Study On Theory And Method Of GNSS Integer Least Squares Ambiguity Resolution

The fast and accurate resolution of carrier phase ambiguity is the key problem of GNSS(Global Navigation Satellite System)real-time high-precision dynamic positioning,and it is also a hot issue in GNSS research field for many years.Only the carrier phase ambiguity is fixed accurately,the carrier phase observations can be converted to millimeter-level precision pseudorange observations,thus on this basis to achieve high-precision navigation and positioning.At present,with the GPS,GLONASS,BDS and GALILEO four systems gradually updated and completed,the number of satellites in orbit is expected to exceed 100,will greatly enhance the precision,integrity,reliability and availability of the satellite navigation and positioning services.And the increase of the number of observation equations will inevitably bring about the problem of high-dimensional ambiguity resolution.The existing ambiguity estimation and validation method have some problems such as slow operation speed and low reliability for high-dimensional ambiguity resolution.Therefore,this paper studies the fast estimation and validation of high-dimensional ambiguity,and also studies the baseline constrained LAMBDA(CLAMBDA)for attitude measurement.Aiming at the above research objectives,the main contents of this paper are as follows:(1)In terms of GNSS positioning solution model,the mathematical model of GNSS observations is introduced;the explicit expression of parameter estimation is deduced;that increasing the number of observation equations can improve the precision of ambiguity resolution is theoretically proved,which provides theoretical support for high-dimensional ambiguity has a higher precision of real-value;and the mixed integer least squares(ILS)quadratic decomposition is deduced from three aspects:orthogonal decomposition method,derivative method and least-squares method,which deepens the understanding of ILS ambiguity resolution theory.(2)In terms of high-dimensional ambiguity lattice reduction,the detailed integer transformation procedures of LAMBDA decorrelation algorithm and the LLL lattice reduction algorithm are described.Two key factors influencing the ambiguity reduction quality:the size reduction and the reduced basis vector swapping,are analyzed theoretically,and the results show that ambiguity search efficiency depends on the exchanging condition of the basis vector,size reduction is used to help improve exchanging strength of the basis vector.The relationship between the ambiguity precision and the reduction time and search time is analyzed,it turns out that the key point of improving the high-dimensional ambiguity resolution efficiency is to reduce the computational complexity of reduction algorithm.Based on the above analysis of the characteristics of reduction algorithm for high-dimensional ambiguity resolution,three efficient reduction algorithms are proposed to solve the high-dimensional ambiguity resolution,i.e.,the LLL algorithm based on the block matrix to reduce the ambiguity dimension,the LLL algorithm based on the partial size reduction and the greedy selection strategy to reduce computational complexity of reduction algorithm,and a new reduction algorithm based on the whole minimum basis vector deep insertion to reduce the swapping number among basis vector and improve reduction quality.Finally,the basis vector length ratio is proposed as an evaluation index to reasonably measure the reduction quality.(3)In terms of ambiguity search,the four depth-first search algorithms of FP,SE,VB and SEVB are analyzed based on measured data of high-dimensional ambiguity.The relationship between the ellipsoid volume and the number of candidate vectors in the corresponding search space is studied,and points out that there is no approximately equal relationship between the two of them.However,there is a proportional coefficient change over the dimension between the ellipsoid volume and the number of candidate vectors,and the proportionality coefficient table of different dimension is calculated according to the discrete characteristic of the ambiguity integer vector.Aiming at the SEVB algorithm have a high time-consuming in high dimension,low Bootstrapping success rate situations,the SEVB algorithm is modified by setting the initial search space and changing the calculating process of conditional expectation of ambiguity real-valued.The k-best algorithm based on the breadth-first search is analyzed.The results show that the increase of k value does not significantly improve the global optimality of the estimated solution,but it will reduce the efficiency of the solution.(4)In terms of ambiguity validation,three kinds of integer estimation methods are introduced,the statistical properties of the parameters such as ambiguity floating point solution and residuals are analyzed,and eight ambiguity validation methods based on integer aperture(IA)estimation:Ratio test IA(RTIA),Difference test IA(DTIA),Projector test IA(PTIA),W-test IA(WTIA),Ellipsoidal aperture estimation(EIA),IA Bootstrapping(IAB),IA Least-Squares(IALS)and optimal integer aperture(OIA)estimation and the geometrical structure of two-dimensional IA pull-in region are detailed study and explained.Based on the fixed failure rate,the ambiguity fixed performance of the eight kinds of IA estimation methods under two-dimensional ambiguities are compared.Finally,the validation threshold of multi-dimensional ambiguity for RTIA,DTIA,WTIA and PTIA is calculated,and established a threshold look-up table for real-time application.(5)In terms of baseline constraint ambiguity resolution,the basic principle of CLAMBDA under hard constraint and weighted constraint model is introduced,and the formula of baseline components based on hard constraint model is deduced.When CLAMBDA initial search space is too large,the use of BFS search space shrinks slowly,resulting in a longer time-consuming,hence the ASS algorithm of adaptive search space is proposed.The experimental results show that CLAMBDA can significantly improve the fixed success rate of ambiguity under single frequency and single epoch,the hard constraint model can obtain good solution,and the efficiency of the proposed ASS algorithm is about 2 times higher than that of the BFS algorithm.