Doppler Frequency Shift Research Articles

Исследование алгоритмов предварительной частотной синхронизации в приемнике спутниковой связи в условиях негеостационарной орбиты космического аппарата

The work is devoted to a comparative study of various algorithms for compensating for frequency shift in a single-frequency radio channel under conditions of varying Doppler frequency shift. The resulting characteristics of frequency offset compensation algorithms based on the Fitz method and the least squares method were studied. Using the method of numerical experiment, the accuracy characteristics of the operation of the studied algorithms in situations of constant and changing frequency shifts were obtained. The best accuracy characteristics of the algorithm based on the Fitz method were revealed in comparison with those built on the basis of the least squares method. At the same time, the algorithm based on the least squares method showed satisfactory accuracy characteristics of operation under conditions of changing frequency shift, under which the algorithm based on the Fitz method turns out to be ineffective.

Flexible Conformal Multifunctional Time‐Varying Phase‐Modulated Metasurface with Polarization Control for Radar Feature Transformation

AbstractReconfigurable metasurfaces have shown unprecedented capabilities in controlling electromagnetic (EM) waves in recent years and play an essential role in information manipulation. However, most research on reconfigurable metasurfaces is limited to planar rigid structures, with only one control function and suitable for specific single polarization. Achieving simultaneous control of phase, polarization, and frequency in the conformal structure has significant practical implications in many applications, but remains obviously challenging. In this paper, a flexible multifunctional time‐varying phase‐modulated metasurface (MTPM) with orthogonal polarization control is proposed for conformal applications to manipulate the spectrum distribution. It enables time encoding capability in controlling the phase characteristics of x‐ and y‐polarized EM waves individually by switching the bias voltage of the PIN diode in two directions. Discrete harmonic spectrum and continuous Doppler frequency shifts are implemented separately on two orthogonal polarizations by applying different time coding sequences. As a practical application, a conformal MTPM for radar feature transformation is explored. Multiple discrete false targets and defocusing phenomena can be realized respectively for x‐ and y‐polarized waves. Both simulated and measured results verify the validity of the proposed method and prototype.

Photonic Measurement for Doppler Frequency Shift and Angle of Arrival Based on Integrated Dual-Parallel Dual-Drive Modulator

A microwave photonic Doppler frequency shift (DFS) and angle of arrival (AOA) measurement method based on a dual-parallel dual-drive Mach–Zehnder modulator (DP-DDMZM) is proposed and demonstrated. A sawtooth wave signal is used to drive the DC port of the modulator to realize the optical frequency shift, and thus the direction discrimination of DFS is realized. Due to single-sideband modulation, the proposed system can avoid periodic power fading and the separation of the remote antenna unit (RAU) and central office (CO) can be achieved. In the experiment, the microwave DFS is estimated with a clear direction and a maximum measurement error of 0.25 Hz over an ultrawide operation frequency from 6 to 36 GHz. The experiment also proves that the phase error of AOA measurement is less than 1.5 degrees. Compared with the traditional electronic microwave measurement scheme, the proposed scheme has great competitive advantages in future broadband electronic applications due to the features of multifunction, large bandwidth and anti-interference.

Multi-Frequency Doppler Velocimetry Based on a Mode-Locked Distributed Bragg Reflector Laser

A differential multi-frequency laser Doppler velocimetry is demonstrated, utilizing the synchronized multimode of a mode-locked distributed Bragg reflector laser. This scheme enables the simultaneous detection of multiple Doppler frequency shifts. Multiple differential Doppler shifts of 0.6 Hz, 1.3 Hz, and 1.9 Hz are obtained, with an average speed of 3.677 mm/s and a standard deviation of 0.122 mm/s, demonstrating a cross-referenced velocity measurement capability. The measurement results are also compared with the dual-frequency laser Doppler velocimetry scheme using electro-optical modulation.

OFDM-Based Massive Connectivity for LEO Satellite Internet of Things

Low earth orbit (LEO) satellite has been considered as a potential supplement for the terrestrial Internet of Things (IoT). In this paper, we consider grant-free non-orthogonal random access (GF-NORA) in the orthogonal frequency division multiplexing (OFDM) system to increase access capacity and reduce access latency for LEO satellite-IoT. We focus on the joint device activity detection (DAD) and channel estimation (CE) problem at the satellite access point. The delay and the Doppler effect of the LEO satellite channel are assumed to be partially compensated. We propose an OFDM-symbol repetition technique to better distinguish the residual Doppler frequency shifts, and present a grid-based parametric probability model to characterize channel sparsity in the delay-Doppler-user domain, as well as to characterize the relationship between the channel states and the device activity. Based on that, we develop a robust Bay esian message-passing algorithm named modified variance state propagation (MVSP) for joint DAD and CE. Moreover, to tackle the mismatch between the real channel and its on-grid representation, an expectation–maximization (EM) framework is proposed to learn the grid parameters. Simulation results demonstrate that our proposed algorithms significantly outperform the existing approaches in both activity detection probability and channel estimation accuracy.

Tensor-Train Decomposition-Based Hybrid Beamforming for Millimeter-Wave Massive Multiple-Input Multiple-Output/Free-Space Optics in Unmanned Aerial Vehicles with Reconfigurable Intelligent Surface Networks

Unmanned aerial vehicles (UAVs) can support low-cost, highly mobile communications while making it possible to establish dedicated terrestrial networks. To overcome the pointing error (PE) and beam misalignment of millimeter-wave large-scale multiple-input multiple-output/free-space optics (MIMO/FSO) caused by UAV jitter, a millimeter-wave massive MIMO/FSO hybrid beamforming method based on tensor train decomposition is proposed. This approach is used for reconfigurable intelligent surface (RIS) network-assisted UAV millimeter-wave massive MIMO/FSO to improve system spectral efficiency. Firstly, the high-dimensional channel of RIS-assisted millimeter-wave massive MIMO/FSO in UAV is represented as a low-dimensional channel by tensor training decomposition. Secondly, the two-way gated recursive unit attention neural network model can effectively solve the FSO PE caused by UAV jitter, and the fast fading channel and Doppler frequency shift are estimated by the Fast Cyclic Tensor Power Method (FCTPM) based on tensor training decomposition. Finally, the RIS phase shift matrix is optimized by singular value decomposition. The hybrid beamforming and RIS phase-shift matrices were estimated by using the low-complexity phase extraction alternating minimization method to solve the beam misalignment problem. Simulation results show that by using the proposed method, the spectrum utilization rate is improved by 23.6% compared with other methods.

Optimizing Task Completion Time in Disaster-Affected Regions with the WMDDPG-GSA Algorithm for UAV-Assisted MEC Systems

In this paper, we investigate a UAV-assisted Mobile Edge Computing (MEC) system that is deployed with multiple UAVs to provide timely data processing services to disaster-stricken areas. In our model, since base stations are unavailable in disaster-affected areas, we solely employ UAVs as MEC servers, as well as enable real-time data transmission during UAV flights by estimating and compensating for the Doppler Frequency Shift (DFS). Subsequently, an optimization problem is formulated to jointly optimize the trajectories and offloading strategies of multiple UAVs to minimize the task completion time. We enhance the performance of the Multi-Agent Deep Deterministic Policy Gradient (MADDPG) algorithm by using a weighted strategy algorithm, and we thus propose the Weighted-Strategy-Based Multi-Agent Deep Deterministic Policy Gradient (WMDDPG) algorithm for optimizing UAV trajectories. We employ the Greedy-Based Simulated Annealing (GSA) algorithm to overcome the limitations of the greedy algorithm and to obtain the best offloading strategy. The results demonstrate the effectiveness of the proposed WMDDPG-GSA algorithm, as it outperforms benchmark algorithms.

Timing‐deviation and frequency‐offset estimations for multicarrier transmission in high mobility environments using deep neural network

SummaryThe multicarrier technology used in fourth‐generation (4G) and fifth‐generation (5G) communications is quite susceptible to multipath fading and Doppler frequency shift, which is more prominent in high mobility environments. Therefore, the accuracy of timing and frequency synchronization impacts the overall system performance significantly. Existing synchronization methods rely on the correlation of the preamble sequences and are, hence, vulnerable to severe multipath effect and Doppler effect. In this article, we propose a novel scheme leveraging deep neural network (DNN) to achieve high‐precision synchronization in high mobility environments. Concretely, a convolutional neural network (CNN) architecture is proposed to extract the hidden features of received signals for timing deviation estimation. In the following, a fully connected (FC) model is demonstrated to classify the optimal carrier frequency offset (CFO) estimate from several CFO candidates. The proposed synchronization scheme is assessed under extended vehicular A (EVA) channel with various Doppler frequency shifts. Simulation results corroborate that the proposed DNN‐based scheme achieves a significant performance gain over the conventional correlation methods, and the proposed timing deviation estimation scheme exhibits an excellent complexity reduction; wherefore, it is extremely promising for multicarrier transmission systems in high mobility environments.

Virtual Space-Time DiversityTurbo Equalization Using Cluster Sparse Proportional Recursive Least Squares Algorithm for Underwater Acoustic Communications

The oceanic positioning, navigation and timing (PNT) network requires high-quality underwater acoustic message transmission. Turbo equalization technology has exhibited superior performance for underwater acoustic (UWA) communications compared with conventional channel equalizers. To overcome the performance reduction caused by severe doubly selective UWA channels, the virtual space-time diversity soft direct-adaptation turbo equalization is proposed for UWA communications. The proposed scheme improves the ability of the typical turbo equalizer to deal with both Doppler and multipath effects for time varying channels. We utilize a fractionally spaced soft interference cancellation equalizer (FS-SE) instead of a hard decision to constitute the soft-input soft-output (SISO) equalizer. Combined with another virtual time-reversal mirror equalizer component, we can obtain virtual space and time diversity with only a single receiving transducer and mitigate the error propagation phenomenon of the feedback filter. To satisfy the sparse UWA channel, the ℓp,q-PRLS algorithm is applied to adaptive updates for FS-SE. In the proposed scheme, an adjustable interpolator and digital phase-locked loop are embedded into the equalizer to overcome the residual Doppler frequency shift and recover the timing distortion. Results of simulations and field lake trial show that the proposed scheme achieves better performance than existing ones under the same equalizer order.

Robust Doppler compensation for low frequency underwater communications

Impairment caused by Doppler frequency shift and harsh channel condition distinguish underwater acoustic communications from radio communications. Slow speed of acoustic waves produces relatively high Doppler shift and result in expansion or compression in time samples, which is known as Doppler scaling. In particular, the Doppler scaling causes significant carrier frequency offset (CFO) in orthogonal frequency division modulation (OFDM). To compensate the CFO, it is essential to resample signal samples according to the Doppler scale. In theory, the Doppler scale can be estimated by measuring the distance between peaks of the matched filter output of consecutive Doppler-invariant preambles. In practice, multi-path reflections and non-orthogonality between the HFM and OFDM payload produce large numbers of local false peaks. In this paper, we propose a robust Doppler estimation technique by employing constant false alarm rate (CFAR) filter to remove false peaks. We validate the performance of the proposed scheme through two sea-trials carried out in shallow water near Jervis Bay, Australia. In the sea-trials, a slow-moving towed hydrophone array was deployed as the receiver and the source was a stationary, low source level, vertical transmit array. Sea-trial results demonstrated up to 112bps information rate using bit-interleaved coded OFDM over 400 Hz bandwidth.

Intensity-Modulated Direct-Detection Doppler LiDAR Using Pseudo-Random Code and Optical Direct Down-Conversion of Modulation Frequency for Range and Speed Measurement of a Hard Target

Intensity-modulated direct-detection Doppler LiDAR (IM-DDDL) with pseudo-random code is demonstrated for range and speed measurement of a hard target. This IM-DDDL has key features of (i) long-time coherent signal accumulation without requirement of narrow-linewidth laser source, (ii) high receiving sensitivity with optical direct down-conversion of modulation frequency, (iii) ranging using pseudo-random code, and (iv) Doppler shift detection at baseband frequency. These features are demonstrated in preliminary experiments with fiber-based circuit at 1550 nm wavelength which has eye-safety. The employment of fiber-based configuration contributes to compactness and reliability of the instrument. Ranging function using pseudo-random code is suitable for prevention from interference between multiple LiDARs. The condition for detecting Doppler frequency shift is also shown. A moving stroke of a target within a measurement time needs to be enough larger than the wavelength of modulation frequency. Process for future practical use and application to volumetric target sensing are additionally investigated.

Experimental demonstration of weak-light inter-spacecraft clock jitter readout for TianQin.

The space-based gravitational wave detection mission, TianQin, requires high-level synchronization between independent clocks of all spacecrafts to extract the gravitational wave signals. It is necessary to measure the inter-spacecraft relative clock jitter based on laser phase-sideband clock transfer. The main challenge is the tracking and locking of clock sideband beatnote signals with low signal-to-noise ratio and frequency variation. In this paper, a systematic scheme of inter-spacecraft clock jitter readout is reported. The requirement of the clock transfer link for TianQin based on the time-delay interferometry algorithm is derived. A bi-directional laser interferometer system with a transmission optical power below 1 nW and a time delay of ∼50 µs is built up to demonstrate the weak-light clock transfer. In this scheme, frequency modulation is performed on the laser to simulate the inter-spacecraft Doppler frequency shift and its variation. Based on electrical and optical clock transfer comparison experiments, it is demonstrated that the GHz frequency synthesizer is the main noise source below the 50 mHz frequency range. The residual clock jitter noise introduced by the optical transfer link is below 40 fs/Hz1/2 above the 6 mHz frequency range, and the fractional frequency instability is less than 6.7 × 10-17 at 1000 s, which meets the requirement of the TianQin mission. Ultimately, The carrier phase measurement accuracy reaches 1 × 10-4 cycles/Hz1/2 above 6 mHz after differential clock noise correction using measured clock jitter.

Research on absolute ranging technology of resampling phase comparison method based on FMCW

Abstract As an advanced optical precision ranging method, FMCW (frequency-modulated continuous-wave) laser interferometric ranging technology can achieve a large-scale and high-precision absolute distance measurement, so it has high research and application value in the field of coordinate measurement in large space. How to improve the resolution and stability of laser interferometry is a research difficulty in this technology. Based on FMCW laser interferometry relative distance technology, a method for achieving absolute distance measurement through phase comparison after repeated sampling is proposed. Using the FMCW laser distance measuring system, two interference optical paths of measuring interferometer and auxiliary interferometer are constructed, respectively. Synchronous sampling is performed on two interference signals, and the phase ratio of the two interference signals is obtained through the extracted frequency information. The optical path difference of the unknown measurement interferometer is derived from the known auxiliary interferometer information. This method uses a triangular wave modulation laser to reduce the influence of Doppler frequency shift and eliminate quantization errors. By using the fixed-point repeated sampling, the optical path difference information is quickly extracted, and the nonlinear error of laser interference frequency modulation is effectively reduced.

Proposal for a Doppler Shift Compensation Method Using Non-Uniform FFT with Pilot Carrier Frequency for OFDM-Based Underwater Acoustic Communication Systems

In this paper, we propose a method that uses the non-uniform Fast Fourier Transform (FFT) to compensate for Doppler frequency shifts in orthogonal frequency division multiplexing (OFDM) based underwater acoustic (UWA) communication systems. To estimate the Doppler frequency shift, the paper proposes using a pilot carrier frequency (PCF) that is identified by transmitting with greater power in the frequency domain compared to other subcarriers. This identifier helps estimate both the Doppler frequency shift and the channel. The paper proposes estimating and compensating for the Doppler frequency shift in two steps: Step 1 performs coarse frequency synchronization, where the Doppler frequency shift is determined by using PCF signal. The Doppler shift correction is obtained by re-sampling the received signal, and then interpolating re-sampled signal. However, the Doppler shift compensation in the step 1 cannot correct the phase distortion of the measured PCF signal. Therefore, performing step 2, known as fine frequency synchronization, is necessary. In this step, the correction for the phase distortion is determined based on the phase difference between the two consecutive OFDM signals in one frame. The remaining Doppler frequency shift is adjusted based on the phase deviation, using the non-uniform FFT. By using the non-uniform FFT, the complexity of the ICI compensation is significantly reduced, and the quality of Doppler shift compensation is improved. The experience results show that the transmitted text will be decoded correctly by using the proposed technique

Dual-Frequency Signal Enhancement Method of Moving Target Echoes for GNSS-S Radar

The GNSS-S radar utilizes the signals of a global navigation satellite system (GNSS) to carry out target detection. Due to the very low power of GNSS signals, long-term accumulation is needed to improve the gain of the echo signals. However, when it is used for moving object detection, the random movement of the target will cause residual Doppler frequency after the echoes are correlated and compressed through the direct signal. The residual Doppler frequency will cause two problems: on the one hand, the signal coherence will deteriorate, affecting the coherent accumulation gain; on the other hand, the amplitude of the signal after compression will decrease due to the sensitivity of GNSS signals to Doppler frequency. Therefore, how to increase the signal amplitude and eliminate the phase fluctuation caused by the Doppler frequency shift in the GNSS echoes of moving targets is an important issue for GNSS-S radar to detect moving targets. This paper proposes a dual-frequency GNSS echo enhancement method that uses the dual-frequency signals transmitted by the GNSS satellites to enhance and regularize the target echo. First, the phase relationship model of the GNSS dual-frequency echo is constructed, and the phase difference is made to the compressed dual-frequency echo signal to obtain the differential phase without fluctuation; then, the amplitudes of the dual-frequency echo signals are added together; and finally, a new signal with enhanced amplitude and consistent phase is constructed by using the dual-frequency additive amplitude and differential phase, and the long-term coherent accumulation of the signal is carried out, which can improve the processing gain of the weak echo signal of the moving target. The simulation and field experiments show that this method makes full use of the energy of the GNSS dual-frequency signal and eliminates the phase fluctuation in the echo signal of the moving target so that the compressed signal energy remains consistent in the slow-time dimension. After long-term coherent accumulation, the echo SNR was greatly improved, which enabled the detection of two high-speed cars by GNSS-S radar in the experiment.

A Space–Time–Range Joint Adaptive Focusing and Detection Method for Multiple Input Multiple Output Radar

The Multiple Input Multiple Output (MIMO) radar, as a new type of radar, emits orthogonal waveforms, which provide it with waveform diversity characteristics, leading to increased degrees of freedom and improved target detection performance. However, it also poses challenges such as difficulty in meeting higher data demand, separating waveforms, and suppressing the multidimensional sidelobes (range sidelobes, Doppler sidelobes, and angle sidelobes) of targets. Phase-coded signals are frequently employed as orthogonal transmission signals in the MIMO radar. However, these signals exhibit poor Doppler sensitivity, and the intra-pulse Doppler frequency shift can have an impact on the effectiveness of the matching filtering process. To address the aforementioned concerns, this paper presents a novel approach called the Space–Time–Range Joint Adaptive Focusing and Detection (STRJAFD) method. The proposed method utilizes the Mean Square Error (MSE) criterion and integrates spatial, temporal, and waveform dimensions to achieve efficient adaptive focusing and detection of targets. The experimental results demonstrate that the proposed method outperforms conventional cascaded adaptive methods in effectively addressing the matching mismatch issue caused by Doppler frequency shift, achieving super-resolution focusing, possessing better suppression effects on three-dimensional sidelobes and clutter, and exhibiting better detection performance in low signal-to-clutter ratio and low signal-to-noise ratio environments. Furthermore, STRJAFD is unaffected by coherent sources and demands less data.

Dynamic surface displacement measurement using carrier optical vortex interferometer: A numerical study

The measurement of dynamic surface displacement is crucial in understanding mechanical and thermophysical dynamics at nanometre to micrometer-scale. Interferometers using optical vortices are gaining attention due to their ability to demodulate fringe patterns with helical phase profiles. In this paper, we propose a novel carrier optical vortex interferometer (COVI) that overcomes the limitations of conventional pixelated morphological operations for demodulating fringe patterns. The COVI introduces a carrier frequency by placing a rotating chopper, a collecting lens and a point photodetector at the exit of the interferometer when there is no surface displacement. When the surface moves, the time-dependent total intensity of the chopped fringe pattern produces a Doppler frequency shift with respect to the carrier frequency. Moreover, a high-order Laguerre-Gaussian (LG) beam exhibiting multiple concentric rings is employed to extend the COVI to the dynamic measurement of non-uniform surface displacement with an axisymmetric profile. In this case, the Doppler frequency shift splits into multiple peaks corresponding to the radii of the rings of the LG beam. Locating the Doppler frequency peaks gives an immediate indication of the surface displacement velocities at those radii. Accordingly, the dynamic surface displacement can be retrieved by integrating the velocities over time. The basic principle and the performance of the COVI are theoretically analysed and numerically demonstrated. In addition, the effect of surface misalignment on the displacement measurement is studied thoroughly and the limitations of the measurable velocity are discussed. Although the proposed approach requires further development to make it more applicable in practice, our study provides a first insight into how to measure a dynamic surface displacement using the COVI.

Single-channel system for joint unambiguous measurement of DFS and AOA based on serrodyne modulation.

In this paper, a photonic-assisted system for simultaneous and unambiguous measurement of the Doppler frequency shift (DFS) and angle-of-arrival (AOA) using a dual-parallel dual-drive Mach-Zehnder modulator (DP-DDMZM) is proposed and investigated. The echo signals received by two receiving antennas are applied to the radio frequency ports of one sub-DDMZM of the DP-DDMZM. The bias port of the sub-DDMZM is fed by a binary electrical signal that is used to construct two different mapping curves on the relationship between the phase difference and the power of the output intermediate frequency (IF) signal. Therefore, unambiguous AOA measurement with extended range can be realized. The transmitted signal is input into the other sub-DDMZM to implement single-sideband modulation, which is then frequency shifted based on serrodyne modulation. Both the value and direction of DFS can be derived intuitively from the frequency of the output IF signal. Simulation results show that the measurement error of unambiguous DFS measurement is no more than ±0.008H z in the range of -100k H z to 100kHz, and the measurement error of unambiguous AOA is less than ±0.2∘ in the range of -70.8∘ to 70.8°. Moreover, since the scheme does not involve the construction of multi-channels or use of any filter or polarization dependent device, the system has concise structure, high accuracy, large operating bandwidth, and strong robustness, and can be considered as a very promising solution for actual applications.

Adaptive DLMS equalizer based on modern FPGA

A simple and effective way to implement adaptive equalization schemes in digital communication systems is to implement them on general-purpose microcontrollers. However, increasing the order of the equalizer, which leads to increase the time to obtain the output sample, at the same time leads to decreasing maximum allowable symbol rate. It makes the implementation based on microcontrollers impractical for use in modern high-speed communication protocols. A more suitable computing platform for implementing LMS algorithms is FPGA, where there is no dependence of output sample obtaining time on equalizer order. In order to derive the error signal at the equalizer output from the last (actual) output sample, the estimation of the error signal in the FPGA is required to occur during the same clock period as the calculation of the output signal sample. Trying to fit all the necessary operations into one clock period leads to decrease maximum allowable clock frequency and inefficient using of computing resources within the FPGA. The solving of this problem is to use the Delayed LMS (DLMS) algorithm, invented in the late 80s. The essence of DLMS algorithm is to pipeline both the blocks for calculating the equalizer coefficients and the output samples. The meaning of pipelining is to install synchronous delay elements (D-flip-flops) between the elements of combinatorial logic, which makes it possible to increase the clock and symbol frequency of the equalized signal. The disadvantage of this method is the presence of the synchronous delay of several clock cycles and, as consequence, using of irrelevant error signal for updating coefficients. Retiming procedure is used to optimally distribute synchronous delays to maximize system clock frequency. This article describes the DLMS equalizer and shows the effectiveness of DLMS algorithms implementation on FPGA. The effectiveness of algorithms, which have been used for the retiming procedure is shown. Diagrams of BER(SNR) and BER (Doppler frequency shift) of LMS and DLMS equalization circuits are presented. Obtained results facilitate transfer of demodulator circuit of existing modem from the Zynq microcontroller part built into the Xilinx XC7Z020 FPGA to its programmable logic part in order to increase the performance of the modem receiver to solve current and future challenges.

Estimation of Target Motion Parameters from the Tonal Signals with a Single Hydrophone.

In the shallow-water waveguide environment, the tonal signals radiated by moving targets carry modal interference and Doppler shift information. The modal interference can be used to obtain the time of the closest point of approach (tCPA) and the ratio of the range at the closest point of approach to the velocity of the source (rCPA/v). However, parameters rCPA and v cannot be solved separately. When tCPA is known, the rCPA and the v of the target can be obtained theoretically by using the Doppler information. However, when the Doppler frequency shift is small or at a low signal-to-noise ratio, there will be a strong parametric coupling between rCPA and v. In order to solve the above parameter coupling problem, a target motion parameter estimation method from tonal signals with a single hydrophone is proposed in this paper. The method uses the Doppler and modal interference information carried by the tonal signals to obtain two different parametric coupling curves. Then, the parametric coupling curves can be used to estimate the two motion parameters. Simulation experiments verified the rationality of this method. The proposed method was applied to the SWellEx-96 and speedboat experiments, and the estimation errors of the motion parameters were within 10%, which shows the method is effective in its practical applications.