates parameters, achieving good adaptability in time-varying sea clutter environments.

However, applying existing radar feature detection techniques to scanning radars still faces two challenges. First, these methods are designed for longer observation durations in staring mode, where detection performance is influenced by accumulation time. In airborne scanning radar scenarios, limited single-pass dwell time significantly degrades detector performance. Second, these techniques focus solely on current-frame features and fail to effectively utilize historical scan information, despite the fact that multiple observations are a core advantage of scanning radars. Reference [18] uses integral bispectrum features for small target detection. It utilizes cumulative sum and total variance to integrate historical scan data and re-express features. This improves detection performance in scanning modes. Reference [19] uses a forgetting factor for inter-frame, multi-feature iteration to improve feature detector performance in scenarios with short observation times. Reference [20] extends the method from [21] to multidimensional features. It uses kernel density estimation (KDE) to fit a prior feature distribution model for sea clutter using historical scan data. This model is then used to optimize scan features iteratively, enhancing their stability and reliability. Reference [22] uses an auto-regressive (AR) model to take advantage of the temporal correlation between historical and current frame data. This model provides prior information for calculating current frame feature values. However, these approaches have limitations. First, they neglect distance variation between targets in different scan frames. Second, they fail to make full use of target integrability across multiple scans. Third, they lack validation with real radar scan data because the data in these studies is derived by segmenting long-duration radar data from stationary mode into short-pulse scan frames using sliding windows and time segmentation.

In order to address the challenges posed by low signal-to-noise ratio in airborne scanning radar target detection and the strong spatio-temporal non-stationarity of sea clutter, as well as the limitations of existing scanning radar feature detection algorithms, this paper proposes a multi-feature detection method based on trajectory prediction integration. Initially, three features are extracted from the Margenau–Hill Spectrogram (MHS). Subsequently, a trajectory prediction matrix is constructed to correlate cross-scan distance changes of targets. When combined with a scan weight matrix, this approach facilitates the integration of multiple scans for target features. A greedy convex hull algorithm is finally employed for target detection. This paper utilizes a comparative analysis of feature separability and detection results by employing real-world data to demonstrate the proposed algorithm’s effectiveness and superiority over alternative scanning methods.

The structure of this paper is as follows: Section 2 introduces the airborne elevation-scanning radar system; Section 3 presents the Multi-Feature Detection Method Based on Multi-Scanning Trajectory Prediction Integration; Section 4 covers airborne experimental results and analysis; Section 5 conducts a discussion; and Section 6 provides a summary of the entire paper.

2. Airborne Elevation-Scanning Radar Detection

2.1. Airborne Elevation-Scanning Radar Scenario

To address the core requirements of “wide-area coverage and real-time tracking” for marine monitoring, this study adopts the airborne elevation-scanning operating mode, which achieves wide-swath coverage and multi-revisit capability by sacrificing single-frame resolution. This mode exhibits differences from traditional staring radar, Scanned Synthetic Aperture Radar (ScanSAR), and other conventional modes: by implementing continuous linear scanning in the elevation direction, it enables the antenna beam to scan rapidly across a wide range of incident angles, ultimately forming an observational geometry characterized by “wide swath and multiple repeated visits” that aligns with the spatiotemporal characteristics required for maritime target detection.

The operational mode of the airborne elevation-scanning radar is illustrated in Figure 1a, employing continuous linear scanning in the radar’s elevation direction to achieve wide-swath detection. As a case in point, the radar’s right-side view may be considered. In this view, $h$ denotes the aircraft’s flight altitude, $v$ signifies the flight velocity, $[φ_{1}, φ_{2}]$ indicates the incidence angle range (i.e., the continuous scanning angle range in the elevation direction), $θ$ is the grazing angle, w denotes the scanning angular velocity, $W_{R}$ represents the range beam width, $ϕ$ denotes the elevation beam width, and $δ$ indicates the azimuth beam width. The radar detection area is illustrated in Figure 1b, where rectangles of varying colors represent antenna footprints at different sampling times. The black line situated centrally within each rectangle denotes the centre of the antenna footprint, which undergoes a shift over the course of time. The primary parameters of the radar are enumerated in Table 1.

From radar knowledge, the range-wise detection swath width is expressed as follows:

(1) $W_{R} = h (\tan φ_{2} - \tan φ_{1} + \frac{ϕ}{2} (\frac{1}{\cos^{2} φ_{1}} + \frac{1}{\cos^{2} φ_{2}}))$

Based on the radar parameters listed in Table 1, it can be calculated that the range-wise detection swath width of the airborne elevation-scanning mode is 3.39 km. By contrast, the traditional staring mode with a fixed 40° incident angle has a range-wise detection swath width of only 0.43 km.

In addition to meeting the width requirements, seamless coverage within the radar detection range must be ensured. The swing angle range of the servo system is $[φ_{1}, φ_{2}]$ . One scanning cycle T is defined as the movement from $φ_{1}$ to the return to $φ_{1}$ .The condition for achieving complete coverage of the detection area is

(2) $\frac{v T h}{\cos φ_{1}} δ \leq 1$

The simulated airborne platform employs scanning radar to detect surface naval targets. The simulated target is defined as a vessel measuring 120 m in length (azimuth projection) and 20 m in width (range projection). Its initial position is located at a radar range of 2500 m and an azimuth direction of 420 m, moving at a constant velocity of 6 m/s in both the range and azimuth directions. The radar echo diagram is shown in Figure 2. The interlaced bright bands visually represent the illumination trajectory of the radar beam across the sea surface during continuous elevation scanning, while also illustrating the wide coverage capability of this operating mode. The red box delineates the target area. The dwell time per scan for a target is contingent on the radar beam width, the target’s range dimension, the scan speed, and the target’s position within the antenna footprint. The frequency with which a target is detected is contingent upon the radar beam width, the angle of target observation, the scan speed, the flight speed, the target’s azimuth dimension, and the azimuth velocity. As illustrated in Figure 2, the characteristics of airborne scanning radar are evident, including a short target dwell time and discontinuous observation time.

The performance of the airborne elevation-scanning mode is jointly determined by “dwell time” and “revisit frequency”. The calculation formulas for the dwell time $T_{C P I}$ and detection count (revisit frequency) $N$ of stationary point targets in the detection area is as follows.

(3) $T_{C P I} = \frac{ϕ}{w}$

(4) $N \approx 2 \cdot ⌊\frac{\frac{h}{\cos φ} σ}{v \cdot T}⌋$

(5) $T_{t o t a l} = N * T_{C P I} = 2 \cdot ⌊\frac{\frac{h}{\cos φ_{c}} σ}{v \cdot T}⌋ \times \frac{ϕ}{w} = 2 \cdot ⌊\frac{h w σ}{2 v △ φ \cos φ}⌋ * \frac{ϕ}{w}$

$⌊⌋$ denotes the floor function. Since the radar beam centerline cannot pass through all areas of the detection region, the revisit count for some areas may be one or two times higher than the calculated value, which is related to the relative initial position of the target. The total dwell time $T_{t o t a l}$ is independent of the scanning angular velocity, and the detection strategy can be dynamically optimized by adjusting the scanning angular velocity according to the target type.

Thus, the airborne elevation-scanning mode has three characteristics: firstly, it possesses seamless wide-swath coverage and continuous observation capability. ScanSAR achieves wide-swath coverage through sub-swath segmentation, which requires subsequent stitching and is prone to intensity inhomogeneity at sub-swath boundaries. In contrast, this mode directly forms a continuous wide-swath detection strip via continuous linear scanning in the elevation direction, eliminating the need for stitching and ensuring stronger observation continuity, making it suitable for continuous search in large-scale marine areas; secondly, it features flexible adjustability of revisit frequency and dwell time. Compared with ScanSAR, this mode achieves higher scanning efficiency and revisit frequency at the cost of sacrificing azimuth resolution; furthermore, it does not require time-division beam switching (as ScanSAR does), and its servo control logic is simpler and more flexible. It can adapt to different target characteristics by adjusting the scanning angular velocity: for moving targets or large targets, increasing the scanning angular velocity shortens the dwell time and improves the revisit frequency to meet real-time tracking needs; for weak or stationary targets, decreasing the scanning angular velocity extends the dwell time, while increasing the transmitted signal bandwidth enhances target echoes through high resolution and long-time energy integration, thereby improving detection capability; thirdly, it is associated with the strong spatiotemporal non-stationarity of sea clutter. Sea clutter characteristics are highly dependent on incident angles, and the wide incident angle range of this mode intensifies the strong spatiotemporal non-stationarity of sea clutter. Additionally, the short dwell time of a single scan further increases the difficulty of target detection.

Given the dual detection requirements of “large coverage (large-scale search) and high update rate (real-time tracking)” arising from the inherent characteristics of maritime targets—high mobility, wide spatial distribution, and sparse distribution—the airborne elevation-scanning mode overcomes the narrow coverage of traditional staring mode, the sub-swath stitching defects of ScanSAR, and the insufficiency of ScanSAR’s revisit rate. By flexibly adjusting dwell time and revisit frequency to adapt to real-time tracking of moving targets and accurate detection of weak targets, it serves as a detection method for large-scale, rapid search of sea surface targets. For the strong spatio-temporal non-stationarity of sea clutter, this mode achieves target feature accumulation through multiple revisits, which can not only counteract the low signal-to-clutter ratio caused by short single-frame dwell time, but also perform statistical averaging of sea clutter, thereby suppressing its interference.

Based on the advantages of wide-swath coverage and flexible parameters, and with the capability of tracking multiple targets simultaneously, the airborne elevation-scanning mode can be widely applied to maritime monitoring scenarios such as maritime situational awareness, high-resolution SAR imaging guidance, maritime search and rescue, ocean escort, and waterway traffic management. By matching the core needs of each scenario, it significantly enhances the comprehensive effectiveness of various maritime monitoring tasks.

2.2. Airborne Scanning Radar Detection Modeling

It is assumed that during each scan, the radar transmits a coherent pulse sequence of length N at each beam position and receives complex signals through the I/Q channels. The echo signal in the sea clutter cell (SCC) consists exclusively of sea clutter and noise components; for the cell containing the target, the echo comprises the target scattering signal, sea clutter, and noise. The problem of target detection within sea clutter can be mathematically simplified to the following binary hypothesis test:

(6) $\begin{array}{l} H_{0} : \{\begin{array}{l} z^{r, i, k} (n) = c^{r, i, k} (n), & n = 1, 2, \dots, N \\ z_{p}^{r, i, k} (n) = c_{p}^{r, i, k} (n), & p = 1, 2, \dots, P \end{array} \\ H_{1} : \{\begin{array}{l} z^{r, i, k} (n) = s^{r, i, k} (n) + c^{r, i, k} (n), & n = 1, 2, \dots, N \\ z_{p}^{r, i, k} (n) = c_{p}^{r, i, k} (n), & p = 1, 2, \dots, P \end{array} \end{array}$

$H_{0}$ indicates that the Cell Under Test (CUT) is a sea clutter cell, while $H_{1}$ indicates that the CUT is the target cell. $z^{r, i, k} (n)$ , $s^{r, i, k} (n)$ , and $c^{r, i, k} (n)$ represent the time series of the received signal, target echo, and sea clutter, respectively. The superscripts $r$ , $i$ , and $k$ are used to denote the distance gate position, scan beam position, and scan sequence number, respectively. $1 \leq r \leq R$ , $1 \leq i \leq I$ , $1 \leq k \leq K$ , it is evident that the $R$ , $I$ and $K$ represent the number of distance gates, the number of beams, and the number of scans, respectively. The $z_{p}^{r, i, k} (n)$ is used to denote signals within pure clutter cells surrounding the CUT, which are used to estimate sea clutter characteristics. The $p$ indicates the number of reference cells (RCs).

In radar scanning modes, a trade-off exists between dwell time and scanning efficiency. Airborne scanning radars with dwell times ranging from tens to hundreds of milliseconds present three challenges for traditional coherent detection. Initially, Doppler broadening and frequency-time variation caused by platform motion render precise phase alignment between pulses during coherent integration challenging, thereby significantly reducing the gain of selective integration. Secondly, the long distance between the airborne scanning radar and the target, coupled with the brief dwell time at the target location, limits the coherent integration time. This results in a low signal-to-noise ratio for the target, making detection difficult. The non-stationary and spatially non-uniform nature of sea clutter, when combined with the dynamically changing incidence angle of the airborne scanning radar, serves to further complicate and diversify the sea clutter. This limitation restricts the number of reference cells available in the vicinity of the target for estimating sea clutter characteristics, thereby hindering the construction of an accurate sea clutter model.

3. Multi-Feature Detection Method Based on Multi-Scanning Trajectory Prediction Integration

3.1. Radar Data Processing Flow

The detection process of the radar feature detection method based on trajectory prediction integration is illustrated in Figure 3. Following pulse compression, the radar echo is subjected to smoothing of sea clutter spike interference through uniformized MHS time–frequency analysis. The following three feature parameters are extracted from the time–frequency image: The following methodologies were employed: Ridge Integration (RI), Scanning Slice Time–Frequency Entropy (SSTFE), and Maximal Size of Connected Regions (MS). Feature normalization is performed using a reference unit. In consideration of the substantial variations in sea clutter energy and characteristics across disparate elevation angles, continuous observation data is segmented by beam spatial position. Each segment corresponds to a specific elevation angle range, ensuring that sea clutter samples within the data exhibit approximately the same statistical distribution. At the same beam position, features extracted from multiple consecutive scans undergo multi-scanning trajectory prediction integration to obtain scan gain. Prior to the implementation of formal radar detection, a sufficient quantity of sea clutter data is collected for the purpose of training samples. The decision regions satisfying preset false alarm rate constraints are obtained by employing a greedy convex hull learning algorithm. During the detection process, the feature vectors obtained from scan integration at the CUT are input into a classification detector to complete target detection. In order to address the variations in sea clutter caused by dynamic sea surface conditions, a false alarm-driven dynamic update strategy is employed. This approach facilitates adaptive adjustment through the updating or restarting of the convex hull model. Furthermore, in the event that prior feature distribution information for specific target types is available, the detection probability for such targets can be enhanced by optimizing the boundary of the lead region in the greedy convex hull learning algorithm.

3.2. Time–Frequency Analysis and Feature Extraction

In circumstances where target echoes exhibit time-varying Doppler shifts and bandwidths, in addition to those containing non-stationary sea clutter characteristics, time–frequency analysis serves as an effective tool for revealing temporal Doppler differences between target echoes and sea clutter. In comparison with the STFT, the Margenau–Hill spectrum offers enhanced time–frequency concentration, thereby providing superior temporal and frequency resolution in accordance with the Heisenberg-Gabor uncertainty principle [23,24]. The MHS suppresses cross-terms through inverse kernel transformation and conjugate multiplication of two window functions, thereby enhancing time–frequency concentration. Concurrently, the spectrum signifies the distribution of signal energy, thereby offering enhanced interpretability in comparison to SPWVD. Consequently, the present study employs MHS as the time–frequency analysis instrument. The expression is as follows:

(7) ${MHS}_{x} (t, ν) = Re \{K_{g h}^{- 1} F_{x} (t, ν; g) F_{x}^{*} (t, ν; h)\}$

(8) $K_{g h} = \int h (u) g^{*} (u) d u F_{x} (t, ν; h) = \int_{- \infty}^{+ \infty} x (u) h^{*} (u - t) e^{- i 2 π ν u} d u$

$Re$ denotes the real-part operation, $g$ and $h$ represent the time and frequency analysis windows, respectively, the $K_{g h}$ term is the integral of the window function, and normalization preserves the signal’s energy.

Rapid changes in scan mode elevation angle, the non-stationary temporal and spatial characteristics of sea clutter, and disturbances from the airborne platform result in complex variations in the time–frequency diagram of sea clutter. Adjacent distance-time time–frequency distributions exhibit significant differences. Therefore, the sea clutter suppression method that normalizes the time–frequency diagram and models the sea clutter time series as a random process described by mean and standard deviation functions is not applicable. In actual measurement data, the spectral energy distribution of targets is concentrated in both time and frequency, while sea clutter energy is relatively dispersed. Exploiting the slower spectral variation of target units relative to sea clutter and the spatial-temporal energy non-uniformity of sea clutter, a multi-adjacent-cell time–frequency map averaging method is employed. This approach amplifies the time–frequency map differences between targets and clutter. Target energy concentrates along the target’s instantaneous frequency curve (IFC). In scenes with strong signal-to-clutter ratios, this manifests as a bright, relatively narrow strip exhibiting slight frequency jitter over time. Conversely, the rapid changes in sea clutter units result in a more chaotic energy distribution after uniformization, while the amplitude of the energy is smoothed. Consequently, time–frequency uniformization smooths the sharp peaks in the sea clutter MDS diagram, enhancing the contrast between targets and sea clutter. This provides an improved background model for feature extraction.

The spectrogram reflects the energy distribution of the signal in the time–frequency domain. Due to the presence of IFC, the first feature employs ridge integration (RI) to distinguish signals based on their energy magnitude [9].

(9) $RI (z) = \sum_{t = 1}^{T} {MHS}_{z} (t, {\arg \max}_{ν} \{{MHS}_{z} (t, ν)\}),$

By leveraging the distinct characteristics of sea clutter energy distribution—discrete and isolated—versus target energy distribution—continuous and clustered—in the time–frequency spectrum, two key features are extracted using the binary image of significant time–frequency points (STFPs): the Maximal Size of Connected Regions (MS) and the Scanning Slice Time–Frequency Entropy (SSTFE). The MS metric quantifies the maximum concentration of energy within the time–frequency plot, while SSTFE describes the disorder in time–frequency energy distribution during the maximum effective dwell time of the scan via time–frequency entropy. Together, these features effectively characterize the structural differences between sea clutter and target echoes in the time–frequency domain, complementing the energy magnitude features described by RI. The MS feature is extracted from the STFP image using the eight-region rule to describe the geometric properties of the time–frequency map. Assuming connected regions in the binary image are denoted as $\{Ω_{1}, Ω_{2}, Ω_{3,} \dots, Ω_{w}\}$ , MS is defined as

(10) ${MS (z) = \max}_{k = 1, 2, \dots, w} {# Ω_{k}},$

Time–frequency entropy quantifies the disorder in the energy distribution within the time–frequency domain—higher entropy values indicate greater dispersion of signal energy. Addressing the limited dwell time characteristic of scanning radars, we propose the Scanning Slice Time–Frequency Entropy (SSTFE). By focusing on the time–frequency features within the target’s effective dwell period, this approach enhances detection accuracy while reducing computational load. The specific process is as follows: First, select the top K largest connected regions in the STFP image and obtain their pixel spatiotemporal indices. Next, calculate the maximum dwell time of the target within the radar beam (obtained via Equation (3)), and construct a time window using the median of the time indices for each connected region. Then, compute the spatiotemporal entropy values within each time window across the entire frequency axis. Finally, the minimum value from this set of entropy values is selected as the SSTFE feature. The specific calculation formula is as follows:

(11) $SSTFE (z) = m i n_{k = 1, 2, \dots K} (H_{k})$

(12) $H_{k} = - \sum_{t = t_{1} - T_{m a x} / 2}^{t_{1} + T_{m a x} / 2} \sum_{v = v_{1}}^{ν_{2}} P (t, ν) * \log_{2} P (t, ν)$

(13) $P (t, ν) = \frac{{MHS}_{z} (t, ν)}{\sum_{t = t_{1} - T_{m a x} / 2}^{t_{1} + T_{m a x} / 2} \sum_{ν = ν_{1}}^{ν_{2}} {MHS}_{z} (t, ν)}$

It should be noted that due to differences in dynamic range among the three features, the classifier may become overly sensitive to features with high magnitude and large dynamic range (RI). The impact of dynamic range is mitigated by implementing feature domain normalization methods for both the guard cells and reference cells. Additionally, the local spatial correlation of sea clutter is utilized to suppress sea clutter to some extent while reducing false alarms caused by secondary units of the target. The specific calculation formula is as follows:

(14) $\bar{η} = {[\frac{RI - {\hat{μ}}_{RI}}{{\hat{σ}}_{RI}}, \frac{SSTFRE - {\hat{μ}}_{SSTFE}}{{\hat{σ}}_{SSTFRE}}, \frac{MS - {\hat{μ}}_{MS}}{{\hat{σ}}_{MS}}]}^{T},$

where

\hat{μ}

and

\hat{σ}

represent the mean and standard deviation of the reference unit, respectively. The selection of guard cells should be based on the radar range gate size, radar range resolution, vessel dimensions, and the number of target subunits. The selection of reference units should be appropriately adjusted according to the sea conditions of the measured data, and reference units should, in principle, ensure that they can characterize the statistical properties of the unit under test.

3.3. Multi-Scanning Trajectory Prediction Integration

To fully utilize information between multiple target scans, this paper supplements weight matrix based on Reference [15] and introduces it into the three-dimensional feature space, completing feature integration across multiple scans along the target’s trajectory. Under the scanning radar test scenario described in Section 2.2, where the maximum relative velocity between the target and radar in the range direction is $V_{\max}$ , and $N$ denotes the number of scans during which the target remains detectable, the active range of the target across these $N$ scans is defined as $⌈2 * (V_{\max} * (N - 1) + e_{\max}) / Δ r + 1⌉$ , where $⌈⌉$ represents rounding up, $e_{\max}$ indicates the maximum error, and is defined as the active window $W$ . Taking the feature matrix of the three-dimensional radar echo data matrix defined in Section 2.2, perform operations on the three features sequentially. Within a single beam, centered on each range gate, extract a column vector of length $W$ in the range dimension. Stack the $N$ scan results from the same position vertically to form an $N W$ -length column vector. The column vectors generated by the range gate are horizontally concatenated to form the feature observation matrix Z of size $N W \times R$ . Different scanning periods are stacked frame by frame to assemble the three-dimensional matrix B.

For airborne scanning radars, due to the short scanning cycle and high aircraft velocity, the relative velocity of the target is considered constant between scans. For the velocity range, a velocity resolution $d v$ is selected; if $d v$ is sufficiently small, even if the target’s velocity is non-uniform during observation, as long as the distance gate containing the target matches the performance of a predetermined velocity across multiple scans, the target’s echo characteristics can be correctly superimposed. Therefore, exhaustively enumerate the target’s H possible trajectories and integrate the results of $N$ scans along the actual trajectory. Centered on the target’s initial position, determine the target’s location within each scan cycle based on the preset velocity, with each scan still spanning a $W$ -length window. Horizontally concatenating the $N$ vectors of length $W$ corresponding to each preset velocity forms a velocity vector of length $N W$ . Vertically stacking all preset velocities creates the $H \times N W$ trajectory prediction matrix A.

The beam pointing of airborne scanning radars dynamically changes with each scan cycle. The position where targets fall within the beam (observation angle) varies across different scans, causing fluctuations in antenna gain and target RCS. This results in fluctuating echo intensities for the same target across multiple scans. Introducing a weight matrix enables inter-scan weight allocation: it enhances the contribution of scans with a high signal-to-clutter ratio while suppressing energy spillover from strong echoes into adjacent scans through weighting, thereby reducing false alarm risk. The selection of the weight matrix must be based on the radar scenario, antenna pattern characteristics, or the variation pattern of target signal strength with the number of scans. The structure adopts a block diagonal form: the overall matrix J is an $N W \times N W$ matrix composed of $N$ smaller diagonal matrices of size $W \times W$ . The diagonal elements of each block correspond to the weighting for a single scan. The scan integration formula is as follows:

(15) $Q = A \times J \times Z,$

Here, Q represents the feature scan integration matrix, A denotes the trajectory prediction matrix, J is the scan weighting matrix, and Z signifies the feature observation matrix. The Q matrix is an H × R matrix, where rows correspond to the number of trajectories and columns represent range gates. When the target’s actual trajectory overlaps with one or more trajectories in A, the results from multiple scans are integrated after being weighted by J. Take the extreme value of each column in Q (based on its features’ properties) as the output of the integration result.

3.4. False Alarm-Driven Dynamic Update for Greedy Convex Hull Algorithms

Due to the imbalance between the number of data samples and target samples in maritime clutter, the application of object detection in maritime clutter is more suitable for using a single classifier. Faced with the challenges of being unable to precisely statistically describe feature vectors, the presence of numerous target types, and sample deficiencies, the greedy convex hull learning algorithm [9] is adopted as the detector. The greedy convex hull learning algorithm recursively removes vertices that maximize the reduction in the volume of the intersection between the convex hull of the remaining samples and the target prior region. This process continues until the number of removed samples reaches a threshold determined by the false alarm rate. The resulting convex set, encompassing the sea clutter training samples, serves as the null hypothesis decision region for a single-class classifier. The lead region is predefined based on theoretical and practical considerations, utilizing the three features described in Section 3.2: targets exhibiting large RI and MS values with small SSTFE. Combined with feature domain normalization, regions satisfying RI > 0, MS > 0, and SSTFE < 0 are designated as the lead region. This configuration allows flexible adjustment according to specific target characteristics, demonstrating the method’s adaptability.

To address the rapidly changing maritime scenes detected by airborne radar, false alarm-driven dynamic convex hull updates are employed. For detection points outside the convex hull, if their distance cell and domain fail to reappear within consecutive K frames, they are classified as false alarms and assigned to sea clutter. A dynamic time window is set to monitor the false alarm rate. If the false alarm rate exceeds the configured threshold, the convex hull is updated using new echo characteristics, and changes in the convex hull volume are recorded. Simultaneously, the time window is reduced and slid. If the false alarm rate remains above the threshold for multiple consecutive scans, accumulated sea clutter data from the scans is used to initialize the convex hull. If the false alarm rate check falls below the threshold, the time window is expanded and slid without updating the convex hull. After multiple scans, the volume difference between the recent sea clutter convex hull and the existing convex hull is calculated. If this volume difference exceeds a preset value, the recent data is used to initialize a new convex hull. This prevents excessive convex hull expansion due to data updates.

4. Field Experiment and Results

4.1. Experimental Scene and Data Processing

The data presented in this paper were obtained from airborne scanning radar experiments conducted by our laboratory in a certain sea area in November 2024, under specific marine environmental conditions: a significant wave height of 0.68 m, sea state 3, an average wind wave period of 1.99 s, an average wind speed of 3.90 m/s, and a gust wind speed of 6.09 m/s. The experimental scene is illustrated in Figure 4. The yellow color identifies the flight direction and flight velocity of the airborne platform, as well as the radar detection area; the blue area presents the antenna beam pointing and antenna footprint, while the red color represents the detected target. During the experiments, a GNSS/INS integrated navigation and positioning system was used to obtain the aircraft’s position information, while positions were determined via the Automatic Identification System (AIS) data to validate the methodology. A 150-s segment of airborne radar test data was selected, with the first 90 s serving as the sea clutter training set and the subsequent 60 s used for target detection tasks. In C-band dual-polarization mode, 13 targets appeared a total of 152 times. The definition of Average Signal-to-Clutter Ratio (ASCR) is given in Equation (16), where $x (n)$ denotes the time sequence of CUT (with the sequence length equal to the target dwell time), ${\bar{p}}_{c}$ represents the average sea clutter power in the region adjacent to the CUT, and ASCR is the ratio of the average power of the CUT to the average sea clutter power [21]. The average signal-to- clutter ratio (SCR) per scan and its variation with occurrence times are shown in Figure 5 below.

(16) $ASCR = 10 \log 10 (\frac{\frac{1}{N} \sum_{n = 1}^{N} {|x (n)|}^{2}}{{\bar{p}}_{c}})$

Beam position one corresponds to an incident angle range of 40–60°, while beam position two corresponds to an incident angle range of 20–40°. The paper employs Trajectory Prediction Integration as the scanning method, selecting cumulative sum and total variance features [18], forgetting factor iteration [19], and kernel density estimation [20,21] as comparison methods. All approaches utilize the time–frequency analysis features employed herein, performing time–frequency analysis on 512 pulses per beam position at each iteration. The time–frequency analysis window function selection depends on airborne radar parameters and sea conditions. The time window function should be close to the maximum residence time, while the frequency window should match the frequency variation range during the target residence time. This paper employs Kaiser windows with shape parameter 25 and lengths of 211 and 199 as the time and frequency windows, respectively. Detection uniformly uses a greedy convex hull algorithm with a false alarm rate of 0.001. For RI and MS features, cumulative sum and total variance features were obtained through inter-scan accumulation. For SSTFE features exhibiting strong randomness in sea clutter, total variance features were employed to assess stability. For the forgetting factor iterative algorithm, iteration was set to 4 with a forgetting factor of 0.35 to minimize the sea clutter convex hull volume and achieve optimal detection probability. The KDE kernel density estimation algorithm parameters employ the empirical formula provided in article [20], with a sliding window size of 128 and 4 iterations. The article uses the trajectory prediction integration scan integration method, processing 4 scans with a maximum single-scan movement range of 2 range gates and a velocity resolution set to 0.05 range gates.

The detection process of the airborne elevation-scanning radar is shown in Figure 6. Figure 6a presents the data pulse compression diagram under the airborne elevation-scanning radar scenario (only capturing the small incidence angle scenario). The signal intensity reflects the illumination trajectory of the radar beam across the sea surface during continuous elevation-scanning, consistent with the simulation results in Section 2.1 of the paper. In contrast, the scenario exhibits additional sidelobe interference. The blue box highlights target echoes, demonstrating the target’s short dwell time and discontinuous observation periods. Figure 6b presents the uniform MDS plot of target units. Although the target’s time–frequency energy lacks a fixed frequency, it exhibits a relatively concentrated distribution in the time–frequency diagram. Figure 6c,d show scatter plots of multiple targets and sea clutter at beam position 2, before and after the scanning algorithm. Compared to the original features, the three features of targets and sea clutter after scanning integration exhibit more distinct separation. Detection of Target 3 across multiple scans in this scenario is illustrated in Figure 6e,f. In Figure 6e, sea clutter points outside the convex hull represent those excluded at the specified false alarm rate. Figure 6f demonstrates that integrating historical scan frame information enables the three combined features to separate low signal-to-clutter ratio targets from the sea clutter convex hull.

4.2. Feature Space Separability

Data separability refers to the separability between two categories of data samples, which can predict detector performance and serves as a crucial metric for feature detectors. This paper employs the Bhattacharyya distance (B-distance) between computational sea clutter and targets to measure their separability, as expressed by the following formula.

(17) $\begin{array}{l} μ_{0} = mean (S_{0}), C_{0} = cov (S_{0}) \\ μ_{1} = mean (S_{1}), C_{1} = cov (S_{1}) \end{array},$

(18) $d_{B} (S_{0}, S_{1}) = \frac{1}{4} {(μ_{0} - μ_{1})}^{T} {(C_{0} + C_{1})}^{- 1} (μ_{0} - μ_{1}) + \frac{1}{2} \ln (\frac{\det (0.5 (C_{0} + C_{1}))}{\sqrt{\det (C_{0}) \det (C_{1})}}),$

Figure 7 presents the B-distance comparison results of five feature processing methods across four datasets: VV polarization (Beams 1 and 2) and VH polarization (Beams 1 and 2). It is evident that the feature separability of the Trajectory prediction integration achieves an average improvement of 54.27% compared to the three-feature detection based on single-frame information, demonstrating superior performance across all four datasets relative to other algorithms. The three-feature detection, which does not utilize inter-scan information, exhibits the lowest B-distance across all datasets, validating the inherent limitation of relying solely on single-scan information for distinguishing features in complex sea clutter backgrounds.

Although the cumulative sum and total variance, forgetting factor iteration, and KDE kernel density estimation methods outperform the single-frame three-feature approach, they all fall short of the proposed method. This is because while the cumulative sum and total variance and forgetting factor iteration methods incorporate multiple scan information, they fail to account for target range changes. In scenarios with dynamic target positions, they cannot correlate with the true target trajectory, resulting in inefficient information fusion. The KDE kernel density estimation method enhances detection quality per scan by optimizing new features using clutter prior information. However, it neglects the integrability of multiple detections for the same target, resulting in limited B-range improvement. The KDE kernel density model exhibits smaller peaks, poorly matching the distribution characteristics of maritime clutter in airborne scanning radars. Compared to other energy-accumulating scanning methods, it faces probability model matching issues, is more sensitive to parameters, and demonstrates lower versatility. Additionally, kernel density estimation requires finer grids when handling widely distributed marine clutter features from airborne scanning radars.

To quantitatively analyze the computational complexity of the algorithms, we define $O (F)$ as the feature extraction complexity for a single range cell in one frame, which includes time–frequency analysis, feature extraction, and normalization. Based on this, both the cumulative sum and total variance algorithm and the forgetting factor iteration algorithm have a complexity of $O (R C + K R)$ where $R$ denotes the number of range gates and $K$ represents the number of scan frames involved in multi-frame fusion (or the number of iterations); the proposed algorithm in this paper has a complexity of $O (R C + K R H W)$ (where $H$ is the number of trajectories, determined by velocity resolution and velocity search range, and $W$ is the length of the cross-scan range-wise active window); while the KDE algorithm has a complexity of $O (K R C + R K N_{R})$ (where $N_{R}$ is the number of reference samples used for KDE model fitting, the first term represents the overhead of repeatedly performing time–frequency analysis and feature extraction in each iteration, and the second term represents the complexity of KDE fitting and iteration) [20]. It can be seen that the KDE algorithm needs to recompute the time–frequency map and re-extract features in each iteration, and coupled with the overhead of reference sample density estimation, its computational complexity is significantly higher than that of other scanning methods.

4.3. Detection Performance Analysis

The detection results of each target are shown in Figure 8. In the airborne elevation-scanning radar scenario described in Section 4.1, 13 targets appeared a total of 152 times under the dual-polarization modes (VV/VH) of the C-band, and individual targets under different polarization modes were counted independently. The statistical results of each detection method are presented in Table 2: the single-frame three-feature detector successfully detected 25 targets, with a total of 108 successful detections; the cumulative sum and total variance detector achieved 142 successful detections; the forgetting factor iteration method had a total of 127 successful detections; the trajectory prediction integration scan-integration detection method proposed in this paper successfully detected 26 targets, with a total of 147 successful detections. Compared with the single-frame three-feature detector, the proposed method improves the detection performance by 36.11% and effectively captures one low signal-to-clutter ratio (SCR) target that was missed by the single-frame detection method. Compared with other scanning algorithms, the proposed method improves the performance by 3.52% compared with the cumulative sum and total variance method, and by 15.74% compared with the forgetting factor iteration method, which verifies the superiority of the trajectory prediction integration method in the ship target detection task of airborne scanning radar.

From the perspective of detection results under different polarization modes and beam positions, various detection methods exhibit significant performance differences. Specifically, the detection results of each method under different beam positions and polarization modes are presented in Table 2: the trajectory prediction integration method proposed in this study achieves optimal performance in three out of the four datasets (combinations of VV/VH polarizations and two beam positions) and sub-optimal performance in the remaining one dataset, demonstrating prominent overall performance advantages.

Notably, the 1st beam position (incident angle range 40–60°) under the VH polarization mode is the scenario where the number of detections of each method shows the largest improvement: the single-frame three-feature detector only achieves 18 successful detections, while the three scanning-based methods increase their detection counts to 34 (with a relative improvement of 88.9%), 29 (with a relative improvement of 61.1%), and 32 (with a relative improvement of 77.8%), respectively. As analyzed in Figure 5b, the average signal-to-clutter ratio (ASCR) of Target 2, Target 3, Target 4, and Target 8 at this beam position under the VH polarization mode is mainly distributed in the range of 2–5 dB, and the ASCR of some scan frames is even lower than 2 dB. Under the dual constraints of low signal-to-clutter ratio (SCR) and short target dwell time, the features extracted within the single-frame observation window cannot effectively distinguish targets from sea clutter, resulting in a low detection rate of the single-frame method. In contrast, scanning-based methods realize the effective accumulation of target features by integrating multi-frame historical scan information, ultimately enabling the successful separation of low-SCR targets from the sea clutter background.

In comparison, the average signal-to-clutter ratio (ASCR) of targets under the VV polarization mode is generally higher than that under the VH polarization mode, so the differences in the number of detections among various methods are relatively small. Among them, the method proposed in this study achieves the highest number of detections (40) at the beam position 2 under the VV polarization mode, representing a relative improvement of 33.33% compared with the single-frame three-feature detector (30 detections). During the same period, the cumulative sum and total variance method achieves 38 detections, and the forgetting factor iteration method achieves 32 detections. It should be noted that the beam position 2 corresponds to a small incident angle scenario, where the VV-polarized (co-polarized) sea clutter is significantly affected by altitude-line clutter interference, leading to drastic fluctuations in statistical characteristics. However, the method proposed in this study still maintains stable detection performance in the environment of strong non-stationary sea clutter, which verifies the environmental adaptability of the algorithm.

Scanning methods exhibit distinct detection mechanisms for targets with different signal-to-clutter ratio (SCR) characteristics. For targets with low average signal-to-clutter ratio (ASCR), such as Target 2, Target 3, and Target 4 under VH polarization, the radar scanning period is much longer than the sea clutter correlation time. As a result, the statistical characteristics of sea clutter between different scan frames are relatively independent, while target echoes maintain a strong correlation. Through multi-frame feature integration, the random fluctuations of sea clutter are statistically averaged, and target features are effectively accumulated and enhanced—this significantly improves the distinguishability between the Maximum Size of Connected Regions (MS) and Scanning Slice Time–Frequency Entropy (SSTFE) features of low-ASCR targets and sea clutter. This also explains why, in the low-ASCR scenario of Beam Position 1 under VH polarization, scanning methods achieve a significant improvement of 61–89% compared to the single-frame method. For targets with large ASCR fluctuations (e.g., Target 7), the single-frame three-feature detector can only detect frames with high ASCR and fails to detect frames with low ASCR, leading to poor detection continuity for such targets. In contrast, the method proposed in this study correlates the position changes of the target across multiple scan frames and integrates the strong Ridge Integral (RI) features from historical high-ASCR frames with the features of the current frame. This compensates for the insufficient SCR of the current frame and effectively suppresses the impact of SCR fluctuations on detection.

As can be seen from the horizontal comparison in Table 2, there are differences in the performance of the three scanning algorithms. The cumulative sum and total variance method improves distinguishability through feature accumulation and stability evaluation, and performs reasonably well in airborne scanning radar scenarios characterized by significant spatiotemporal differences and strong non-stationarity. However, it assigns equal weights to all historical frames, which easily leads to the simultaneous accumulation of noise from low-quality frames; moreover, it fails to consider the cross-frame distance changes of targets. In the experimental scenario, the number of range gates for the displacement of ships between frames is small, and ship targets have a certain size and sufficient sub-units. Therefore, this method without distance compensation can still capture target energy in some range gates and obtain a certain scanning gain, but its performance is greatly limited when dealing with highly maneuverable targets.

The forgetting factor iteration method conducts exponentially weighted iterative updates on historical features by introducing a forgetting factor, but it also does not consider target trajectory information. Although its forgetting factor parameter adopts the strategy from Reference [19], which is “minimizing the sea clutter convex hull volume to achieve optimal detection probability”, in the sea clutter scenario of airborne scanning radar, a fixed forgetting factor cannot adapt to the differences in sea clutter characteristics under different incident angles. For example, in the detection of Target 3 under VH polarization and Target 10 under VV polarization, the number of successful detections is even less than that of the single-frame detector.

The core advantage of the proposed method lies in correlating the cross-frame distance changes of targets and optimizing the allocation of multi-frame contributions, thereby effectively accumulating target features. Compared with the single-frame three-feature detector and the other two scanning algorithms, the proposed method not only has the optimal feature space separability, but also demonstrates the optimal detection performance in both measured experiments and subsequent simulation experiments, verifying its effectiveness.

To further evaluate the algorithm’s performance, we selected an additional 30 s beam position 2 airborne pure sea clutter data outside the training set and added simulated targets for detection. The simulated targets were configured according to the following formula [21,22]:

(19) $S_{k} (n) = a_{k} (n) + H_{k} e^{2 π i (f_{d} n Δ t + φ_{k})},$

Here, $S_{k} (n)$ and $a_{k} (n)$ represent the time-sequence data and sea clutter sequence after adding simulated targets, respectively, with the subscript $k$ denoting the scan frame. $H_{k}$ denotes the amplitude of the simulated target sequence, while $f_{d}$ and $Δ t$ represent the Doppler shift and pulse repetition time, respectively. $φ_{k}$ indicates the initial phase. The simulated target’s generation position is randomized. The first appearance of the target occurs in a randomly selected scan frame, followed by four consecutive appearances. The timing of the target’s appearance within the scan frame must satisfy the condition that the radar beam illuminates the target’s distance gate. The target’s velocity is randomly generated within the range [−18 m/s, 18 m/s]. The ASCR calculation method for targets follows Section 3.1, employing the Swerling 0 and Swerling 1 models: Swerling 0 represents non-undulating targets, while Swerling 1 describes slow-undulating targets (pulse-to-pulse correlation, scan-to-scan independence), suitable for characterizing ships and other large-volume targets. The generated simulated target scenario is shown in Figure 9 below, with the white box indicating the generated simulated targets. The simulation targets were set with ASCR values of 2 dB and 4 dB, using the Swerling 0 model and Swerling 1 model respectively. Each model and ASCR value underwent 100 experiments in both VV and VH polarizations, totaling 400 experiments. The detection results are shown in Table 3 and Table 4.

As shown in Table 3 and Table 4, the fluctuating characteristics of the target SCR reduce detection probability, exhibiting a decreasing trend across all scanning algorithms. Comparing Figure 9a,b, cross-polarization demonstrates significant suppression of altitude-line clutter near 2 km. Under identical ASCR conditions, cross-polarization (VH) demonstrates superior detection performance compared to co-polarization (VV). This phenomenon can be attributed to cross-polarization’s suppression of altitude-line clutter and its more stable sea clutter characteristic distribution. This result aligns with the analysis conclusions regarding B-distance in Section 3.2. Figure 10 quantitatively demonstrates the performance gains of different scanning algorithms, with percentage improvements labeled relative to the single-frame baseline. Across all experimental groups, the trajectory prediction integration feature detector demonstrated significant performance improvements compared to the single-frame three-feature detection: an average increase of 103.67% under VV polarization and 6.97% under VH polarization. It also achieved optimal performance relative to other scanning algorithms.

5. Discussion

5.1. Improvement Mechanism of Detection Performance by Trajectory Prediction Integration

The multi-feature detection method based on trajectory prediction integration proposed in this study demonstrates advantages in maritime ship target detection tasks, with its core performance enhancement stemming from the effective utilization of multi-frame information from scanning radars. Mechanically, this method correlates target distance variations across scans through a behavior prediction matrix, effectively addressing the shortcomings of other scanning algorithms (such as cumulative sum and total variance, or a forgetting factor iteration) that neglect target distance changes. In this practical test scenario, the ship’s displacement across scan cycles was minimal, and a sufficient number of sub-units were present. This allowed other scanning algorithms without distance variation compensation to achieve some scanning gain. The KDE method disregards the integrability of multiple detections of the same target, exhibits poor matching with the sea clutter characteristic distribution of airborne scanning radars, and involves high computational complexity. In the experimental scenario, the trajectory prediction integration method demonstrated an average improvement of 54.27% in feature space separability (B-distance) and a 36.11% increase in detection success rate compared to the single-frame three-feature detector. In low SCR scenarios, successful separation of targets from sea clutter’s convex hull was achieved by correlating MS features with SSTFE features from historical scan frames. Concurrently, the introduction of a scan weight matrix optimized multi-frame contribution allocation. By enhancing the contribution of high SCR scan frames, missed alarms caused by SCR fluctuations were reduced. Finally, leveraging the characteristic that sea clutter correlation duration is shorter than the scan period, fusing information from multiple scan frames can average sea clutter characteristics. This partially mitigates the impact of sea spikes and reduces false alarms.

5.2. The Effect of Polarization Mode and Beam Position on Detection Performance

Experimental results demonstrate that polarization mode and beam position significantly impact detection performance by altering sea clutter characteristics.

Regarding polarization mode differences, although VV polarization generally yields higher target signal-to-clutter ratio (ASCR) than VH polarization, VH polarization exhibits superior feature separability (B-distance) and detection success rate. This stems from the stronger tailing and spiking in the VV-polarized feature distribution, leading to higher overlap between target and clutter probability distributions. Conversely, the smaller variance and smoother distribution of VH-polarized sea clutter characteristic distribution offset the disadvantage in ASCR. This finding suggests that prioritizing VH polarization can enhance detection performance in complex coastal or high-sea-state scenarios with intricate sea clutter characteristic distributions.

From the perspective of beam position (incidence angle range), VV polarization exhibits significantly reduced distinguishability in beam position two (incidence angles 20–40°) compared to beam position one. This occurs because at low incidence angles, the radar-to-target distance shortens. The relatively short distance combined with the high reflectivity of clutter during near-vertical incidence amplifies both main-beam clutter and sidelobe clutter (such as altitude-line clutter). This results in more complex clutter statistical characteristics, compressing the difference between targets and clutter and degrading detector performance. Conversely, in VH polarization, beam position two exhibits stronger feature distinguishability. This is because cross-polarization significantly suppresses altitude-line clutter, and the stronger echo energy at the shorter distance of beam position two makes target features easier to distinguish from the steady clutter background. Results indicate that spatial inhomogeneity of sea clutter significantly impacts feature processing performance, demonstrating that algorithm performance depends on specific local clutter environments.

As previously established, the feature distribution of local sea clutter exerts a significant impact on detection performance, and there exist distinct differences in the sea clutter feature distribution across different beam positions. This implies that the traditional coarse-grained beam position division scheme cannot adequately adapt to the spatial heterogeneity of sea clutter, thereby restricting the improvement of detection performance. This indicates that through beam position refinement—decomposing the originally continuously scanned incidence angle range into smaller beam position units—the statistical characteristics of sea clutter features within each refined beam position tend to become homogeneous. This approach can enhance the feature distinguishability between targets and clutter, as well as improve the effectiveness of multi-scan feature fusion and overall detection performance. From the perspective of subsequent engineering optimization implementation, the “clutter feature B-distance between refined beam positions” can be adopted as the core criterion (supplemented by statistical indicators such as sea clutter power coefficient of variation and distribution goodness-of-fit if necessary), aiming to achieve a balance between the statistical homogeneity of beam positions and engineering computational efficiency. The specific process is as follows: first, based on the radar antenna beamwidth and target radial displacement characteristics (the maximum number of range gates moved per scan cycle), the scanned incidence angle range is initially divided into several coarse-grained beam positions; subsequently, the clutter B-distance between adjacent coarse-grained beam positions is calculated. If the B-distance is less than the merging threshold, the two are merged into a single beam position; if the B-distance exceeds the splitting threshold, the coarse-grained beam position is further split using the 5-range-gate sliding window method. This iteration is repeated until the B-distance between any adjacent refined beam positions falls within the range between merging threshold and splitting threshold. Finally, parameters (e.g., the number of reference cells, the scope of guard cells, and the coefficients of the scan weight matrix) are independently configured for each refined beam position, and each beam position performs feature processing and detection through an independent workflow—ensuring the accurate adaptation of feature processing to the clutter environment of the corresponding beam position.

5.3. Limitations of the Method and Future Directions for Improvement

Although this method demonstrates good performance in both experimental and simulation studies, three limitations require further optimization. First, “energy leakage” occurs during the scanning integration process. This phenomenon means that the characteristic energy of high-SCR targets may spill over into subsequent scan frames, leading to detection counts exceeding the actual occurrence times. This is difficult to avoid in scanning algorithms. Future improvements could involve dynamically adjusting weighting coefficients (e.g., increasing the weight proportion of the current frame) or introducing an incidence angle-dependent maximum detection count threshold. Second, the selection of reference and guard cells during feature normalization relies on empirical parameters. Current methods adjust these parameters based on the distance gate size, ship dimensions, and sea conditions. Future research could explore adaptive cell selection algorithms that dynamically determine cell quantity and range according to the local spatial correlation of sea clutter, thereby enhancing the method’s robustness. In target-dense scenarios, reference cells for multiple targets may overlap, introducing features from other targets into the reference cell and causing target masking effects. Future work could explore multi-target joint detection strategies, such as grouping target points in feature space using clustering algorithms before performing separate trajectory prediction integration for each group to reduce cross-interference. Third, the synergistic fusion potential of multi-polarization channels has not been fully exploited. Current methods only utilize VV and VH polarization data separately for detection, failing to consider the complementary nature of these two polarization features (e.g., VV polarization excels in energy characteristics, while VH polarization excels in clutter suppression). A multi-polarization feature fusion model could be constructed, such as through feature-level fusion (e.g., combining VV polarization’s RI with VH polarization’s SSTFE) or decision-level fusion, to further enhance the detection probability of low SCR targets. Building on this, adaptive fusion mechanisms based on environmental perception could be explored to dynamically adjust the contribution weights of different polarization channels according to real-time sea state estimation. Finally, to improve the utilization of inter-frame data, the inter-frame consistency of the target spatial scale will be leveraged. Unlike the random morphological deformations of sea clutter speckles over time, target echoes typically maintain a relatively stable geometric size across consecutive frames. Consequently, the target size features extracted within frames can be employed as key constraints for temporal association to further reduce false alarm rates and confirm real targets. Simultaneously, the spatiotemporal correlations of inter-frame sea clutter can be incorporated to dynamically optimize integration weights for more precise clutter suppression. Furthermore, advanced data-driven techniques, such as Recurrent Neural Networks (RNN), could be explored to capture deep non-linear dependencies between scans, further enhancing the detection capability for weak targets in strong clutter.

6. Conclusions

To address challenges such as low signal-to-noise ratio and strong spatio-temporal non-stationarity of sea clutter encountered by airborne scanning radars in ship target detection, this paper proposes a multi-feature detection method based on trajectory prediction integration. The study begins by introducing and modeling airborne elevation-scanning radar scenarios. Building upon this foundation, the method first employs Margenau–Hill Spectrogram (MHS) for time–frequency analysis and uniformization processing. It extracts three features—Ridge Integral (RI), Maximum Size of Connected Region (MS), and Scan Slice Time–Frequency Entropy (SSTFE)—across three dimensions: energy intensity, spatial clustering, and distribution disorder. Feature normalization is performed using surrounding cells to mitigate the impact of dynamic range variations. Subsequently, by constructing a trajectory prediction matrix to correlate distance changes across scans and dynamically adjusting multi-frame contributions via a scan weight matrix, the method achieves effective accumulation of target features across multiple scans. Finally, a greedy convex hull algorithm is employed to realize target detection with controllable false alarm rates. The paper validated the proposed method using C-band dual-polarization airborne measurement data: compared to single-frame three-feature detection, feature separability improved by 54.27% and detection success increased by 36.11%. Among existing scanning algorithms, it demonstrated optimal performance in both feature space separability and total detection success. The paper also analyzes the impact of polarization modes and beam positions on detector performance, along with the method’s limitations. Future work may involve constructing a multi-polarization feature fusion model to leverage complementary information from different polarization channels, thereby enhancing the detection performance of airborne scanning radars.

Author Contributions

Conceptualization, F.Z., Z.X. and S.J.; design and implementation of radar systems, F.Z., Z.X., X.L. and Z.Z.; methodology, F.Z., C.Z. and H.F.; data analysis, F.Z., Z.X., X.L. and Z.Z.; validation, K.X., Z.L. and C.X.; writing—original draft preparation, F.Z.; writing—review and editing, F.Z., Z.X., T.Z. and Z.C. All authors have read and agreed to the published version of the manuscript.

Data Availability Statement

The original contributions presented in this study are included in the article. Further inquiries can be directed to the corresponding author.

Conflicts of Interest

The authors declare no conflicts of interest.

Abbreviations

The following abbreviations are used in this manuscript:

MHS	Margenau–Hill Spectrogram
STAP	Space-Time Adaptive Processing
FRFT	Fractional Fourier Transform
CFAR	Constant False Alarm Ratio
SVM	Support Vector Machine
CNN	Convolutional Neural Network
H	Horizontal
V	Vertical
RI	Ridge Integral
MS	Maximum Size of Connected Regions
SSTFE	Scanning Slice Time–Frequency Entropy
SCC	Sea Clutter Cell
CUT	Cell Under Test
RCs	Reference Cells
AR	Auto-Regressive
KDE	Kernel Density Estimation
SCR	Signal-to-Clutter Ratio
ASCR	Average Signal-to-Clutter Ratio
IFC	Instantaneous Frequency Curve
STFP	Significant Time–Frequency Points
B-distance	Bhattacharyya distance
RNN	Recurrent Neural Networks

Footnotes

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content.

Figures and Tables

Figure 1 Schematic diagram of airborne elevation—scanning radar scene. (a) Radar Operating Modes Diagram. (b) Schematic Diagram of Radar Detection Scenario.

Figure 2 Schematic diagram of airborne scanning radar echo simulation.

Figure 3 The flowchart of the feature detection method based on multi-scanning trajectory prediction integration.

Figure 4 The radar airborne experiment scene.

Figure 5 Target ASCR changes with the number of occurrences. (a) VV polarization. (b) VH polarization.

Figure 6 Schematic diagram of the airborne scanning radar data processing process. (a) C-band VV-polarized pulse compression diagram. (b) C-band VV-polarized Target Uniformization MDS Map. (c) Feature scatter plot. (d) Feature scatter plot after scanning integration. (e). Greedy convex hull training graph. (f) Convex hull detection visualization.

Figure 7 Comparison of B distances of different methods on the dataset.

Figure 8 Comparison of target detection results of different methods.

Figure 9 Simulated target scene diagram under actual sea clutter conditions. (a) VV. (b) VH.

Figure 10 Performance Comparison of Different Methods.

Table 1

Scanning radar main parameters.

Parameter	Value
Flight Altitude (km)	2.0
Frequency Band (GHz)	5.4
Polarization	VV, VH
Beam Width (°)	7.3
Pulse Width (μs)	5.0
Incidence Angle Range (°)	20.0–60.0
Pulse Repetition Frequency (Hz)	500.0
Scan Cycle (s)	4.2

Table 2

Statistics of successful detection times by different methods.

PolarizationBeam Position	VV1 BeamPosition	VV2 BeamPosition	VH1 BeamPosition	VH2 BeamPosition	Total
Single-frame three-feature detector	28	30	18	32	108
Cumulative sum and total variance	35	38	34	35	142
Forgetting factor iteration	34	32	22	39	127
Trajectory prediction integration	36	40	32	39	147

Table 3

The successful detections of each method for Swerling 0-type simulation targets.

PolarizationTarget ModelASCR (dB)	VVSwerling 02 dB	VVSwerling 04 dB	VHSwerling 02 dB	VHSwerling 04 dB
Single-frame three-feature detector	54	146	314	398
Cumulative sum and total variance	110	247	352	398
Forgetting factor iteration	75	223	340	395
Trajectory prediction integration	142	339	381	400

Table 4

The successful detections of each method for Swerling 1-type simulation targets.

PolarizationTarget ModelASCR (dB)	VVSwerling 12 dB	VVSwerling 14 dB	VHSwerling 12 dB	VHSwerling 14 dB
Single-frame three-feature detector	73	181	316	390
Cumulative sum and total variance	118	222	313	395
Forgetting factor iteration	69	144	231	309
Trajectory prediction integration	123	277	331	395

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