共查询到16条相似文献，搜索用时 109 毫秒
1.
改进的GPS模糊度降相关LLL算法 总被引：2，自引：1，他引：1
模糊度降相关技术可以有效提高模糊度求解的效率及成功率,LLL(A.K.Lenstra,H.W.Lenstra,L.Lovasz)算法是新出现的模糊度降相关方法。详细分析LLL算法,针对该算法中存在的缺陷,提出逆整数乔勒斯基、整数高斯算法和升序调整矩阵辅助的改进LLL算法。利用谱条件数及平均相关系数为准则,以300个随机模拟的对称正定矩阵作为模糊度方差-协方差矩阵,对LLL算法和改进的LLL算法进行仿真计算。比较与分析结果表明,改进LLL算法模糊度降相关处理更加彻底,能有效地加速整周模糊度搜索及成功解算。 相似文献
2.
由于多频多模GNSS观测数据解算的模糊度具有较高的维数和精度,当采用常规的LLL算法进行模糊度整数估计时,规约耗时显著大于搜索耗时,成为限制高维模糊度解算计算效率的主要因素。针对这一问题,通过分析规约耗时与模糊度维数和精度之间的关系,提出了一种LLL分块处理算法。该算法通过对模糊度方差协方差阵进行分块处理,降低单个规约矩阵的维数,以减少规约耗时,从而提高模糊度解算计算效率。通过两组实测高维模糊度数据对本文提出的分块处理算法进行了效果验证。结果显示,当分块选择合理时,本文提出的算法相对于LLL算法的解算效率分别可提高65.2%和60.2%。 相似文献
3.
模糊度降相关的整数分块正交化算法 总被引：1，自引：1，他引：0
随着模糊度实数解协方差矩阵维数的增加,由于取整运算舍入误差的影响,LLL降相关算法的成功率低、降相关效果差。本文引入分块正交的思想,设计了整数分块Gram-Schmidt正交化算法,同时联合LLL算法提出了基于整数分块正交化的LLL降相关算法（IBGS-LLL）。利用随机模拟的方法,分析了不同维数下不同分块方式的降相关效果,明确了不同模式下算法的分块方式。在动态和静态模式下与改进的LLL算法进行了比较,证明了IBGS-LLL算法在模糊度协方差矩阵降相关方面具有更优的效果和更高的成功率。 相似文献
4.
针对差分全球定位系统(DGPS)模糊度解算过程中效率低,搜索慢的问题,对鸡群优化算法(CSO)进行适应性改进,并将改进后的鸡群优化算法(ICSO)应用到整周模糊度的快速解算中,利用卡尔曼滤波求出双差模糊度的浮点解和协方差矩阵,采用Lenstra-Lenstra-Lovasz (LLL)降相关算法对模糊度的浮点解和方差协方差矩阵进行降相关处理,以降低模糊度各分量之间的相关性,在基线长度固定的情况下,利用ICSO搜索整周模糊度的最优解. 采用经典算例进行仿真,仿真结果表明,与已有文献相比在整周模糊度的解算过程中改进的鸡群优化算法能有效提高搜索速度和求解成功率. 相似文献
5.
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
6.
在GNSS模糊度解算的过程中,由于模糊度之间存在相关性,为减少搜索时间需要对模糊度的协方差矩阵进行降相关处理。降相关算法的优劣将直接影响到模糊度搜索的效率。本文基于Householder正交变换提出了一种新的降相关算法,并利用随机模拟数据和北斗实测数据,从谱条件数、平均相关系数和规约时间3个方面将Householder算法与目前较为流行的LLL算法以及逆整数Cholesky算法进行了对比。通过实验分析得出,Householder算法能够明显改善降相关处理的效果。但是该算法仍存在规约时间较长的不足,需要进一步完善。 相似文献
7.
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.
《武汉大学学报(信息科学版)》2016,(8)
针对Lenstra-Lenstra-Lovász(LLL)规约算法在高维情况下规约耗时较大的特点,采用贪心算法和部分列向量规约,减少LLL算法规约过程中的基向量交换和尺度规约次数,以降低LLL算法的计算复杂度。通过模拟和实测的数据验证,该改进方法可以降低LLL算法的规约耗时,因而对高维模糊度的快速解算具有一定的参考应用价值。 相似文献
10.
提出一种用于整周模糊度OTF求解的整数白化滤波改进算法。该算法首先对整周模糊度的协方差矩阵进行整数白化滤波处理 ,以降低整周模糊度间的相关性 ,然后构造搜索空间来判定是否需要进行搜索。如果需要 ,则通过搜索来确定变换后的整周模糊度 ;如果不需要 ,则通过直接取整来确定整周模糊度 ,进而得到原始的整周模糊度和基线分量的固定解。初步试验结果显示 ,采用改进方法解算整周模糊度可以提高成功率和解算效率 相似文献
11.
利用矩阵分解理论分别对整数高斯法、联合去相关法、基于矩阵乔里斯基分解的迭代法、逆整数乔里斯基法和LLL法等降相关算法进行了分类和比较。仿真计算表明：逆整数乔里斯基分解法优于联合去相关法,联合去相关法优于LLL法。 相似文献
12.
Random simulation and GPS decorrelation 总被引：13，自引：1，他引：13
Peiliang Xu 《Journal of Geodesy》2001,75(7-8):408-423
(i) A random simulation approach is proposed, which is at the centre of a numerical comparison of the performances of different
GPS decorrelation methods. The most significant advantage of the approach is that it does not depend on nor favour any particular
satellite–receiver geometry and weighting system. (ii) An inverse integer Cholesky decorrelation method is proposed, which
will be shown to out-perform the integer Gaussian decorrelation and the Lenstra, Lenstra and Lovász (LLL) algorithm, and thus
indicates that the integer Gaussian decorrelation is not the best decorrelation technique and that further improvement is
possible. (iii) The performance study of the LLL algorithm is the first of its kind and the results have shown that the algorithm
can indeed be used for decorrelation, but that it performs worse than the integer Gaussian decorrelation and the inverse integer
Cholesky decorrelation. (iv) Simulations have also shown that no decorrelation techniques available to date can guarantee
a smaller condition number, especially in the case of high dimension, although reducing the condition number is the goal of
decorrelation.
Received: 26 April 2000 / Accepted: 5 March 2001 相似文献
13.
A. Lannes 《Journal of Geodesy》2013,87(4):323-335
The LLL algorithm, introduced by Lenstra et al. (Math Ann 261:515–534, 1982), plays a key role in many fields of applied mathematics. In particular, it is used as an effective numerical tool for preconditioning the integer least-squares problems arising in high-precision geodetic positioning and Global Navigation Satellite Systems (GNSS). In 1992, Teunissen developed a method for solving these nearest-lattice point (NLP) problems. This method is referred to as Lambda (for Least-squares AMBiguity Decorrelation Adjustment). The preconditioning stage of Lambda corresponds to its decorrelation algorithm. From an epistemological point of view, the latter was devised through an innovative statistical approach completely independent of the LLL algorithm. Recent papers pointed out some similarities between the LLL algorithm and the Lambda-decorrelation algorithm. We try to clarify this point in the paper. We first introduce a parameter measuring the orthogonality defect of the integer basis in which the NLP problem is solved, the LLL-reduced basis of the LLL algorithm, or the $\Lambda $ -basis of the Lambda method. With regard to this problem, the potential qualities of these bases can then be compared. The $\Lambda $ -basis is built by working at the level of the variance-covariance matrix of the float solution, while the LLL-reduced basis is built by working at the level of its inverse. As a general rule, the orthogonality defect of the $\Lambda $ -basis is greater than that of the corresponding LLL-reduced basis; these bases are however very close to one another. To specify this tight relationship, we present a method that provides the dual LLL-reduced basis of a given $\Lambda $ -basis. As a consequence of this basic link, all the recent developments made on the LLL algorithm can be applied to the Lambda-decorrelation algorithm. This point is illustrated in a concrete manner: we present a parallel $\Lambda $ -type decorrelation algorithm derived from the parallel LLL algorithm of Luo and Qiao (Proceedings of the fourth international C $^*$ conference on computer science and software engineering. ACM Int Conf P Series. ACM Press, pp 93–101, 2012). 相似文献
14.
Mixed Integer-Real Valued Adjustment (IRA) Problems: GPS Initial Cycle Ambiguity Resolution by Means of the LLL Algorithm 总被引：4，自引：0，他引：4
Erik W. Grafarend 《GPS Solutions》2000,4(2):31-44
In order to achieve to GPS solutions of first-order accuracy and integrity, carrier phase observations as well as pseudorange
observations have to be adjusted with respect to a linear/linearized model. Here the problem of mixed integer-real valued
parameter adjustment (IRA) is met. Indeed, integer cycle ambiguity unknowns have to be estimated and tested. At first we review
the three concepts to deal with IRA: (i) DDD or triple difference observations are produced by a properly chosen difference
operator and choice of basis, namely being free of integer-valued unknowns (ii) The real-valued unknown parameters are eliminated
by a Gauss elimination step while the remaining integer-valued unknown parameters (initial cycle ambiguities) are determined
by Quadratic Programming and (iii) a RA substitute model is firstly implemented (real-valued estimates of initial cycle ambiguities)
and secondly a minimum distance map is designed which operates on the real-valued approximation of integers with respect to
the integer data in a lattice. This is the place where the integer Gram-Schmidt orthogonalization by means of the LLL algorithm (modified LLL algorithm) is applied being illustrated by four examples. In particular, we prove
that in general it is impossible to transform an oblique base of a lattice to an orthogonal base by Gram-Schmidt orthogonalization where its matrix enties are integer. The volume preserving Gram-Schmidt orthogonalization operator constraint to integer entries produces “almost orthogonal” bases which, in turn, can be used to produce the integer-valued
unknown parameters (initial cycle ambiguities) from the LLL algorithm (modified LLL algorithm). Systematic errors generated
by “almost orthogonal” lattice bases are quantified by A. K. Lenstra et al. (1982) as well as M. Pohst (1987). The solution point of Integer Least Squares generated by the LLL algorithm is = (L')−1[L'◯] ∈ ℤ
m
where L is the lower triangular Gram-Schmidt matrix rounded to nearest integers, [L], and = [L'◯] are the nearest integers of L'◯, ◯ being the real valued approximation of z ∈ ℤ
m
, the m-dimensional lattice space Λ. Indeed due to “almost orthogonality” of the integer Gram-Schmidt procedure, the solution point is only suboptimal, only close to “least squares.” ? 2000 John Wiley & Sons, Inc. 相似文献
15.
GNSS模糊度降相关算法及其评价指标研究 总被引：4，自引：0，他引：4
针对Gauss、LDL和LLL算法构造整数阵存在的实数阵元素计算、实数至整数阵转换的排序问题,分别研究了相应的元素升序降相关算法和整逆型(先求逆后取整)降相关算法。分析了谱条件数、降相关系数和平均相关系数等降相关算法评价指标的优缺点,提出了等效相关系数评价指标。研究结果表明,等效相关系数较其他3种指标能更有效地评价不同维数方差阵,尤其是高维情况的降相关算法效果;逆整型优于整逆型降相关算法,升序(逆整型)降相关算法更佳,且优劣顺序为升序LDL、升序Gauss和升序LLL算法。 相似文献
16.
The LLL reduction of lattice vectors and its variants have been widely used to solve the weighted integer least squares (ILS)
problem, or equivalently, the weighted closest point problem. Instead of reducing lattice vectors, we propose a parallel Cholesky-based
reduction method for positive definite quadratic forms. The new reduction method directly works on the positive definite matrix
associated with the weighted ILS problem and is shown to satisfy part of the inequalities required by Minkowski’s reduction
of positive definite quadratic forms. The complexity of the algorithm can be fixed a priori by limiting the number of iterations.
The simulations have clearly shown that the parallel Cholesky-based reduction method is significantly better than the LLL
algorithm to reduce the condition number of the positive definite matrix, and as a result, can significantly reduce the searching
space for the global optimal, weighted ILS or maximum likelihood estimate. 相似文献