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%.

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.

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 variance- covariance 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 integer- vector. 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 be 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.

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。

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.

不同截止高度角下天线阵列RTK定位分析

针对天线阵列实时动态(RTK)的定位性能评估问题,将天线阵列RTK的数学模型与RTK的数学模型进行对比分析,并在不同截止高度角下采用天线阵列RTK与RTK对一组静态实测数据进行单历元解算.结果表明:相较于RTK,天线阵列RTK能够增加双差观测方程的冗余度从而增加模型强度,达到提高模糊度固定成功率与定位精度的效果.基于GPS+北斗卫星导航系统(BDS)组合的天线阵列RTK在50°大截止高度角下,其模糊度固定成功率达到93.6%,并且固定解水平精度优于1 cm、高程精度优于2 cm,能够满足高精度定位需求,进一步提高了RTK在城市峡谷等环境中的适用性.

BDS-2/BDS-3非组合观测模型的中距离相对定位

为了弥补北斗三号全球卫星导航系统(BDS-3)全星座、多频率相对定位以及组合定位方式相关研究的不足,提出一种BDS-2/BDS-3非组合观测模型的中距离相对定位方法:对BDS-3四频和北斗卫星导航(区域)系统(BDS-2)/BDS-3组合双频观测数据,采用多频载波相位观测数据非组合模型进行相对定位解算;分析BDS-2/BDS-3组合的定位性能,并与BDS-2三频、全球定位系统(GPS)双频解算结果进行对比;然后选取4条不同长度基线进行不同系统相对定位解算,对54km基线充分考虑大气延迟误差的影响,并对定位性能进行分析。实验结果表明,BDS-3收敛速度相较于BDS-2有一倍的提升,并略优于GPS,定位精度相较BDS-2可提升大约40%,但略低于GPS;BDS-2/BDS-3组合模式收敛速度最快、定位精度最高,相较GPS在天顶(U)方向可有8.3%的提升,与BDS-3相比在U方向可有22.1%的提升;BDS-2/BDS-3双频组合定位性能优于GPS、BDS-2和BDS-3多频定位结果。

CDMA+FDMA非差非组合区域PPP-RTK

为顺应多频多模发展趋势,PPP-RTK技术正逐步由传统的消电离层组合数据处理模式发展为非差非组合模式。现有非差非组合PPP-RTK研究多针对码分多址(CDMA)系统,而频分多址(FDMA)PPP-RTK受频率间偏差的影响难以实现。本文针对区域参考网,提出了一种CDMA+FDMA多系统非差非组合PPP-RTK模型,该模型能灵活处理多频多模两类信号体制的数据。为了实现FDMA PPP-RTK,本文利用整数可估理论保证了模糊度固定的严密性,该FDMA PPP-RTK模型适用于同款接收机的参考网。本文采集了香港地区连续运行参考网的GPS、BDS、Galileo、GLONASS数据进行试验,数据采样率为30 s。服务端结果表明,由于各产品之间高度相关,对组合产品进行精度评估是有必要的。组合卫星钟差、卫星相位偏差和电离层产品后,精度达到毫米级,满足用户精密改正的要求。用户端仿动态定位结果表明,GPS、BDS和Galileo单系统PPP-RTK分别在5、1和3 min实现了模糊度首次固定,定位误差收敛至厘米级。GLONASS组合GPS实现了首历元模糊度固定,定位精度比GPS单系统提升了9%、12%、14%(东、北、天3个方向)。BDS组合GPS同样能实现首历元模糊度固定,定位精度比GPS单系统提升了29%、22%、18%,额外加入Galileo观测值,定位精度进一步提升了12%、8%、16%。再加入GLONASS观测值,定位精度仍有小幅提升(4%、3%、8%)。

一种用于DGPS整周模糊度解算的混合策略麻雀搜索算法

针对麻雀搜索算法(SSA)在计算差分全球定位系统(DGPS)整周模糊度过程中出现的全局搜索能力弱、易陷入局部最优等问题,提出了混合策略麻雀搜索算法(HSSSA)。首先,通过引入Circle混沌映射初始化种群,提高初始种群的多样性,增强算法的全局寻优能力;其次,将粒子群算法中各个粒子的速度策略引入发现者位置更新公式中,提升算法寻优能力;最后,使用高斯变异策略对最优麻雀位置进行扰动,增强了跳出局部最优的能力。将所提算法应用于9个不同特征的基准函数进行实验,结果表明,HSSSA算法有着良好的寻优精度和收敛速度。在GPS/BDS实测数据的3000个历元的解算中,相比传统LAMBDA算法和SSA算法,HSSSA算法有着更高的解算成功率,可达99.2%。

BDS-2/BDS-3组合长基线三频RTK算法

针对在长基线动态实时差分定位技术(RTK)中,由于整周模糊度容易受到大气延迟误差的影响,导致其固定率偏低,从而影响定位精度的问题,提出一种基于北斗卫星导航(区域)系统即北斗二号(BDS-2)和北斗三号全球卫星导航系统(BDS-3)组合的长基线定位方法:组合方法中BDS-2采用B1I、B2I和B3I 3种信号,BDS-3采用B1I、B2b和B3I 3种信号,充分利用三频中存在电离层延迟极小且具有整数特性的组合,同时考虑对流层延迟的影响,建立基于弱电离层组合的几何相关中长基线解算模型,并利用卡尔曼(Kalman)模型对天顶对流层延迟误差、三维坐标和弱电离层组合模糊度进行参数估计;再结合部分模糊度固定方法加快模糊度搜索效率,最终实现长基线RTK定位。实验结果表明,该方法能够在长基线下基本实现单历元模糊度固定,定位结果与流动站真值之间的定位偏差可达到厘米级。

测量精度约束的模糊度搜索定位算法

为了快速且准确地固定整周模糊度,针对LAMBDA算法存在整周模糊度搜索范围过广、搜索效率低等问题,提出一种基于测量精度约束的模糊度搜索算法。该算法在最小二乘问题得到最佳加权的情况下,以标准差分进化(DE)算法为基础、载波相位测量精度为约束条件进行模糊度固定解的检验。该算法解决了不同卫星高度角产生的影响,在解算三维整周模糊度时能够达到99%的解算成功率。相比于MLAMBDA、DE、自适应加权的差分进化(AWDE)算法,该算法进一步提高了模糊度的解算效率和成功率。

GPS/Galileo双系统三频实时PPP固定解性能分析

针对实时精密单点定位模糊度解算方法未能较好兼容多频多系统GNSS观测数据这一问题,提出了一种双系统三频GNSS实时PPP模糊度解算方法,实现了GPS/Galileo双系统三频实时PPP固定解.实验结果表明,GPS/Galileo双系统三频实时PPP固定解平均首次固定时间为19.3 min,首次固定时在E、N和U方向上定位精度分别可达到3.0、2.5和3.2 cm,相比单GPS三频实时PPP固定解,首次固定时间可缩短23.2%,首次固定时E、N和U方向上定位精度可分别提高约11.8%、13.8%和13.5%.

多基准站相对定位算法及先验基线向量偏差影响分析

为提高单基准站短基线相对定位解算的可靠性,研究了多基准站约束的相对定位算法。将基准站间可提前测量的先验基线信息融入观测模型中,给出了多基准站相对定位的函数模型和随机模型,在此基础上推导了模糊度精度因子的解析表达式,揭示了基准站数量的增加对模糊度浮点解精度提升的作用;从理论上分析了基准站间先验基线信息中的偏差对模糊度解算的影响,分析表明,当先验基线各分量偏差的绝对值之和小于5 cm时,模糊度解算几乎不受影响;通过仿真和实测数据进行了验证。试验结果表明,增加基准站数量不仅能有效提升模糊度解算成功率和收敛速度,并且对先验基线信息中的偏差具有较好的抑制作用,当基线各分量偏差均增加到4 cm时,实测数据模糊度解算成功率仍能达到92%以上。研究结论为特殊场景下多基准站间的快速非精确标定提供了理论依据。

RTK在不同场景下的定位精度分析

重点论述了RTK定位的基本原理,着重介绍几种定位精度的影响因素,并通过案例分析和总结了各类因素对RTK定位精度的影响情况,从而大致了解GNSS的定位水平,其成果在一定程度上对CORS系统的建立起到了重要的参考作用。