Research On Key Methods Of GNSS Integer Ambiguity Estimation

The fast and effective resolution of carrier phase ambiguity is the primary basis of GNSS precise positioning,and it is also a hotspot and difficulty of GNSS research field.Ambiguity resolution is the process which recoveries the integer solution from real number.Only the carrier phase observations of which the ambiguity is fixed can be used as millimeter-sized distance observations to participate in the navigation and positioning.This is very critical for the data processing and application of satellite precise positioning.With the modernization of four major navigation satellite systems and the promotion of GNSS service,the user requirements for the precision,reliability and practicability of GNSS positioning results is more and more higher.The technological development of multi-system and multi-frequency results in the change of ambiguity dimension and calculation accuracy.And the existing ambiguity resolution has the problem of inefficiency and instability in the case of high dimension.Based on the problems above,this paper studies the set of ambiguity initial search space,ambiguity lattice reduction,ambiguity search and the developing software for ambiguity resolution applications.And the carrier phase smoothing pseudo-range algorithm affected by the influence of ionospheric delay is analysed.The main research contents and achievements are as follows:1.In connection to GNSS positioning models and error source,the mathematical model of GNSS observations is introduced,and the corresponding error source is analysed.On the issue of the low accuracy of the traditional single-frequency carrier phase smoothing pseudo-range algorithm,a self-modelling algorithm for single-frequency carrier phase smoothing pseudorange with ionospheric delay variation is proposed.The algorithm uses the ionospheric delay information contained in the pseudo-range and carrier observations to model the ionospheric delay,and deducts the ionospheric delay variation between epochs from the smooth pseudo-range,thus effectively avoiding the divergence of the smooth pseudo-range.Static and dynamic observation data are used to carry out analysis.The result shows that the positioning accuracy can reach sub-decimeter level in both static and dynamic NEU directions by using the proposed algorithm for epoch-by-epoch single-frequency smoothing pseudo-range single-point positioning.2.In connection to setting the initial ambiguity search space,the basis process and the deductive methods of converting mixed integer model to integer model are introduced.The characteristics of the search space of LAMBDA method is analysed.The two setting methods based on objective function and ellipsoid volume are analysed and compared.The advantages and disadvantages of the methods above are evaluated.On this basis,a new search space impact factor is defined to express the comprehensive influence of the dimension,the conditional value component rounding and the conditional variance magnitude.And the corrected fomula of determining the ambiguity search space is provided by combining the hierarchy rounding method based on project function.Experiments with simulated and real data are executed,the consequence shows that the improved space setting method can separate superfluous integer resolution from the initial search space.And the actual number of ambiguity candidate vectors can be reduced effectively according to the requirement of the expected value,which is beneficial to the fast ambiguity resolution.3.In connection to ambiguity lattice reduction,the basic conception of lattice theory is introduced,and the basic process of ambiguity resolution under the framework of lattice theory is designed.The detaied integer transformation procedures of LAMBDA decorrelation algorithm and the LLL lattice reduction algorithm are described.The performance feature of the lattice reduction in helping ambiguity resolution is analysed.It turns out that the ambiguity search efficiency essentially depends on the exchange of base vectors,and the goal of size reduction is to make the exchange of base vectors more fully.The dimension and precidion of ambiguity resolution are analysed,and it turns out that the size reduction has a greater impact on the resolution efficiency of the high-dimensional ambiguity resolution.At the same time,a new performance evaluation is proposed to measure the overall ordering effect,which is based on the smoothness of the alinement curve on the length of orthogonal basis vectors.On this basis,the delayed size reduction,the partial size reduction and the QR factorization with minimum column pivoting are introduced.And the whole size reduction LLL algorithm with minimum column pivoting(WMLLL)and the delayed and partial LLL algorithm with minimum column pivoting(DPLLL)are proposed according to reasonable combination,respectively.The high efficiency of the improved algorithms are verified by using simulated and real data.4.In connection to ambiguity search,the characteristics of three kinds of ambiguity estimation methods are analysed,including the rounding method,the integer Bootstrapping rounding method and the integer least-square method.The FP,VB and SE-VB strategies as well as their algorithms based on depth-first mode are introduced.And the performance of several kinds of depth-first algorithms is compared,which shows that the SE-VB strategy has the highest search efficiency.The K-best algorithm based on the breadth-first mode is introduced.And the influence of the different choice of k is analysed,it turns out that there is no necessary connection between the expanding of k and the overall optimal results of K-best algorithm.According to the problem of the redundant computation in the MLAMBDA algorithm under SE-VB strategy,the calculation method of the conditional values is improved properly.Experiments with simulated and real data are executed to verify the effectiveness of the improved search algorithm.5.In connection to software development of related application with ambiguity resolution,combined with the theory and method mentioned above,the positioning application function related to the ambiguity resolution is developed and realized further based on the GNSSer(GNSS Date Parallel Processer)platform.The basic function modules and technical features of the software are introduced.The software has a map visualization function and supports fast parallel computing under multi-core multi-node resources based on the parallel network environment The precision positioning resolution service about multi-system undifferenced and double difference model are provided.The high-precision positioning function of the software is analyzed in detail,taking the GPS double-difference solution and the undifferenced solution under the four GNSS systems as an example.Finally,the reliability,practicability and high efficiency of the positioning results in the double-difference mode can be verified through the application analysis of the Crustal Movement Observation Network of China(CMONOC)and a high-speed railway engineering GNSS control network.