A Doppler Location Method Based on Virtual Path Difference

This paper presents a Doppler passive location method for moving targets with fixed single station using the Doppler frequency shift and time difference information.First,based on the relationship between frequency shift and path difference,the virtual path difference is calculated from the measured value of Doppler frequency shift by means of mean value correction.Then,under the assumption that the target is moving at a constant speed along a straight line,two coaxial virtual double base arrays are constructed by using the moving track of the moving target based on the method of fixed period time difference.On this basis,the moving distance of the moving target can be calculated by using the ratio relationship between the frequency difference and the radial distance between the two adjacent detection points in the middle of the array,and the linear solution of the two double base path difference positioning equations.At this point,the relative coordinate position of the moving target can be obtained by directly using the linear solution of the double base path difference positioning equation again.

Design and implementation of code acquisition using sparse Fourier transform

Code acquisition is the kernel operation for signal synchronization in the spread-spectrum receiver.To reduce the computational complexity and latency of code acquisition,this paper proposes an efficient scheme employing sparse Fourier transform(SFT)and the relevant hardware architecture for field programmable gate array(FPGA)and application-specific integrated circuit(ASIC)implementation.Efforts are made at both the algorithmic level and the implementation level to enable merged searching of code phase and Doppler frequency without incurring massive hardware expenditure.Compared with the existing code acquisition approaches,it is shown from theoretical analysis and experimental results that the proposed design can shorten processing latency and reduce hardware complexity without degrading the acquisition probability.

A Method to Obtain the Moving Speed of Uncooperative Target Based on Only Two Measurements

The existing research results show that a fixed single station must conduct three consecutive frequency shift measurements and obtain the target’s moving speed by constructing two frequency difference equations. This article proposes a new method that requires only two consecutive measurements. While using the azimuth measurement to obtain the angular difference between two radial distances, it also conducts two consecutive Doppler frequency shift measurements at the same target azimuth. On the basis of this measurement, a frequency difference equation is first constructed and solved jointly with the Doppler frequency shift equation. By eliminating the velocity variable and using the measured angular difference to obtain the target’s lead angle, the target’s velocity can be solved by using the Doppler frequency shift equation again. The new method avoids the condition that the target must move equidistantly, which not only provides an achievable method for engineering applications but also lays a good foundation for further exploring the use of steady-state signals to achieve passive positioning.

Computations on the Earth Terrain Return of Pulse Doppler Radar Altimeter

Concerning the PDRA (pulse doppler radar altimeter) designing and evaluation, owing to that the specifications of PDRA should be adaptively fixed according to the ETR (earth terrain return), and that in certain stages of product evaluation of PDRA which means the designations of PDRA are successful or not, the usage of ETR are indispensable, so the terrain return from spherical earth is critically important. A complete analytic derivation of the antenna shot section model of PDRA and the bright section model constrained by pulse emitted from antenna are given. Furthermore, the doppler effect mode and the earth terrain RCF (radar crossing factor) model are constructively analyzed. Then, the computing methodology on PDRA, which are used to compute the scattering power, scattering doppler spectrum, and the scattering signal, is studied. Besides, in order to check the correctness and efficiency of the algorithm, computing examples of ETR (earth terrain return) under the supposing premises are furnished. Finally, the conclusion is drawn that the models and algorithm are rational, the computational precise is satisfactory, the cost of computing time is low.

Adaptive compensating method for Doppler frequency shift using LMS and phase estimation

The novel compensating method directly demodulates the signals without the carrier recovery processes, in which the carrier with original modulation frequency is used as the local coherent carrier. In this way, the phase offsets due to frequency shift are linear. Based on this premise, the compensation processes are： firstly, the phase offsets between the baseband neighbor-symbols after clock recovery is unbiasedly estimated among the reference symbols; then, the receiving signals symbols are adjusted by the phase estimation value; finally, the phase offsets after adjusting are compensated by the least mean squares （LMS） algorithm. In order to express the compensation processes and ability clearly, the quadrature phase shift keying （QPSK） modulation signals are regarded as examples for Matlab simulation. BER simulations are carried out using the Monte-Carlo method. The learning curves are obtained to study the algorithm＇s convergence ability. The constellation figures are also simulated to observe the compensation results directly.

Doppler frequency offset estimation and diversity reception scheme of high-speed railway with multiple antennas on separated carriage

The challenges of severe Doppler effects in high-speed railway are considered. By building a cooperative antenna system; an algorithm of joint channel estimation and Doppler frequency offset （DFO） estimation is proposed based on Ricean channel model. First, a maximum likelihood estimation （MLE） algorithm for DFO is designed, show- ing that the Doppler estimation can be obtained by estimating moving velocity of the train and the path loss with the exploitation of pilots that are placed inside the frame. Then a joint detection algorithm for the receiver is proposed to exploit multi-antenna diversity gains. Last, the theoretical Crammer Rao bound （CRB） for joint channel estimation and DFO estimation is derived. The steady performance of the system is confirmed by numerical simulations. In particular, when the Ricean fading channel parameter equals 5 and the velocities of train are 100 m/s and 150 m/s, the estimation variances of DFO are very close to the theoretical results obtained by using CRB. Meanwhile, the corresponding sig- nal to noise ratio loss is less than 1.5 dB when the bit error rate is 10-5 for 16QAM signals.

Novel Doppler Frequency Extraction Method Based on Time-Frequency Analysis and Morphological Operation

A novel method of Doppler frequency extraction is proposed for Doppler radar scoring systems. The idea is that the time-frequency map can show how the Doppler frequency varies along the time-line, so the Doppler frequency extraction becomes curve detection in the image-view. A set of morphological operations are used to implement curve detection. And a map fusion scheme is presented to eliminate the influence of strong direct current （DC） component of echo signal during curve detection. The radar real-life data are used to illustrate the performance of the new approach. Experimental results show that the proposed method can overcome the shortcomings of piecewise-processing-based FFT method and can improve the measuring precision of miss distance.

Estimation of DOA and Doppler Frequency on Nonideal UCA

The problem of estimating direction of arrivals (DOA) and Doppler frequency for many sources is considered in the presence of general array errors (such as amplitude and phase error of sensors, setting position error of sensors). Adopting direct array manifold in a uniform circular array (UCA), the estimation of Doppler frequency can be obtained by DOA matrix. Based on analyzing the statistic characters of general array errors, the estimation of DOA can be obtained by Weight Total Least Squares. Numerical results illustrate that the estimator is robust to general array errors and show the capabilities of the estimator.

Velocity estimation of moving targets with stepped-frequency radar based on Doppler frequency difference

By analyzing the signal model of stepped-frequency waveform, a novel method for velocity measurement is proposed. The method is based on Doppler frequency difference which is achieved by using Hough transform. As the estimated velocity is inversely proportional to the frequency step size instead of the carrier frequency of the transmitted signal as the pulse-Doppler （PD） processing, the new algorithm can achieve much wider unambiguous velocity range. Furthermore, non-coherent integration of the sub-pulses with different carrier frequencies can be implemented by Hough trans- form to improve the anti-noise performance. Besides, field experimental results show that the high range resolution profile （HRRP） of a bullet with high speed can be reconstructed correctly without distortion.

ESTIMATION OF DOPPLER CENTROID FREQUENCY IN SPACEBORNE SCANSAR

Doppler centroid frequency is an essential parameter in the imaging processing of the Scanning mode Synthetic Aperture Radar (ScanSAR). Inaccurate Doppler centroid frequency will result in ghost images in imaging result. In this letter, the principle and algorithms of Doppler centroid frequency estimation are introduced. Then the echo data of ScanSAR system is analyzed. Based on the algorithms of energy balancing and correlation Doppler estimator in the estimation of Doppler centroid frequency in strip mode SAR, an improved method for Doppler centroid frequency estimation in ScanSAR is proposed. The method has improved the accuracy of Doppler centroid frequency estimation in ScanSAR by zero padding between burst data. Finally, the proposed method is validated with the processing of ENVIronment SATellite Advanced Synthetic Aperture Radar (ENVISAT ASAR) wide swath raw data.

ATTITUDE RATE ESTIMATION BY GPS DOPPLER SIGNAL PROCESSING

A method is presented for near-Earth spacecraft or aviation vehicle's attitude rate estimation by using relative Doppler frequency shift; of the Global Positioning System (GPS) carrier. It comprises two GPS receiving antennas, a signal processing circuit and an algorithm. The whole system is relatively simple, the cost and weight, as well as power consumption, are very low.

A novel high precision Doppler frequency estimation method based on the third-order phase-locked loop

In deep space exploration,many engineering and scientific requirements require the accuracy of the measured Doppler frequency to be as high as possible.In our paper,we analyze the possible frequency measurement points of the third-order phase-locked loop(PLL)and find a new Doppler measurement strategy.Based on this finding,a Doppler frequency measurement algorithm with significantly higher measurement accuracy is obtained.In the actual data processing,compared with the existing engineering software,the accuracy of frequency of 1 second integration is about 5.5 times higher when using the new algorithm.The improved algorithm is simple and easy to implement.This improvement can be easily combined with other improvement methods of PLL,so that the performance of PLL can be further improved.

A new Doppler frequency anomaly algorithm for surface current measurement with SAR

Values for Doppler center frequency are calculated from the echo signal at the satellite using the Doppler centroid method and so include the predicted Doppler frequency caused by the relative motion of the satellite and the Earth,which is the main component of Doppler center frequency and must be removed to obtain the Doppler frequency anomaly for ocean current measurement.In this paper,a new Doppler frequency anomaly algorithm was proposed when measuring surface currents with synthetic aperture radar(SAR).The key of the proposed algorithm involved mean filtering method in the range direction and linear fitting in the azimuth direction to remove the radial and the azimuthal component of predicted Doppler frequency from the Doppler center frequency,respectively.The basis is that the theoretical Doppler center frequency model of SAR exhibits an approximately linear characteristic in both the range direction and in the azimuth direction.With the help of the new algorithm for predicted Doppler frequency removal,the estimation error of Doppler frequency anomaly can be reduced by avoiding employing the theoretical antenna pattern and imperfect satellite attitude parameters in the conventional Doppler frequency method.SAR measurement results demonstrated that,compared to the conventional Doppler frequency with/without error correction method,the proposed algorithm allows for a pronounced improvement in the current measuring accuracy in comparison with the global ocean multi-observation(MOB)products.In addition,the eff ectiveness and robustness of the proposed Doppler algorithm has been demonstrated by its application in the high velocity current in the Kuroshio region.

Radial velocity of ocean surface current estimated from SAR Doppler frequency measurements—a case study of Kuroshio in the East China Sea

Ocean currents are a key element in ocean processes and in meteorology,affecting material transport and modulating climate change patterns.The Doppler frequency shift information of the synthetic aperture radar(SAR)echo signal can reflect the dynamic characteristics of the sea surface,and has become an essential sea surface dynamic remote sensing parameter.Studies have verified that the instantaneous Doppler frequency shift can realize the SAR detection of the sea surface current.However,the validation of SAR-derived ocean current data and a thorough analysis of the errors associated with them remain lacking.In this study,we derive high spatial resolution flow measurements for the Kuroshio in the East China Sea from SAR data using a theoretical model of shifts in Doppler frequency driven by ocean surface current.Global ocean multi observation(MOB)products and global surface Lagrangian drifter(GLD)data are used to validate the Kuroshio flow retrieved from the SAR data.Results show that the central flow velocity for the Kuroshio derived from the SAR is 0.4–1.5 m/s.The error distribution between SAR ocean currents and MOB products is an approximate standard normal distribution,with the 90%confidence interval concentrated between–0.1 m/s and 0.1 m/s.Comparative analysis of SAR ocean current and GLD products,the correlation coefficient is 0.803,which shows to be significant at a confidence level of 99%.The cross-validation of different ocean current dataset illustrate that the SAR radial current captures the positions and dynamics of the Kuroshio central flow and the Kuroshio Counter Current,and has the capability to monitor current velocity over a wide range of values.

Curvelet Transform-Based Denoising Method for Doppler Frequency Extraction

A novel image denoising method based on curvelet transform is proposed in order to improve the performance of Doppler frequency extraction in low signal-noise-ratio (SNR) environment. The echo can be represented as a gray image with spectral intensity as its gray values by time-frequency transform. And the curvelet coefficients of the image are computed. Then an adaptive soft-threshold scheme based on dual-median operation is implemented in curvelet domain. After that, the image is reconstructed by inverse curvelet transform and the Doppler curve is extracted by a curve detection scheme. Experimental results show the proposed method can improve the detection of Doppler frequency in low SNR environment.

INSTANTANEOUS DOPPLER FREQUENCY FOR SQUINT SAR IMAGING

Instantaneous Doppler frequency for squint SAR imaging has been found with ChirpScaling Algorithm (CSA). Because the azimuth sample is not perpendicular to the range sample,the range signal must impact on the azimuth signal in the squint SAR data processing, andthe different slant range targets have different Doppler frequencies. From the mathematicalmodel of SAR echo signal, this paper carefully analyzes the instantaneous azimuth frequency, theinstantaneous Doppler frequency component of the azimuth frequency and the impact of rangechirp on azimuth frequency, which explains that Doppler frequency should be properly selected forcorrect SAR imaging in the squint SAR. The results of point target simulation experiments showthat the way is reasonable for the squint SAR and can effectively complete range compressionand azimuth focusing, and improve images' quality.

Deep learning based Doppler frequency offset estimation for 5G-NR downlink in HSR scenario

In the fifth-generation new radio(5G-NR) high-speed railway(HSR) downlink,a deep learning(DL) based Doppler frequency offset(DFO) estimation scheme is proposed by using the back propagation neural network(BPNN).The proposed method mainly includes pre-training,training,and estimation phases,where the pre-training and training belong to the off-line stage,and the estimation is the online stage.To reduce the performance loss caused by the random initialization,the pre-training method is employed to acquire a desirable initialization,which is used as the initial parameters of the training phase.Moreover,the initial DFO estimation is used as input along with the received pilots to further improve the estimation accuracy.Different from the training phase,the initial DFO estimation in pre-training phase is obtained by the data and pilot symbols.Simulation results show that the mean squared error(MSE) performance of the proposed method is better than those of the available algorithms,and it has acceptable computational complexity.

Iterative physical optics model for electromagnetic scattering and Doppler analysis

An iterative physical optics（IPO） model is proposed to solve extra large scale electric electromagnetic（EM） scattering from randomly rough surfaces. In order to accelerate the convergence of the IPO model, the forward-backward methodology and its modification with underrelaxation iteration are developed to simulate the rough surface scattering; the local iteration methodology and the fast far field approximation（Fa FFA） in the matrix-vector product are proposed to reduce greatly the computational complexity. These techniques make Monte Carlo simulations possible. Thus, the average Doppler spectra of backscattered signals obtained from the simulations are compared for different incident angles and sea states. In particular, the simulations show a broadening of the Doppler spectra for a more complicated sea state at a low grazing angle（LGA）.

Thin-film lithium niobate dual-parallel Mach-Zehnder modulator for a simple photonic system measuring Doppler frequency shift

In recent years,thin-film lithium niobate(TFLN)electro-optic(EO)modulators have developed rapidly and are the core solution for the next generation of microwave photonics(MWP)problems.We designed and fabricated a dual-parallel Mach-Zehnder modulator(DPMZM)based on TFLN,achieving a 3 dB electro-electro(EE)bandwidth of 29 GHz and a low drive voltage(Vπ=6 V).The device we manufactured is metal-encapsulated.It is noteworthy that we proposed a single-channel Doppler frequency shift(DFS)measurement system based on this device and conducted verification experiments.We coupled light from an external laser into the chip and passed it through each of the two sub-MZMs of the DPMZM.These lights were modulated by echo signals and reference signals.By measuring the frequency of the output signal,we can obtain a DFS value without directional ambiguity.The success of this experiment marks a key step in the practical application of TFLN modulators in MWP.

Fast multi-parameter estimation and localization for MIMO radar

This paper addresses the problem of four-dimensional angle and Doppler frequency estimation for bistatic multiple-input multiple-output （MIMO） radar with arbitrary arrays in spatial co- lored noise. A novel method for joint estimation of Doppler fre- quency, two-dimensional （2D） direction of departure and 2D direc- tion of arrival based on the propagator method （PM） for arbitrary arrays is discussed. A special matrix is constructed to eliminate the influence of spatial colored noise. The four-dimensional （4D） angle and Doppler frequency are extracted from the matrix and the three- dimensional （3D） coordinates of the targets are then calculated on the basis of these angles. The proposed algorithm provides a lower computational complexity and has a parameter estimation very close to that of the ESPRIT algorithm and the DOA-matrix al- gorithm in the high signal to noise ratio and the Cramer-Rao bound （CRB） is given. Furthermore, multi-dimensional parameters can be automatically paired by this algorithm to avoid performance degra- dation resulting from wrong pairing. Simulation results demonstrate the effectiveness of the proposed method.