Global Positioning System Integer Ambiguity Resolution Using Factorized Least-Squares Techniques

2007 ◽  
Vol 30 (2) ◽  
pp. 346-356 ◽  
Author(s):  
Mark L. Psiaki ◽  
Shan Mohiuddin
Keyword(s):  
Least Squares ◽  
Global Positioning System ◽  
Ambiguity Resolution ◽  
Integer Ambiguity Resolution ◽  
Integer Ambiguity ◽  
Positioning System ◽  
Global Positioning ◽  
Least Squares Techniques

scholarly journals Ambiguity of Residual Constraint-Based Precise Point Positioning with Partial Ambiguity Resolution under No Real-Time Network Corrections Using Real Global Positioning System (GPS) Data

Sensors ◽  
2020 ◽  
Vol 20 (11) ◽  
pp. 3220
Author(s):  
Honglei Qin ◽  
Peng Liu ◽  
Li Cong ◽  
Xia Xue
Keyword(s):  
Real Time ◽  
Global Positioning System ◽  
Ambiguity Resolution ◽  
Precise Point Positioning ◽  
Convergence Time ◽  
Positioning System ◽  
Post Processing ◽  
Partial Ambiguity Resolution ◽  
Global Positioning ◽  
Point Positioning

Although precise point positioning (PPP) is a well-established and promising technique with the use of precise satellite orbit and clock products, it costs a long convergence time to reach a centimeter-level positioning accuracy. The PPP with ambiguity resolution (PPP-AR) technique can improve convergence performance by resolving ambiguities after separating the fractional cycle bias (FCB). Now the FCB estimation is mainly realized by the regional or global operating reference station network. However, it does not work well in the areas where network resources are scarce. The contribution of this paper is to realize an ambiguity residual constraint-based PPP with partial ambiguity resolution (PPP-PARC) under no real-time network corrections to speed up the convergence, especially when the performance of the float solution is poor. More specifically, the update strategy of FCB estimation in a stand-alone receiver is proposed to realize the PPP-PAR. Thereafter, the solving process of FCB in a stand-alone receiver is summarized. Meanwhile, the influencing factors of the ambiguity success rate in the PPP-PAR without network corrections are analyzed. Meanwhile, the ambiguity residual constraint is added to adapt the particularity of the partial ambiguity-fixing without network corrections. Moreover, the positioning experiments with raw observation data at the Global Positioning System (GPS) globally distributed reference stations are conducted to determine the ambiguity residual threshold for post-processing and real-time scenarios. Finally, the positioning performance was verified by 22 GPS reference stations. The results show that convergence time is reduced by 15.8% and 26.4% in post-processing and real-time scenarios, respectively, when the float solution is unstable, compared with PPP using a float solution. However, if the float solution is stable, the PPP-PARC method has performance similar to the float solution. The method shows the significance of the PPP-PARC for future PPP applications in areas where network resource is deficient.

scholarly journals Estimating satellite and receiver differential code bias using a relative Global Positioning System network

2019 ◽  
Vol 37 (6) ◽  
pp. 1039-1047 ◽  
Author(s):  
Alaa A. Elghazouly ◽  
Mohamed I. Doma ◽  
Ahmed A. Sedeek
Keyword(s):  
Least Squares ◽  
Global Positioning System ◽  
Gps Data ◽  
Electron Content ◽  
Positioning System ◽  
Total Electron ◽  
Gps Network ◽  
Global Positioning ◽  
The Mean ◽  
Mean Differences

Abstract. Precise total electron content (TEC) is required to produce accurate spatial and temporal resolution of global ionosphere maps (GIMs). Receivers and satellite differential code biases (DCBs) are one of the main error sources in estimating precise TEC from Global Positioning System (GPS) data. Recently, researchers have been interested in developing models and algorithms to compute DCBs of receivers and satellites close to those computed from the Ionosphere Associated Analysis Centers (IAACs). Here we introduce a MATLAB code called Multi Station DCB Estimation (MSDCBE) to calculate satellite and receiver DCBs from GPS data. MSDCBE based on a spherical harmonic function and a geometry-free combination of GPS carrier-phase, pseudo-range code observations, and weighted least squares was applied to solve observation equations and to improve estimation of DCB values. There are many factors affecting the estimated values of DCBs. The first one is the observation weighting function which depends on the satellite elevation angle. The second factor is concerned with estimating DCBs using a single GPS station using the Zero Difference DCB Estimation (ZDDCBE) code or using the GPS network used by the MSDCBE code. The third factor is the number of GPS receivers in the network. Results from MSDCBE were evaluated and compared with data from IAACs and other codes like M_DCB and ZDDCBE. The results of weighted (MSDCBE) least squares show an improvement for estimated DCBs, where mean differences from the Center for Orbit Determination in Europe (CODE) (University of Bern, Switzerland) are less than 0.746 ns. DCBs estimated from the GPS network show better agreement with IAAC than DCBs estimated from precise point positioning (PPP), where the mean differences are less than 0.1477 and 1.1866 ns, respectively. The mean differences of computed DCBs improved by increasing the number of GPS stations in the network.

scholarly journals Iterative least squares method for global positioning system

2011 ◽  
Vol 9 ◽  
pp. 203-208 ◽  
Author(s):  
Y. He ◽  
A. Bilgic
Keyword(s):  
Linear System ◽  
Least Squares ◽  
Global Positioning System ◽  
Least Squares Method ◽  
Positioning System ◽  
System Of Equations ◽  
Linear System Of Equations ◽  
Global Positioning ◽  
Non Linear ◽  
Non Linear System

Abstract. The efficient implementation of positioning algorithms is investigated for Global Positioning System (GPS). In order to do the positioning, the pseudoranges between the receiver and the satellites are required. The most commonly used algorithm for position computation from pseudoranges is non-linear Least Squares (LS) method. Linearization is done to convert the non-linear system of equations into an iterative procedure, which requires the solution of a linear system of equations in each iteration, i.e. linear LS method is applied iteratively. CORDIC-based approximate rotations are used while computing the QR decomposition for solving the LS problem in each iteration. By choosing accuracy of the approximation, e.g. with a chosen number of optimal CORDIC angles per rotation, the LS computation can be simplified. The accuracy of the positioning results is compared for various numbers of required iterations and various approximation accuracies using real GPS data. The results show that very coarse approximations are sufficient for reasonable positioning accuracy. Therefore, the presented method reduces the computational complexity significantly and is highly suited for hardware implementation.

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