Coherent Integration Time Research Articles

Internal Waves' Role in Determining Probability Distribution of Coherent Integration Time Near 133 Hz and 3709 km in North Pacific Ocean

The hypothesis tested is that internal gravity waves limit the coherent integration time of sound at 3709 km in the Pacific ocean at 133 Hz and a pulse resolution of 0.06 s. Five days of continuous transmissions at 2-min intervals are examined. The source and the receiver are mounted on the bottom of the ocean with timing governed by atomic clocks. Measured variability is only due to fluctuations in the ocean. A model for the propagation of sound through fluctuating internal waves is run without any tuning with data. Excellent resemblance is found between the model and data's probability distributions of integration time up to a day, which is the largest lag explored. The probability that the integration exceeds a day or more is about 0.15. The model underpredicts the probability of occurrence of integration times shorter than 10 min. However, the overwhelming agreement at longer times supports the conclusion that the standard spectrum of internal waves accurately explains almost all of the distribution of measured integration time.

On the Use of GNSS-R Data to Correct L-Band Brightness Temperatures for Sea-State Effects: Results of the ALBATROSS Field Experiments

Sea surface salinity is a key oceanographic parameter that can be measured by means of L-band microwave radiometry. The measured brightness temperatures over the ocean are influenced by the sea state, which can entirely mask the salinity signature. Sea-state corrections parameterized in terms of wind speed and/or significant wave height have proven not to be fully satisfactory. In 2003, it was proposed to use reflectometry using navigation opportunity signals [Global Navigation Satellite System Reflectometer (GNSS-R)] for sea-state determination and correction of the measured L-band brightness temperature changes associated to the sea state. The novelty of the approach relies in the measurement of the whole Delay-Doppler Map that captures the scattering of the GNSS signals in the whole glistening zone. In this framework, the “Advanced L-BAnd emissiviTy and Reflectivity Observations of the Sea Surface” (ALBATROSS) field experiments were undertaken in 2008 and 2009, collecting an extensive data set of collocated radiometric and reflectometric measurements over the Atlantic Ocean, as well as oceanographic and meteorological data. In this paper, the experimental results and conclusions of the ALBATROSS 2009 field experiment are compiled and presented, showing the great potential of this technique to perform the necessary corrections in future salinity missions. Empirical relationships are derived among measured brightness temperature variations due to the sea-state effect and direct GNSS-R observables, and the sea surface correlation time at L1 band, a key parameter for GNSS-R data processing since it determines the maximum coherent integration time, was experimentally determined.

Partial-correlation-result reconstruction technique for weak global navigation satellite system long pseudo-noise-code acquisition

In global navigation satellite system (GNSS), the signals are very weak. In particular, when the signals are interfered by other signals or shadowed by heavy vegetation, mountains, buildings etc., they will be significantly attenuated and become much weaker. In the situation, for GNSS pseudo-noise (PN)-code acquisition, detection performance is critical. In the study, to improve the detection performance of the previously published double block zero-padding (DBZP) method for weak GNSS long PN-code signals, the authors propose to reconstruct the correlation results of DBZP. Taking the advantage of utilising the correlation results that correspond to part of received signal aligning with local signal and are discarded by DBZP, the technique expands coherent integration time. The effect of the proposed technique on detection and mean acquisition time performance is analysed. It is shown that after reconstructing correlation results the proposed technique expands coherent integration time to twice, improves detection performance about 1.3 dB and consequently further shortens mean acquisition time, whereas it does not increase the implementation complexity of a GNSS receiver. The technique is also applicable to other GNSS long PN-code acquisition methods such as the previously published direct average method and the overlap average method.

Assessing Three New GPS Combined L1/L2C Acquisition Methods

This paper presents three new global positioning system acquisition methods that make use of both L1 C/A and L2C signals in a combined way. The methods perform joint estimation of the Doppler frequencies and code delays on L1 and L2 without increasing the coherent integration time. Each method is assessed in terms of theoretical probabilities of false alarm and detection as well as through testing with real intermediate frequency data. The first method is a noncoherent summation of L1 and L2 correlator outputs. The second method implements an independent differential summation of L1/L2 correlator outputs, and the third method uses a noncoherent plus dependent differential summation. While each method provides increased detection performance compared with the standard noncoherent acquisition applied on L1 C/A, the noncoherent plus dependent differential summation method outperforms all of the others in the scenarios investigated.

Simulation and detection of tsunami signatures in ocean surface currents measured by HF radar

High-frequency (HF) surface wave radars provide the unique capability to continuously monitor the coastal environment far beyond the range of conventional microwave radars. Bragg-resonant backscattering by ocean waves with half the electromagnetic radar wavelength allows ocean surface currents to be measured at distances up to 200 km. When a tsunami propagates from the deep ocean to shallow water, a specific ocean current signature is generated throughout the water column. Due to the long range of an HF radar, it is possible to detect this current signature at the shelf edge. When the shelf edge is about 100 km in front of the coastline, the radar can detect the tsunami about 45 min before it hits the coast, leaving enough time to issue an early warning. As up to now no HF radar measurements of an approaching tsunami exist, a simulation study has been done to fix parameters like the required spatial resolution or the maximum coherent integration time allowed. The simulation involves several steps, starting with the Hamburg Shelf Ocean Model (HAMSOM) which is used to estimate the tsunami-induced current velocity at 1 km spatial resolution and 1 s time step. This ocean current signal is then superimposed to modelled and measured HF radar backscatter signals using a new modulation technique. After applying conventional HF radar signal processing techniques, the surface current maps contain the rapidly changing tsunami-induced current features, which can be compared to the HAMSOM data. The specific radial tsunami current signatures can clearly be observed in these maps, if appropriate spatial and temporal resolution is used. Based on the entropy of the ocean current maps, a tsunami detection algorithm is described which can be used to issue an automated tsunami warning message.

Internal waves’ role in determining probability distribution of coherent integration time near 133 Hertz and 3709 kilometers in North Pacific Ocean.

The hypothesis tested is that internal gravity waves limit the coherent integration time of sound at 3709 km in the Pacific Ocean at 133 Hz and a pulse resolution of 0.06 s. Five days of continuous transmissions at 2 min intervals are examined. The source and receiver are mounted on the bottom of the ocean with timing governed by atomic clocks. Measured variability is only due to fluctuations in the ocean. A model for the propagation of sound through fluctuating internal waves is run without any tuning with data. Excellent resemblance is found between the model and data’s probability distributions of integration time up to a day, which is the largest lag explored. The probability that the integration exceeds a day or more is about 0.15. The model under‐predicts the probability of occurrence of integration times less than 10 min. However, the overwhelming agreement at longer times supports the conclusion that the standard spectrum of internal waves accurately explains almost all of the distribution of measured integration time. The ocean supports very long coherent integration times because its fluctuations cause the acoustic phasors to fluctuate following non‐canceling probability distributions. [Work supported by the Office of Naval Research Contracts N00014‐06‐C‐0031 and N00014‐10‐C‐0480.]

Radon-Fourier Transform for Radar Target Detection, I: Generalized Doppler Filter Bank

Based on the coupling relationship among radial velocity, range walk, and Doppler frequency of the moving target's echoes, a novel method is proposed, i.e., Radon-Fourier transform (RFT), to realize the long-time coherent integration for radar target detection. The RFT realizes the echoes spatial-temporal decoupling via joint searching along range and velocity directions, as well as the successive coherent integration via the Doppler filter bank. Besides, four equivalent RFTs are obtained with respect to the different searching parameters. Furthermore, a generalized form of RFT, i.e., generalized Radon-Fourier transform (GRFT), is also defined for target detection with arbitrary parameterized motion. Due to the similarity between the RFT and the well-known moving target detection (MTD) method, this paper provides detailed comparisons between them on five aspects, i.e., coherent integration time, filter bank structure, blind speed response, detection performance, and computational complexity. It is shown that MTD is actually a special case of RFT and RFT is a kind of generalized Doppler filter bank processing for targets with across range unit (ARU) range walk. Finally, numerical experiments are provided to demonstrate the equivalence among four kinds of RFTs. Also, it is shown that the RFT may obtain the coherent integration gain in the different noisy background and the target's blind speed effect may be effectively suppressed. In the meantime, both the weak target detection performance and the radar coverage of high-speed targets may be significantly improved via RFT without change of the radar hardware system.

M-Sequence and Secondary Code Constraints for GNSS Signal Acquisition

In this paper, the problem of coherently extending the integration time for the acquisition of new Global Navigation Satellite System (GNSS) signals is addressed. Unlike the acquisition of legacy GNSS signals, the presence of secondary codes allows the polarity of the transmitted signal to change each primary code period. These polarity changes have to be recovered, and symbol combinations have to be tested before extending the coherent integration time. The hierarchical structure imposed by secondary codes and the presence of data/pilot channels are exploited to improve the acquisition process. A new algorithm based on the fast m-sequence and Walsh-Hadamard (WH) transforms is developed and used for efficiently testing all the possible symbol combinations. Secondary code constraints are included to further reduce the computational complexity of enumerating all symbol combinations. The proposed algorithms are analyzed in terms of receiver operating characteristics (ROC), and an approximate expression for the probability of false alarm is derived exploiting results from extreme value theory.

Coherent integration time limit of a mobile receiver for indoor GNSS applications

There is an emerging requirement for processing global navigation satellite system (GNSS) signals indoor where the signal is very weak and subjected to spatial fading. Typically, longer coherent integration intervals provide the additional processing gain required for the detection and processing of such weak signals. However, the arbitrary physical motion of the handset imputed by the user limits the effectiveness of longer coherent integration intervals due to the spatial decorrelation of the multipath-faded GNSS signal. In this paper, limits of coherent integration due to spatial decorrelation are derived and corroborated with experimental verification. A general result is that the processing gain resulting from direct coherent integration saturates after the antenna has moved through a certain distance, which for typical indoor propagation, is about half a carrier wavelength. However, a refined Doppler search coupled with a prolonged coherent integration interval extends this limit, which is effectively a manifestation of selective diversity.

Choosing the coherent integration time for Kalman filter-based carrier-phase tracking of GNSS signals

Carrier phase---based positioning using Global Navigation Satellite System (GNSS) signals can provide centimeter-level accuracy; however, to do so requires robust, continuous tracking of the phase ...

Experimental Determination of the Sea Correlation Time Using GNSS-R Coherent Data

The feasibility of the Global Navigation Satellite Signal Reflectometry (GNSS-R) techniques has been proven for remote determination of sea state. When using GNSS-R techniques, coherent integration time is limited by the correlation time of the surface under observation which, in the case of the ocean, depends on sea state. In this letter, a new technique to retrieve the sea correlation time at L-band using GNSS-R coherent data is presented along with experimental results.

Micro-Doppler parameter estimation from a fraction of the period

Radar micro-Doppler (m-D) signatures are of great potential for identifying properties of unknown targets. All the techniques developed for extracting m-D features for the past decade rely primarily on the assumption that the time series of the signal contains at least one oscillation or more during the coherent integration time or imaging time. However, many applications in real-world scenarios involve short duration signals and often require the detection and the estimation of m-D characteristics. Short duration signals may contain only a fraction of an oscillation. In this study, the authors develop two techniques to estimate the m-D parameters from a fraction of the period. In these scenarios, the coherent integration will cover only 1/4 and 1/2 of the oscillation. The performance of the proposed methods are evaluated using both synthetic and experimental data.

Advanced architectures for real-time Delay-Doppler Map GNSS-reflectometers: The GPS reflectometer instrument for PAU (griPAU)

In recent years Global Navigation Satellite System’s signals Reflectometry (GNSS-R) has stood as a potential powerful remote sensing technique to derive scientifically relevant geophysical parameters such as ocean altimetry, sea state or soil moisture. This has brought out the need of designing and implementing appropriate receivers in order to track and process this kind of signals in real-time to avoid the storage of huge volumes of raw data. This paper presents the architecture and performance of the Global Positioning System (GPS) Reflectometer Instrument for PAU (griPAU), a real-time high resolution Delay-Doppler Map reflectometer, operating at the GPS L1 frequency with the C/A codes. The griPAU instrument computes 24 × 32 complex points DDMs with configurable resolution (Δ f Dmin = 20 Hz, Δ τ min = 0.05 chips) and selectable coherent (minimum = 1 ms, maximum = 100 ms for correlation loss Δ ρ < 90%) and incoherent integration times (minimum of one coherent integration period and maximum not limited but typically <1 s). A high sensitivity (DDM peak relative error = 0.9% and DDM volume relative error = 0.03% @ T i = 1 s) and stability (Δ ρ/Δ t = −1 s −1) have been achieved by means of advanced digital design techniques.

Implementation and Testing of an Unaided Method for the Acquisition of Weak GPS C/A Code Signals

Fast Modified Double Block Zero Padding (FM-DBZP) is presented as a method for unaided acquisition of weak GPS C/A signals. FM-DBZP uses frequency-domain techniques for coherent integration over integer multiples of the data bit period to perform a search in code delay, Doppler frequency, bit combination, and bit edge. The FFT operation count grows linearly with coherent integration time. The Zoom FFT (ZFFT) further reduces the multiplication count by 28% and the addition count by 37%. The coherent integration time is set to minimize the total computational cost, given a specified acquisition threshold. Successful acquisition, at a design C/N0 of 15 dB-Hz, is demonstrated using a GPS signal simulator. The signal is further attenuated until the algorithm failed to acquire a satellite with a success rate better than 50%. This occurs at a C/N0 of 12.5 dB-Hz.

A test-bed implementation of an acquisition system for indoor positioning

Indoor GNSS signals are typically received with poor signal-to-noise ratio, which impairs the acquisition stage of common global positioning system (GPS) receivers. Extending the coherent integration time increases the acquisition sensitivity, but the data-bit-rate limits the maximum achievable performance. Non-coherent processing also improves the detection performance, but indoor signals require a large amount of accumulations resulting in significant squaring loss. Moreover, both strategies have high computational complexity which fixes demanding requirements for stand alone mass-market terminals operating in real time. A sensitivity–complexity trade-off is therefore mandatory. Assisted-GPS, which is included in 3GPP specifications, reduces the overall acquisition complexity and enhances sensitivity. In this paper we describe a low-complexity-assisted data-wipe-off technique that enables the high-sensitivity acquisition of GPS signals. The method is based on the acquisition of the strongest signal in order to obtain information that eases the acquisition of the weaker ones. The analysis also addresses sources of sensitivity loss, such as Doppler effects and local oscillator inaccuracies. A test campaign with real signals and integration times up to 2 s validates the method, demonstrating the effectiveness of the proposed technique in indoor environments.

Einstein@Home search for periodic gravitational waves in early S5 LIGO data

This paper reports on an all-sky search for periodic gravitational waves from sources such as deformed isolated rapidly-spinning neutron stars. The analysis uses 840 hours of data from 66 days of the fifth LIGO science run (S5). The data was searched for quasi-monochromatic waves with frequencies f in the range from 50 Hz to 1500 Hz, with a linear frequency drift \dot{f} (measured at the solar system barycenter) in the range -f/\tau < \dot{f} < 0.1 f/\tau, for a minimum spin-down age \tau of 1000 years for signals below 400 Hz and 8000 years above 400 Hz. The main computational work of the search was distributed over approximately 100000 computers volunteered by the general public. This large computing power allowed the use of a relatively long coherent integration time of 30 hours while searching a large parameter space. This search extends Einstein@Home's previous search in LIGO S4 data to about three times better sensitivity. No statistically significant signals were found. In the 125 Hz to 225 Hz band, more than 90% of sources with dimensionless gravitational-wave strain tensor amplitude greater than 3e-24 would have been detected.

Einstein@Home search for periodic gravitational waves in LIGO S4 data

A search for periodic gravitational waves, from sources such as isolated rapidly spinning neutron stars, was carried out using 510 h of data from the fourth LIGO science run (S4). The search was for quasimonochromatic waves in the frequency range from 50 to 1500 Hz, with a linear frequency drift f˙ (measured at the solar system barycenter) in the range -f/τ<f˙<0.1f/τ, where the minimum spin-down age τ was 1000 yr for signals below 300 Hz and 10 000 yr above 300 Hz. The main computational work of the search was distributed over approximately 100 000 computers volunteered by the general public. This large computing power allowed the use of a relatively long coherent integration time of 30 h, despite the large parameter space searched. No statistically significant signals were found. The sensitivity of the search is estimated, along with the fraction of parameter space that was vetoed because of contamination by instrumental artifacts. In the 100 to 200 Hz band, more than 90% of sources with dimensionless gravitational-wave strain amplitude greater than 10-23 would have been detected.

Dual-folding based rapid search method for long PN-code acquisition

For long PN-code, rapid acquisition is difficult due to large search space. To speed up the search process, extended replica folding acquisition search technique (XFAST), which directly reduces the code phases to be searched by folding local signal, provides an efficient approach to rapid acquisition. Nevertheless, after folding the correlation properties of PNcode are degraded; hence, the detection performance of XFAST to weak signal is worse than that of nonfolding methods. To improve the detection performance, a dual-folding acquisition method (DF) is proposed. By folding both incoming signal and local signal, DF extends coherent integration time to enhance detection performance and indirectly reduce mean acquisition time. Numerical results demonstrate the enhancement of the proposed method with respect to other methods such as serial search (SS), zero-padding method (ZP), and XFAST.

Real-time motion compensation, image formation and image enhancement of moving targets in ISAR and SAR using S-method-based approach

The commonly used technique for inverse synthetic aperture radar (ISAR)/synthetic aperture radar signal analysis is a two-dimensional Fourier transform (FT), which results in an image of the target&apos;s reflectivity mapped onto a range and cross-range plane. However, in cases where the line-of-sight projections of the target&apos;s point velocities change or there is uncompensated movement within the coherent integration time, the FT produces blurred images. For target recognition applications, mainly those in military surveillance and reconnaissance operations, a blurred ISAR image has to be refocused quickly so that it can be used for real-time target identification. Two standard techniques used for improvement of blurred ISAR images are motion compensation and the use of quadratic time–frequency representations. Both are computationally intensive. The authors present an effective quadratic time–frequency representation, the S-method. This approach performs better than the Fourier transform method by drastically improving images of fast manoeuvring targets and by increasing the SNR in both low and high noise environments. These advantages are a result of the S-method&apos;s ability to automatically compensate for quadratic and all even higher-order phase terms. Thus, targets with constant acceleration will undergo full motion compensation and their point scatterers will each be localised. It should be noted that the source of the quadratic term can come not only from acceleration, but also from non-uniform rotational motion and the cosine term in wide-angle imaging. The method is also computationally simple, requiring only slight modifications to the existing FT-based algorithm. The effectiveness of the S-method is demonstrated through application to simulated and experimental data sets.

A Novel Architecture for Ultra-Tight HSGPS-INS Integration

Global Positioning System (GPS) currently fulfills the positioning requirements of many applications under Line-Of-Sight (LOS) environments. However, many Location-Based Services (LBS) and navigation applications such as vehicular navigation and personal location require positioning capabilities in environments where LOS is not readily available, e.g., urban areas, indoors and dense forests. Such environments either block the signals completely or attenuate them to a power level that is 10-30 dB lower than the nominal signal power. This renders it impractical for a standard GPS receiver to acquire and maintain signal tracking, which causes discontinuous positioning in such environments. In order to address the issue of GPS tracking and positioning in degraded signal environments, a novel architecture for ultra-tight integration of a High Sensitivity GPS (HSGPS) receiver with an inertial navigation system (INS) is proposed herein. By enhancing receiver signal tracking loops through the use of optimal estimators and with external aiding, the capabilities of the receiver can be substantially improved. The proposed approach is distinct from the commonly used ultra-tightly coupled GPS/INS approaches and makes use of different tracking enhancement technologies used in typical HSGPS receivers, multichannel cooperated receivers and the current ultra-tightly coupled GPS/INS methods. Furthermore, the effects of inertial measurement unit (IMU) quality, receiver oscillator noise and coherent integration time on weak signal tracking are also analyzed. Simulated test results in both static and dynamic testes show that, the designed INS-aided GPS receiver can track the incoming weak GPS signals down to 15 dB-Hz without carrier phase locked, or 25 dB-Hz with carrier phase locked. When there are multiple strong GPS signals in view, the other weak signals can be tracked down to 15 dB-Hz with carrier phase locked.