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1.
On lattice reduction algorithms for solving weighted integer least squares problems: comparative study 总被引：2，自引：1，他引：1
Decorrelation or reduction theory deals with identifying appropriate lattice bases that aid in accelerating integer search to find the optimal integer solution of the weighted integer least squares problem. Orthogonality defect has been widely used to measure the degree of orthogonality of the reduced lattice bases for many years. This contribution presents an upper bound for the number of integer candidates in the integer search process. This upper bound is shown to be a product of three factors: (1) the orthogonality defect, (2) the absolute value of the determinant of the inverse of the generator matrix of the lattice, and (3) the radius of the search space raised to the power of the dimension of the integer ambiguity vector. Four well-known decorrelation algorithms, namely LLL, LAMBDA, MLAMBDA, and Seysen, are compared. Many simulated data with varying condition numbers and dimensions as well as real GPS data show that the Seysen reduction algorithm reduces the condition number much better than the other algorithms. Also, the number of integer candidates, before and after the reduction process, is counted for all algorithms. Comparing the number of integer candidates, condition numbers, and orthogonality defect reveals that reducing the condition number and the orthogonality defect may not necessarily result in decreasing the number of integer candidates in the search process. Therefore, contrary to the common belief, reducing the orthogonality defect and condition number do not always result in faster integer least squares estimation. The results indicate that LAMBDA and MLAMBDA perform much better in reducing the number of integer candidates than the other two algorithms, despite having a larger orthogonality defect and condition number in some cases. Therefore, these two algorithms can speed up the integer least squares estimation problem in general and the integer ambiguity resolution problem in particular. 相似文献
2.
Fast integer least-squares estimation for GNSS high-dimensional ambiguity resolution using lattice theory 总被引：4，自引：0，他引：4
GNSS ambiguity resolution is the key issue in the high-precision relative geodetic positioning and navigation applications.
It is a problem of integer programming plus integer quality evaluation. Different integer search estimation methods have been
proposed for the integer solution of ambiguity resolution. Slow rate of convergence is the main obstacle to the existing methods
where tens of ambiguities are involved. Herein, integer search estimation for the GNSS ambiguity resolution based on the lattice
theory is proposed. It is mathematically shown that the closest lattice point problem is the same as the integer least-squares
(ILS) estimation problem and that the lattice reduction speeds up searching process. We have implemented three integer search
strategies: Agrell, Eriksson, Vardy, Zeger (AEVZ), modification of Schnorr–Euchner enumeration (M-SE) and modification of
Viterbo-Boutros enumeration (M-VB). The methods have been numerically implemented in several simulated examples under different
scenarios and over 100 independent runs. The decorrelation process (or unimodular transformations) has been first used to
transform the original ILS problem to a new one in all simulations. We have then applied different search algorithms to the
transformed ILS problem. The numerical simulations have shown that AEVZ, M-SE, and M-VB are about 320, 120 and 50 times faster
than LAMBDA, respectively, for a search space of dimension 40. This number could change to about 350, 160 and 60 for dimension
45. The AEVZ is shown to be faster than MLAMBDA by a factor of 5. Similar conclusions could be made using the application
of the proposed algorithms to the real GPS data. 相似文献
3.
Since its introduction in 1993, the LAMBDA method has found widespread use across the world. The method has been employed
in many geodetic and navigation applications, with lots of satisfied users. Independent tests show that it is considered the
best method for integer carrier phase ambiguity resolution available. But every now and then we still notice some misunderstandings
concerning the principles and potential of the method. In this contribution we will briefly summarize the principles underlying
the LAMBDA method, go into some of the frequently asked questions on the LAMBDA method and try to clarify some of the existing
misunderstandings.
Electronic Publication 相似文献
4.
5.
用LAMBDA改进算法固定GPS整周模糊度 总被引：1，自引：0，他引：1
介绍了LAMBDA算法原理，结合国土资源调查的工程实践，对常规的LAMBDA方法作了两点改进，即扩大超椭球的体积En和以点位的先验信息检验坐标解算结果。实测数据分析表明，两点改进均能有效地提高基线解算的可靠性，具有一定的理论价值。 相似文献
6.
本文提出了一种改进LAMBDA方法:在确定Z变换后的模糊度时,改变以往对所有历元的模糊度全部进行搜索的做法,而是通过设置合理的条件,将搜索与直接归整有效地结合起来,从而减少了模糊度的解算时间,提高了解的效率。文章最后利用实测GPS数据验证了改进效果。 相似文献
7.
单频GPS快速定位中病态问题的解法研究 总被引：20，自引：3，他引：17
研究只利用少数历元GPS载波相位观测值进行快速定位时的新解法.在分析病态法矩阵结构特性的基础上,基于TIKHONOV正则化原理,提出一种选择正则化矩阵R的新方法,减弱法方程的病态性.与其他方法相比,新方法得到与模糊度准确值更接近的浮动解及其相应的均方误差矩阵.结合LAMBDA方法,用均方误差矩阵代替协方差阵确定模糊度的搜索范围,可准确快速地确定模糊度,最后得到基线向量的解.结合算例,将新解法与最小二乘估计、岭估计和截断奇异值法分别结合LAMBDA方法解算模糊度的结果进行比较分析,展示新解法的效果. 相似文献
8.
下三角Cholesky分解的整数高斯变换算法 总被引：1，自引：0，他引：1
针对全球导航卫星系统(GNSS)载波相位测量中,基于整数最小二乘估计准则解算整周模糊度问题。目前以LAMBDA降相关算法和Lenstra-Lenstra-Lovász(LLL)为代表的规约算法应用最为广泛。由于不同算法采用的模糊度方差-协方差阵的分解方式不同,导致难以合理地进行不同算法性能的比较。该文通过分析LAMBDA算法的降相关特点,从理论上推出基于下三角Cholesky分解多维情形下的整数高斯变换的降相关条件及相应公式,并与分解方式不同的LAMBDA和LLL算法作了对比。实验结果表明,降相关采用的分解方式将会直接影响计算复杂度和解算性能,因此该文推导的整数高斯变换算法便于今后基于下三角Cholesky分解的降相关算法间的合理比较。 相似文献
9.
基于整周模糊度概率特性的有效性检验 总被引：1，自引：0，他引：1
准确确定载波相位整周模糊度是快速高精度GPS定位的关键,已有的检验GPS整周模糊度有效性的方法几乎均是基于其为非随机常量建立的,因而都存在一定的缺陷。本文在研究整周模糊度概率特性的基础上,提出一种基于LABMBAD算法的整周模糊度概率分布函数的检验方法。实际演算表明该方法简单有效,统计概念明确。 相似文献
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Partial integer decorrelation: optimum trade-off between variance reduction and bias amplification 总被引：2，自引：2，他引：0
Different techniques have been developed for determining carrier phase ambiguities, ranging from float approximations to the
efficient solution of the integer least square problem by the LAMBDA method. The focus so far was on double-differenced measurements.
Practical implementations of the LAMBDA method lead to a residual probability of wrong fixing of the order one percent. For
safety critical applications, this probability had to be reduced by eight orders of magnitude, which could be achieved by
linear multi-frequency code–carrier combinations. Scenarios with single or no differences include biases due to orbit errors,
satellite clock offsets, as well as residual code and phase biases. For this case, a linear combination of Galileo E1 and
E5 code and carrier phase measurements with a wavelength of 3.285 m and a noise level of a few centimeters is derived. This
ionosphere-free combination preserves the orbit and clock errors, and suppresses the E1 code multipath by 12.6 dB. Since integer
decorrelation transformations, as used in the LAMBDA method, inflate biases, the number of such transformations must be limited,
and applied in a judicious order. With a Galileo type constellation, this leads to a vertical standard deviation of ca. 20 cm,
while keeping the probability of wrong fixing extremely low for code biases of 10 cm, and phase biases of 0.1 cycle, combined
in a worst case. 相似文献
12.
Precise GRACE baseline determination using GPS 总被引：13，自引：1，他引：13
Precision relative navigation is an essential aspect of spacecraft formation flying missions, both from an operational and a scientific point of view. When using GPS as a relative distance sensor, dual-frequency receivers are required for high accuracy at large inter-satellite separations. This allows for a correction of the relative ionospheric path delay and enables double difference integer ambiguity resolution. Although kinematic relative positioning techniques demonstrate promising results for hardware-in-the-loop simulations, they were found to lack an adequate robustness in real-world applications. To overcome this limitation, an extended Kalman Filter modeling the relative spacecraft dynamics has been developed. The filter processes single difference GPS pseudorange and carrier phase observations to estimate the relative position and velocity along with empirical accelerations and carrier phase ambiguities. In parallel, double difference carrier phase ambiguities are resolved on both frequencies using the least square ambiguity decorrelation adjustment (LAMBDA) method in order to fully exploit the inherent measurement accuracy. The combination of reduced dynamic filtering with the LAMBDA method results in smooth relative position estimates as well as fast and reliable ambiguity resolution. The proposed method has been validated with data from the gravity recovery and climate experiment (GRACE) mission. For an 11-day data arc, the resulting solution matches the GRACE K-Band Ranging System measurements with an accuracy of 1 mm, whereby 83% of the double difference ambiguities are resolved. 相似文献
13.
The Indian Regional Navigation Satellite System (IRNSS) has recently (May 2016) reached its full operational capability. In this contribution, we provide the very first L5 attitude determination analyses of the fully operational IRNSS as a standalone system and also in combination with the fully operational GPS Block IIF along with the corresponding ambiguity resolution results. Our analyses are carried out for both a linear array of two antennas and a planar array of three antennas at Curtin University, Perth, Australia. We study the noise characteristics (carrier-to-noise density, measurement precision, time correlation), the integer ambiguity resolution performance (LAMBDA, MC-LAMBDA) and the attitude determination performance (ambiguity float and ambiguity fixed). A prerequisite for precise and fast IRNSS attitude determination is the successful resolution of the double-differenced integer carrier-phase ambiguities. In this contribution, we will compare the performance of the unconstrained and the multivariate-constrained LAMBDA method. It is therefore also shown what improvements are achieved when the known body geometry of the antenna array is rigorously incorporated into the ambiguity objective function. As our ambiguity-fixed outcomes show consistency between empirical and formal results, we also formally assess the precise attitude determination performance for several locations within the IRNSS service area. 相似文献
14.
单频GPS快速定位方程是严重病态的,应用最小二乘原理得到的模糊度浮点解大大偏离其准确值,应用LAMBDA方法难以正确地固定模糊度。本文将GPS载波相位双差观测量在不同的小波空间和尺度空间进行分解和重构,去除高频测量噪声,可减小测量噪声对GPS快速定位中病态方程解的影响,提高模糊度浮点解的精度,缩小模糊度搜索空间。实验表明,对于GPS短基线,仅利用1min左右的单频载波观测数据,经过基于haar、db4、coif4和sym4小波的5尺度小波变换后,可获得较准确的模糊度浮点解,应用LAMBDA法可正确地固定模糊度,达到厘米级定位精度。 相似文献
15.
16.
利用两种z变换算法的PS-DInSAR相位解缠与等价性证明 总被引：1，自引：1，他引：0
在介绍PS-DInSAR相位解缠函数模型的基础上,给出了应用LAMBDA方法求解模糊度和形变参数的过程,并将两种改进的z变换降相关算法——逆整乔列斯基和LLL应用于PS-DInSAR相位解缠。以z变换过程的迭代次数、z变换后的模糊度向量间的平均相关系数和协因数阵的谱条件数为准则,对两种算法进行仿真模拟和分析,结果表明逆整乔列斯基算法和LLL算法等价。最后从理论上对两种降相关算法的一致性进行了解释。 相似文献
17.
GPS快速定位方程的病态性对整周模糊度及基线解的影响 总被引：2，自引：0，他引：2
GPS快速定位的数据处理一般是基于整数最小二乘理论,参数估计通过浮点解、整周模糊度的搜索、固定解三个步骤实现。当观测时间较短时,观测量间具有较强的相关性,用LS估计未知数的法方程严重病态,导致模糊度及基线浮点解与其正确值差距较大。本文通过实例研究了不同观测时间的GPS快速定位方程的病态性程度及其对模糊度和基线解的影响,计算结果表明当观测时间少于2分钟时,采用LS结合LAMBDA法难以求出可靠的固定解。 相似文献
18.
The network-based real-time kinematic (RTK) positioning has been widely used for high-accuracy applications. However, the precise point positioning (PPP) technique can also achieve centimeter to decimeter kinematic positioning accuracy without restriction of inter-station distances but is not as popular as network RTK for real-time engineering applications. Typically, PPP requires a long initialization time and continuous satellite signals to maintain the high accuracy. In case of phase breaks or loss of signals, re-initialization is usually required. An approach of instantaneous cycle slips fixing using undifferenced carrier phase measurements is proposed, which leads to instantaneous re-initialization for real-time PPP. In the proposed approach, various errors such as real-time orbit and clock errors, atmosphere delay and wind-up effects are first refined and isolated from integer cycle slips. The integer values of cycle slips can then be estimated and fixed with the LAMBDA technique by applying a cascade cycle slip resolution strategy. Numerical experiments with different user dynamics are carried out to allow a comprehensive evaluation of efficiency and robustness of the cycle slip fixing algorithm. The results show that the cycle slips can be fixed correctly in all cases considered and that data gaps of up to 300?s can be connected with high confidence. As a result, instantaneous re-initialization is achieved in the real-time PPP processing. 相似文献
19.
In the context of ambiguity resolution (AR) of global navigation satellite systems (GNSS), decorrelation among entries of an ambiguity vector, integer ambiguity search, and ambiguity validations are three standard procedures for solving integer least-squares problems. This paper contributes to AR issues from three aspects. Firstly, the orthogonality defect is introduced as a new measure of the performance of ambiguity decorrelation methods and compared with the decorrelation number and with the condition number, which are currently used as the judging criterion to measure the correlation of ambiguity variance–covariance matrix. Numerically, the orthogonality defect demonstrates slightly better performance as a measure of the correlation between decorrelation impact and computational efficiency than the condition number measure. Secondly, the paper examines the relationship of the decorrelation number, the condition number, the orthogonality defect, and the size of the ambiguity search space with the ambiguity search candidates and search nodes. The size of the ambiguity search space can be properly estimated if the ambiguity matrix is decorrelated well, which is shown to be a significant parameter in the ambiguity search progress. Thirdly, a new ambiguity resolution scheme is proposed to improve ambiguity search efficiency through the control of the size of the ambiguity search space. The new AR scheme combines the LAMBDA search and validation procedures together, which results in a much smaller size of the search space and higher computational efficiency while retaining the same AR validation outcomes. In fact, the new scheme can deal with the case there are only one candidate, while the existing search methods require at least two candidates. If there are more than one candidate, the new scheme turns to the usual ratio-test procedure. Experimental results indicate that this combined method can indeed improve ambiguity search efficiency for both the single constellation and dual constellations, respectively, showing the potential for processing high-dimension integer parameters in multi-GNSS environment. 相似文献
20.
单频GPS短基线快速定位中的少数历元算法 总被引：2，自引：0，他引：2
研究了短基线时利用少数历元的单频GPS载波相位观测值进行快速定位的一种算法。基于TIK-HONOV正则化原理，选择了一种具有物理意义的正则化矩阵，以减弱法矩阵的病态性。新算法只需解算几个历元的单频GPS相位数据，就可得到比较准确的模糊度浮动解及其相应的均方误差矩阵，用均方误差矩阵代替协方差阵，结合LAMBDA方法，可准确、快速地确定模糊度，最后得到基线向量的解。结合短基线算例，将少数历元算法与最小二乘估计的结果作了比较分析，得出了新解法的有效性。 相似文献