Phase Ambiguity Research Articles

Low-Cost GNSS and PPP-RTK: Investigating the Capabilities of the u-blox ZED-F9P Module

GNSS has become ubiquitous in high-precision applications, although the cost of high-end GNSS receivers remains a major obstacle for many applications. Recent advances in GNSS receiver technology have led to the development of low-cost GNSS receivers, making high-precision positioning available to a wider range of users. One such technique for achieving high-precision positioning is Precise Point Positioning-Real Time Kinematic (PPP-RTK). It is a GNSS processing technique that combines the PPP and RTK approaches to provide high-precision positioning in real time without the need for a base station. In this work, we aim to assess the performance of the low-cost u-blox ZED-F9P GNSS module in PPP-RTK mode using the low-cost u-blox ANN-MB antenna. The experiment was designed to investigate both the time it takes the receiver to resolve the phase ambiguity and to determine the positioning accuracies achievable. Results showed that the u-blox ZED-F9P GNSS module could achieve centimeter-level positioning accuracy in about 60 s in PPP-RTK mode. These results make the PPP-RTK technique a good candidate to fulfill the demand for mass-market accurate and robust navigation since uses satellite-based corrections to provide accurate positioning information without the need for a local base station or network. Furthermore, due to its rapid acquisition capabilities and accurate data georeferencing, the technique has the potential to serve as a valuable method to improve the accuracy of the three-S techniques (GIS, remote sensing, and GPS/GNSS).

A Graph-Space Optimal Transport Approach Based on Kaniadakis κ-Gaussian Distribution for Inverse Problems Related to Wave Propagation.

Data-centric inverse problems are a process of inferring physical attributes from indirect measurements. Full-waveform inversion (FWI) is a non-linear inverse problem that attempts to obtain a quantitative physical model by comparing the wave equation solution with observed data, optimizing an objective function. However, the FWI is strenuously dependent on a robust objective function, especially for dealing with cycle-skipping issues and non-Gaussian noises in the dataset. In this work, we present an objective function based on the Kaniadakis κ-Gaussian distribution and the optimal transport (OT) theory to mitigate non-Gaussian noise effects and phase ambiguity concerns that cause cycle skipping. We construct the κ-objective function using the probabilistic maximum likelihood procedure and include it within a well-posed version of the original OT formulation, known as the Kantorovich-Rubinstein metric. We represent the data in the graph space to satisfy the probability axioms required by the Kantorovich-Rubinstein framework. We call our proposal the κ-Graph-Space Optimal Transport FWI (κ-GSOT-FWI). The results suggest that the κ-GSOT-FWI is an effective procedure to circumvent the effects of non-Gaussian noise and cycle-skipping problems. They also show that the Kaniadakis κ-statistics significantly improve the FWI objective function convergence, resulting in higher-resolution models than classical techniques, especially when κ=0.6.

BD-CVSA: A Broadband Direction Finding Method Based on Constructing Virtual Sparse Arrays

As the electromagnetic environment becomes more complex, radio direction finding systems need to cover a wide frequency range. However, the phase ambiguity of high frequency limits the development of broadband direction finding technology. The existing methods in solving the phase ambiguity problem heavily rely on designing the precise actual sparse array structure by theoretical derivation, which is expensive and time-consuming. To solve this problem, we propose a broadband direction finding method based on constructing virtual sparse arrays. First, we perform the convolutional operation on the direction feature matrix to achieve the weighted summation of the original baselines, which generates numerous virtual array elements and virtual baselines with different directions. The virtual array elements are combined to form virtual sparse arrays with different aperture sizes. Second, we optimize the parameters through the error backpropagation algorithm and obtain the optimal combination of virtual sparse arrays, which eliminates the phase ambiguity. Meanwhile, the virtual sparse arrays can maintain the advantages of sparse arrays, which can accomplish high-precision broadband direction finding. The experimental results demonstrate that the proposed method can solve the phase ambiguity problem effectively. It has high accuracy and strong robustness in simulation environment.

Self-Location Based on Grid-like Representations for Artificial Agents

Self-location plays a crucial role in a framework of autonomous navigation, especially in a GNSS/radio-denied environment. At the current time, self-location for artificial agents still has to resort to the visual and laser technologies in the framework of deep neural networks, which cannot model the environments effectively, especially in some dynamic and complex scenes. Instead, researchers have attempted to transplant the navigation principle of mammals into artificial intelligence (AI) fields. As a kind of mammalian neuron, the grid cells are believed to provide a context-independent spatial metric and update the representation of self-location. By exploiting the mechanism of grid cells, we adopt the oscillatory interference model for location encoding. Furthermore, in the process of location decoding, the capacity of autonomous navigation is extended to a significantly wide range without the phase ambiguity, based on a multi-scale periodic representation mechanism supported by a step-wise phase unwrapping algorithm. Compared with the previous methods, the proposed grid-like self-location can achieve a much wider spatial range without the limitation imposed by the spatial scales of grid cells. It is also able to suppress the phase noise efficiently. The proposed method is validated by simulation results.

Multi-point scattering measurements for effective property extraction from metamaterials with skin effects

Scattering experiments can be leveraged to extract the effective properties of a heterogeneous metamaterial slab based on multi-point measurements in surrounding media. In this technique, two measurements are made in the ambient media on each side of a finite thickness micro-structured slab to decompose incoming and outgoing waves. The method is applied to an example with locally resonant micro-structured inclusions while paying close attention to parameters that influence the extracted material parameters. It is observed that the extracted overall parameters converge to limiting values when the number of unit cells across the slab thickness or ambient media modulus are increased. Dependence of extracted material parameters on the number of cells through thickness or ambient media properties are attributed to the different response of boundary (skin) and interior cells. A method is presented which represents a finite array with different effective properties for the skin regions vs. the interior regions with great success in reproducing the scattering for different slab thicknesses, and through which the interior regions properties become independent of ambient media properties. In stop bands with lower material loss, challenges arise that are associated with extremely small transmission. The assumption of continuity in transmission phase is enforceable to remove phase ambiguity, although in certain cases (associated with nearly lossless specimens) this assumption appears to fail. In such cases, interference from coupled shear modes may lead to apparent higher longitudinal transmission within the stop band. This work provides a proof of concept for the development of an experimental methodology capable of extracting the effective properties and dispersion behavior of heterogeneous mechanical metamaterials without any knowledge of the internal fields.

Applicability of the Meniscus-Removal Method for Q-Band Liquid Characterization in Semi-Open Waveguide Cell

We present the broadband transmission-reflection meniscus-removal method for liquid characterization in a semi-open rectangular waveguide. The algorithm utilizes 2-port scattering parameters measured with a calibrated vector network analyzer for three states of the measurement cell: empty and filled with two liquid levels. The method enables the mathematical de-embedding of a symmetrical sample of a liquid, not distorted with a meniscus, and provision of its permittivity and permeability, as well as its height. We validate the method for propan-2-ol (IPA), a 50% aqueous solution of IPA, and distilled water in the Q-band (33–50 GHz). We investigate typical problems for in-waveguide measurements, such as phase ambiguity.

A deep learning-based approach to solve the height-slope ambiguity in phase measuring deflectometry

Phase measuring deflectometry (PMD) shows excellent performance in measuring the shape of specular surfaces. However, the existing height-slope ambiguity affects the measurement of PMD. In this paper, we propose a deep learning-based method to solve the ambiguity and reconstruct the specular surface. A neural network was built to reconstruct the surface. A set of simulation surfaces were generated using two-dimensional Legendre polynomials to train and test the network. A spherical-shaped surface was reconstructed in a simulation to evaluate the validity of the proposed method and compare our method to the state-of-the-art method. Experimental results demonstrate a 35.88% improvement in this method’s accuracy. Our method provides a great improvement in measurement accuracy.

Energy receiver positioning using a spatial search strategy in MWPT

This paper proposes a space search method combining the Г-type layout of receiving antenna array of pilot signal for energy receiver positioning in MWPT systems. Based on the retrodirective technology, the spatial coordinate identification function (SCIF) of the energy receiver is generated. The study also investigates how to determine the spatial search range and search point interval. In addition, we propose a Criss-cross space search strategy (CSSS) to accelerate target positioning by summarizing the distribution features of the results obtained by SCIF. The simulation and physical experiment results demonstrate that the proposed method effectively overcomes the phase ambiguity problem and greatly improves the speed and accuracy of energy receiver positioning.

A Dynamic Continuous Constrained Phase Factor Graph Optimization Method for GNSS Kinematic Precise Point Positioning

Carrier phase measurements play a more critical role in achieving precise positioning for lower noise and insensitivity to multipath error over code (pseudorange) measurements. Real-time kinematic (RTK) is the most used precise positioning technique. However, the application costs are increased due to the demands for differential base stations. The undifferenced precise point positioning (PPP) does not require differential station assistance but is typically for static use. This paper proposes a dynamic continuous constrained phase (DCCP) method based on factor graph optimization for kinematic positioning without differential stations, even in the presence of cycle slips. The precise velocity estimated via integral doppler and the time correlation of phase ambiguity are regarded as the probability constraints in the factor graph. A real-world experiment was carried out to verify the feasibility of the DCCP method. Experimental results show that the proposed method had a better performance than the kinematic PPP method and window carrier phase (WCP) optimization method with 0.034m standard deviation and 1.338m mean error. It is our hope that this approach provides new insight into the study of other time-correlated state estimation problems.

AVALIAÇÃO DA ACURÁCIA DA TÉCNICA DE POSICIONAMENTO GNSS PPP-RTK COM O USO DO SERVIÇO DE CORREÇÃO TRIMBLE CENTERPOINT RTX

The use of only one receiver at the user level, together with the solution of phase ambiguities as integer values, are among the main advantages of the PPP-RTK GNSS Positioning Technique. However, it is necessary to have a Geodetic Network at a global level for the generation of products, such as precise orbits and satellite clocks. Furthermore, to accurately estimate geodetic coordinates, all errors involved with the propagation of GNSS signals and with ground stations must be properly modeled and treated. Thus, the main objective of this work is to evaluate the accuracy of the PPP-RTK Positioning Technique, using corrections from the Trimble Centerpoint RTX Service in Brazil. For this, GNSS surveys were carried out in all states of the Federation in Geodetic Stations belonging to the SGB, whose coordinates were considered as reference in the evaluation process. Student's t statistical tests were applied – to detect possible trends (systematic errors) in the data, and Chi-Square to assess the precision of the coordinates. Finally, the results show that the horizontal accuracy improves gradually with increasing convergence time, reaching 0.025m ± 0.018m (Trend and Precision) for 15 minutes of convergence.

Polarimetric L-Band ALOS2-PALSAR2 for Discontinuous Permafrost Mapping in Peatland Regions

Recently, it has been shown that the long penetrating polarimetric L-band ALOS is very promising for boreal and subarctic peatland mapping and monitoring. The unique information provided by the Touzi decomposition, and the dominant-scattering-type phase in particular, on peatland subsurface water flow permits an enhanced discrimination of bogs from fens, two peatland classes that can hardly be discriminated using conventional optical remote sensing sensors and C-band polarimetric SAR. In this study, the dominant and medium-scattering phases generated by the Touzi decomposition are investigated for discontinuous permafrost mapping in peatland regions. Polarimetric ALOS2, LiDAR, and field data were collected in the middle of August 2014, at the maximum permafrost thaw conditions, over discontinuous permafrost distributed within wooded palsa bogs and peat plateaus near the Namur Lake (Northern Alberta). The ALOS2 image, which was miscellaneously calibrated with antenna cross talk (−33 dB) much higher than the actual ones, was recalibrated. This led to a reduction of the residual calibration error (down to −43 dB) and permitted a significant improvement of the dominant and medium-scattering-type phase (20∘ to −30∘) over peatlands underlain by discontinuous permafrost. The Touzi decomposition, Cloude–Pottier α-H incoherent target scattering decomposition, and the HH-VV phase difference were investigated, in addition to the conventional multipolarization (HH, HV, and VV) channels, for discontinuous permafrost mapping using the recalibrated ALOS2 image. A LiDAR-based permafrost classification developed by the Alberta Geological Survey (AGS) was used in conjunction with the field data collected during the ALOS2 image acquisition for the validation of the results. It is shown that the dominant- and scattering-type phases are the only polarimetric parameters which can detect peatland subsurface discontinuous permafrost. The medium-scattering-type phase, ϕs2, performs better than the dominant-scattering-type phase, ϕs1, and permits a better detection of subsurface discontinuous permafrost in peatland regions. ϕs2 also allows for a better discrimination of areas underlain by permafrost from the nonpermafrost areas. The medium Huynen maximum polarization return (m2) and the minimum degree of polarization (DoP), pmin, can be used to remove the scattering-type phase ambiguities that might occur in areas with deep permafrost (more than 50 cm in depth). The excellent performance of polarimetric PALSAR2 in term of NESZ (−37 dB) permits the demonstration of the very promising L-band long-penetration SAR capabilities for enhanced detection and mapping of relatively deep (up to 50 cm) discontinuous permafrost in peatland regions.

Estimation of underwater acoustic direction-of-arrival using the probe beam deflection technique.

This paper proposes a method of estimating the underwater acoustic direction-of-arrival using several laser beams impinging on a propagating underwater acoustic wave. The deflection of the laser beam caused by the spatial variation of the optical refractive index, which is further due to the modulation of the acoustic wave, reflects the information of direction-of-arrival and is sensed by the position sensitive detector (PSD). The sensing of the minute displacement on the PSD, in fact, introduces an extra dimension in the depth direction, which is a significant advantage over the conventional piezoelectric sensing regime. The employment of the extra sensing dimension can overcome several shortcomings, represented by spatial aliasing and phase ambiguity, existing in the current direction-of-arrival estimating methods. In addition, the ringing phenomenon of the piezoelectric effect is greatly reduced in the proposed laser-based sensing regime. By the flexibility of placing the laser beams, a prototype of the hydrophone is designed and manufactured, and a series of testing is performed. The results show that, benefiting from the probe beam deflection technique and combining the rough estimate and fine calculation, the resolution of the underwater acoustic direction-of-arrival can be improved to better than 0.016°, which can support and reform many underwater applications such as underwater acoustic communication, underwater detection, and ocean monitoring.

Single-shot dense depth sensing with a tricolor RGB fringe pattern

A single-shot fringe pattern composed of red (R), green (G), and blue (B) is proposed for dynamic scene depth acquisition. A tricolor binary fringe is adopted and filtered in the frequency domain to obtain sinusoidal fringes. A Gabor filter is employed to estimate the wrapped phase. To overcome the phase ambiguity, we use the color-encoded De Bruijn sequence to denote the period of the phase information and assign the sequence to two channels of the pattern, while the third channel is equal to the inverse of the composition of the two channels. Benefiting from this coding strategy, two disparity maps with different phase shifts can be acquired in only one shot, and a disparity consistency check is used to eliminate errors. Quantitative and qualitative experiments are conducted to verify the performance of the proposed method and prove that it can achieve a high accuracy and dense depth map.

Phase ambiguity resolution and mixed pixel detection in EDM with multiple modulation wavelengths

Distance measurement based on the accumulated phase of intensity-modulated continuous-wave lasers is an established approach for pointwise geometry acquisition in uncontrolled conditions, enabling some of the most accurate Lidar/laser-scanning solutions. Inherently affected by cycle ambiguities due to the modulo 2π phase observations, several modulation wavelengths are typically used in practical implementations to extend the measurement range. One of the main limitations of these systems arises from their inability to decouple mixed signals affected by different delays. This is especially relevant when the laser beam illuminates simultaneously two or more surfaces at significantly different distances, producing mixed-pixel measurements in which the estimated distance does not reliably correspond to any of the involved scatterers. Algorithms for detection and filtering of mixed pixels within point-cloud data have been proposed based on analyzing consistency across local neighborhoods. The resolution of multiple scatterers on individual measurements, however, has not been yet reported nor is provided by undisclosed commercial implementations. In this work, we analyze the problem of signal mixing in multi-wavelength phase-based distance estimation, and propose an algorithm for joint phase ambiguity resolution and mixed pixel detection based on mixed integer linear programming. We first analyze theoretically the performance limits of the proposed solution, demonstrating unbiasedness in the presence of noise and robustness in the presence of multiple scatterers. In addition, we investigate empirically the impact of noise, mixed measurements and choice of modulation wavelengths on the performance of the proposed algorithm. The results demonstrate the capacity of the presented approach, given an adequate wavelength selection, to provide unambiguous distance estimates under realistic noise conditions and to identify measurements affected by mixed pixels while approximating the position of the dominant scatterer. Aside from contributing to improving the reliability and resolution capability of Lidar and laser-scanning data, the proposed solution sets a promising step towards fully resolved multi-target distance measurement.

Channel Imbalance Calibration Based on the Zero Helix of Bragg-like Targets

The calibration of channel imbalances is currently the main concern in polarimetric calibration (POLCAL) since the crosstalk of recent polarimetric synthetic aperture radar (Pol-SAR) systems is lower than −20 dB. The existing channel imbalance calibration method without corner reflectors utilizes both volume-dominated and Bragg-like targets. However, there are two limitations to using volume-dominated targets. One is that the inaccurate selection of volume-dominated areas in the uncalibrated Pol-SAR images has a negative influence on the estimation of cross-polarization (x-pol) channel imbalance, which subsequently impacts the estimation of copolarization (copol) channel imbalance. The other is that there are minimal volume-dominated areas in some special applications of Pol-SAR, such as planetary exploration. Thus, only selecting Bragg-like targets to estimate the values of both transmitting and receiving channel imbalances, which is proposed in this paper, can avoid the uncertainty brought about by selecting other distributed targets in an uncalibrated imaginary. In addition, the reciprocity assumption and characteristics corresponding to H/α¯ decomposition are introduced to eliminate the phase ambiguity for the first time. Compared with previous methods, our method had an obvious advantage in terms of universality, since Bragg-like targets are common in the most illuminating areas. The novel method was applied to both the simulated data from the L-band Advanced Land Observing Satellite (ALOS) and C-band GaoFen-3 (GF-3), and to real data with corner reflectors on site. The results from the simulated data showed that the errors of the amplitude and phase estimation were less than 0.5 dB and 5.0° in most topographical features. Meanwhile, the VV/HH terms from all trihedral corner reflectors were less than 0.3 dB for amplitude, and 5.5° for phase after calibration by using the estimated channel imbalances.

Full-Period Quantum Phase Estimation.

Quantum sensing can provide the superior sensitivity for sensing a physical quantity beyond the shot-noise limit. In practice, however, this technique has been limited to the issues of phase ambiguity and low sensitivity for small-scale probe states. Here, we propose and demonstrate a full-period quantum phase estimation approach by adopting the Kitaev's phase estimation algorithm to eliminate the phase ambiguity and using the GHZ states to obtain phase value, simultaneously. For an N-party entangled state, our approach can achieve an upper bound of sensitivity of δθ=sqrt[3/(N^{2}+2N)], which beats the limit of adaptive Bayesian estimation. By performing an eight-photon experiment, we demonstrate the estimation of unknown phases in a full period, and observe the phase superresolution and sensitivity beyond the shot-noise limit. Our Letter provides a new way for quantum sensing and represents a solid step towards its general applications.

Parallel unambiguous generalized phase-shifting and T-spline fitting algorithms for optical micro-structured surface 3D topography metrology.

3D topography metrology of optical micro-structured surfaces is critical for controlled manufacturing and evaluation of optical properties. Coherence scanning interferometry technology has significant advantages for measuring optical micro-structured surfaces. However, the current research faces difficulties of designing high accuracy and efficient phase shifting, and characterization algorithms for optical micro-structured surface 3D topography metrology. In this paper, parallel unambiguous generalized phase-shifting and T-spline fitting algorithms are proposed. To avoid phase ambiguity and improve the accuracy of the phase-shifting algorithm, the zero-order fringe is determined by the iterative envelope fitting with Newton's method, and the accurate zero optical path difference is determined by a generalized phase-shifting algorithm. In particular, the calculation procedures of the multithreading iterative envelope fitting with Newton's method and generalized phase shifting are optimized with the graphics processing unit-Compute Unified Device Architecture kernel function. Additionally, to fit the base form of optical micro-structured surfaces and characterize the surface texture and roughness, an effective T-spline fitting algorithm is proposed by optimizing the preimage of the T-mesh with image quadtree decomposition. Experimental results show that the surface reconstruction of optical micro-structured surfaces using the proposed algorithm is more accurate, and the efficiency is 10 times higher than that of current algorithms; the time of the surface reconstruction is less than 1s. Compared with the current B-spline method, the accuracy of roughness characterization using the proposed T-spline algorithm is improved by more than 10%.

An Operational Processing Framework for Spaceborne SAR Formations

The paper proposes a flexible and efficient wavenumber domain processing scheme suited for close formations of low earth orbiting (LEO) synthetic aperture radar (SAR) sensors hosted on micro-satellites or CubeSats. Such systems aim to generate a high-resolution image by combining data acquired by each sensor with a low pulse repetition frequency (PRF). This is usually performed by first merging the different channels in the wavenumber domain, followed by bulk focusing. In this paper, we reverse this paradigm by first upsampling and focusing each acquisition and then combining the focused images to form a high-resolution, unambiguous image. Such a procedure is suited to estimate and mitigate artifacts generated by incorrect positioning of the sensors. An efficient wave–number method is proposed to focus data by adequately coping with the orbit curvature. Two implementations are provided with different quality/efficiency. The image quality in phase preservation, resolution, sidelobes, and ambiguities suppression is evaluated by simulating both point and distributed scatterers. Finally, a demonstration of the capability to compensate for ambiguities due to a small across-track baseline between sensors is provided by simulating a realistic X-band multi-sensor acquisition starting from a stack of COSMO-SkyMed images.

Phase refractive index measurement of thick glass plates with a spectrally resolved interferometer

Measurements of phase refractive indexes of thick objects by using fitting method have been reported in many papers, but the fitting method produces errors in the fitted coefficients of a fitting function. In this paper it is made clear that the thickness of object, for which the phase refractive index can be measured exactly, is limited by the errors. Phase refractive indexes of three kinds of glass plates of 1 mm thickness are measured directly from spectral phases detected with a spectrally resolved interferometer. Instead of using the fitting method, the 2π phase ambiguity contained in a detected spectral phase is determined by using an assumption that an actual refractive index measured in experiment is almost the same as well-known data of the refractive index. The actual refractive indexes measured with an error less than 8 × 10−5 are slightly different from the well-known data about the slope and the constant value in the distributions.

Robust and efficient waveform-based velocity-model building by optimal transport in the pseudotime domain: Methodology

Full-waveform inversion (FWI) aims at a broadband reconstruction of the subsurface physical properties by fitting the entire recorded wavefield. In realistic exploration seismic surveys, however, conventional FWI often fails to retrieve the deep velocity model due to the limited penetration depth of diving waves. Joint FWI (JFWI) unifies reflection-waveform inversion and early arrival waveform inversion to reconstruct simultaneously the shallow and deep subsurface kinematics. However, several factors limit the appeal of JFWI velocity-model building: (1) conflict between fixed reflectivity and evolving kinematics, creating phase ambiguity at short offsets; (2) susceptibility to cycle skipping at mid-to-long offsets, thus reliance on the quality of the starting model; and (3) cost of building and updating the reflective model. We have developed a fully operational JFWI-based methodology that systematically addresses the aforementioned issues. JFWI is reformulated in the pseudotime domain, to enforce consistency between velocity and reflectivity in a cost-effective fashion, without repeated least-squares migrations. A JFWI graph-space optimal transport (GSOT) objective function is designed to avert cycle skipping, whereas nonuniqueness is mitigated at no extra cost by smoothing the velocity gradient along the structures extracted from the reflective model. A dedicated asymptotic-based preconditioner is developed for impedance waveform inversion, making it possible to obtain sharp and balanced reflective images in a fraction of the time. We determine that pseudotime GSOT-JFWI retrieves complex velocity macromodels from limited-offset data sets with minimal preprocessing, starting from noninformative initial solutions. Compared with depth-domain JFWI, the computing cost is reduced significantly, along with a simpler and less subjective design of data weighting and inversion strategy. Pseudotime GSOT-JFWI provides FWI with the necessary low wavenumbers to converge to the broadband model, reducing the need for accurate starting models, on the road to a fully waveform-based imaging workflow.