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To investigate the characteristics of sea clutter, based on ocean surface electromagnetic scattering theory, the first- and second-order ocean surface scattering cross sections for bistatic high-frequency (HF) radar incorporating a multi-frequency six degree-of-freedom (DOF) oscillation motion model are mathematically derived. The derived radar cro...
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... to the interaction between the ocean floating platform and complex ocean environment, based on the seakeeping theory of deep-water floating platform, the motion of the ocean floating platform can be viewed as the superposition of sway, surge, heave, yaw, pitch, and roll with a multifrequency model [32,33]. Figure 1 shows the diagram of six DOF motion for a transmitting sensor on a floating platform. It is assumed that the source is at ( ) , , a b h . ...
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... 2 i N = represents two frequency components. Figure 10 displays the simulated first-and second-order RCSs for bistatic HF radar incorporating a dual-frequency six DOF oscillation motion model. From Figure 10a, the LF motion-induced peaks appear not only near the Bragg peaks but also near the WF motion-induced peaks, which agrees well with Equation (62). ...
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... 10 displays the simulated first-and second-order RCSs for bistatic HF radar incorporating a dual-frequency six DOF oscillation motion model. From Figure 10a, the LF motion-induced peaks appear not only near the Bragg peaks but also near the WF motion-induced peaks, which agrees well with Equation (62). Furthermore, the amplitudes of the Bragg peaks and the WF motion-induced peaks are lower than those of the LF motion-induced peaks due to the modulation effect, which may 'break' Bragg scatter mechanism. ...
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... the amplitudes of the Bragg peaks and the WF motion-induced peaks are lower than those of the LF motion-induced peaks due to the modulation effect, which may 'break' Bragg scatter mechanism. A comparison of Figures 8f and 10b shows that the WF motion is the dominant factor affecting the second-order RCS. Figure 10c shows the total RCS containing the first-and second-order RCSs. From Figure 10c, it can be seen that a dual-frequency six DOF oscillation motion may have a more significant effect than a single-frequency case in Figure 9. ...
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... comparison of Figures 8f and 10b shows that the WF motion is the dominant factor affecting the second-order RCS. Figure 10c shows the total RCS containing the first-and second-order RCSs. From Figure 10c, it can be seen that a dual-frequency six DOF oscillation motion may have a more significant effect than a single-frequency case in Figure 9. ...
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... comparison of Figures 8f and 10b shows that the WF motion is the dominant factor affecting the second-order RCS. Figure 10c shows the total RCS containing the first-and second-order RCSs. From Figure 10c, it can be seen that a dual-frequency six DOF oscillation motion may have a more significant effect than a single-frequency case in Figure 9. In addition, the effects of different wind directions, wind speeds, and radar parameters on RCS for bistatic HF radar incorporating a dualfrequency six DOF oscillation motion model are similar to the sway case [30,31] and are not further discussed here. ...
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... addition, the effects of different wind directions, wind speeds, and radar parameters on RCS for bistatic HF radar incorporating a dualfrequency six DOF oscillation motion model are similar to the sway case [30,31] and are not further discussed here. Figure 11 shows the simulated total RCSs containing the first-and second-order RCSs for different bistatic angles. It is obvious that the Bragg peaks, both the hydrodynamic and electromagnetic peaks for the second-order scatter and additional peaks caused by six DOF oscillation motion move closer to zero Doppler frequency while the bistatic angle is increasing. ...
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... as the bistatic angle increases, the amplitudes of the second-order RCSs decrease, and the modulation effect caused by the platform motion is weakened. It should be noted that, from Equation (58), the second-order electromagnetic peaks may be far away from the Bragg peaks or even diminished from the total RCS curve for a large bistatic angle, for example 0 85 φ = ° as shown in Figure 11. ...
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Citations
... In order to further expand the detection range of HFSW, further development of current inversion based on mobile platforms has farreaching significance [2,3]. However, six degree-of-freedom (DOF) will cause complex modulations which will set the barrier for later ocean surface current inversion [4]. All these modulations are dependent on the arrival direction, hence in this paper, we focus on the three DOF rotations that may influence the direction-of-arrival estimation. ...
High-frequency surface wave radar (HFSWR) has been widely used for ocean surface current inversion. Floating this radar can realize the ocean surface inversion among large areas far away from the coastline. However, six degree-of-freedom (DOF) movements will set the barrier for the ocean current inversion on its radial velocity estimation and direction of arrival estimation. Among these movements, three DOF rotations can cause both Doppler modulation and azimuth modulation while three DOF translations only cause Doppler modulation which is dependent on the arrival direction of echoes. Hence, the analysis and compensation for three DOF rotations are first to be solved. In this paper, we analyse the Doppler modulation and azimuth modulation of three DOF rotations and further develop the global adaptive beamforming method to compensate for these rotations. Adaptive beamforming is used to compensate for rotations to make the real-time beams fixed to the ground when the platform is rotating. Simulations indicate that the global adaptive beamforming can perfectly compensate for the reasonable rotations, among which the yaw rotation is the dominant factor for both Doppler spectrum modulation and azimuth modulation. The rotation compensation using global adaptive beamforming can greatly improve the precision of ocean surface inversion.
... In light of these considerations, this paper introduces a forward-modeling approach tailored for dynamic and complex maritime targets on time-varying sea surfaces, with applications in remote sensing and recognition. Initially, the six-degrees-of-freedom motion analysis from maritime hydrodynamics [33][34][35] is employed to elucidate the ship dynamics atop fluctuating ocean waves. Subsequently, these dynamic movements are transformed into the ship's rotational and heaving attitudes on the sea surface, leveraging Open Graphics Library (OpenGL) technology to craft an integrated ship-sea geometry model for any given moment. ...
This paper presents a forward modeling method for the scattering center (SC) model of dynamic ships on time-varying sea surfaces, tailored for remote sensing and target-recognition applications. Grounded in ship hydrodynamics, the methodology delineates ship movements amidst fluctuating waves, harnessing computer graphics to integrate ship–sea geometries across diverse temporal instances. Utilizing the four-path model, the composite scattering effects are segregated into distinct ship and sea contributions, along with their mutual interactions. Augmented by high-frequency electromagnetic principles, the paper quantifies and deduces SC parameters, culminating in a 3-D parameterized SC model for complex maritime targets. Unlike conventional inverse methods, this approach employs a “cause-to-effect” forward strategy, establishing clear links between SCs and local geometries, enhancing the model’s physical clarity. Using the fishing ship as a case, this research compared the normalized similarity index and position-matching rate between the reconstructed synthetic aperture radar (SAR) image and the simulated SAR image. The results indicate that all computed results exceeded 90%. Furthermore, a comparison was conducted between the reconstructed radar cross-sections (RCS) obtained by expanding the model within a large angular range and the simulated results. The root mean square error between the two was less than 3 dB, affirming the accuracy and effectiveness of the proposed model. Additionally, the research examines the variations in SCs during the six-degrees-of-freedom motions, providing a detailed quantitative analysis of their temporal trends in amplitude and position. In summary, this investigation furnishes an efficient and economical framework for rapid radar characterization in dynamic, variable marine environments, fostering advancements in remote sensing and maritime target identification.
... It is found that the RCS and Doppler spectrum at different wind speeds have distinct characteristics due to the different attitudes of the target. Ji et al. [4] and Yao et al. [5] simulated target echoes under different motion conditions and found that the nonuniform linear motion broadened the target echo, and reduced the signal-to-noise ratio (SNR). Walsh et al. [6] and Chang et al. [7] modeled the backscattered Doppler spectrum of high-frequency surface wave radar (HFSWR). ...
... Because the projection of the motion of the trimaran in the 75° incidence plane decreases compared to the 55° incidence, especially the pitch (we compared the effects of heave, roll, and pitch on the Doppler spectrum at this angle and found that the effect of the pitch was the largest), resulting in a decrease in the spectrum width of the trimaran. This is similar to the conclusion of the simulation of the monohull signal in reference [5]. The essence of both is that the spectrum energy of the target signal is more concentrated when the modulation effect of the 6-DOF motion decreases as the angle changes. ...
The trimaran is an advanced ship with high hydrodynamic performance, but the study of its electromagnetic characteristics and Doppler spectrum is insufficient. This study presents a new procedure for evaluating the scattering echo and Doppler spectrum of a trimaran in a time-varying ocean environment. First, based on the Reynolds-averaged Navier-Stokes (RANS) equations, the interpolation wave-making method (IWMM) is proposed for the prediction of the six degrees of freedom (6-DOF) motion of the trimaran. The method takes into account the viscous effect of the flow field and the complexity of wave motion, which applies to the seakeeping prediction of high-speed trimaran under different sea states. Second, an accelerated geometrical optics and physical optics algorithm using the light source function (GO-PO/LSF) is proposed, which uses the light source function to realize the visibility judgment of surfaces and greatly reduces the computation time. Then, the influence of different motion conditions on the backscattering echo of the composite scene is demonstrated by the capillary wave modification facet scattering model (CWMFSM) and GO-PO/LSF. Finally, the Doppler spectrum characteristics of the trimaran are presented by the standard spectrum estimation method, which provides a reference for radar detection and identification of ships in the microwave band.
... Based on this foundation and considering uniform motion and six-degree-offreedom motion for the ship, the generation mechanism of the first-order RCS of shipborne monostatic HFSWR has been extensively investigated in [13][14][15]. For bistatic HFSWR with either transmitter or receiver on a ship or floating platform, corresponding first-order RCS models have been developed [16][17][18][19]. Ji et al. analyzed the spreading effect of first-order sea clutter and frequency shift of target echo for a shore-ship HFSWR based on simulated and experimental data [20]. ...
A bistatic high-frequency surface wave radar (HFSWR) with both receiving and transmitting stations placed on different ships (platforms) is a new radar system and referred to as shipborne bistatic HFSWR. In this paper, a first-order ocean surface cross section of shipborne bistatic HFSWR was derived. The first-order cross-section models for three different cases, i.e., ships moving with uniform, periodic, and hybrid motion states, respectively, are presented. The corresponding first-order Doppler spectra were simulated, and the spread width of the first-order spectrum was investigated. The simulation results show that the characteristics of the first-order spectrum are similar to those of a shore-based bistatic HFSWR when the transmitting and receiving platforms move in opposite directions. The first-order spectral spread width in the case of platforms with opposite directions is much smaller than that in the case of platforms with the same direction. This finding is useful for reducing HFSWR first-order spectrum spread due to platform motion, thus improving the target detection performance of the shipborne bistatic HFSWR. In addition, periodic oscillation motion of both platforms will cause complex motion-induced peaks in the first-order spectrum, which may be detrimental to target detection and ocean remote sensing. These results have important implications for the application of shipborne bistatic HFSWR.
... In this study, the yaw rotation is the predominant motion in the six-DOF platform motion and can cover a broad range. In recent years, Yao et al. [35,36,37] revealed the additional peaks caused by oscillations of yaw rotation. In this study, the calibration of the phased array is combined with the yaw rotation. ...
Prior studies have highlighted the importance of calibrating receiver antennas in target direction-of-arrival (DOA) estimation and surface current measurement for high-frequency (HF) radar systems. It is worth noting that the calibration contributes to the performance of both shore-based HF radar and platform-mounted HF radar. Compared with shore-based HF radar, the influence of six-degrees-of-freedom (six-DOF) platform motion should be considered in the calibration of platform-mounted HF radar. This paper initially describes a calibration scheme that receives phasedarray antennas for an anchored platform-mounted HF radar incorporating a model of free rotation, which is called yaw rotation and dominates the six-DOF platform motion in this study. In the presence of yaw rotation, the amplitude and phase of the source calibration signal from the other shore-based radar sites reveal the directional sensitivity of the receiver phased-array antennas. The calibration of receiver phased-array antennas is composed of channel calibration (linking cables and receiver hardware calibration) and antenna pattern calibration. The antenna pattern at each bearing can be represented by the Fourier series. The estimation of channel calibration and antenna pattern calibration depends on an overdetermined HF radar system consisting of observed values and theoretical constraints, so the least-squares fits of the channel calibration coefficients and antenna pattern calibration coefficients are obtained. The experimental results show that the target DOA estimation and surface current measurement can be improved if the phased-array platform-mounted HF radar system is calibrated.
... According to the electric field theory, Walsh et al. proposed the first-order and second-order RCS of the ocean surface under surge motion [12,13] and pointed out that surge motion would generate additional motion-induced peaks on the range-Doppler (RD) spectrum. Following that, researchers have derived different models of shipborne HFSWR first-order RCS containing 6-DOF motion [3,[14][15][16][17][18]. These models can be divided into frequency domain models and time domain models. ...
The echo of shipborne high-frequency surface wave radar (HFSWR) is modulated by six-degrees-of-freedom (6-DOF) motion, affecting the detection of the target and the remote sensing of ocean surface dynamics parameters. Commonly, motion compensation methods of shipborne HFSWR describe each aspect of the 6-DOF motion as the superposition of sinusoidal motion, which results in the effect of motion compensation affected by the precision of 6-DOF motion parameters. A motion compensation method based on dual reference radio frequency (RF) signals is proposed in this paper, without depending on a sinusoidal motion model to describe the 6-DOF motion. By using the motion compensation parameters, which are relevant to the motion attitude and calculated from the information of dual reference RF signals located onshore, the method realizes the compensation of shipborne HFSWR echo modulated by platform 6-DOF motion. This paper proposes the extraction of reference RF signals from radar echo and analyzes the influence of the location of the reference RF signals’ emission source on the motion compensation method. The result shows that a good motion compensation effect is achieved in eliminating the influence of 6-DOF motion modulation. In addition, a traversal of different reference RF signals’ emission source locations is conducted, and the simulation results show that the method proposed in this paper has universality.
... The actual motion parameters of the ship are time-varying, and it is so complicated that it can hardly be expressed through analytical expressions. However, due to the interaction between ship and complex ocean environment, based on seakeeping theory of deep-water platform, ship motion can be generally viewed as the superposition of surge, sway, heave, roll, pitch, and yaw with a multi-frequency motion [3,4]. Therefore, it is possible to approximately derive the phase distortions introduced by 6-DOF oscillation and make a qualitative analysis of their effects. ...
... The linear oscillation of a ship along its transverse axis. 3 Heave ...
... Due to the interaction between ship and complex ocean environment, based on seakeeping theory of deep-water platform, ship motion is generally viewed as the superposition of surge, sway, heave, roll, pitch, and yaw with a multi-frequency motion [3,4]. As an ideal rigid target, the displacements caused by ship linear oscillation can be expressed as follows: ...
Ship targets are high-value military and civilian targets with broad application prospects. However, the precise focusing of ships is still a difficult issue because of their complicated six-degree-of-freedom motions on the sea surface. This paper focused on investigating the effect of ship six-degree-of-freedom oscillation on Synthetic Aperture Radar imaging. Firstly, based on the six-degree-of-freedom motions, the accurate range models for ship linear oscillation and angular oscillation were built, and the superiority was verified by comparing them with the models described in published literature. Secondly, we used the Taylor formula and Bessel function to expand the phase error introduced by ship oscillation, then their effects on imaging were further analyzed. Finally, based on the measured ship attitude data, we generated the semi-physical echoes of the oscillatory ship to validate the analysis throughout this article. Based on the proposed range model, we also made some tentative on the phase compensation method by fitting ship attitude angles with multiple sinusoidal functions.
... They pointed out that there would be more symmetrical peaks caused by the combined motion in the radar Doppler spectra. Yao et al. derived the first-and second-order bistatic RCS models with multi-frequency six-DOF oscillation motion and described platform motion with a more realistic motion model [19]. Chang et al. derived the firstorder shipborne HFSWR time-domain RCS model, including six-DOF platform motion, which was based on the modulation of motion for the antenna pattern and array steering vector [20]. ...
... The motion parameters of rotation were obtained by INS IMU720-G. Since the INS cannot obtain the motion parameters of translation (including surge and sway), the motion parameters of translation were selected according to [19], the real ship and the sea state in the experiment were also fully considered. Table 2 shows the preliminary identification results of the motion parameter a and ω , which were directly identified by the reference RF signal. ...
The shipborne high-frequency surface wave radar (HFSWR) platform produces six degrees of freedom (DOF) motion at sea, which affects the performance of radar target detection and remote sensing of ocean surface dynamics parameters. Motion compensation can mitigate the effect of six-DOF motion, but motion parameters (including amplitude and angular frequency) need to be known. Motion parameters obtained by using high precision sensors are affected by the precision error and time delay, thus affecting the effect of motion compensation. To obtain the motion parameters accurately and in real time, a method of identifying the motion parameters by using an artificially transmitted reference radio frequency (RF) signal generated at the shore is proposed. Based on the results of the parameter identification, the reference RF signal and the first-order radar cross-sections (RCSs) modulated by six-DOF motion of the shipborne HFSWR platform can be compensated. The identification of angular frequency is divided into two steps: (1) Preliminary identification results are obtained by using the reference RF signal; (2) the pattern search method is used to further improve the identification accuracy of angular frequency. The amplitude of translation (including surge and sway) can be identified accurately through the reference RF signal. Due to the small amplitude of rotation (including roll, pitch, and yaw), it needs to be identified by the reference RF signal and pattern search method. After identifying the motion parameters, division in the time domain is used for motion compensation. Through the simulation results, both translation and rotation have good motion compensation effects. In addition, the method of using high precision sensors to obtain motion parameters and compensation is compared with the method in this paper, the simulation results of motion compensation show that the latter is better.
... The first-order and second-order ocean-surface cross sections for shipborne HFSWR with uniform linear motion and sway motion were derived by Xie, Sun and Ji [8][9][10]; (J) E. Khoury et al. presented a model of received signal from a floating HFSWR and assessed the effect of antenna motion on the first-order Bragg lines [11]. Over the years, the effects of forward motion, sway motion, surge motion, rotation motion and other motions caused by ocean dynamics on both monostatic and bistatic shipborne HFSWR have been studied [12][13][14][15][16][17]. These analyses provide guidance for target detection in shipborne HFSWR. ...
Due to the motion of the platform, the spectrum of first-order sea clutter will widen and mask low-velocity targets such as ships in shipborne high-frequency surface-wave radar (HFSWR). Limited by the quantity of qualified training samples, the performance of the generally used clutter-suppression method, space–time adaptive processing (STAP) degrades in shipborne HFSWR. To deal with this problem, an innovative training sample acquisition method is proposed, in the area of joint domain localized (JDL) reduced-rank STAP. In this clutter-suppression method, based on a single range of cell data, the unscented transformation is introduced as a preprocessing step to obtain adequate homogeneous secondary data and roughly estimated clutter covariance matrix (CCM). The accurate CCM is calculated by integrating the approximate CCM of different range of cells. Compared with existing clutter-suppression algorithms for shipborne HFSWR, the proposed approach has a better signal-to-clutter-plus-noise ratio (SCNR) improvement tested by real data.
... This raises practical issues in terms of the coastal space required for installation of both the transmitting and the receiving antenna arrays, as well as the problem of mutual interference between antennas. These issues can be overcome by resorting to a bistatic radar system in which the transmitter and the receiver are located some distance apart [3][4][5]. In a bistatic HFSWR system, the receiver has robust anti-active directional jamming and anti-destruction characteristics because of the physical separation of the transmitter and the receiver, giving it unique advantages and potential regarding anti-electronic interference. ...
The coast–ship bistatic high-frequency surface wave radar (HFSWR) not only has the anti-interference advantages of the coast-based bistatic HFSWR, but also has the advantages of maneuverability and an extended detection area of the shipborne HFSWR. In this paper, theoretical formulas were derived for the coast–ship bistatic radar, including the first-order sea clutter scattering cross-section and the Doppler frequency shift of moving targets. Then, simulation results of the first-order sea clutter spectrum under different operating conditions were given, and the range of broadening of the first-order sea clutter spectrum and its influence on target detection were investigated. The simulation results show the broadening ranges of the right sea clutter spectrum and left sea clutter spectrum were symmetric when the shipborne platform was anchored, whereas they were asymmetric when the shipborne platform was underway. This asymmetry is primarily a function of platform velocity and radar frequency. Based on experimental data of the coast–ship bistatic HFSWR conducted in 2019, the broadening range of the sea clutter and the target frequency shift were analyzed and compared with simulation results based on the same parameter configuration. The agreement of the measured results with the simulation results verifies the theoretical formulas.
