ALGORITHM FOR AMBIGUITY RESOLUTION IN RANGE AND VELOCITY

For enhancing performances and increasing functions of PD radar, High PRF, medium PRF and low PRF are commonly applied into system ambiguity appeared in range and velocity in some PRF. Based on clustering, a sliding window correlator algorithm for resolving the radar object ambiguity in range and velocity is described. Slide window algorithm is a searching algorithm. The probability of ambiguity resolution for targets and the computational efficiency are discussed. The relations between the probability of ambiguity resolution of this algorithm and PRF, the range of interest, and the width of sliding window are analyzed. Simulational results are also given.

Ambiguity Resolution in Direction of Arrival Estimation with Linear Antenna Arrays Using Differential Geometry

Linear antenna arrays(LAs)can be used to accurately predict the direction of arrival(DOAs)of various targets of interest in a given area.However,under certain conditions,LA suffers from the problem of ambiguities among the angles of targets,which may result inmisinterpretation of such targets.In order to cope up with such ambiguities,various techniques have been proposed.Unfortunately,none of them fully resolved such a problem because of rank deficiency and high computational cost.We aimed to resolve such a problem by proposing an algorithm using differential geometry.The proposed algorithm uses a specially designed doublet antenna array,which is made up of two individual linear arrays.Two angle observation models,ambiguous observation model(AOM)and estimated observation model(EOM),are derived for each individual array.The ambiguous set of angles is contained in the AOM,which is obtained from the corresponding array elements using differential geometry.The EOM for each array,on the other hand,contains estimated angles of all sources impinging signals on each array,as calculated by a direction-finding algorithm such as the genetic algorithm.The algorithm then contrasts the EOM of each array with its AOM,selecting the output of that array whose EOM has the minimum correlation with its corresponding AOM.In comparison to existing techniques,the proposed algorithm improves estimation accuracy and has greater precision in antenna aperture selection,resulting in improved resolution capabilities and the potential to be used more widely in practical scenarios.The simulation results using MATLAB authenticates the effectiveness of the proposed algorithm.

Precise orbit determination of Haiyang‑2D using onboard BDS‑3 B1C/B2a observations with ambiguity resolution

The Haiyang-2D altimetry mission of China is one of the first Low Earth Orbit(LEO)satellites that can receive new B1C/B2a signals from the BeiDou-3 Navigation Satellite System(BDS-3)for Precise Orbit Determination(POD).In this work,the achievable accuracy of the single-receiver ambiguity resolution for onboard LEO satellites is studied based on the real measurements of new BDS-3 frequencies.Under normal conditions,six BDS-3 satellites on average are visible.However,the multipath of the B1C/B2a code observations presents some patchy patterns that cause near-field variations with an amplitude of approximately 40 cm and deteriorate the ambiguity-fixed rate.By modeling those errors,for the B2a code,a remarkable reduction of 53%in the Root Mean Square(RMS)is achieved at high elevations,along with an increase of 8%in the ambiguity-fixed rates.Additionally,an analysis of the onboard antenna’s phase center offsets reveals that when compared to the solutions with float ambiguities,the estimated values in the antenna’s Z direction in the solutions with fixed ambiguities are notably smaller.The independent validation of the resulting POD using satellite laser ranging at 16 selected high-performance stations shows that the residuals are reduced by a minimum of 15.4%for ambiguity-fixed solutions with an RMS consistency of approximately 2.2 cm.Furthermore,when compared to the DORIS-derived orbits,a 4.3 cm 3D RMS consistency is achieved for the BDS-3-derived orbits,and the along-track bias is reduced from 2.9 to 0.4 cm using ambiguity fixing.

Performance investigation of LAMBDA and bootstrapping methods for PPP narrow-lane ambiguity resolution

Precise point positioning with ambiguity resolution(PPP-AR)is a powerful tool for geodetic and time-constrained applications that require high precision.The performance of PPP-AR highly depends on the reliability of the correct integer carrier-phase ambiguity estimation.In this study,the performance of narrow-lane ambiguity resolution of PPP using the Least-squares AMBiguity Decorrelation(LAMBDA)and bootstrapping methods is extensively investigated using real data from 55 IGS stations over one-month in 2020.Static PPP with 24-,12-,8-,4-,2-,1-and½-h sessions using two different cutoff angles(7°and 30°)was conducted with three PPP modes:i.e.ambiguity-float and two kinds of ambiguity-fixed PPP using the LAMBDA and bootstrapping methods for narrow-lane AR,respectively.The results show that the LAMBDA method can produce more reliable results for 2 hour and shorter observation sessions com-pared with the bootstrapping method using a 7°cutoff angle.For a 30°cutoff angle,the LAMBDA method outperforms the bootstrapping method for observation sessions of 4 h and less.For long observation times,the bootstrapping method produced much more accurate coordinates compared with the LAMBDA method without considering the wrong fixes cases.The results also show that occurrences of fixing the wrong integer ambiguities using the bootstrapping method are higher than that of the LAMBDA method.

Precise orbit determination for LEO satellites:single-receiver ambiguity resolution using GREAT products

In recent years,the large Low Earth Orbit(LEO)constellations have become a hot topic due to their great potential to improve the Global Navigation Satellite Systems(GNSS)positioning performance.One of the important focus is how to obtain the accurate and reliable orbits for these constellations with dozens of LEO satellites.The GNSS-based Precise Orbit Determination(POD)will be exclusively performed to achieve this goal,where the Integer Ambiguity Resolution(IAR)plays a key role in acquiring high-quality orbits.In this study,we present a comprehensive analysis of the benefit of the single-receiver IAR in LEO POD and discuss its implication for the future LEO constellations.We perform ambiguity-fixed LEO POD for four typical missions,including Gravity Recovery and Climate Experiment(GRACE)Follow-On(GRACE-FO),Swarm,Jason-3 and Sentinel-3,using the Uncalibrated Phase Delay(UPD)products generated by our GREAT(GNSS+REsearch,Application and Teaching)software.The results show that the ambiguity fixing processing can significantly improve the accuracy of LEO orbits.There are negligible differences between our UPD-based ambiguity-fixed orbits and those based on the Observable Signal Bias(OSB)and Integer Recovery Clock(IRC)products,indicating the good-quality of UPD products we generated.Compared to the float solution,the fixed solution presents a better consistency with the external precise science orbits and the largest accuracy improvement of 5 mm is achieved for GRACE-FO satellites.Meanwhile,the benefit can be observed in laser ranging residuals as well,with a Standard Deviation(STD)reduction of 3–4 mm on average for the fixed solutions.Apart from the absolute orbits,the relative accuracy of the space baseline is also improved by 20–30%in the fixed solutions.The result demonstrates the superior performance of the ambiguity-fixed LEO POD,which appears as a particularly promising technique for POD of future LEO constellations.

Indirect-Inversion A lgorithm via Precise Integration for Ill-Conditioned Matrix in Ambiguity Resolution

Global navigation satellite system(GNSS)positioning depends on the correct integer ambiguity resolu-tion(AR).If the double difference equation for solving the float solution remains il-conditioned,often happening due to the environment complexity and the equipment mobility,the corrcct AR is difficult to achieve.Concern-ing the il-conditioned problem,methods of modifying the equation cofficient matrix are widely applied,whose effects are heavily dependent on modifying parameters.Besides,the direct inversion of the il-conditioned coef-ficient matrix can lead to a reduction in the accuracy and stability of the float solution.To solve the problem of il-conditioned matrix inversion and further improve the accuracy,the present study for the first time proves the positive definite symmetry of the coefficient matrix in AR model and employs precise integration method to the indirect inverse of cofficient matrix.AR model for the GNSS positioning and the general resolving strate-gies introduction are briefly introduced.An indirect-inversion algorithm via precise integration for il-conditioned coefficient matrix is proposed.According to the simulations and comparisons,the proposed strategy has higher precision and stability on foat solution,and less dependence on modifying parameters.

A Combined Antenna Array Deployment with High Positioning Accuracy and Low Angular Measurement Error

In this paper,an antenna array composed of circular array and orthogonal linear array is proposed by using the design of long and short baseline“orthogonal linear array”and the circular array ambiguity resolution design of multi-group baseline clustering.The effectiveness of the antenna array in this paper is verified by sufficient simulation and experiment.After the system deviation correction work,it is found that in the L/S/C/X frequency bands,the ambiguity resolution probability is high,and the phase difference system error between each channel is basically the same.The angle measurement error is less than 0.5°,and the positioning error is less than 2.5 km.Notably,as the center frequency increases,calibration consistency improves,and the calibration frequency points become applicable over a wider frequency range.At a center frequency of 11.5 GHz,the calibration frequency point bandwidth extends to 1200 MHz.This combined antenna array deployment holds significant promise for a wide range of applications in contemporary wireless communication systems.

An improved GNSS ambiguity best integer equivariant estimation method with Laplacian distribution for urban low-cost RTK positioning

The integer least squares(ILS)estimation is commonly used for carrier phase ambiguity resolution(AR).More recently,the best integer equivariant(BIE)estimation has also attracted an attention for complex application scenarios,which exhibits higher reliability by a weighted fusion of integer candidates.However,traditional BIE estimation with Gaussian distribution(GBIE)faces challenges in fully utilizing the advantages of BIE for urban low-cost positioning,mainly due to the presence of outliers and unmodeled errors.To this end,an improved BIE estimation method with Laplacian distribution(LBIE)is proposed,and several key issues are discussed,including the weight function of LBIE,determination of the candidates included based on the OIA test,and derivation of the variance of LBIE solutions for reliability evaluation.The results show that the proposed LBIE method has the positioning accuracy similar to the BIE using multivariate t-distribution(TBIE),and significantly outperforms the ILS-PAR and GBIE methods.In an urban expressway test with a Huawei Mate40 smartphone,the LBIE method has positioning errors of less than 0.5 m in three directions and obtains over 50%improvements compared to the ILS-PAR and GBIE methods.In an urban canyon test with a low-cost receiver STA8100 produced by STMicroelectronics,the positioning accuracy of LBIE in three directions is 0.112 m,0.107 m,and 0.252 m,respectively,with improvements of 17.6%,27.2%,and 26.1%compared to GBIE,and 23.3%,28.2%,and 30.6%compared to ILS-PAR.Moreover,its computational time increases by 30–40%compared to ILS-PAR and is approximately half of that using TBIE.

Orbit and clock products for quad-system satellites with undifferenced ambiguity fixing approach

Integer Ambiguity Resolution(IAR)can significantly improve the accuracy of GNSS Precise Orbit Determination(POD).Traditionally,the IAR in POD is achieved at the Double Differenced(DD)level.In this contribution,we develop an Un-Differenced(UD)IAR method for Global Positioning System(GPS)+BeiDou Navigation Satellite System(BDS)+Galileo navigation satellite system(Galileo)+Global'naya Navigatsionnaya Sputnikovaya Sistema(GLONASS)quad-system POD by calibrating UD ambiguities in the raw carrier phase and generating the so-called carrier range.Based on this method,we generate the UD ambiguity-fixed orbit and clock products for the Wuhan Innovation Application Center(IAC)of the International GNSS Monitoring and Assessment System(iGMAS).One-year observations in 2020 from 150 stations are employed to investigate performance of orbit and clock products.Notably,the UD Ambiguity Resolution(AR)yields more resolved integer ambiguities than the traditional DD AR,scaling up to 9%,attributable to its avoidance of station baseline formation.Benefiting from the removal of ambiguity parameters,the computational efficiency of parameter estimation undergoes a substantial 70%improvement.Compared with the float solution,the orbit consistencies of UD AR solution achieve the accuracy of 1.9,5.2,2.8,2.1,and 2.7 cm for GPS,BeiDou-2 Navigation Satellite System(BDS-2),BeiDou-3 Navigation Satellite System(BDS-3),Galileo,and GLONASS satellites respectively,reflecting enhancements of 40%,24%,54%,34%,and 42%.Moreover,the standard deviations of Satellite Laser Ranging(SLR)residuals are spanning 2.5–3.5 cm,underscoring a comparable accuracy to the DD AR solution,with discrepancies below 5%.A notable advantage of UD AR lies in its capability to produce the Integer Recovered Clock(IRC),facilitating Precise Point Positioning(PPP)AR without requiring additional Uncalibrated Phase Delay(UPD)products.To assess the performance of quad-system kinematic PPP based on IRC,a network comprising 120 stations is utilized.In comparison to the float solution,the IRC-based PPP AR accelerates convergence time by 31%and enhance positioning accuracy in the east component by 54%.

PERFORMANCE ANALYSIS OF INTEGRATED GPS/GLONASS CARRIER PHASE-BASED POSITIONING

Due to the different signal frequencies for the GLONASS satellites,the commonly-used double-differencing procedure for carrier phase data processing can not be implemented in its straightforward form,as in the case of GPS.In this paper a novel data processing strategy,involving a three-step procedure,for integrated GPS/GLONASS positioning is proposed.The first is pseudo-range-based positioning,that uses double-differenced (DD) GPS pseudo-range and single-differenced (SD) GLONASS pseudo-range measurements to derive the initial position and receiver clock bias.The second is forming DD measurements (expressed in cycles) in order to estimate the ambiguities,by using the receiver clock bias estimated in the above step.The third is to form DD measurements (expressed in metric units) with the unknown SD integer ambiguity for the GLONASS reference satellite as the only parameter (which is constant before a cycle slip occurs for this satellite).A real-time stochastic model estimated by residual series over previous epochs is proposed for integrated GPS/GLONASS carrier phase and pseudo-range data processing.Other associated issues,such as cycle slip detection,validation criteria and adaptive procedure(s) for ambiguity resolution,is also discussed.The performance of this data processing strategy will be demonstrated through case study examples of rapid static positioning and kinematic positioning.From four experiments carried out to date,the results indicate that rapid static positioning requires 1 minute of single frequency GPS/GLONASS data for 100% positioning success rate.The single epoch positioning solution for kinematic positioning can achieve 94.6% success rate over short baselines (<6 km).

Monopulse instantaneous 3D imaging for wideband radar system

To avoid the complicated motion compensation in interferometric inverse synthetic aperture(InISAR)and achieve realtime three-dimensional(3 D)imaging,a novel approach for 3 D imaging of the target only using a single echo is presented.This method is based on an isolated scatterer model assumption,thus the scatterers in the beam can be extracted individually.The radial range of each scatterer is estimated by the maximal likelihood estimation.Then,the horizontal and vertical wave path difference is derived by using the phase comparison technology for each scatterer,respectively.Finally,by utilizing the relationship among the 3 D coordinates,the radial range,the horizontal and vertical wave path difference,the 3 D image of the target can be reconstructed.The reconstructed image is free from the limitation in InISAR that the image plane depends on the target's own motions and on its relative position with respect to the radar.Furthermore,a phase ambiguity resolution method is adopted to ensure the success of the 3 D imaging when phase ambiguity occurs.It can be noted that the proposed phase ambiguity resolution method only uses one antenna pair and does not require a priori knowledge,whereas the existing phase ambiguity methods may require two or more antenna pairs or a priori knowledge for phase unwarping.To evaluate the performance of the proposed method,the theoretical analyses on estimation accuracy are presented and the simulations in various scenarios are also carried out.

A New GPS System for Continuous Deformation Monitoring

This paper presents a multi-antenna GPS based system developed for local continuous deformation monitoring. Due to a large number of points that needs to be monitored, the standard approaches of using permanent GPS receiver arrays will cause high cost. It eventually becomes the limiting factor for large-scale use of GPS in these application areas. Multi-antenna GPS system allows a number of GPS antennas to be linked to one GPS receiver by a specially designed electronic component, i. e. the so-called GPS multi-antenna switch (GMS), The receiver takes data sequentially from each of the antennas attached to the receiver. A distinctive advantage of the approach is that one GPS receiver can be used to monitor more than one point. The cost per monitored point (i. e. the expenses of hardware) is therefore significantly reduced.

Combined GPS/GLONASS Data Processing

To obtain the GLONASS satellite position at an epoch other than reference time,the satellite’s equation of motion has to be integrated with broadcasting ephemerides.The iterative detecting and repairing method of cycle slips based on triple difference residuals for combined GPS/GLONASS positioning and the iterative ambiguity resolution approach suitable for combined post processing positioning are discussed systematically.Experiments show that millimeter accuracy can be achieved in short baselines with a few hours’ dual frequency or even single frequency GPS/GLONASS carrier phase observations,and the precision of dual frequency observations is distinctly higher than that of single frequency observations.

Performance Analysis of GNSS/MIMU Tight Fusion Positioning Model with Complex Scene Feature Constraints

In order to meet the requirements of high-precision vehicle positioning in complex scenes,an observation noise adaptive robust GNSS/MIMU tight fusion model based on the gain matrix is proposed considering static zero speed,non-integrity,attitude,and odometer constraint models.In this model,the robust equivalent gain matrix is constructed by the IGG-Ⅲmethod to weaken the influence of gross error,and the on-line adaptive update of observation noise matrix is carried out according to the change of actual observation environment,so as to improve the solution performance of filtering system and realize high-precision position,attitude and velocity measurement when GNSS signal is unlocked.A real test on a road over 600 km demonstrates that,in about 100 km shaded environment,the fixed rate of GNSS ambiguity resolution in the shaded road is 10%higher than that of GNSS only ambiguity resolution.For all the test,the positioning accuracy can reach the centimeter level in an open environment,better than 0.6 m in the tree shaded environment,better than 1.5 m in the three-dimensional traffic environment,and can still maintain a positioning accuracy of 0.1 m within 10 s when the satellite is unlocked in the tunnel scene.The proposal and verification of the algorithm model show that low-cost MIMU equipment can still achieve high-precision positioning when there are scene feature constraints,which can meet the problem of high-precision vehicle navigation and location in the urban complex environment.

A new approach of single epoch GPS posi- tioning for landslide monitoring

When the deformation of landslide becomes larger, the conventional static GPS surveying cannot satisfy the real-time requirement in landslide monitoring. In this paper we present a new method for single epoch GPS posi- tioning combining with the accuracy of approximate coordinates of monitored station in landslide monitoring. This algorithm does not consider troublesome cycle-slip problem of carrier phase, and integer ambiguities can be solved at a single epoch, so the centimeter level accurate coordinates can be calculated instantaneously. By means of fil- tering or smoothing, this method can be extended to detect millimeter level deformation and velocity. In order to test the new method, low-cost single frequency receivers have been used in a real landslide, which happened in Jiangxi Province, China.

A whole-net cooperative positioning method based on CDGNSS and inter-vehicle ranging

Relative positioning is recognized as an important issue for vehicles in urban environments.Multi-vehicle Cooperative Positioning(CP)techniques which fuse the Global Navigation Satellite System(GNSS)and inter-vehicle ranging have attracted attention in improving the performance of baseline estimation between vehicles.However,current CP methods estimate the baselines separately and ignore the interactions among the positioning information of different baselines.These interactions are called’information coupling’.In this work,we propose a new multivehicle precise CP framework using the coupled information in the network based on the Carrier Differential GNSS(CDGNSS)and inter-vehicle ranging.We demonstrate the benefit of the coupled information by deriving the Cramer-Rao Lower Bound(CRLB)of the float estimation in CP.To fully use this coupled information,we propose a Whole-Net CP(WN-CP)method which consists of the Whole-Net Extended Kalman Filter(WN-EKF)as the float estimation filter,and the Partial Baseline Fixing(PBF)as the ambiguity resolution part.The WN-EKF fuses the measurements of all baselines simultaneously to improve the performance of float estimation,and the PBF strategy fixes the ambiguities of the one baseline to be estimated,instead of full ambiguity resolution,to reduce the computation load of ambiguity resolution.Field tests involving four vehicles were conducted in urban environments.The results show that the proposed WN-CP method can achieve better performance and meanwhile maintain a low computation load compared to the existing methods.

Integrity monitoring of fixed ambiguity Precise Point Positioning(PPP)solutions

Traditional positioning methods,such as conventional Real Time Kinematic(cRTK)rely upon local reference networks to enable users to achieve high-accuracy positioning.The need for such relatively dense networks has significant cost implications.Precise Point Positioning(PPP)on the other hand is a positioning method capable of centimeter-level positioning without the need for such local networks,hence providing significant cost benefits especially in remote areas.This paper presents the state-of-the-art PPP method using both GPS and GLONASS measurements to estimate the float position solution before attempting to resolve GPS integer ambiguities.Integrity monitoring is carried out using the Imperial College Carrier-phase Receiver Autonomous Integrity Monitoring method.A new method to detect and exclude GPS base-satellite failures is developed.A base-satellite is a satellite whose measurements are differenced from other satellite’s measurements when using between-satellite-differenced measurements to estimate position.The failure detection and exclusion methods are tested using static GNSS data recorded by International GNSS Service stations both in static and dynamic processing modes.The results show that failure detection can be achieved in all cases tested and failure exclusion can be achieved for static cases.In the kinematic processing cases,failure exclusion is more difficult because the higher noise in the measurement residuals increases the difficulty to distinguish between failures associated with the base-satellite and other satellites.

Synthetic UWB Range Profile Using SFPTs and Class MUSIC for High-resolution Velocity Estimation

A method, called class multiple signal classification （CMUSIC）, is proposed to estimate high-resolution radial velocity in each pulse train （subband, i.e. narrowband） with M pulses based on stepped frequency pulse trains （SFPTs） signal. A synthetic ultra-wideband （UWB） high-resolution range profile （HRRP） is then obtained by fast Fourier transform （FFT） processing along the subbands after compensating the range-Doppler coupling and Doppler dispersion with the estimated velocity. Compared with the other methods, CMUSIC has fine performance of velocity estimation at low signal-to-noise ratio （SNR） level. This method also has excellent performance with small Mas long as the requirement, i.e. Mis large than Q, is able to be fulfilled, where Q is the number of targets with different radial velocities. In addition, through a radial velocity resolving, the method can be well suitable for targets moving at high radial velocities, which has significant practical value with considerable progress made in the national defence technology and the advanced vehicles moving at high speed springing up. Simulation results demonstrate the feasibility and effectiveness of the method.

A method of improving ambiguity fixing rate for post-processing kinematic GNSS data

Global Navigation Satellite System precise positioning using carrier phase measurements requires reliable ambiguity resolution.It is challenging to obtain continuous precise positions with a high ambiguity fixing rate under a wide range of dynamic scenes with a single base station,thus the positioning accuracy will be degraded seriously.The Forward-Backward Combination(FBC),a common post-processing smoothing method,is simply the weighted average of the positions of forward and backward filtering.When the ambiguity fixing rate of the one-way(forward or backward)filter is low,the FBC method usually cannot provide accurate and reliable positioning results.Consequently,this paper proposed a method to improve the accuracy of positions by integrating forward and backward AR,which combines the forward and backward ambiguities instead of positions-referred to as ambiguity domain-based integration(ADBI).The purpose of ADBI is to find a reliable correct integer ambiguities by making full use of the integer nature of ambiguities and integrating the ambiguities from the forward and backward filters.Once the integer ambiguities are determined correctly and reliably with ADBI,then the positions are updated with the fixing ambiguities constrained,in which more accurate positions with high confidence can be achieved.The effectiveness of the proposed approach is validated with airborne and car-borne dynamic experiments.The experimental results demonstrated that much better accuracy of position and higher ambiguity-fixed success rate can be achieved than the traditional post-processing method.

Performance analysis of frequency‑mixed PPP‑RTK using low‑cost GNSS chipset with different antenna configurations

Low-cost Global Navigation Satellite System(GNSS)devices offer a cost-effective alternative to traditional GNSS systems,making GNSS technology accessible to a wider range of applications.Nevertheless,low-cost GNSS devices often face the challenges in effectively capturing and tracking satellite signals,which leads to losing the observations at certain frequencies.Moreover,the observation peculiarities of low-cost devices are in contradistinction to those of traditional geodetic GNSS receivers.In this contribution,a low-cost PPP-RTK model that considers the unique characteristics of different types of measurements is developed and its performance is fully evaluated with u-blox F9P receivers equipped with three distinctive antenna configurations:vertical dipole,microstrip patch,and helix antennas.Several static and kinematic experiments in different scenarios are conducted to verify the effectiveness of the proposed method.The results indicate that the mixed-frequency PPP-RTK model outperforms the traditional dual-frequency one with higher positioning accuracy and fixing percentage.Among the three low-cost antennas tested,the vertical dipole antenna demonstrates the best performance under static conditions and shows a comparable performance as geodetic antennas with a positioning accuracy of 0.02 m,0.01 m and 0.07 m in the east,north,and up components,respectively.Under low-speed kinematic scenarios,the helix antenna outperforms the other two with a positioning accuracy of(0.07 m,0.07 m,0.34 m).Furthermore,the helix antenna is also proved to be the best choice for vehicle navigation with an ambiguity fixing rate of over 95%and a positioning accuracy of(0.13 m,0.14 m,0.36 m).