Ambiguity Resolution Algorithm Research Articles

Multiple integer candidates ambiguity resolution: a unification ambiguity resolution algorithm

Among all the ambiguity resolution techniques, the Full Ambiguity Resolution (FAR), Partial Ambiguity Resolution (PAR) and Best Integer Equivariant (BIE) estimator are widely used. Although the researches have been done on the different classes of ambiguity resolution, we still hope to find the relationships among these specific algorithms. In this work, we unify the PAR and FAR algorithms under a whole framework of BIE by applying multiple integer candidates. A concise estimation formula of the variance of Gaussian BIE estimator based on the variance of float solution and the probability distribution of the candidates is first derived. Then, we propose an algorithm named Multiple Integer Candidates Ambiguity Resolution (MICAR) to discover as many ambiguities in the BIE as possible that can be estimated more precisely by PAR (FAR) algorithm instead of BIE. In the experiments, we utilize the simulated data of GPS (Global Positioning System) + BDS (BeiDou Navigation Satellite System) + Galileo (Galileo navigation satellite system) to contrast the effects of MICAR and single candidate estimator, i.e., FAR. By taking the threshold of 5 cm at 95% confidence level as an example, MICAR accelerates the convergence process by about 3.0 min. When the positioning sequence converges, MICAR reduces the root mean square of the positioning error by 9.8% in horizontal directions and 3.5% in vertical direction, which is attributed to more fixed NL.

Results of experimental processing of phase measurements of the GLONASS system using a non-brute force integer ambiguity resolution algorithm for high-precision absolute location

Results of experimental processing of phase measurements of the GLONASS system using a non-brute force integer ambiguity resolution algorithm for high-precision absolute location

4D High-Resolution Imagery of Point Clouds for Automotive mmWave Radar

In the community of automotive millimeter wave radar, the recently developed concept of four-dimensional (4D) radar can provide high-resolution point clouds image with enhanced imaging performance. Currently, the density of point clouds for single-frame image is usually too sparse to satisfy the demands of target classification and recognition due to the limitation of Doppler and angle resolutions. To address the aforementioned issues, a novel algorithm is proposed for 4D high-resolution imagery generation of point clouds with extremely high Doppler and angle resolutions in this paper. For high Doppler resolution with high-dynamic, a novel velocity ambiguity resolution algorithm is proposed using a dual pulse repetition frequency (dual-PRF) waveform design embedded in an innovative time-division multiplexing & Doppler-division multiplexing MIMO (TDM-DDM-MIMO) framework. Meanwhile, an attractive complex-valued deep convolutional network (CV-DCN) of super-resolution direction-of-arrival (DOA) estimation is proposed only using single-frame data. To be specific, a spatial smoothing operator on array data is applied as input of the network, and a CV-DCN is designed to learn the transformation of the spatial spectrum from the end-to-end to effectively protect the spectrum extraction. Furthermore, experimental analysis is performed to confirm the effectiveness of the proposed super-resolution DOA estimation algorithm. Finally, the 4D high-resolution imagery of point clouds is obtained by experiments in the parking lot.

A Velocity Ambiguity Resolution Algorithm Based on Improved Hypothetical Phase Compensation for TDM-MIMO Radar Traffic Target Imaging

A Velocity Ambiguity Resolution Algorithm Based on Improved Hypothetical Phase Compensation for TDM-MIMO Radar Traffic Target Imaging

Research on the Real-Time Ambiguity Resolution Algorithm of GPS/Galileo/BDS Based on CNES Real-Time Products

Real-Time (RT) Precise Point Positioning (PPP) uses precise satellite orbits and clock corrections, and employs a separate receiver for positioning. With the growing demand, RT PPP is becoming an increasingly popular research topic. The ambiguity resolution (AR) can significantly improve the positioning accuracy and convergence time of PPP, so it is essential to study PPPAR in RT mode. In this paper, 37 MGEX stations from around the world are chosen, and the RT orbit, clock, and phase biases products broadcast by the Centre National d’Etudes Spatiales (CNES) are applied to PPPAR. Additionally, the residuals of the RT phase biases products, convergence time, and positioning accuracy are investigated. The results indicate that GPS products have the best quality of AR, with wide-lane (WL) and narrow-lane (NL) residuals of 98.9% and 95.3%, respectively, within ±0.25 cycles. Within ±0.25 cycles, the WL and NL residuals of the Galileo are 98.2% and 94.3%, respectively. Within ±0.25 cycles, the (Beidou Navigation Satellite System) BDS has a poor quality of AR, with WL and NL residuals of 97.3% and 73.1%, respectively. Due to the poor quality of the BDS AR, the convergence time of the BDS is not calculated in this paper. The convergence time of other systems is significantly reduced after AR processing, and the convergence time of the GPS/Galileo combination is the fastest, being 17.14 min in kinematic mode and only 11.85 min in static mode. The positioning accuracy of the GPS, Galileo, GPS/Galileo, and GPS/Galileo/BDS in the E and U directions is significantly improved after PPPAR.

High-Resolution and Wide-Swath 3D Imaging for Urban Areas Based on Distributed Spaceborne SAR

Tomographic synthetic aperture radar (TomoSAR) obtains elevation resolution by adding multiple baselines successively in the direction perpendicular to the line of sight, thereby realizing three-dimensional (3D) reconstruction of complex scenes and significantly promoting the development of the 3D application field. However, a large data redundancy and long mapping time in traditional 3D imaging lead to a large data transmission burden, low efficiency, and high costs. To solve the above problems, this paper proposes a distributed SAR high-resolution and wide-swath (HRWS) 3D imaging technology scheme. The proposed scheme overcomes the size limitation of traditional single-satellite antennas through the multi-channel arrangement of multiple satellites in the elevation direction to achieve HRWS imaging; meanwhile, the distributed SAR system is integrated with tomographic processing technology to realize 3D imaging of difficult areas by using the elevation directional resolution of TomoSAR systems. HRWS 3D SAR increases the baseline length and channel number by transmission in turn, which leads to excessive pulse repetition frequency and causes echoes of different pulse signals to overlap in the same receiving cycle, resulting in range ambiguity and thus seriously affecting the quality of the 3D reconstruction. To solve this problem, this paper proposes a range ambiguity resolution algorithm based on multi-beam forming and verifies it on the measured data from airborne array SAR. Compared with the traditional TomoSAR, the distributed HRWS 3D SAR scheme proposed in this paper can obtain a greater mapping bandwidth with the same resolution in a single flight, thereby enhancing the time correlation, reducing data redundancy, and greatly improving mapping efficiency.

An Improved Ambiguity Resolution Algorithm for Smartphone RTK Positioning.

Ambiguity resolution based on smartphone GNSS measurements can enable various potential applications that currently remain difficult due to ambiguity biases, especially under kinematic conditions. This study proposes an improved ambiguity resolution algorithm, which uses the search-and-shrink procedure coupled with the methods of the multi-epoch double-differenced residual test and the ambiguity majority tests for candidate vectors and ambiguities. By performing a static experiment with Xiaomi Mi 8, the AR efficiency of the proposed method is evaluated. Furthermore, a kinematic test with Google Pixel 5 verifies the effectiveness of the proposed method with improved positioning performance. In conclusion, centimeter-level smartphone positioning accuracy is achieved in both experiments, which is greatly improved compared with the float and traditional AR solutions.

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.

Track‐Before‐Resolving: Doppler ambiguity resolution at low SNR

This study introduces a new scheme for resolving the ambiguity in a pulse-Doppler radar. While ambiguity resolution is typically performed before tracking, the proposed approach, Track-Before-Resolving, is resolving ambiguity utilising tracking filters. A specific Doppler ambiguity resolution algorithm is provided for demonstrating that the Track-Before-Resolving method is useful. In order to resolve the ambiguity, which is equivalent to finding the ambiguity number, this algorithm investigates the maximum probability calculated in the multiple model estimation, each with a tracking filter of a different ambiguity number. Simulation shows that the proposed algorithm performs effectively, even at low SNR.

A Partial Ambiguity Resolution Algorithm Based on New-Breadth-First Lattice Search in High-Dimension Situations.

With the development and integration of GNSS systems in the world, the positioning accuracy and reliability of GNSS navigation services are increasing in various fields. Because the current multisystem fusion leads to an increase in the ambiguity dimension and the ambiguity parameters have discrete characteristics, the current conventional search algorithm leads to low search efficiency when the ambiguity dimension is large. Therefore, this paper describes a new algorithm that searches the optimal lattice points by lattice theory through the breadth-first algorithm and reduces the search space of ambiguity by calculating and judging the Euclidean distance between each search variable and the target one so as to propose a new lattice ambiguity search algorithm based on the breadth-first algorithm. The experimental results show that this method can effectively improve the search efficiency of ambiguity in high-dimension situations.

Interferometer direction‐finding system with time‐division multiplexing of spread spectrum signals

AbstractA single channel interferometer direction‐finding (DF) system is proposed in this article. The interferometer DF system adopts time‐division multiplexing to receive different antenna phase information, which can effectively eliminate the differences in time delay and channel gain due to different channels. In addition, the spread spectrum signal and integer ambiguity resolution algorithm are used to make the system suitable for low carrier‐to‐noise ratios (CNRs) and high‐frequency signals. The simulations show that the system can measure the angle with root mean square error accuracy at a CNR of 50 dB‐Hz.

Optimized Algebraic Algorithm for Ambiguity Resolution and DOA Computation in Baseline Interferometer

Background: Interferometer is the most preferred technique for high accuracy direction finding. For broadband direction finding (DF) applications, multiple antennas forming a number of baselines are used to achieve better accuracy in measuring the direction of arrival (DOA). Ambiguity resolution in multi-element interferometers is a crucial algorithm for the computation of DOA. Objective: This paper introduces a fast, algebraic Common Minimum Modulo Search (CMMS) algo-rithm for ambiguity resolution and DOA computation. LabVIEW-based tool for Monte Carlo simula-tion of the algorithm over various parameters is described. Method: The CMMS is a computationally efficient algorithm, where the longest baseline phase difference is used for accuracy, and the phase difference data from all other baselines are used for resolving the ambiguities in the longest baseline. A hybrid approach using correlation and minimum algebraic search is used to determine the best fit set of ambiguities to the measured phase difference data. Results: Case studies have been presented in the literature and the performance of the CMMS algo-rithm was validated against established algorithms. This paper discusses the FPGA implementation as well as its simulation results. Analysis is performed on the 6-18 GHz frequency band. Moreover, the sources of errors and resulting limitations regarding the applicability of the algorithm are also discussed. Conclusion: Simulation results establish the algorithm's effectiveness in ambiguity resolution and applicability to diverse array configurations. The short nine-clock cycle processing latency in FPGA is demonstrated by the simulation results.

A Novel Two-Stage Adaptive Filtering Model-Based GNSS/INS Tightly Coupled Precise Relative Navigation Algorithm for Autonomous Aerial Refueling

Autonomous aerial refueling (AAR) has generated great interest in recent years. However, much research has focused on the vision-based close docking stage; few studies have been conducted on the navigation algorithm for the rendezvous and following stages. High-precision relative navigation in following stage can provide favourable conditions for successful docking. Aiming at precise relative navigation in the complex high dynamic environment of aerial refueling rendezvous and following stages, a two-stage adaptive filtering architecture is exploited in this paper. An adaptive main Kalman filter (AKF) is realized for ambiguity eliminated GNSS/INS tightly coupled integrated system, and a robust adaptive subfilter is developed for GNSS individually. Particularly, aiming at the influence of pseudorange observation multipath outliers and state abnormal disturbances in unmanned air vehicle- (UAV-) tanker proximity, an INS-aided bifactor robust and classified factor adaptive filtering (IBRCAF) algorithm for single-frequency ambiguity resolution is proposed. Finally, the effectiveness of the algorithm is verified by the simulation experiments for UAV-tanker. The results indicate that the IBRCAF algorithm can efficiently suppress the influence of pseudorange multipath gross errors and abnormal state disturbances and greatly raise the success rate of ambiguity resolution, and the two-stage adaptive filtering algorithm of IBRCAF-AKF can significantly improve relative navigation performance and achieve centimeter-level accuracy.

A New Rapid Integer Ambiguity Resolution of GNSS Phase-Only Dynamic Differential Positioning

The methods using the linear combination or simultaneous equations of GNSS carrier phase and pseudorange as the observations have become the main technology applied in GNSS dynamic differential positioning. Though the usage of pseudorange measurements can improve the efficiency of the integer ambiguity resolution, it may cause larger positioning errors than only using carrier phase. In response, we propose a new rapid integer ambiguity resolution algorithm that only using carrier phase for GNSS differential positioning. Based on weighted constrained least-squares ambiguity decorrelation adjustment (WC-LAMBDA), this method utilizes the baseline resolution of GNSS pseudorange differential positioning to constrain the integer ambiguity resolution of phase-only differential positioning. This method can make full use of the pseudorange constraints to improve the efficiency of phase-only integer ambiguity resolution. Besides, it can avoid the large error in positioning results caused by errors of pseudorange measurements. The experimental results show that the proposed method can shorten the initialization time of the integer ambiguity resolution and achieve a rapid and high precision phase-only differential positioning.

Sequential Ambiguity Resolution Method for Poorly-Observed GNSS Data

Integer ambiguity resolution is required to obtain precise coordinates for the global navigation satellite system (GNSS). Poorly observed data cause unfixed integer ambiguity and reduce the coordinate accuracy. Previous studies mostly used denoise filters and partial ambiguity resolution algorithms to address this problem. This study proposes a sequential ambiguity resolution method that includes a float solution substitution process and a double-difference (DD) iterative correction equation process. The float solution substitution process updates the initial float solution, while the DD iterative correction equation process is used to eliminate the residual biases. The satellite-selection experiment shows that the float solution substitution process is adequate to obtain a more accurate float solution. The iteration-correction experiment shows that the double-difference iterative correction equation process is feasible with an improvement in the ambiguity success rate from 28.4% to 96.2%. The superiority experiment shows significant improvement in the ambiguity success rate from 36.1% to 83.6% and a better baseline difference from about 0.1 m to 0.04 m. It is proved that the proposed sequential ambiguity resolution method can significantly optimize the results for poorly-observed GNSS data.

A Dynamic Range Ambiguity Resolution Algorithm for Radar Seeker Based on Vote Accumulation

A Dynamic Range Ambiguity Resolution Algorithm for Radar Seeker Based on Vote Accumulation

Effect Analysis of GNSS/INS Processing Strategy for Sufficient Utilization of Urban Environment Observations.

The occlusion of buildings in urban environments leads to the intermittent reception of satellite signals, which limits the utilization of observations. This subsequently results in a decline of the positioning and attitude accuracy of Global Navigation Satellite System (GNSS)/Inertial Navigation System (INS) integrated system (GNSS/INS). This study implements a smooth post-processing strategy based on a tightly coupled differential GNSS/INS. Specifically, this strategy used the INS-estimated position to reinitialize integer ambiguity. The GNSS raw observations were input into the Kalman filter to update the measurement. The Rauch–Tung–Striebel smoothing (RTSS) algorithm was used to process the observations of the entire period. This study analyzed the performance of loosely coupled and tightly coupled systems in an urban environment and the improvement of the RTSS algorithm on the navigation solution from the perspective of fully mining the observations. The experimental results of the simulation data and real data show that, compared with the traditional tightly coupled processing strategy which does not use INS-aided integer ambiguity resolution and RTSS algorithm, the strategy in this study sufficiently utilized INS observations and GNSS observations to effectively improve the accuracy of positioning and attitude and ensure the continuity of navigation results in an obstructed environment.

Метод раскрытияфазовых неоднозначностей, использующий обработку псевдодальностей по коду и фазе несущей в фильтре калмановского типа

The main problem of implementing high-precision pseudoranges by carrier phase lies in their ambiguity associated with the ambiguity of the phase measurements of the navigation receiver. Thus, the development of new methods for phase ambiguity resolution becomes a very important element of high-precision positioning. The paper considers relative methods for estimating the coordinates of a stationary object that involve the use of both user and base (network in the case of a network of base receivers) receivers with precisely known coordinates located at a distance of several thousand kilometers from each other. We propose an algorithm for phase ambiguity resolution (integer type) based on the use of a Kalman-type filter (KTF), which receives ionosphere-free combinations of code and carrier phase pseudoranges. It is shown that traditional methods of ambiguity resolution require a significant observation period (about 2,000 seconds). We propose a method for evaluating the linear combination of phase ambiguities in the L1 and L2 bands obtained from instantaneous phase measurements. Its application along with the estimation of KTF parameters makes it possible to resolve phase ambiguities from as early as 50 seconds of observation. Set forth are the results of an experiment, in which code pseudorange measurements are used prior to the resolution of phase ambiguities and carrier phase pseudorange measurements are used after ambiguity resolution.

Применение теории решетчатых упаковок в задаче высокоточного абсолютного местоопределения по ионосферосвободным измерениям в ГНСС с кодовы м разделением

The paper considers the use of the lattice packing theory for Integer Precise Point Positioning (Integer PPP) with the errors usually not exceeding 1–3 cm based on GNSS signals with code division multiple access (CDMA). Positioning is carried out by processing ionosphere-free linear combinations of code and phase measurements with ambiguity resolution employing satellite corrections. The main issue of PPP algorithms is overcoming the rank deficiency problem of the linear equation system obtained by linearization of nonlinear mathematical models of measurements. Nowadays Float PPP is quite well developed, where rank deficiency is tackled by combining systematic biases in measurement models with integer carrier phase ambiguities. As a result, the number of unknowns is reduced to the rank of design matrix, which allows unambiguous estimation of precise user coordinates and values of new variables generated by the performed combinations. However, under such conditions the information about integer nature of carrier phase ambiguities is lost, and this leads to a significant increase in convergence time to obtain user coordinates estimates with the errors of 1–3 cm. It is possible to involve the information on the integer nature of phase ambiguities into processing by applying ambiguity resolution algorithms. Though, as a result of the conducted combinations, the integer nature is destroyed, which makes it impossible to apply these algorithms. In Integer PPP rank deficiency is overcome by projecting the state space of the initial linear equation system onto a so-called S-space, whose dimension is equal to the rank of this system. The orientation of the S-space and the direction of projecting are chosen so that the variables of the initial system corresponding to user coordinates are not changed during the projecting and the projections of integer variables remain integer. This makes it possible to estimate precise user coordinates involving information on the integer nature of phase ambiguities. In the literature on Integer PPP based on CDMA GNSS signals processing the description of the S-space orientation with the desired properties is given, but there is no description of the method to determine this orientation. This paper based on the notions of the lattice packing theory considers an algorithm for determining the S-space with the desired properties. It is shown that there exists an infinite set of such S-spaces connected by unimodular transformations, and a technique is proposed to enable selection from this set the S-space, which requires minimal computational cost. The use of the lattice packing theory to the Integer PPP network solution with CDMA GNSS signals will be considered in the following publication of the authors.

Research on Ambiguity Resolution Algorithm by Quaternion Based on Acoustic Vector Sensor

The increase in element spacing can increase the aperture of the array and improve its resolution performance. However, phase ambiguity will occur when the array element interval is larger than the minimum half wavelength of the incident signal. The three acoustic velocity components of the acoustic vector are ingeniously constructed into a new kind of quaternions because of the special structure of the acoustic vector sensor array, and the rough estimation of the direction of arrival (DOA) is obtained using the rotation relationship between the subarray steering vectors corresponding to quaternion data. The rough estimate is used to resolve the phase ambiguity of the spatial phase difference between the array elements, and the high-precision DOA estimation of the signal can be obtained. Simulation results show that the method is effective.