The total optimal search criterion in solving the mixed integer linear model with GNSS carrier phase observations
The total optimal search criterion in solving the mixed integer linear model with GNSS carrier phase observations
复制标题
GNSS载波相位观测值求解混合整数线性模型的总最优搜索准则
DOI：
10.1007/s10291-008-0115-y
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发表时间：
2009-01
期刊：
影响因子：
4.9
通讯作者：
Hu, Congwei
中科院分区：
文献类型：
--
作者：
Cai, Jianqing;Grafarend, Erik W.;Hu, Congwei
现有的GPS模糊度确定算法可以分为三类，即测量域、坐标域和模糊域的模糊度求解。有许多技术可用于搜索模糊域，例如FARA(Frei和Beutler在Muscr GeoD 15(4)：325-356,1990)，LSAST(Hatch in KIS‘90，Banff，Canada，第299-308页，1990)，修改的Cholesky分解方法(Euler和Landau在第六届国际大地测量卫星定位研讨会论文集，俄亥俄州哥伦布市，第650-659页，1992)，Lambda(Teunissen in特邀讲座，第四部分理论和方法，IAG大会，北京，中国，1993)，FASF(Chen和Lachale in J Inst Navig 42(2)：371-390，pp650-659,1992)1995)和改进的LLL算法(GPS解决方案4(2)中的Grafarend：31-44,2000；Lou和Grafarend在Zeitschrift für VerMessungswesen 3：203-210,2003)。广泛应用的LAMBDA方法基于最小二乘模糊搜索(LSAS)准则，并采用了一种有效的解相关技术。G.Xu(J Glob Position Syst 1(2)：121-131,2002)还提出了一个新的模糊搜索通用准则及其等价目标函数，该准则可以在坐标域和/或模糊域中进行。徐的目标函数与LSAS函数不同，导致了不同的数值结果。这一差异的原因在这一贡献中得到了确认和纠正。经过更正，徐的方法与Lambda中隐含的方法是相同的。给出了在坐标和模糊域中求解整周模糊度的混合整数线性模型的全局最优搜索准则，并从代数和几何的角度推导了目标函数的正交分解和相关的最小表达式。用实际的GPS相位数据对该判据进行了验证。理论和数值结果表明：(1)在整周模糊度参数固定的约束下，LSAS目标函数可以从全局最优搜索准则得到；(2)Xu对等价目标函数的推导是错误的，导致搜索过程不正确。讨论了总体最优准则对GPS载波相位数据处理的影响，并给出了具体的实现方法。
Existing algorithms for GPS ambiguity determination can be classified into three categories, i.e. ambiguity resolution in the measurement domain, the coordinate domain and the ambiguity domain. There are many techniques available for searching the ambiguity domain, such as FARA (Frei and Beutler in Manuscr Geod 15(4):325–356, 1990), LSAST (Hatch in Proceedings of KIS’90, Banff, Canada, pp 299–308, 1990), the modifiedCholeskydecomposition method (Euler and Landau in Proceedings of the sixth international geodetic symposium on satellite positioning, Columbus, Ohio, pp 650–659, 1992), LAMBDA (Teunissen in Invited lecture, section IV theory and methodology, IAG general meeting, Beijing, China, 1993), FASF (Chen and Lachapelle in J Inst Navig 42(2):371–390, 1995) and modified LLL Algorithm (Grafarend in GPS Solut 4(2):31–44, 2000; Lou and Grafarend in Zeitschrift für Vermessungswesen 3:203–210, 2003). The widely applied LAMBDA method is based on theLeast Squares Ambiguity Search(LSAS) criterion and employs an effective decorrelation technique in addition. G. Xu (J Glob Position Syst 1(2):121–131, 2002) proposed also a new general criterion together with its equivalent objective function for ambiguity searching that can be carried out in the coordinate domain, the ambiguity domain or both. Xu’s objective function differs from the LSAS function, leading to different numerical results. The cause of this difference is identified in this contribution and corrected. After correction, the Xu’s approach and the one implied in LAMBDA are identical. We have developed a total optimal search criterion for the mixed integer linear model resolving integer ambiguities in both coordinate and ambiguity domain, and derived the orthogonal decomposition of the objective function and the related minimum expressions algebraically and geometrically. This criterion is verified with real GPS phase data. The theoretical and numerical results show that (1) the LSAS objective function can be derived from the total optimal search criterion with the constraint on the fixed integer ambiguity parameters, and (2) Xu’s derivation of the equivalent objective function was incorrect, leading to an incorrect search procedure. The effects of the total optimal criterion on GPS carrier phase data processing are discussed and its practical implementation is also proposed.
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DOI：
--
发表时间：
2003-06
期刊：
--
影响因子：
--
作者：
L. Lou;E. Grafarend
通讯作者：
L. Lou;E. Grafarend
DOI：
10.1007/978-1-4612-3102-8_27
发表时间：
1991
期刊：
--
影响因子：
--
作者：
R. Hatch
通讯作者：
R. Hatch
DOI：
10.1016/0021-9169(95)90017-9
发表时间：
1995
影响因子：
1.9
作者：
D. Allerton
通讯作者：
D. Allerton
影响因子：
4
作者：
K. Koch
通讯作者：
K. Koch
影响因子：
1.6
作者：
Shaowei Han;C. Rizos
通讯作者：
Shaowei Han;C. Rizos