Phase Bias Research Articles

Observation of Soliton Molecules in a Robust All PM Mode-Locked Fiber Laser With Nonreciprocal Phase Bias

We report the first experimental observation, to the best of our knowledge, of soliton molecules in a robust all polarization-maintaining (PM) mode-locked fiber laser with a nonreciprocal phase bias that results in a low self-starting threshold and stable mode locking. Through elaborately tuning the waveplate in the cavity, calibrating the laser pulse from conventional soliton to soliton molecules is implemented, and versatile soliton molecules including harmonic soliton pairs, tightly or loosely bound soliton quartets, multipulse bound solitons are achieved and manipulated at different pump powers. Theoretical investigations are established to elucidate the soliton molecules spectral characteristics with various phase differences and time separations in the cavity that elicit good concurrence with achieved experimental results. The achieved results both rich the nonlinear dynamics in fiber lasers and pave the potential applications for this excellent architecture fiber laser.

Fast calibration of between-receiver GPS/Galileo/BDS differential phase bias with millimeter accuracy based on short baseline mode

The differential code and phase biases induced by the receiver hardware (including receiver, antenna, firmware, etc.) of the Global Navigation Satellite System (GNSS) have significant effects on precise timing and ionosphere sensing, thus deserve careful treatment. In this contribution, we propose an approach to fast fix the single-difference ambiguity to finally obtain the unbiased estimates of between-receiver differential phase bias (BR-DPB) and between-receiver differential code-phase bias (BR-DCPB) based on the short baseline mode. The key to this method is that the error sources can be significantly eliminated due to the length of the baseline is very short. At the same time, the empirical constraints and random characteristics of BR-DPB/BR-DCPB were considered, which is conducive to the resolution of single-difference ambiguity. Several sets of GNSS data (GPS L1/L2, Galileo E1/E5b, and BDS B1/B3), recorded by the short baselines in an interval of 30 s and covered a broad range of receiver/antenna types (JAVA, SEPT, LEIC, and TRIM), were used to verify the effectiveness of the proposed method. The numerical tests show that the proposed method is capable of fast fixing the single-difference ambiguity successfully within a few epochs and then providing the unbiased estimates of BR-DPB and BR-DCPB in an epoch-by-epoch manner. Experiments show that the estimated BR-DPB is in millimeter accuracy, which is of great significance for the millimeter-accuracy phase time transfer and ionospheric delay estimation. Furthermore, the calibrated BR-DPB/BR-DCPB can be treated as the known products for long-distance precise timing and ionosphere sensing based on the inter-station single-difference model.

Rapid and Accurate Measurement of Polarization and Fading of Weak VHF Signals Obliquely Reflected From Sporadic-E Layers

In the E-region of the ionosphere, at heights between 90 and 130 km, thin patches of enhanced ionization occur intermittently. The electron density in these sporadic-E (Es) clouds can sometimes be so high that radio waves with frequencies up to 150 MHz are obliquely reflected. While this phenomenon is well known, the reflection mechanism itself is not well understood. To investigate this question, an experimental system has been developed for accurate polarimetric and fading measurements of 50 MHz radio waves obliquely reflected by mid-latitude Es layers. The overall sensitivity of the system is optimized by reducing environmental electromagnetic noise, giving the ability to observe weak, short-lived 50 MHz Es propagation events. The effect of the ground reflection on observed polarization is analyzed and the induced amplitude and phase biases are compensated. It is found that accurate measurements are only possible below the pseudo-Brewster angle. To demonstrate the effectiveness of the system, initial empirical results are presented which provide clear evidence of magneto-ionic double refraction.

A novel phase bias estimation method for multichannel HRWS SAR system in azimuth based on RDS analysis

ABSTRACT Multichannel synthetic aperture radar (SAR) systems in azimuth can realize high-resolution and wide-swath (HRWS) imaging, which has attracted intensive research interests. The azimuth ambiguities caused by non-uniform sampling can be suppressed by digital beamforming technique. However, the presence of inevitable channel errors in the multichannel SAR system deteriorates the performance of ambiguity suppression. Based on the analysis of the characteristics of the multichannel SAR echoes, it was found that phase bias among channels can cause jumping in the reconstructed Doppler spectrum (RDS). This letter presents a novel data-based phase bias estimation method for HRWS SAR system. With the assumption that the splice of echo energy inside the Doppler bandwidth is continuous, there is no jumping in the RDS. The estimation of phase biases in the multichannel HRWS SAR system can be translated into the optimization solution issue. Simulation experiments and real data processing results validated the effectiveness of the proposed method.

Griffiths phase and spontaneous exchange bias in La1.5Sr0.5CoMn0.5Fe0.5O6

La1.5Sr0.5CoMn0.5Fe0.5O6 (LSCMFO) compound was prepared by solid state reaction and its structural, electronic and magnetic properties were investigated. The material forms in rhombohedral structure, and the presence of distinct magnetic interactions leads to the formation of a Griffiths phase above its FM transition temperature (150 K), possibly related to the nucleation of small short-ranged ferromagnetic clusters. At low temperatures, a spin glass-like phase emerges and the system exhibits both the conventional and the spontaneous exchange bias (EB) effects. These results resemble those reported for La1.5Sr0.5CoMnO6 but are discrepant to those found when Fe partially substitutes Co in La1.5Sr0.5(Co1−x Fe x )MnO6, for which the EB effect is observed in a much broader temperature range. The unidirectional anisotropy observed for LSCMFO is discussed and compared with those of resembling double-perovskite compounds, being plausibly explained in terms of its structural and electronic properties.

Fraunhofer oscillations of the critical current at a varying Zeeman field in a spin-orbit coupled Josephson junction

The Zeeman interaction results in spontaneous current through a Josephson contact with a spin-orbit coupled normal metal, even in the absence of any voltage, or phase bias. In the case of the Rashba spin-orbit coupling of electrons in a two-dimensional (2D) electron gas this effect takes place for the Zeeman field which is parallel to the 2D system and to superconducting contacts. At the same time, the spontaneous current is absent when this field is perpendicular to the contacts. It is shown that in the latter case it may manifest itself in oscillations of the critical Josephson current at varying Zeeman energy. These oscillations have a form of the Fraunhofer diffraction pattern. The Josephson current under the phase bias was calculated based on the semiclassical Green's functions for a disordered 2D electron gas with the strong spin-orbit coupling, as well as for surface electrons of a three-dimensional topological insulator. In the latter case the diffraction pattern was found to be most pronounced, while in the Rashba gas the oscillations of the critical current are weaker.

On correcting the phase bias of GCC in spatially correlated noise fields

Generalized cross correlation (GCC) is arguably the most widely used time difference of arrival (TDOA) estimators. Most studies on GCC assume spatially uncorrelated noises, and focus on the design of weighting functions. However, real world noises tend to be spatially correlated, and such correlation introduces phase bias to the cross phase spectra used in GCC. This paper proposes a simple closed-form maximum likelihood (ML) cross phase spectra estimator for GCC by only assuming the prior knowledge of noise spatial complex coherence function, which can be predicted in theory or measured in advance. TDOA estimation experimental results on real world speech recordings confirm the usefulness of this simple new phase estimator.

Assessing the Performance of Multi-GNSS PPP-RTK in the Local Area

The benefits of an increased number of global navigation satellite systems (GNSS) in space have been confirmed for the robustness and convergence time of standard precise point positioning (PPP) solutions, as well as improved accuracy when (most of) the ambiguities are fixed. Yet, it is still worthwhile to investigate fast and high-precision GNSS parameter estimation to meet user needs. This contribution focuses on integer ambiguity resolution-enabled Precise Point Positioning (PPP-RTK) in the use of the observations from four global navigation systems, i.e., GPS (Global Positioning System), Galileo (European Global Navigation Satellite System), BDS (Chinese BeiDou Navigation Satellite System), and GLONASS (Global’naya Navigatsionnaya Sputnikova Sistema). An undifferenced and uncombined PPP-RTK model is implemented for which the satellite clock and phase bias corrections are computed from the data processing of a group of stations in a network and then provided to users to help them achieve integer ambiguity resolution on a single receiver by calibrating the satellite phase biases. The dataset is recorded in a local area of the GNSS network of the Netherlands, in which 12 stations are regarded as the reference to generate the corresponding corrections and 21 as the users to assess the performance of the multi-GNSS PPP-RTK in both kinematic and static positioning mode. The results show that the root-mean-square (RMS) errors of the ambiguity float solutions can achieve the same accuracy level of the ambiguity fixed solutions after convergence. The combined GNSS cases, on the contrary, reduce the horizontal RMS of GPS alone with 2 cm level to GPS + Galileo/GPS + Galileo + BDS/GPS + Galileo + BDS + GLONASS with 1 cm level. The convergence time benefits from both multi-GNSS and fixing ambiguities, and the performances of the ambiguity fixed solution are comparable to those of the multi-GNSS ambiguity float solutions. For instance, the convergence time of GPS alone ambiguity fixed solutions to achieve 10 cm three-dimensional (3D) positioning accuracy is 39.5 min, while it is 37 min for GPS + Galileo ambiguity float solutions; moreover, with the same criterion, the convergence time of GE ambiguity fixed solutions is 19 min, which is better than GPS + Galileo + BDS + GLONASS ambiguity float solutions with 28.5 min. The experiments indicate that GPS alone occasionally suffers from a wrong fixing problem; however, this problem does not exist in the combined systems. Finally, integer ambiguity resolution is still necessary for multi-GNSS in the case of fast achieving very-high-accuracy positioning, e.g., sub-centimeter level.

Dual-wavelength Mach-Zehnder interferometry-assisted photothermal spectroscopy for characterization of surface contaminants.

Photothermal spectroscopy (PTS) working in the mid-infrared region is an effective technique for in-situ characterization of the chemical composition of surface contaminants. The sensitivity relies on the way that the laser-induced response of the sample is detected. We present a highly-sensitive PTS assisted with a dual-wavelength Mach-Zehnder interferometer (MZI), MZI-PST in short. The MZI aims to sense all the phase delays taking place at the sample and air when the heat produced by resonance absorption of the contaminant is transferred into its surroundings and further to amplify the total phase delay to a large intensity difference of a probe beam. To guarantee a stable quadrature phase bias of the MZI working in the balanced detection mode, we employ two separate wavelengths, one for sensing and the other for phase bias feedback, to lock the working point to the quadrature point in real time. The MZI is expected to have a 7.8-fold sensitivity enhancement compared with the conventional phase-sensitive PTS in theory. The results of the proof-of-concept experiment on the olive oil contaminated on a wafer surface verify the spectral fidelity and the sensitivity enhancement as well as the capability of photothermal spectral imaging of the MZI-PST.

SAR Tomography via Nonlinear Blind Scatterer Separation

Layover separation has been fundamental to many synthetic aperture radar applications, such as building reconstruction and biomass estimation. Retrieving the scattering profile along the mixed dimension (elevation) is typically solved by inversion of the SAR imaging model, a process known as SAR tomography. This paper proposes a nonlinear blind scatterer separation method to retrieve the phase centers of the layovered scatterers, avoiding the computationally expensive tomographic inversion. We demonstrate that conventional linear separation methods, e.g., principle component analysis (PCA), can only partially separate the scatterers under good conditions. These methods produce systematic phase bias in the retrieved scatterers due to the nonorthogonality of the scatterers' steering vectors, especially when the intensities of the sources are similar or the number of images is low. The proposed method artificially increases the dimensionality of the data using kernel PCA, hence mitigating the aforementioned limitations. In the processing, the proposed method sequentially deflates the covariance matrix using the estimate of the brightest scatterer from kernel PCA. Simulations demonstrate the superior performance of the proposed method over conventional PCA-based methods in various respects. Experiments using TerraSAR-X data show an improvement in height reconstruction accuracy by a factor of one to three, depending on the used number of looks.

Synthesis of an Interference-Resistant Space-Time Filter for High-Precision Measurements of Navigation Parameters According to the Signals of Global Navigation Satellite Systems

We study the problems of serviceability of contemporary high-precision terminals of global navigation satellite systems under the conditions of jamming and spoofing interferences. The application of digital antenna arrays with algorithms of space-time signal processing of the signals can be regarded as a solution of the problem of low interference resistance. We describe well-known, most studied, and currently applied algorithms of space-time signal processing. We also formulate the causes that do not enable one to use well-known algorithms in high-precision terminals of satellite systems of global navigation. We propose an algorithm of space-time signal processing based on a space-time filter of finite length with a theoretically justified requirement of Hermitian symmetry for the matrix impulse response. The proposed algorithm guarantees the absence of distortions of signals under any signal and interference conditions. In this case, the impulse response of the space-time filter is computed according to the criterion of optimal suppression of the interference. The characteristics of the proposed space-time filter and other algorithms of space-time signal processing are investigated. For this purpose, we apply the method of mathematical simulation with random search of numerous parameters of signals and interferences (directions to signals, directions to numerous interferences, and to their reflections, remoteness of the reflectors of interferences, the phases of reflections, and the levels of interferences and reflections, etc.). The results of simulations are presented in the form of the distribution functions of the signal-to-interference ratios at the output of the algorithms of space-time signal processing and the distribution functions of the phase and signal-time biases. The obtained dependences substantiate the absence of the phase and signal-time biases in the space-time filter for any signal and interference conditions with interference multipath. It is shown that the space-time filter guarantees a higher interference resistance than the compensating algorithms of space-time signal processing.

On the temperature sensitivity of multi-GNSS intra- and inter-system biases and the impact on RTK positioning

The intra-system biases, including differential code biases (DCBs) and differential phase biases (DPBs), are generally defined as the receiver-dependent hardware delays between different frequencies in a single global navigation satellite system (GNSS) constellation. Likewise, the inter-system biases (ISBs) are the differential code and phase hardware delays between different GNSSs, which are of great relevance for combined processing of multi-GNSS and multi-frequency observations. Although the two biases are usually assumed to remain unchanged for at least 1 day, they sometimes can exhibit remarkable intraday variability, likely due to environmental factors, particularly the ambient temperature. It has been proved that the possible short-term temporal variations of receiver DCBs and DPBs are directly related to ambient temperature fluctuation. We analyze whether the variability of the biases is sensitive to temperature and further identify how this affects the performance of real-time kinematic (RTK) positioning. Our numerical tests, carried out using GPS, BDS-3, Galileo and QZSS observations collected by zero and short baselines, suggest two major findings. First, we found that while ISBs associated with overlapping frequencies are fairly stable, those associated with non-overlapping frequencies can exhibit remarkable variability over a rather short period of time, driven by the changes of ambient temperature. Second, by pre-calibrating and modeling of the biases for the baselines at hand, the empirical success rates and positioning performance can be significantly improved when compared to classical and inter-system differencing, with both models assuming time-invariant receiver DCBs, DPBs and ISBs.

Determination and analysis of front-end and correlator-spacing-induced biases for code and carrier phase observations

Global navigation satellite system (GNSS) biases preclude integer ambiguity resolution and degrade positioning accuracy if they are not corrected in GNSS precise applications. Biases in GNSS positioning applications occur because of imperfections and physical limitations in satellite and receiver hardware. Consequently, these biases will affect the accuracy of positioning solutions, particularly for precise applications due to the existence of biases in the code and carrier phase observations. Various types of biases between systems, frequencies, and satellites have been defined and analyzed. In addition, receiver biases are often assumed to be eliminated by differencing observations between satellites, although this is not always true. This paper investigates the determination of the receiver front-end and correlator-spacing-induced biases in code and carrier phase observations with a focus on how receiver front-end and correlator spacing affect the code and carrier phase measurements, and how such biases vary with respect to the use of different correlator spacings and frontends. Firstly, oscillator, front-end chip, and ADC-induced biases, as well as their observability, will be discussed. Several groups of datasets with different frontends have been collected and used to determine the inter-front-end (including oscillator, chip, and ADC) pseudorange and carrier phase biases. Then, a software receiver that allows the tracking of a satellite with a series of different correlator spacings has been developed to assess measurement biases with different datasets. The results show that the inter-front-end biases and correlator-spacing-induced biases are significantly different among satellites, which can not be ignored during the GNSS positioning. This is because the single-difference of measurements between satellites can not eliminate all these biases. The results with the software receiver connected to different frontends and different correlator spacings indicate that the satellite-dependent biases depend on the configuration of the in-receiver hardware and software.

GPS triple-frequency undifferenced and uncombined precise orbit determination with the consideration of receiver time-variant bias

As the development of the global navigation satellite system (GNSS), the navigation satellite transmitting multi-frequency signals becomes a prevailing trend. Currently, the usual GNSS precise orbit determination (POD) strategy uses dual-frequency (DF) ionosphere-free (IF) linear combination to build up the observation equation. In the area of precise positioning, it has been validated that the third frequency can decrease the convergence time of ambiguity resolution and has a subtle improvement on the positioning accuracy. However, there is no report about the benefits of the third frequency on GNSS POD. Although the precision of dual-frequency POD can meet requirements for generating different types of products, an obvious advantage of multi-frequency observations is that more robust results can be derived. Besides, with the third frequency observations, the improvements of orbits and clocks need to be validated. Thus, a triple-frequency (TF) uncombined (UC) POD method of GNSS satellites is developed. The hardware delay of carrier phase is divided by time-invariant and -variant components. Then the UC observation model is given by re-parameterizing the unknown parameters. The datum of satellite clocks is aligned to IGS products. The step-by-step ambiguity fixing method, i.e. the extra-wide-lane, wide-lane and narrow-lane ambiguities being fixed in sequence, is deduced by using double-differenced ambiguities in a network. We select 74 ground stations and 12 GPS BLOCK IIF satellites to process POD with a length of 20 days. Results of TF-UC POD show that about 10% improvements on orbits and clocks are received compared to L1/L2 DF-IF POD. The time-variant characteristic of phase biases from satellites and stations at the third frequency is analyzed, which shows that the bias at the station has a slight influence on the derived products. These results imply that the precision of orbits and clocks can be improved with observations from the third frequency added.

Triple-Frequency GPS Un-Differenced and Uncombined PPP Ambiguity Resolution Using Observable-Specific Satellite Signal Biases

The new generations of global navigation satellite system (GNSS) space vehicles can transmit three or more frequency signals. Multi-frequency observations bring a significant improvement to precise point positioning ambiguity resolution (PPP AR). However, the multi-frequency satellite code and phase biases need to be properly handled before conducting PPP AR. The traditional satellite bias correction methods, for example, the commonly used differential code biases (DCB), are limited to the dual-frequency ionosphere-free (IF) case and become more and more difficult to extend to multi-GNSS and multi-frequency cases. In this contribution, we propose the observable-specific signal bias (OSB) correction method for un-differenced and uncombined (UDUC) PPP AR. The OSB correction method, which includes observable-specific satellite code and phase bias correction, can directly apply kinds of OSBs to GNSS original observation data, thus, it is more appropriate for multi-GNSS and multi-frequency cases. In order to verify the performance of multi-frequency UDUC-PPP AR based on the OSB correction method, triple-frequency GPS observation data provided by 142 Multi-GNSS Experiment (MGEX) stations were used to estimate observable-specific satellite phase biases at the PPP service end and some of them were also used to conduct AR at the PPP user end. The experiment results showed: the averaged time-to-first-fix (TTFF) of triple-frequency GPS kinematic UDUC-PPP AR with observable-specific satellite code bias (SCB) corrections could reach about 22 min with about 29% improvement, compared with that without observable-specific SCB corrections; TTFF of triple-frequency static UDUC-PPP AR with observable-specific phase-specific time-variant inter-frequency clock bias (IFCB) corrections took about 15.6 min with about 64.3% improvement, compared with that without observable-specific IFCB corrections.

An all polarization-maintaining fiber laser mode locked by nonlinear amplifying loop mirror with different biases

We report on an erbium-doped, mode-locked fiber laser incorporated with various phase-biased nonlinear amplifying loop mirrors. Our cavity employs all polarization-maintaining fibers so that the laser is environmentally stable and insensitive to thermal and mechanical perturbations. The laser with a phase bias directly delivers 1.20 ps pulses at a repetition rate of 88.2 MHz. The output power is 37.0 mW and the single-pulse energy is ∼0.42 nJ, when the pump power is 450 mW. Since the phase bias plays an important role in enhancing self-starting properties, we mainly investigate the self-starting threshold and the phase noise of the fiber oscillator using three diverse phase biases. It is found that compared with and waveplates, the laser employing a waveplate has a lower self-starting threshold and higher phase noise.

A Josephson phase battery.

A classical battery converts chemical energy into a persistent voltage bias that can power electronic circuits. Similarly, a phase battery is a quantum device that provides a persistent phase bias to the wave function of a quantum circuit. It represents a key element for quantum technologies based on phase coherence. Here we demonstrate a phase battery in a hybrid superconducting circuit. It consists of an n-doped InAs nanowire with unpaired-spin surface states, that is proximitized by Al superconducting leads. We find that the ferromagnetic polarization of the unpaired-spin states is efficiently converted into a persistent phase bias φ0 across the wire, leading to the anomalous Josephson effect1,2. We apply an external in-plane magnetic field and, thereby, achieve continuous tuning of φ0. Hence, we can charge and discharge the quantum phase battery. The observed symmetries of the anomalous Josephson effect in the vectorial magnetic field are in agreement with our theoretical model. Our results demonstrate how the combined action of spin-orbit coupling and exchange interaction induces a strong coupling between charge, spin and superconducting phase, able to break the phase rigidity of the system.

Double-ring interference of binary diffractive axicons

We report on the interference between the double rings generated by the Fourier transform of a binary diffractive axicon. These two rings have the same size and correspond to the ± 1 diffracted order beams. The interference condition between both rings can be easily changed by adding a constant phase bias, resulting in a central ring that is either dark or bright. Additionally, this interference condition can be changed along the ring and can be easily tuned, thus allowing greater flexibility. We present experimental results obtained with a binary π-phase liquid-crystal spatial light modulator. These patterns might find applications in optical trapping systems, where the bright or dark regions could trap particles whose refractive index is either higher or lower than the medium.

Analysis of phase bias between GNSS signal components caused by nonideal group delay

Binary offset carrier (BOC) modulations are widely used in the modernized satellite navigation systems. But we find an interesting phenomenon that the signal composed of different BOC modulations suffers larger phase bias than the case that all the components have the same modulation due to the nonideal group delay of the channel. This issue is more obvious in navigation satellites for the use of a narrowband filter to suppress the out-of-band part. The general form of analytic expression that reveals the impact of the nonideal channel on phase bias is presented and validated with simulations. Further, by simplifying the spectrums for the signals like B1 of BeiDou and E1 of Galileo navigation systems, we obtain the concise expression of phase bias and find that the bias is mainly derived from the phase difference between the subcarrier frequencies caused by the odd order terms of group delay.

Real-Time PPP-RTK Performance Analysis Using Ionospheric Corrections from Multi-Scale Network Configurations

The long convergence time required to achieve high-precision position solutions with integer ambiguity resolution-enabled precise point positioning (PPP-RTK) is driven by the presence of ionospheric delays. When precise real-time ionospheric information is available and properly applied, it can strengthen the underlying model and substantially reduce the time required to achieve centimeter-level accuracy. In this study, we present and analyze the real-time PPP-RTK user performance using ionospheric corrections from multi-scale regional networks during a day with medium ionospheric disturbance. It is the goal of this contribution to measure the impact the network dimension has on the ambiguity-resolved user position through the predicted ionospheric corrections. The user-specific undifferenced ionospheric corrections are computed at the network side, along with the satellite phase biases needed for single-receiver ambiguity resolution, using the best linear unbiased predictor. Such corrections necessitate the parameterization of an estimable user receiver code bias, on which emphasis is given in this study. To this end, we process GPS dual-frequency data from four four-station evenly distributed CORS networks in the United States with varying station spacings in order to evaluate if and to what extent the ionospheric corrections from multi-scale networks can improve the user convergence times. Based on a large number of samples, our experimental results showed that sub-10 cm horizontal accuracy can be achieved almost instantaneously in the ionosphere-weighted partially-ambiguity-fixed kinematic PPP-RTK solutions based on corrections from a network with 68 km spacing. Most of the solutions (90%) were shown to require less than 6.0 min, compared to the ionosphere-float PPP solutions that needed 68.5 min. In case of sparser networks with 115, 174 and 237 km spacing, 50% of the horizontal positioning errors are shown to become less than one decimeter after 1.5, 4.0 and 7.0 min, respectively, while 90% of them require 10.5, 16.5 and 20.0 min. We also numerically demonstrated that the user’s convergence times bear a linear relationship with the network density and get shorter as the density increases, for both full and partial ambiguity resolution.