REGULARIZATION APPROACH FOR FAST INTEGER AMBIGUITY RESOLUTION OF MEDIUM-LONG BASELINE GPS NETWORK RTK

An improved method based on the Tikhonov regularization principle and the precisely known reference station coordinate is proposed to design the regularized matrix. The ill-conditioning of the normal matrix can be improved by the regularized matrix. The relative floating ambiguity can be computed only by using the data of several epochs. Combined with the LAMBDA method, the new approach can correctly and quickly fix the integer ambiguity and the success rate is 100% in experiments. Through using measured data sets from four mediumlong baselines, the new method can obtain exact ambiguities only by the Ll-frequency data of three epochs. Compared with the existing methods, the improved method can solve the ambiguities of the medium-long baseline GPS network RTK only using L1-frequency GPS data.

Research on the method of dual-frequency microwave diagnosis of plasma for solving phase integer ambiguity

In this work,microwaves and terahertz waves have performed a dual-frequency combineddiagnosis in high-temperature,large-scale plasma.According to the attenuation and phase shift of electromagnetic waves in the plasma,the electron density and collision frequency of theplasma can be inversely calculated.However,when the plasma size is large and the electron density is high,the phase shift of the electromagnetic wave is large(multiple times 2πperiod).Due to the limitations of the test equipment,the true phase shift is difficult to test accurately or to recover reality.That is,there is a problem of phase integer ambiguity.In order to obtain a phase shift of less than 180°,a higher electromagnetic wave frequency(terahertz wave with 890 GHz)is used for diagnosis.However,the attenuation of the terahertz wave diagnosis is too small(less than 0.1 d B),only the electron density can be obtained,and the collision frequency cannot be accurately obtained.Therefore,a combined diagnosis was carried out by combining twofrequencies(microwave with 36 GHz,terahertz wave with 890 GHz)to obtain electron density and collision frequency.The diagnosis result shows that the electron density is in the range of(0.65–1.5)×1019m^(-3),the collision frequency is in the range of 0.65–2 GHz,and the diagnostic accuracy is about 60%.

Research on ambiguity resolution aided with triple difference

The ambiguity resolution in the field of GPS is investigated in detail. A new algorithm to resolve the ambiguity is proposed. The algorithm first obtains the floating resolution of the ambiguity aided with triple difference measurement. Decorrelation of searching space is done by reducing the ambiguity covariance matrix＇s dimension to overcome the possible sick factorization of the matrix brought by Z-transformation. In simulation, the proposed algorithm is compared with least-squares ambiguity decorrelation adjustment （LAMBDA）. The result shows that the proposed algorithm is better than LAMBDA because of lesser resolving time, which approximately reduces 20% resolving time. Thus, the proposed algorithm adapts to the high dynamic real-time applications.

Solving single-frequency phase ambiguity using parameter weights fitting and constrained equation ambiguity resolution methods

Based on the structural characteristics of the double-differenced normal equation, a new method was proposed to resolve the ambiguity float solution through a selection of parameter weights to construct an appropriate regularized matrix, and a singular decomposition method was used to generate regularization parameters. Numerical test results suggest that the regularized ambiguity float solution is more stable and reliable than the least-squares float solution. The mean square error matrix of the new method possesses a lower correlation than the variancecovariance matrix of the least-squares estimation. The size of the ambiguity search space is reduced and the search efficiency is improved. The success rate of the integer ambiguity searching process is improved significantly when the ambiguity resolution by using constraint equation method is used to determine the correct ambiguity integervector. The ambiguity resolution by using constraint equation method requires an initial input of the ambiguity float solution candidates which are obtained from the LAMBDA method in the new method. In addition, the observation time required to fix reliable integer ambiguities can he significantly reduced.

Adaptive Robust Filtering Algorithm for BDS Medium and Long Baseline Three Carrier Ambiguity Resolution

For classical TCAR(three carrier ambiguity resolution)algorithm is affected by ionospheric delay and measurement noise,it is difficult to reliably fix ambiguity at medium and long baselines.An improved TCAR algorithm which takes the influence of ionospheric delay into account and has good adaptive robustness is proposed.On the basis of the non-geometric TCAR model,ionospheric delay is obtained by linearly combining extra-wide-lane with fixed ambiguity,and then wide-lane ambiguity is solved.Solving narrow-lane ambiguity by adaptive robust filtering by constructing optimal combination observation,which can effectively improve the fixed success rate of narrow-lane ambiguity and reduce the adverse effects of gross error.Experimental results show that the improved TCAR algorithm can guarantee a high fixed correct rate of wide-lane ambiguity,effectively improve fixed success rate of narrow-lane ambiguity,and has a good ability to resist gross error.

Information Protection Based on Extraction of Square Roots of Gaussian Integers

A cryptosystem based on computation of square roots of complex integers modulo composite n is described in this paper. This paper provides an algorithm extracting a square root of Gaussian integer. Various properties of square roots and a method for finding Gaussian generators are demonstrated. The generators can be instrumental in constructing other cryptosystems. It is shown how to significantly reduce average complexity of decryption per each block of ciphertext.

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.

一种RTK单历元整周模糊度快速确定MAXCOM-DC组合算法

本文针对传统的RTK单历元整周模糊度确定主辅频相关法(MAXCOM)观测卫星数增多导致单历元整周模糊度确定效率降低的问题,提出了一种单历元卫星分类筛选处理方法;将单历元所有卫星分类为参考星、主星和辅星,应用MAXCOM算法单历元确定主星整周模糊度和DC算法确定辅星整周模糊度,并提出了一种新的RTK单历元整周模糊度快速确定算法,称为MAXCOM-DC组合算法。对一组BDS-3实测数据900个连续观测历元进行动态定位试验,结果分析表明,MAXCOM-DC组合算法可避免在应用MAXCOM算法时辅星对主星整周模糊度搜索效率的影响,将主星数设为6时,单历元整周模糊度快速确定效率平均提升了98.5%,且单历元模糊度成功率达99.9%。本文为高采样数据单历元RTK快速定位提供了一种新算法。

A variant of raw observation approach for BDS/GNSS precise point positioning with fast integer ambiguity resolution

The Precise Point Positioning(PPP)technique uses a single Global Navigation Satellite System(GNSS)receiver to collect carrier-phase and code observations and perform centimeter-accuracy positioning together with the precise satellite orbit and clock corrections provided.According to the observations used,there are basically two approaches,namely,the ionosphere-free combination approach and the raw observation approach.The former eliminates the ionosphere effects in the observation domain,while the latter estimates the ionosphere effects using uncombined and undifferenced observations,i.e.,so-called raw observations.These traditional techniques do not fix carrier-phase ambiguities to integers,if the additional corrections of satellite hardware biases are not provided to the users.To derive the corrections of hardware biases in network side,the ionosphere-free combination operation is often used to obtain the ionosphere-free ambiguities from the L1 and L2 ones produced even with the raw observation approach in earlier studies.This contribution introduces a variant of the raw observation approach that does not use any ionosphere-free(or narrow-lane)combination operator to derive satellite hardware bias and compute PPP ambiguity float and fixed solution.The reparameterization and the manipulation of design matrix coefficients are described.A computational procedure is developed to derive the satellite hardware biases on WL and L1 directly.The PPP ambiguity-fixed solutions are obtained also directly with WL/L1 integer ambiguity resolutions.The proposed method is applied to process the data of a GNSS network covering a large part of China.We produce the satellite biases of BeiDou,GPS and Galileo.The results demonstrate that both accuracy and convergence are significantly improved with integer ambiguity resolution.The BeiDou contributions on accuracy and convergence are also assessed.It is disclosed for the first time that BeiDou only ambiguity-fixed solutions achieve the similar accuracy with that of GPS/Galileo combined,at least in China's Mainland.The numerical analysis demonstrates that the best solutions are achieved by GPS/Galileo/BeiDou solutions.The accuracy in horizontal components is better than 6 mm,and in the height component better than 20 mm(one sigma).The mean convergence time for reliable ambiguity-fixing is about 1.37 min with 0.12 min standard deviation among stations without using ionosphere corrections and the third frequency measurements.The contribution of BDS is numerically highlighted.

基于改进蝴蝶搜索算法的DGPS整周模糊度快速解算

为了快速准确地解算差分全球定位系统(DGPS)整周模糊度,提出了一种改进蝴蝶搜索算法(IBOA)求解整周模糊度。首先在蝴蝶优化算法(BOA)的香味系数中加入一个自适应权重,弥补BOA算法觅食行为中较弱的搜索能力;其次使用动态切换概率权衡BOA算法中全局搜索与局部搜索的比例;最后在全局搜索和局部搜索阶段引入新的迭代位置更新策略,提升了算法全局搜索能力和跳出局部最优能力。与最小二乘模糊度降相关平差算法(LAMBDA)算法进行1000个历元数据的解算对比实验,结果表明所提算法的平均搜索成功率比LAMBDA算法提高了5.07%。

基于PSO与AFSA的GNSS整周模糊度种群融合优化算法

载波相位测量是实现全球导航卫星系统(Global navigation satellite system, GNSS)快速高精度定位的重要途径,而准确解算整周模糊度是其中的关键步骤之一.粒子群算法(Particle swarm optimization, PSO)收敛速度快但易陷入局部最优,人工鱼群算法(Artificial fish swarm algorithm, AFSA)全局优化性能好但收敛速度慢,因此融合两种算法的优点,提出一种GNSS整周模糊度种群融合优化算法(PSOAF).首先,通过载波相位双差方程求解整周模糊度的浮点解和对应的协方差矩阵.然后,采用反整数Cholesky算法对模糊度浮点解作降相关处理.其次,针对整数最小二乘估计的不足通过优化适应度函数来提高算法的收敛性和搜索性能.最后,通过PSOAF算法对整周模糊度进行解算.通过经典算例和试验研究表明:PSOAF算法可以更快地收敛于最优解,搜索效率也更为出色,解算的基线精度可以控制在10 mm以内,在短基线的实际情况下具有较高的应用价值.

约束双差整周模糊度的GNSS单差载波相位时间比对方法

GNSS时间比对是目前应用最为广泛的时间比对方法.虽然GNSS单差载波相位时间比对技术的性能会随着基线长度的增加而恶化,但是在短基线条件下该技术在时间比对精度和收敛时间方面仍具有明显的优势.传统GNSS单差载波相位时间比对技术需要使用双频观测值完成单差模糊度的固定,为了能够在仅使用单频观测值的条件下实现高精度的时间比对,本文提出了约束双差整周模糊度的GNSS单差载波相位时间比对方法.该方法通过约束双差整周模糊度减小待估计参数的维度,进而提高单差模糊度浮点解的估计精度.实测结果表明,本文所提方法的时间比对精度可达到0.03 ns,并且能够在100 s左右使时间比对误差收敛到0.2 ns以内,适合近距离条件下要求高精度快速时间同步的应用领域.

基于载波相位的视距内动态无线时间比对关键技术研究

针对视距内动态时间比对用伪距观测量解算钟差噪声较大的问题,用载波相位观测量可以大幅度减小解算钟差的噪声,但载波相位存在求解整周模糊度和周跳等问题。本文首先研究了双向伪距和载波相位测量原理以及配对解算钟差的方法,并提出了一种采样提取双向载波相位观测量的新方法,减小了双向载波相位因采样时刻不一致导致的链路非对称对钟差测量结果的影响。针对载波相位双向时间比对中整周模糊度的求解和周跳探测与修正2个技术难点,用改进的伪距法估算整周模糊度,并用卡尔曼滤波实时的探测修正周跳。最后搭建车载试验平台验证动态时间比对效果,载波相位相较于伪距双向时间比对的精度提升了71.3%,测量钟差的均方根误差达到了百皮秒量级。

基于天牛须种群算法的整周模糊度解算算法

如何快速、准确地固定整周模糊度是载波相位测量中的一个关键问题。为了提高整周模糊度搜索速率,提出了一种基于天牛须种群算法(beetle antennae colony search, BACS)的整周模糊度解算算法。通过与BAS算法、BAS-Nadam算法、LAMBDA算法以及MLAMBDA算法进行解算速率、稳定性的对比实验,在三维模糊度解算时,BACS算法在与LAMBDA和MLAMBDA算法解算成功率相当的情况下,能利用更少的时间搜索到模糊度最优解。为了验证BACS算法在高维模糊度解算以及工程解算情况下是否适用,进行了高维模糊度解算的实验以及单频单GPS系统下BACS算法的应用实验。分析及实验表明,BACS算法能很好保证高维模糊度解算的实时性和鲁棒性,对于12维模糊度解算,平均解算时间0.068 s,解算成功率为92%,对于低维模糊度解算,解算速率更快,解算成功率更高。在单频单GPS系统工程解算中,x、y、z方向定位精度分别为±0.008、±0.01、±0.01 m,能达到厘米级精度定位。

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%.

基于C-LAMBDA算法的GNSS相对定位增强方法

针对相对定位场景下载体天线间先验基线信息利用不充分问题,提出基于约束的最小二乘模糊度降相关平差算法(C-LAMBDA)的全球卫星导航系统(GNSS)相对定位增强方法:对于双天线载体,采用C-LAMBDA算法进行基线长度约束的定向解算,将求解得到的模糊度向量和基线矢量作为先验信息融入相对定位观测方程,从而将基线长度先验信息辅助提升解算效果的先天优势从测姿领域扩展到相对定位领域,由此给出基于C-LAMBDA算法的GNSS相对定位增强模型;通过推导相对定位增强模型糊度精度因子(ADOP)与传统单天线载体相对定位模型ADOP的数学关系,从理论上揭示了增强模型对于模糊度浮点解精度的提升作用。仿真与实测试验结果表明,与传统单天线载体相对定位相比,该方法在不同可视卫星数观测条件下均能够提高模糊度浮点解的精度,有效提升模糊度解算成功率,从而增强相对定位的可靠性。

GPS单历元双差整周模糊度确定主辅频相关算法研究

针对GPS现代化增加的L_(5)频率观测值,提出一种GPS单历元双差整周模糊度确定新算法,称为GPS主辅频相关算法。该算法仅采用GPS单历元数据的伪距观测值及主频率与辅频率的相位观测值,通过扩展双频相关法思想,将L_(1)设为主频率、L_(2)或L_(5)选为辅频率,建立GPS主频率与辅频率的双差相位观测值内在相关关系模型,在观测值平差值域和模糊度值域作交叉搜索,并利用Ratio显著性检验法单历元确认GPS主频率双差整周模糊度。算例表明,针对GPS现代化后可观测的L_(1)、L_(2)和L_(5)三种原始相位观测值,优选L_(5)为算法辅频率在模糊度解算效率及成功率上均略优于L_(2),本文算法是行之有效的。

一种提高模糊度解算成功率的新方法——优选拟合因子获取最大Ratio值

模糊度整数解高效高成功率的固定算法是实现GNSS快速甚至实时精密定位的关键技术,而Ratio检验是判定最优模糊度整数解可靠性的技术指标之一.为提高模糊度解算的可靠性和成功率,本文在基于选权拟合法求解模糊度的基础上,提出了一种提高模糊度解算成功率的新策略,即利用优选选权拟合因子值来获取较大Ratio值,并选取最大的Ratio值对应的整数解为最可靠解.理论分析和实验结果显示,该方法虽然会影响计算效率,但能显著地提高模糊度整数解固定的可靠性和成功率,实现双频观测短基线单历元模糊度解算成功率99.96%以上.新算法能促进精密的动态实时定位技术拓展应用.

网络RTK参考站间模糊度动态解算的卡尔曼滤波算法研究

提出一种适用于参考站网络的站间模糊度解算方法,该方法使用CA码与相位的电离层无关组合解算宽巷模糊度,利用多路径效应的周期性削弱CA码多路径效应。在宽巷模糊度得到固定后,利用卡尔曼滤波对L1模糊度进行估计,并使用模糊度失相关搜索算法,动态地确定模糊度。这种方法已经应用在自主开发的网络RTK软件上,并以四川GPS综合服务网络SIGN(Sichuan Integrated GPS Network)作为试验网络,进行了试验和分析。

LAMBDA整周模糊度解算方法中的整数Z变换算法

利用整数Z变换对高度相关的整周模糊度进行降相关,是LAMBDA算法的核心之一。阐述了联合去相关法和迭代法两种整数Z变换算法的基本原理及具体实现过程,通过实际算例从条件数、去相关数等方面对其降相关性能进行了评估和分析,结果表明两种算法去相关水平相当,迭代次数上也无明显差异,总体上讲联合去相关法的处理成功率高于迭代法。