Coherent Integration Time Research Articles

A Two-Stage Kalman Filter-Based Carrier Tracking Loop for Weak GNSS Signals.

For global navigation satellite system receivers, Kalman filter (KF)-based tracking loops show remarkable advantages in terms of tracking sensitivity and robustness compared with conventional tracking loops. However, to improve the tracking sensitivity further, increasing the coherent integration time is necessary, but it is typically limited by the navigation data bit sign transition. Moreover, for standard KF-based tracking receivers, the KF parameters are initialized by the acquired results. However, especially under weak signal conditions, the acquired results have frequency errors that are too large for KF-based tracking to converge rapidly to a steady state. To solve these problems, a two-stage KF-based tracking architecture is proposed to track weaker signals and achieve faster convergence. In the first stage, coarse tracking refines the acquired results and achieves bit synchronization. Then, in the second stage, fine tracking initializes the KF-based tracking by using the coarse tracking results and extends the coherent integration time without the bit sign transition limitation. This architecture not only utilizes the self-tuning technique of the KF to improve the tracking sensitivity, but also adopts the two-stage to reduce the convergence time of the KF-based tracking. Simulation results demonstrate that the proposed method outperforms conventional tracking techniques in terms of tracking sensitivity. Furthermore, the proposed method is compared with the standard KF-based tracking approach, proving that the proposed method converges more rapidly.

Galileo E5 Signal Acquisition using Intermediate Coherent Integration Time

The acquisition of modern Global Navigation Satellite System (GNSS) signals may be difficult due to the presence of a secondary code. Indeed, short coherent integration times should be used without non-coherent integration, which implies a low sensitivity; or long coherent integration times should be used, requiring synchronisation with the secondary code and thus a full correlation, which implies a significant computational burden, especially for signals with long secondary codes such as the Galileo E5 signal. A third option that lies between the previous two is to perform a partial correlation using less than one secondary code period as input, however this is less efficient in terms of complexity than using an entire secondary code period, and the code's autocorrelation properties are completely changed. The authors recently proposed a method based on combining secondary code correlations, allowing the use of intermediate coherent integration times with the possibility to do non-coherent integrations, and the method was successfully applied to the Global Positioning System (GPS) L5 signal. This paper studies the application of the method to the Galileo E5 signal, compares it with the partial correlation method, and discusses the case where less than one secondary code period is used as an input

Carrier Phase Recovery for Array Navigation Receiver: A Fast Phase Retrieval Approach

A fast carrier phase recovery scheme is developed for satellite navigation receiver using an antenna array based on the phase retrieval theory, in which the antenna array provides sufficient measurement information for the phase recovery algorithm. First, the complex satellite signal model after coherent integration is established using the antenna array. Then, considering symbol uncertainty of the navigation data during the coherent integration time, the carrier phase estimation is formulated as a typical phase retrieval problem. At last, using the squared iterative method (SQUAREM), which is capable of superlinear convergence, a fast variant of the Wirtinger Flow (WF) algorithm is derived to solve the phase recovery problem efficiently without compromising the balance between simplicity and stability. As demonstrated by numerical results, the proposed algorithm outperforms the state-of-the-art in terms of the mean squared error (MSE) convergence. Moreover, the adjustment processes of the carrier phase in the proposed method is validated.

Geometric Distortion Correction of Spaceborne GNSS-R Delay-Doppler Map Using Reconstruction

For spaceborne Global Navigation Satellite System-Reflectometry (GNSS-R), the delay difference of direct and reflected GNSS signals among successive snapshots changes rapidly because of the high dynamics of low earth orbital and GNSS satellites. This change has to be compensated to avoid the distortion of incoherently averaged delay-Doppler map (DDM). The method to refresh the correlation window on each coherent integration time period may require too many instrument resources or too much data to be uploaded from the ground station. This letter proposes a new postprocessing approach based on the motion degradation model of DDM and the reconstruction to replace real-time compensation. Raw sampled data from UK TechDemoSat-1 are used to verify the availability of proposed approach. The results show that after reconstruction for the distorted DDM, the DDM accuracies relative to that compensated in real time are significantly improved.

Performance of GNSS-R GLORI data for biomass estimation over the Landes forest

The Above-Ground Biomass (AGB) is a key parameter used for the modeling of the carbon cycle. The aim of this study is to make an experimental assessment of the sensitivity of Global Navigation Satellite System (GNSS) reflected signals to forest AGB. This is based on the analysis of the data recorded during several GLORI airborne campaigns in June and July 2015, over the Landes Forest (France). Ground truth measurements of tree height, density and diameter at breast height (DBH), as well as AGB, were carried out for 100 maritime pine forest plots of various ages. The GNSS-R data were used to obtain the right-left (ΓRL) and right-right (ΓRR) reflectivity observables, which are geo-referenced in accordance with the known positions of relevant GPS satellites and the airborne receiver. The correlations between forest AGB and the GNSS-R observables yield the highest sensitivity at high elevation angles (70°-90°). In this case, for (ΓRL) and the reflectivity polarization ratio (PR = ΓRL/ΓRR) estimated with a coherent integration time Tc = 20 ms, the coefficients of determination R2 are equal to 0.67 and 0.51, with a sensitivity of −0.051 dB/[106g (Mg) ha−1], and −0.053 dB/[Mg ha−1], respectively. The relationships between AGB and the observables are confirmed through the use of a 5-fold cross validation approach, with several different coherent integration times.

Computationally efficient coherent detection and parameter estimation algorithm for maneuvering target

In this paper, a computationally efficient coherent detection and parameter estimation algorithm via symmetric autocorrelation function (SAF) and scaled Fourier transform (i.e., SAF-SFT) is proposed, involving range cell migration (RCM) and Doppler spread (DS) within the coherent integration (CI) time. In particular, the first SAF and SFT operations are applied to achieve the range and velocity estimations after the generalized keystone transform. With the estimations, the remaining RCM induced by target’s velocity could be removed and the target signal could be extracted along the range cell. Then the second SAF and SFT operations are performed on the extracted signal, where the target energy could be coherent integrated and the acceleration estimation can be obtained. Cross term of SAF-SFT is also analyzed and its characteristic indicates the applicability in the scenario of multi-targets. Detailed comparisons of SAF-SFT with several typical algorithms with respect to computational cost, detection probability and parameter estimation ability show that the SAF-SFT could strike a balance between computational cost and detection probability as well as the estimation performance. Simulation results and real test experiment are given to verify the SAF-SFT based approach.

In brief

PAGE 995 The use of long coherent integration times in CZT-based algorithms could have applications for GPS systems operating in weak signal environments. A down-sampling data operation introduced by researchers in China demonstrates that the same signal acquisition can be achieved with a lower carrier-to-noise ratio and reduced computational effort. PAGE 991 Researchers in the UK working with semiconductor-based terahertz emitters have observed that temperature dependent polarity reversal within the material is an intrinsic property. Terahertz emission from various emitters over a range of temperatures revealed the semiconductor's inversion is not influenced by metallic contact, and creates potential for these devices to compete with commercial antennas. Signal detection probability improves with extended coherent integration times. PAGE 1007 A novel design for a simpler, more flexible, high performance microstrip power-divider (PD) has been implemented and tested by researchers in China. The device is composed of two dual-mode filtering PDs lacking any additional matching network, and provides significant design utility and size reduction with applications in wireless communications systems. Spectrometer set up for temperature dependence measurement of metal emitters. PAGE 967 Researchers from China have developed a frequency calibration method for a crystal-less current-controlled ring oscillator utilising a serial data signal from another chip as a reference. This newly presented auto-correlation method outperforms similar literature designs in terms of calibration accuracy, power consumption, and circuit area. Measured and simulated performances of power-divider device channels. PAGE 969 A purely digital approach to ultra-narrow pulse control for use in the picosecond and gigahertz domains has been presented by researchers in China. The digital synthesis method converts pulse-width control to the relative delay control between two signals, and can be applied to ultra-wideband communication systems and pulse radar. Frequency histograms before and after chip signal calibration. Diagram of ideal and real sharpener edge signal outputs.

Benefits of long coherent integration for CZT‐based GPS signal acquisition

Due to its flexibility in calculating frequency spectrum, the chirp z-transform (CZT) has been used in various applications where high-frequency resolution is desirable, e.g. the acquisition of global positioning system (GPS) signals. However, the CZT is very time consuming when dealing with the very large size of input data. Thus, typically, only 1 ms data is used for GPS signal acquisition. In this Letter, the authors improve the acquisition precision and sensitivity of the CZT-based acquisition by extending coherent integration time. To reduce computation load, they introduce a down-sampling operation to the extended data without degrading acquisition performance. Results show that the CZT-based acquisition with a coherent integration time of 10 ms obtains a frequency error of 5.9 Hz for the carrier-to-noise ratio (CNR) of 25 dB-Hz and can acquire signals with a CNR down to 22 dB-Hz.

Adaptive Radon–Fourier Transform for Weak Radar Target Detection

The Radon–Fourier transform (RFT) with a long coherent integration time has recently been proposed for detecting a moving target with an across range cell (ARC) effect. However, without effective clutter suppression, clutter will also be integrated via the RFT, which may affect weak target detection. Based on the maximal signal-to-clutter-plus-noise ratio (SCNR) criteria, a novel adaptive RFT (ARFT) is proposed in this paper to effectively detect a “low-observable” target in a clutter background. The proposed ARFT can combine RFT and adaptive clutter suppression by introducing an optimal filter weight, which is determined from the clutter's covariance matrix as well as a steering vector for a moving target with the ARC effect. In the transformed range-velocity space, the proposed ARFT can suppress background clutter and optimally integrate the target's energy. Nevertheless, with the increase in the integration time, the ARFT needs to address two difficulties in its real implementation. One is the lack of independently and identically distributed (i.i.d.) training samples in a heterogeneous clutter background, and the other is that the computational complexity is too high due to the large number of pulse samples. Therefore, a subaperture ARFT (SA-ARFT) is further proposed in this paper. It divides all coherent pulse samples into several subapertures and accomplishes adaptive clutter suppression in each subaperture. Subsequently, SA-ARFT implements coherent integration among the outputs of different subapertures. The proposed SA-ARFT method can obtain a similar SCNR improvement factor (SCNR IF) with a large number of i.i.d. training samples, while it can obtain a much higher SCNR IF than the ARFT with limited i.i.d. training samples and much lower computational complexity in a heterogeneous clutter background. Finally, some numerical results are provided to demonstrate the effectiveness of the two proposed methods.

Fast GNSS signal acquisition with Doppler frequency estimation algorithm

In both urban and indoor environments, position and navigation technologies that are based on global navigation satellite systems (GNSSs) high requirements for acquisition sensitivity of a GNSS receiver. To increase the acquisition speed and sensitivity of a GNSS receiver, a new method called improved acquisition algorithm with Doppler frequency compensation (IAADFC) is proposed to realize a long coherent integration time (CIT) acquisition algorithm to increase the sensitivity of a GNSS receiver. Its CIT can be larger than the bit length of the navigation message. Based on the parameter estimation theory, the Doppler frequency estimation algorithm (DFEA) is proposed to reduce the Doppler frequency search range (DFSR) to speed-up the acquisition process. Then, the data bit sign transition (DBST) algorithm is proposed to remove the impact of the data bit sign transition to improve acquisition sensitivity. Then, the IAADFC is discussed. Simulation results demonstrate that the IAADFC can improve the sensitivity and speed of weak GNSS signal acquisition. Finally, we provide a detailed comparison between the proposed IAADFC algorithm and the non-coherent integration (NCI) algorithm. Simulation results shown demonstrate that our IAADFC algorithm can detect weaker signals than the NCI algorithm can. This can help meet the high sensitivity requirement for indoor and outdoor seamless position and navigation service.

Lagrange-Polynomial-Interpolation-Based Keystone Transform for a Passive Radar

In this paper, we address the problem of target's range migration in passive bistatic radar exploiting long coherent integration times with fairly wideband signals of opportunity. We resort to the well-known keystone transform (KT) to compensate for the range walk effect and to take advantage of a higher coherent integration gain against targets with nonnegligible radial velocity. Specifically, an efficient implementation of the KT is proposed, based on the Lagrange polynomial interpolation, in order to reduce the computational load of the method that mostly depends on the required slow-time interpolation stage. The analysis conducted against simulated data shows that the conceived approach allows us to achieve theoretical performance, while further reducing the KT complexity with respect to alternative solutions based on cardinal sine functions or chirp-Z transforms. Moreover, the application against experimental datasets collected by a DVB-T-based passive radar proves the practical effectiveness of the proposed algorithm and highlights its suitability for real-time air traffic surveillance applications.

Resampling to accelerate cross-correlation searches for continuous gravitational waves from binary systems

Continuous-wave (CW) gravitational waves (GWs) call for computationally-intensive methods. Low signal-to-noise ratio signals need templated searches with long coherent integration times and thus fine parameter-space resolution. Longer integration increases sensitivity. Low-mass x-ray binaries (LMXBs) such as Scorpius X-1 (Sco X-1) may emit accretion-driven CWs at strains reachable by current ground-based observatories. Binary orbital parameters induce phase modulation. This paper describes how resampling corrects binary and detector motion, yielding source-frame time series used for cross-correlation. Compared to the previous, detector-frame, templated cross-correlation method, used for Sco X-1 on data from the first Advanced LIGO observing run (O1), resampling is about 20x faster in the costliest, most-sensitive frequency bands. Speed-up factors depend on integration time and search setup. The speed could be reinvested into longer integration with a forecast sensitivity gain, 20 to 125 Hz median, of approximately 51%, or from 20 to 250 Hz, 11%, given the same per-band cost and setup. This paper's timing model enables future setup optimization. Resampling scales well with longer integration, and at 10x unoptimized cost could reach respectively 2.83x and 2.75x median sensitivities, limited by spin-wandering. Then an O1 search could yield a marginalized-polarization upper limit reaching torque-balance at 100 Hz. Frequencies from 40 to 140 Hz might be probed in equal observing time with 2x improved detectors.

VLBI Imaging of M81* at λ = 3.4 mm with Source-frequency Phase-referencing

Abstract We report on the first VLBI image of the M81 nucleus (M81*) at a wavelength of 3.4 mm, obtained with the source-frequency phase-referencing (SFPR) technique. Thanks to the SFPR calibration, the coherent integration time eventually could be increased by more than an order of magnitude, which enabled the detection of fringes at the level of 45 mJy beam−1 with a dynamic range higher than 130:1. This paves the way toward future millimeter/submillimeter VLBI observations of weaker sources. From the analysis of the M81* visibilities, a core size of ∼50 μas at 3.4 mm was estimated. This follows the power-law relationship with wavelength, , reported previously at lower frequencies. These results constrain the core size (at 3.4 mm) to a minimum of ∼80 Schwarzschild radii of M81*.

Detection of Slow Radial Velocity Ship by OTHR

In order to detect ship in the spread sea clutter caused by ionospheric disturbance, algorithms of short coherent integration time (CIT) are used in over-the-horizon radar system. Here, ECVC (Estimate Clutter Via Correlation) algorithm is employed to provide higher resolution to detect ship of slow radial velocity. The following two topics are discussed: (1) the model of sea clutter and ECVC algorithm; (2) the detection results of ECVC, compared with Root, SVD (Singular Value Decomposition) and EVD (Eigen-Value Decomposition). Simulation and experiment results demonstrate the usefulness of the proposed approach.

A Stand-Alone Approach for High-Sensitivity GNSS Receivers in Signal-Challenged Environment

To navigate in global navigation satellite systems (GNSS) signal-challenged environment, for example, foliage canopy, urban canyon, indoor, etc., high-sensitivity GNSS receivers are usually preferred for the improved acquisition and tracking capabilities. The core of high-sensitivity GNSS receiver design is to extend integration time coherently, which is optimal for improving post-signal-to-noise ratio, mitigating multipath and cross-correlation false locks, and avoiding squaring loss. In GNSS data channels, extending integration time coherently requires the navigation message data bit wipe-off. For stand-alone high-sensitivity GNSS receivers, bit wipe-off is usually achieved by using estimation algorithms (i.e., bit decoding) rather than accessing external networks (i.e., bit aiding). In this paper, the maximum-likelihood (ML) bit decoding is used to estimate the data bit values for bit wipe-off. Furthermore, the benefits of using advanced tracking algorithms—vector tracking and inertial navigation system (INS)-assisted tracking (i.e., ultratight coupling of GNSS/INS)—to improve ML bit decoding and navigation performance are analyzed. Two vehicular navigation tests are performed in dense foliage and an urban canyon environment. In the context of global positioning system L1 C/A signals, the field test results show that vector tracking and ultratight coupling can improve the successful decoding rate by up to 40% depending on signal strength. This paper also demonstrates how the signal power-based correlator selection method can address high bit error-rate problems when ML bit decoding is used for bit wipe-off in the signal-challenged environment. After implementing this algorithm, the position and velocity accuracy of the stand-alone high-sensitivity GNSS receiver has been improved about 50% after extending coherent integration time from 20 to 100 ms in the vehicular navigation tests.

High‐precision estimation of target range, radial velocity, and azimuth in mechanical scanning LFMCW radar

This study investigates the effects of antenna rotation on range, radial velocity, and azimuth estimation during coherent integration in linear frequency-modulated continuous wave (LFMCW) radars. When antenna scans during the coherent integration time, theoretical analysis indicates that the angle sensing with the traditional sum-difference amplitude-comparison (SDAC) monopulse method and the range, radial velocity estimation with interpolation method are different from that in staring mode. Simulation demonstrates that the estimation performance is heavily impaired by the antenna rotation. In this study, a generalised mathematical model of coherent integration for LFMCW radar is established. Furthermore, a high-precision estimation method, which consists of generalised SDAC monopulse method, radial velocity estimator with modified interpolation curves, and range estimator refined by Doppler frequency, is proposed. A complete signal-processing scheme is proposed for the accurate estimation of the target parameter in mechanical scanning LFMCW radar. A sub-optimal method is provided for practical implementation. Experimental and simulation results show that the proposed method achieves high accuracy and robustness.

Time–frequency analysis for moving ship targets in GEO spaceborne/airborne bistatic SAR imaging based on a GEO satellite transmitter

ABSTRACTThe track of a synthetic aperture radar (SAR) system mounted on a geosynchronous orbit (GEO) satellite can be curvilinear. GEO spaceborne/airborne bistatic (SA-Bi) SAR, which employs a GEO satellite as a transmitter and an aeroplane that works on the ‘receive-only’ mode as a receiver, is distinct from general bistatic SAR systems. During coherent integration time, the rotation of ship targets results in a time-varying Doppler frequency shift that produces a smeared Doppler spectrum and a blurred image after Fourier transform. This article mainly studies the time–frequency characteristics of ship targets in a GEO SA-Bi SAR system. First, the geometric model of a GEO SA-Bi SAR in ship target imaging is built, and the Doppler frequency shift function induced by target rotation is derived in detail. Then, the instantaneous frequency characteristics of moving targets are analytically calculated based on the time–frequency analysis method. Moreover, a rotation target imaging strategy of GEO SA-Bi SAR based on the time–frequency analysis method is proposed and tested with simulation data, which demonstrates the correctness and effectiveness of the proposed method.

A Modified Differential Coherent Bit Synchronization Algorithm for BeiDou Weak Signals with Large Frequency Deviation

BeiDou system navigation messages are modulated with a secondary NH (Neumann-Hoffman) code of 1 kbps, where frequent bit transitions limit the coherent integration time to 1 millisecond. Therefore, a bit synchronization algorithm is necessary to obtain bit edges and NH code phases. In order to realize bit synchronization for BeiDou weak signals with large frequency deviation, a bit synchronization algorithm based on differential coherent and maximum likelihood is proposed. Firstly, a differential coherent approach is used to remove the effect of frequency deviation, and the differential delay time is set to be a multiple of bit cycle to remove the influence of NH code. Secondly, the maximum likelihood function detection is used to improve the detection probability of weak signals. Finally, Monte Carlo simulations are conducted to analyze the detection performance of the proposed algorithm compared with a traditional algorithm under the CN0s of 20~40 dB-Hz and different frequency deviations. The results show that the proposed algorithm outperforms the traditional method with a frequency deviation of 50 Hz. This algorithm can remove the effect of BeiDou NH code effectively and weaken the influence of frequency deviation. To confirm the feasibility of the proposed algorithm, real data tests are conducted. The proposed algorithm is suitable for BeiDou weak signal bit synchronization with large frequency deviation.

Comparison of Spectral Estimation Methods for Rapidly Varying Currents Obtained by High-Frequency Radar

A comparative study of the periodogram method and high-resolution techniques (the autoregressive and multiple signal classification methods) for current mapping by a high-frequency (HF) surface wave radar is undertaken for the case of 66-s-long data. This analysis is extended from a previous study that used the commonly adopted 6–13-min coherent integration times. This reduction in the sample size will result in poor Doppler resolution and reduction in signal-to-noise ratio (SNR) for the conventional periodogram method. Two Bragg-peak identification methods for current estimation, the conventional centroid method and the symmetric-peak-sum (SPS) method, are examined in conjunction with each of the spectral estimation techniques. A weighted sum of the current estimates using the two Doppler shift identification methods is also recommended to provide a lower root mean square (RMS) difference. The weight is optimized using a genetic algorithm. Field data comparison with current measurements obtained from a current meter indicates that the high-resolution spectral estimation method is capable of providing the same RMS difference level for short and long time series, while the RMS difference for currents obtained from the periodogram method increases dramatically for short time series. Significant improvement in the current velocities retrieved from a short time series indicates the potential for measuring rapidly changing currents using the suggested technique.

On-Ground Retracking to Correct Distorted Waveform in Spaceborne Global Navigation Satellite System-Reflectometry

Spaceborne Global Navigation Satellite System-Reflectometry (GNSS-R) has been the research focus of Earth observation because of its unique advantages; however, there are still many challenges to be resolved. The reduction of the impact of the satellite motion on the GNSS-R waveform is the one of key technologies for spaceborne GNSS-R. The proposed delay retracking methods in existing literatures require too many instrument resources and too much priori information to refresh correlation window on each coherent integration time period. This paper aims to propose an on-ground alternative in which less frequency tracking refresh on board is needed. The model of dynamic delay waveform, which is expressed as the convolution of the pure waveform and the point spread function, are described. Based on this, the new methodology, which utilizes the least squares fitting to make the residual error between the dynamic model and measured waveform minimum, is employed to reconstruct the pure waveform. The validity of proposed method is verified using UK-DMC, UK-TDS-1 and simulated data. Moreover, the performances of sea surface height and wind speed retrieval using retracked and non-retracked waveforms are compared. The results show that (1) the MSEs between aligned and retracked waveform reduce to 0.026 and 0.044 from 0.110 and 0.156 between aligned and non-retracked waveform with the TRP of 1 s and 3 s for UK-DMC data, and for UK-TDS-1 data, the MSEs decrease from 161.02 and 227.34 to 70.10 and 61.80; (2) the standard deviation of sea surface height using retracked waveform is lower 5 times than the one using non-retracked waveform; (3) the retracked waveform could lead to a better measurement performance in wind speed retrieval. Finally, the relationship between the performance of retracking and Signal-to-Noise Ratio (SNR) is analyzed. The results show that when the SNR of the waveform is lower than 3 dB, the retrieval accuracies rapidly become worse.