Pseudorandom Noise Code Research Articles

Exploring Time Delay Interferometry ranging as a practical ranging approach in the Bayesian framework

Time Delay Interferometry (TDI) is an indispensable step in the whole data processing procedure of space-based gravitational wave detection, as it mitigates the overwhelming laser frequency noise, which would otherwise completely bury the gravitational wave signals. Knowledge on the inter-spacecraft optical paths (i.e. delays) is one of the key elements of TDI. Conventional method for inter-spacecraft ranging mainly relies on the pseudo-random noise (PRN) code signal modulated onto the lasers. To ensure the reliability and robustness of this ranging information, it would be highly beneficial to develop other methods which could serve as cross-validations or backups. This paper explores the practical implementation of an alternative data-driven approach – time delay interferometry ranging (TDIR) – as a ranging technique independent of the PRN signal. Distinguished from previous research, our TDIR algorithm significantly relaxes the stringent requirement for clock synchronization imposed by traditional TDI procedure. By framing TDIR as a Bayesian parameter estimation problem and employing a general polynomial parametrization, we demonstrate our algorithm with simulated data based on the numerical orbit of Taiji. In the presence of laser frequency noise and secondary noises, the estimated median values of delays are only 5.28 ns away from the ground truths, capable of suppressing laser frequency noise to the desired level. Additionally, we have also analyzed the requirements of mitigating optical bench noise and clock noise on TDIR, and presented an illustrative example for the impact of laser locking.

Ranging sensor fusion in LISA data processing: Treatment of ambiguities, noise, and onboard delays in LISA ranging observables

Interspacecraft ranging is crucial for the suppression of laser frequency noise via time-delay interferometry (TDI). So far, the effects of onboard delays and ambiguities on the Laser Interferometer Space Antenna (LISA) ranging observables were neglected in LISA modeling and data processing investigations. In reality, onboard delays cause offsets and timestamping delays in the LISA measurements, and pseudorandom noise (PRN) ranging is ambiguous, as it determines only the range up to an integer multiple of the PRN code length. In this article, we identify the four LISA ranging observables: PRN ranging, the sideband beat notes at the interspacecraft interferometer, TDI ranging, and ground-based observations. We derive their observation equations in the presence of onboard delays, noise, and ambiguities. We then propose a three-stage ranging sensor fusion to combine these observables in order to gain accurate and precise ranging estimates. We propose to calibrate the onboard delays on ground and to compensate the associated offsets and timestamping delays in an initial data treatment (stage 1). We identify the ranging-related routines, which need to run continuously during operation (stage 2) and implement them numerically. Essentially, this involves the reduction of ranging noise, for which we develop a Kalman filter combining the PRN ranging and the sideband beat notes. We further implement cross-checks for the PRN ranging ambiguities and offsets (stage 3). We show that both ground-based observations and TDI ranging can be used to resolve the PRN ranging ambiguities. Moreover, we apply TDI ranging to estimate the PRN ranging offsets. Published by the American Physical Society 2024

Ionospheric Total Electron Content (TEC) Anomalies as Earthquake Precursors: Unveiling the Geophysical Connection Leading to the 2023 Moroccan 6.8 Mw Earthquake

The study delves into the relationship between ionospheric total electron content (TEC) anomalies and seismic activity, with a focus on Morocco’s 6.8 Mw earthquake on 8 September 2023, lying within a tectonically active region at the convergence of the African and Eurasian Plates. To enhance the reliability of our findings, we incorporate space weather conditions, utilizing indices (Dst, Kp, and F10.7) to pinpoint periods of stable space weather. This minimizes the possibility of erroneously attributing natural ionospheric fluctuations to seismic events. Notably, our TEC analysis unveils positive and negative anomalies, with some occurring up to a week before the earthquake. These anomalies, exceeding predefined thresholds, provide compelling evidence of significant deviations from typical ionospheric conditions. Spatial mapping techniques employing both station-specific vTEC data and pseudorandom noise codes (PRNs) from multiple global navigation satellite system (GNSS) stations highlight a strong correlation between ionospheric anomalies and the earthquake’s epicenter. The integration of PRNs enhances coverage and sensitivity to subtle anomalies. Additionally, the analysis of satellite imagery and ground displacement data using Sentinel-1 confirms significant ground uplift of approximately 15 cm following the earthquake, shedding light on surface responses to seismic events. These findings underscore the potential of ionospheric science in advancing earthquake early warning systems and deepening our understanding of earthquake precursors, thus contributing to the mitigation of seismic event impacts and the protection of lives and infrastructure.

Stepped-Frequency Binary Offset Carrier Modulation for Global Navigation Satellite Systems

In this paper, we propose Stepped-Frequency Binary Offset Carrier (SFBOC) modulation for Global Navigation Satellite Systems (GNSS) that use spread spectrum signals. SFBOC modulation generates a Binary Offset Carrier (BOC) signal of which the subcarrier frequency varies stepwise within each period of the pseudorandom-noise (PRN) code. The generated SFBOC signal can have a sharp autocorrelation function (ACF) output and an almost flat spectrum over a wide frequency band. These characteristics result in correlation properties, multipath mitigation, and anti-interference that are superior to those of conventional GNSS modulations. To testify, we compare the performance of SFBOC in various aspects to conventional GNSS modulations and other time-varying subcarrier frequency (TVSF) modulations. From numerical simulations, we show that the proposed SFBOC has higher ranging accuracy, lower tracking ambiguity, and more robustness to noise, interference, and multipath than the conventional GNSS modulations. In addition, we demonstrate that the proposed SFBOC moulation has two advantages while other modulations with TVSF cannot have both; that SFBOC is robust to code-Doppler and that, when filterbank is employed, SFBOC improves the signal-to-noise ratio (SNR) significantly without any loss of weak early arrival path in the Non-line of sight (NLOS) multipath environments.

Bi-directional PRN laser ranging and clock synchronization for TianQin mission

Laser frequency coupling noise due to unbalanced arm lengths is the dominant noise source for space-based gravitational wave detection. Time-delay interferometry is a proposed technique to eliminate the coupling noise by constructing a virtual equal-arm-length interferometer, where the real-time information of both absolute inter-satellite distance and clock synchronization is required. Inter-satellite laser ranging based on pseudo-random noise (PRN) sequence modulation has become the main technical means for extraction of the inter-satellite distance and clock difference information. This paper shows a bi-directional laser ranging scheme based on PRN code modulation and experimentally demonstrates its function by using an optical fiber of 10 km long. The measured results of the transmission time duration and the clock difference are compared with independent methods of pulse laser ranging and 1PPS signal measurement, respectively, both of which coincide well. It is also evaluated that the laser ranging accuracy is 1.2 m, and the clock synchronization accuracy reaches 6.7 ns, applicable to TianQin with the preliminarily determined requirement of 3 m and 10 ns. This laser ranging scheme can be applied to satellite navigation and space-based gravitational wave detection.

Remote Phase-Shift LiDAR With Communication

The integrated sensing and communication is emerging as a crucial technology due to reduced hardware costs and broad application scenarios. However, there is a contradiction between ranging and communication in phase-shift light detection and ranging (LiDAR) for the utilization of the subcarrier’s phase. A scheme called phase-shift laser ranging with communication (PLRC) is proposed to enable both ranging and communication using the same transmitted signal in this paper. The message encoded with pseudo-random noise code is modulated into the phase of the subcarrier for laser emission, and thus the received signal carries the data and the phase difference due to the distance. The received signal is subject to correlation, waveform recovery, and phase-shift measurement with the local signal at the LiDAR transceiver, and the distance is derived from the complete phase to avoid range ambiguity. The data is extracted from the spread spectrum signal at the communication receiver. The performance in terms of the measured distance and precision of LiDAR, the bit error rate of communication is obtained for the proposed solution. Meanwhile, the optimized light ratio for ranging and communication is derived. The experimental demonstration is carried out, the range precision is <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$3.54\,\,{\times }\,\,10^{-3}$ </tex-math></inline-formula> m, and the communication capability meets 1.43 Mbit/s.

A Superresolution Multipath Estimation Algorithm for DSSS Systems

In direct sequence spread spectrum systems, the multipath interference is known to be one of the most important factors in degrading the measurement accuracy. To resolve this problem, we propose a superresolution multipath estimation method based on waveform replacement and adaptive-filtering. In this method, the continuous pseudorandom noise code autocorrelation waveform of the matched filtering output is first replaced by a designed triangular pulse waveform. Subsequently, a reiterative minimum mean-square error adaptive filtering approach is applied to realize superresolution estimation of multipath parameters. The proposed method can achieve accurate multipath estimation even in complex multipath scenarios containing short-delay multipaths and make a good balance between the computational complexity and the estimation performance of multipath parameters. Simulation results verify the effectiveness of the proposed method.

Estimation of Vertical Phase Center Offset and Phase Center Variations for BDS-3 B1CB2a Signals

The BeiDou Global Satellite Navigation System (BDS-3) broadcast newly developed B1C and B2a signals. To provide a better service for global users, the vertical phase center offset (PCO) and phase center variation (PCV) are estimated for the B1C/B2a ionospheric-free linear combination of the BDS-3 inclined geostationary orbit (IGSO) and medium earth orbit (MEO) satellites in this study. And considering the traditional PCC estimation method needs two Precise orbit determination (POD) processing, based on the correlation between PCO z-offset and PCV, the theoretical analysis and experimental comparison have been made to discuss whether the POD procedure for the PCO estimation can be omitted. The estimated z-offset time series revealed the inadequacy of the solar radiation pressure (SRP) model for the IGSO satellites and the MEO satellites with Pseudo Random Noise code (PRN) C45 and C46. The PCVraws estimated by the traditional method and the PCO estimation omitted method have the same characteristic. The final PCO z-offsets and PCVs calculated by the two schemes agreed very well with differences can be harmlessly ignored, which confirmed that the PCO estimation can be safely omitted to save computation time. The PCC model proposed in this study has been compared with the Test and Assessment Research Center of China Satellite Navigation Office (TARC/CSNO) released model, the qualities of the orbits and BDS-only precise point positioning (PPP) solutions of the new model both show improvements, except for the IGSO orbits. The analysis of the IGSO orbits further verifies the SRP model is not suitable for the IGSO satellites.

A Novel Satellite PRN Code Assignment Method Based on Improved RLF Algorithm.

Low Earth Orbit (LEO) satellites have stronger received signals and more rapid geometry changes than Global Navigation Satellite System (GNSS) satellites, making them attractive for positioning, navigation, and timing (PNT) applications. Due to the low altitude, the LEO constellation requires more satellites to cover the entire globe and more Pseudo Random Noise (PRN) codes to realize Code Division Multiple Access (CDMA), which means greater receiver storage resources and receiver acquisition time. In this paper, different from the traditional methods that assign a unique PRN code to each satellite, we propose a novel method in which several satellites share the same PRN code, and simply demonstrate the feasibility and benefits of this method. To determine the minimum number of PRN codes needed for a constellation, we build a mathematical model. After the algorithm comparison, we improve the recursive largest first (RLF) algorithm so that it has a higher running speed and a smaller approximate optimal solution within a certain time period. By studying polar-orbiting and walker constellations, we find that if other satellite parameters remain the same, the higher the orbital altitude is, the more PRN codes are needed, and no matter what the orbital inclination is, the minimum number of PRN codes remains the same. Overall, it is feasible and meaningful for several satellites sharing the same PRN code to save storage resources and reduce the satellite acquisition time of the receiver. If this new technology is applied, the storage resources and the average satellite acquisition time of the receiver will be, at most, one-third of previous ones.

Randomized Spectral Separation Coefficient for Short Code Acquisition Performance Evaluation

Reliable signal acquisition with low computational complexity is an important design objective for the evolution of global navigation satellite systems (GNSS). Most GNSS signals consist of long pseudorandom noise (PRN) codes whose acquisition is expensive in terms of memory, computation time, and energy. As these resources are particularly scarce in the emerging mass-market user segment, cyclostationary pilot signals with short PRN codes are an attractive option to keep the number of acquisition search bins low. However, reducing the code length degrades the acquisition performance, as multiple access interference (MAI) becomes more pronounced and can lead to an increased false alarm rate. We demonstrate that, quite different from stationary MAI, cyclostationary MAI does not affect each bin of the search space uniformly, and is therefore not easily modeled with the well-known spectral separation coefficient (SSC). We propose a new randomized SSC (SSC-R) based on code/Doppler interference functions, which can be used for simple and accurate acquisition performance evaluation. As an application example, we demonstrate how the SSC-R can be utilized in signal design to minimize the PRN code length under an acquisition performance constraint. We conclude that feasible PRN code lengths for GNSS can be on the order of 300-700.

Pulse Broadening Effects on Ranging Performance of a Laser Altimeter with Return-to-Zero Pseudorandom Noise Code Modulation.

A laser altimeter using code modulation techniques receives a backscattered pulse wider than the transmitted rectangular pulse when scanning a rough or sloped target surface. This leads to degrading the ranging performance in terms of signal-to-noise ratio (SNR) and detection probability. Unlike the pulsed techniques, little work has focused on the pulse broadening effect of the code modulation techniques. In this study, mathematical models were derived to investigate the pulse broadening effect on the ranging performance of a return-to-zero pseudorandom noise (RZPN) laser altimeter. Considering that the impulse response can be approximated by a Gaussian function, the analytical waveform was derived using a new flat-topped multi-Gaussian beam (FMGB) model. The closed-form expressions were also analytically derived for a peak cross-correlation, SNR, and detection probability in terms of the pulse broadening effect. With the use of a three-dimensional model of asteroid Itokawa for practical surface profiles, the analytical expressions were validated by comparing to the results obtained from numerical simulations. It was also demonstrated that the pulse broadening effect dropped down the peak cross-correlation and then deteriorated the ranging performance. These analytical expressions will play an important role in not only designing a laser altimeter using the RZPN code modulation technique but also analyzing its ranging performance.

Measurement of the Sea Surface Height with Airborne GNSS Reflectometry and Delay Bias Calibration

Sea surface height can be measured with the delay between reflected and direct global navigation satellite system (GNSS) signals. The arrival time of a feature point, such as the waveform peak, the peak of the derivative waveform, and the fraction of the peak waveform is not the true arrival time of the specular signal; there is a bias between them. This paper aims to analyze and calibrate the bias to improve the accuracy of sea surface height measured by using the reflected signals of GPS CA, Galileo E1b and BeiDou B1I. First, the influencing factors of the delay bias, including the elevation angle, receiver height, wind speed, pseudorandom noise (PRN) code of GPS CA, Galileo E1b and BeiDou B1I, and the down-looking antenna pattern are explored based on the Z-V model. The results show that (1) with increasing elevation angle, receiver height, and wind speed, the delay bias tends to decrease; (2) the impact of the PRN code is uncoupled from the elevation angle, receiver height, and wind speed, so the delay biases of Galileo E1b and BeiDou B1I can be derived from that of GPS CA by multiplication by the constants 0.32 and 0.54, respectively; and (3) the influence of the down-looking antenna pattern on the delay bias is lower than 1 m, which is less than that of other factors; hence, the effect of the down-looking antenna pattern is ignored in this paper. Second, an analytical model and a neural network are proposed based on the assumption that the influence of all factors on the delay bias are uncoupled and coupled, respectively, to calibrate the delay bias. The results of the simulation and experiment show that compared to the meter-level bias before the calibration, the calibrated bias decreases the decimeter level. Based on the fact that the specular points of several satellites are visible to the down-looking antenna, the multi-observation method is proposed to calibrate the bias for the case of unknown wind speed, and the same calibration results can be obtained when the proper combination of satellites is selected.

Comparative analysis of ionosonde spread F and GPS ionospheric scintillations over Hyderabad

Investigation of the relationship between ionospheric scintillations and equatorial spread F (ESF) during adverse space weather conditions is of paramount significance for developing ionospheric scintillation mitigation strategies for Global Navigation Satellite System (GNSS) receivers. In this paper, we present correlation analysis between equatorial spread F (ESF) and L-band amplitude scintillations conducted at low-latitude Hyderabad station (17.47° N, 78.57° E) during the severe geomagnetic storm event of 17 March 2015 (St. Patrick's Day). Hyderabad location comes under the region between the magnetic equator and the northern crest of equatorial ionization anomaly (EIA). ESF information is derived from ionograms of ionosonde located at the Tata Institute of Fundamental Research (TIFR) Balloon Facility, Hyderabad, whereas amplitude scintillation index (S4) data have been obtained from the GPS receiver at Hyderabad (GAGAN network). Intense spread F (SSF) signatures were observed during post-sunset hours of 16 March (pre-storm day) and 17 March (storm day), 2015, where the spread F (SF) index is higher than 1 MHz. GPS satellite vehicle with pseudo-random noise code (PRN) 24 experienced strong scintillation (S4 = 1.06) at 18:53 UT on the pre-storm day of 16 March 2015. GPS PRN 30 satellite was affected severely on 17 March (storm day), when the observed S4 index is 0.99. Development of ESF and subsequent scintillations are due to the strong eastward prompt penetration electric fields over the Indian region. The inhibition of spread F and scintillations noticed on 18 March 2015 are because of disturbance dynamo electric fields and disturbance winds. The SSF occurrences were well correlated with scintillation index values at Hyderabad station, India. Variations of the virtual height of the F layer (h′F) and drift velocity (Vd) are related to the S4 values during the period of interest. The outcome of the preliminary results would be useful for development of ionospheric scintillation prediction algorithms for GPS users.

A study on TEC reduction during the tail phase of the 21st June 2020 annular solar eclipse

Ionospheric response during the annular solar eclipse of June 21, 2020, has been examined in terms of the Total Electron Content (TEC) obtained from six Global Positioning System (GPS) receivers positioned in the Chinese-Taiwanese region. We have shown TEC variation from satellites designated by PRNs (Pseudo-Random Noise code) 2, 6, and 19. PRN wise TEC trend was observed to depend upon satellite-pass trajectory to the receiver's location during the eclipse period. A time lag of ~15–30 min is also observed in maximum TEC decrement after the phase of maximum eclipse. Instead of the percentage of eclipse magnitude, a reduction in TEC is seen more for the station for which the orbital track of respective satellites was in closer view relative to receivers for more hours of eclipse window. Additionally, the eclipse day diurnal variations are compared with the pre-eclipse day TEC trend, and observed results show a clear decrease in TEC values at all chosen stations after the eclipse onset then reached the lowest value a few minutes afterward the maximum eclipse phase.

GNSS interferometric reflectometry signature‐based defense

Global navigation satellite system (GNSS) signals are vulnerable to radio frequency interference (RFI) and spoofing. RFI detection has become trivial with many detection algorithms available and built into GNSS receivers; this is not the case with spoofing. GNSS spoofing can involve generating false GNSS signals with one or more altered components of GNSS satellite transmissions: radio frequency (RF) carrier, pseudorandom noise codes, and/or the broadcast navigation messages. We present GNSS interferometric reflectometry (GNSS-IR) signature-based defense: a new methodology to defend wireless space-based positioning, navigation, and timing (PNT) transmissions against spoofing by leveraging existing, fixed GNSS receivers used in GNSS-dependent critical infrastructure and key resource sectors. GNSS-IR signature-enabled defense provides spoofing and RFI detection without any changes to existing architecture by conducting input validation of GNSS receiver observables against the generated GNSS-IR truth calibration signatures. This paper includes an overview of the theory, methodology, and results of live-sky signature variability experiments.

Real-Time Detection of Orbital Maneuvers Using Epoch-Differenced Carrier Phase Observations and Broadcast Ephemeris Data: A Case Study of the BDS Dataset.

The orbital maneuvers of the global navigation satellite system (GNSSs) have a significant influence on the performance of the precise positioning, navigation, and timing (PNT) services. Because the Chinese BeiDou Navigation Satellite System (BDS) has three types of satellites in the geostationary orbit (GEO), inclined geosynchronous orbit (IGSO), and medium earth orbit (MEO) maneuvers occur more frequently. Thus, it is essential to determine an effective approach for the detection of orbital maneuvers. This study proposes a method for the detection of orbital maneuvers using epoch-differenced carrier phase observations and broadcast ephemeris data. When using the epoch-differenced velocity estimation as a basic data solution model, the time discrimination and satellite identification factors are defined and used for the real-time detection of the beginning and the pseudorandom noise code (PRN) of satellites. The datasets from four GNSS stations (WUH1, BJF1, POHN, CUT0) from the year 2016 were collected and analyzed. The validations showed that the beginning, the PRN of the orbital maneuver of the satellite can be precisely detected in real time for all GEO, IGSO, and MEO satellites, and the detected results also showed good consistency, with the beginning time at a difference of 1–2 min across different stations. The proposed approach was observed to be more sensitive, and the detected beginning time was about 30 min earlier than the single point positioning approach when the high-precision carrier phase observation was used. Thus, orbital maneuvering can be accurately detected by the proposed method. It not only improves the utilization of the collected data but also improves the performance of PNT services.

A fast method for the acquisition of weak long-code signal

The growing demand for positioning, navigation and timing services is boosting the development of new signal systems that are gradually being adopted by Global Navigation Satellite System (GNSS), such as the BDS, the Galileo and the modernized GPS. A common feature of these new signal systems is that they have longer pseudorandom noise (PRN) code lengths than the old ones, which greatly improves the ranging accuracy and anti-interference ability of signals. However, the longer PRN code length leads to increased computational complexity and reduced acquisition speed, especially in low-carrier-to-noise-ratio (CNR) conditions. A rapid scheme for the acquisition of weak long-code signal is proposed. The reduced Doppler shift and code-phase space are pre-estimated with inertial navigation system (INS) aiding and ephemeris, and an FFT-based parallel time–frequency domain search method is used to realize rapid two-dimensional search. To further reduce the computational complexity of weak long-code signals, a parallel code-phase search (PCS) method with reduced code-phase space based on matrix partition and reconfiguration is proposed inside the correlator, which can realize the rapid coherent operation of signals. The proposed algorithm can greatly reduce the theoretical operands of FFT operation in the acquisition without loss to the relevant peak, to meet the requirements of receiver sensitivity and acquisition speed in the low-CNR conditions. Finally, computer simulations verify the effectiveness of this acquisition scheme.

High-precision orbit determination for a LEO nanosatellite using BDS-3

The Tianping-1B is a 20-kg low earth orbit nanosatellite with a commercial multi-GNSS receiver based on a microelectromechanical system. This receiver collects concurrent code and phase dual-frequency measurements from the global positioning system (GPS) and the second and third generations of the BeiDou Global Navigation Satellite System (i.e., BDS-2 and BDS-3). However, BDS-3 signals with pseudorandom noise code numbers greater than 32 cannot be received. In this study, onboard GPS and BDS measurements from Tianping-1B are collected for days 133–147 of 2019. The performance of the onboard BDS-3 measurements is analyzed, and the potential of the BDS-3-based precise orbit determination (POD) for Tianping-1B is assessed. The carrier-to-noise-density ratio of the BDS-3 is higher than that of the BDS-2 and approaches that of the GPS. The BDS-3 has a smaller code multipath error than the BDS-2 and the GPS and therefore a higher quality of code measurements. The results of the overlap comparison show a GPS-based orbit consistency below 3.5 cm in three dimensions (3D) and below 1.2 cm in the radial direction. The mean of satellite laser ranging validation residual RMS is 1.7 cm. The orbit obtained using onboard BDS measurements is assessed using the GPS-based orbit as a reference: The mean 3D root mean square (RMS) difference between the BDS-3-only-based POD and the reference orbit is 4.57 cm. Thus, a sub-dm-level orbit can be achieved using only onboard BDS-3 measurements. A POD with slightly higher precision than the BDS-3-only-based POD is obtained using both BDS-3 and BDS-2 measurements, using higher weights for the BDS-3 data than the BDS-2 data. Then, the combined BDS-3/GPS POD is performed: The RMS difference between this joint orbit and the GPS-based orbit is 1 cm in 3D. This study can be used as a reference for the development of BDS-3 based POD, which will approve in accuracy and precision upon completion of BDS-3.

Enhanced Passive GNSS-Based Radar Imaging Based on Coherent Integrated Multi-Satellite Signals.

Weak reflected signal is one of the main problems in a recent developing remote sensing tool—passive GNSS-based radar (GNSS radar). To address this issue, an enhanced GNSS radar imaging scheme on the basis of coherently integrating multiple satellites is proposed. In the proposed scheme, to avoid direct signal interference at surveillance antenna, the satellites that used as transmission of opportunity are in backscattering geometry model. To coherently accumulate echo signal magnitudes of the scene center in the targeted sensing region illuminated by the selected satellites, after performing the paralleled range compressions, a coordinates alignment operator is performed to the respective range domains, in which, pseudorandom noise (PRN) code phases are aligned. Thereafter, the coordinates aligned range compressed signals of the selected satellites are coherently integrated along azimuth domain so that imaging gain is improved and azimuth processing can be accomplished in only one state operation. The theoretical analysis and field proof-of-concept experimental results indicate that compared to both conventional bistatic imaging scheme and the state-of-the-art multi-image fusion scheme, the proposed scheme can provide a higher imaging gain; compared to the state-of-the-art multi-image fusion scheme, the proposed scheme has a less computational complexity and faster algorithm speed.

Unambiguous Acquisition/Tracking Technique Based on Sub-Correlation Functions for GNSS Sine-BOC Signals.

The autocorrelation function (ACF) of the Binary Offset Carrier modulation (BOC) signal for Global Navigation Satellite System (GNSS) has multiple peaks, ambiguity is easily generated during the synchronization of the baseband signal. Some methods have been proposed to remove the ambiguity, but the performance is not suitable for high-order BOC signals or does not maintain narrow correlation characteristics. This paper proposes a sub-function reconstruction synchronization algorithm to solve this problem, of which the key is to design a new local auxiliary code: the local Pseudo-Random Noise (PRN) code is divided into several new codes with different delays. The auxiliary code performs a coherent integration operation with the received signal. Then, a correlation function without any positive side peaks is obtained by multiplying the two correlation results to make the acquisition/tracking completely unambiguous. The paper gives a design scheme of navigation signal acquisition/tracking and deduces the theoretical analysis of detection performance. The phase discrimination function is provided. The performance of the method is analyzed from both theoretical and simulation aspects. Compared with the Binary phase shift keying-like (BPSK-LIKE) method, Subcarrier Phase Cancellation (SCPC) method and the Autocorrelation Side-Peak Cancellation Technique (ASPeCT) method, the proposed method has the best detection probability for the acquisition, which is 0.5 dB-Hz better than ASPeCT. For tracking, the proposed method performs best in terms of phase-detection curve, anti-multipath performance, and anti-noise performance. For high-order BOC signals, the SRSA technique successfully removes the false lock points, and there is only one multipath error envelope, and the code tracking error is almost the same as the ASPeCT method.