基于格理论的GNSS模糊度估计方法研究
发布时间：2018-07-28 15:33
【摘要】：随着卫星导航系统的建设和发展，卫星定位技术的应用领域不断扩大，用户对定位结果的精度和可靠性的要求也越来越高。高精度的定位过程中，整周模糊度的正确解算是保证定位精度的关键因素，本文基于数学中的格理论对整周模糊度的估计方法进行了研究，论文的主要成果和创新点概括如下： 1.为了获得最终的位置结果，需要首先将既包含实数未知参数又包含整数未知参数的混合整数模型转化为整数模型进行解算，讨论了基于最小二乘准则和基于Bayesian准则的两种转换过程，并且证明了两类准则下转换得到的整数模型是一致的。 2.针对LLL降相关算法利用整数Gram Schmidt变换进行处理，变换过程受取整舍入误差的影响严重，而导致高维情况下出现降相关失败的问题，提出了一种整数分块正交变换法，并且基于这种变换设计了基于整数分块正交变换的LLL降相关算法。通过计算分析，证明了新方法的降相关性能有了很大的提高。 3.深入研究了格的定义，特点以及格上的两个著名难题，通过对模糊度解算的整数最小二乘模型的分析，对协方差矩阵进行三角分解即可构造出模糊度解算对应的格，而模糊度搜索固定的问题等价于格上的最近向量问题，在此基础上，提出了基于格的模糊度解算方法。 4.分析研究了LLL规约基及两种实现算法。由于格基具有多样性，格基性能的好坏将会影响到格上CVP解算的效率和成功率，对于基于格的模糊度解算来说，需要通过格基规约的方式选择出最适合问题解算的那组基。通过对LLL规约基的分析，掌握了格基规约的原理、过程与根本目标，同时对基于Gram Schmidt变换和基于Householder变换的两种LLL规约基的实现方法进行研究。 5.提出了一种扩展的LLL规约基，其长度规约的约束条件要高于LLL规约，可保证在所有的基向量范围内实现长度规约。为了实现E-LLL规约基，，首先设计了基于系统旋转的Householder变换，其可在规约开始之前就保证基向量能够按照其正交化向量长度由小到大的顺序排列，从而提高规约的效率，其次基于这种变换方式提出了HE-LLL规约算法，该方法在系统旋转变换的辅助下，对基向量逐一进行大小规约和长度规约处理，最终可保证获得E-LLL规约基。通过利用实测数据进行计算，验证了HE-LLL算法不仅提高规约效果，而且提高了规约的效率。 6.提出了一种改进的BKZ规约算法，BKZ规约是在LLL规约的基础上对格基进行进行分块处理，保证每个分块中的基向量能够满足KZ规约的条件，其规约的效果和效率取决于分块的大小，分块越大则效果越好同时效率也越低，为了优化规约的效率，基于HE-LLL进行了改进，通过利用实测和模拟数据的分析，验证了改进的BKZ算法的计算效率要明显优于BKZ规约基，同时其规约效果在理论上也优于HE-LLL规约。 7.研究了基于深度优先搜索模式的VB-SD和SE-SD算法，并且对格基规约过程对其搜索空间的影响进行了分析，证明了格基规约的大小规约过程并不能改善搜索空间，而只有长度规约才会对搜索的效率和成功率产生影响，通过利用实测数据在不同情况下的分析证明了以上结论。 8.提出了基于HE-LLL规约的K-best搜索算法，基于深度优先的搜索算法由于需要进行复杂的迭代分析，在高维情况下效率较低，以K-best算法为代表的基于广度优先模式的球形搜索算法由于每次只搜索k个候选值，所以具有比较固定的复杂度，但是这导致了它是一种次优的算法。为了满足模糊度解算的精度要求，在格基质量和搜索半径约束两个方面进行了改进，利用实测数据进行了计算分析，结果表明本文提出的方法只需选取较小的k值即可获得模糊度的最优解，并且其效率稳定不会随着维数的增加而产生很大的变化，适用于高维的模糊度解算。 9. Voronoi cell作为一种具有对偶性质的凸域几何结构，可用来对格上相关问题进行分析研究。通过对格上向量对应的Voronoi cell的分析，将模糊度CVP求解的问题转化为求解目标向量在原点的Voronoi cell中对应向量的问题。利用Voronoi相关向量来构造原点对应的Voronoi cell，并且在此基础上设计了基于Voronoi cell的模糊度CVP解算方法，利用一组模拟的2维数据，对算法的模糊度解算过程进行了分析，基于其构造的Voronoi cell对结果的可靠性进行评价，同时选取几组实测数据进一步验证了算法的正确性。
[Abstract]:With the construction and development of the satellite navigation system, the application field of satellite positioning technology is expanding, and the requirements for the accuracy and reliability of the positioning results are becoming more and more high. In the high precision positioning process, the correct calculation of the integer ambiguity is the key factor to ensure the positioning accuracy. This paper is based on the lattice theory in mathematics to the whole week. The main results and innovations of the paper are summarized as follows:
1. in order to obtain the final position results, we need to convert the mixed integer model which includes both the unknown parameters of the real number and the unknown integer parameters into the integer model, and discusses the two transformation processes based on the least square criterion and the Bayesian criterion, and proves that the integer model obtained under the two classes of criteria is the integer model. Coincident.
2. to deal with the LLL descending correlation algorithm using integer Gram Schmidt transform, the transformation process is seriously affected by the rounding error, which leads to the problem of falling correlation failure in high dimension. An integer block orthogonal transform is proposed, and based on this transformation, the LLL drop correlation calculation based on integer block orthogonal transform is designed. Calculation and analysis show that the performance of the new method is greatly improved.
3. the definition, the characteristics and the two famous problems on the lattice are deeply studied. By the analysis of the integer least square model of the ambiguity resolution, the triangular decomposition of the covariance matrix can be used to construct the corresponding lattice of the ambiguity solution, and the problem of the nearest vector on the lattice is solved by the fuzzy degree search. On this basis, the problem is proposed. The method of ambiguity resolution based on lattice is presented.
4. analysis and study of the LLL protocol base and two implementation algorithms. Due to the diversity of GI, the performance of GI will affect the efficiency and success rate of the CVP solution. For the lattice based ambiguity resolution, it is necessary to choose the group which is the most suitable for solving the problem through the lattice specification. Through the analysis of the LLL protocol basis, The principle of the GI protocol, the process and the fundamental goal are mastered, and the implementation of the two LLL protocol bases based on Gram Schmidt transform and Householder transform is studied.
5. an extended LLL protocol base is proposed. The constraint condition of its length specification is higher than the LLL specification, which guarantees the implementation of the length specification within all base vector ranges. In order to realize the E-LLL protocol base, the Householder transformation based on the system rotation is designed first, which can ensure that the base vector can be orthogonal to its orthogonalization before the specification begins. The volume length is arranged from small to large, and the efficiency of the protocol is improved. Secondly, the HE-LLL protocol algorithm is proposed based on this transformation. Under the aid of the rotation transformation of the system, the size specification and length specification of the base vector are processed one by one, and the E-LLL protocol base can be obtained, and the calculated data can be calculated by using the measured data. The HE-LLL algorithm is verified not only to improve the effectiveness of the protocol, but also to improve the efficiency of the protocol.
6. an improved BKZ protocol algorithm is proposed. The BKZ protocol is based on the LLL protocol to block the lattice, which ensures that the base vector in each block can meet the conditions of the KZ specification. The effect and efficiency of the protocol depend on the size of the block. The bigger the block, the better the efficiency and the lower the efficiency, in order to optimize the protocol. Efficiency is improved on the basis of HE-LLL. By using the analysis of measured and simulated data, it is proved that the efficiency of the improved BKZ algorithm is obviously superior to the BKZ protocol base, and its protocol effect is also superior to the HE-LLL specification in theory.
7. the VB-SD and SE-SD algorithms based on the depth first search model are studied, and the effect of the GI protocol process on its search space is analyzed. It is proved that the size specification process of the GI protocol does not improve the search space, but only the length specification will affect the efficiency and success rate of the search, and use the measured data by using the measured data. The analysis in different cases proves the above conclusion.
8. the K-best search algorithm based on HE-LLL protocol is proposed. The search algorithm based on the depth first is less efficient because of the need for complex iterative analysis. The spherical search algorithm based on the breadth first model, represented by the K-best algorithm, has a relatively fixed complexity because it only searches for the K candidate values at a time. However, it is a suboptimal algorithm. In order to meet the precision requirement of ambiguity resolution, two aspects of the quality of GI and the constraint of the search radius are improved. The calculation and analysis are carried out by the measured data. The results show that the proposed method only needs to select the smaller K value to obtain the optimal solution of fuzzy degree and its efficiency. The rate stability does not change greatly with the increase of the dimension, and is suitable for solving the ambiguity of high dimension.
9. Voronoi cell, as a dual convex domain geometric structure, can be used to analyze the related problems on the lattice. Through the analysis of the Voronoi cell corresponding to the vector corresponding to the lattice, the problem of the ambiguity resolution is converted to the problem of solving the corresponding vector of the target vector in the origin of the Voronoi cell. The Voronoi correlation vector is used. To construct the Voronoi cell corresponding to the original point, and on this basis, the fuzzy degree CVP calculation method based on Voronoi cell is designed, and a set of simulated 2 dimensional data is used to analyze the ambiguity resolution process of the algorithm. Based on the constructed Voronoi cell, the reliability of the result is evaluated, and several sets of measured data are selected at the same time. The correctness of the algorithm is verified.
【学位授予单位】：解放军信息工程大学
【学位级别】：博士
【学位授予年份】：2013
【分类号】：P228.4
本文编号：2150729
[Abstract]:With the construction and development of the satellite navigation system, the application field of satellite positioning technology is expanding, and the requirements for the accuracy and reliability of the positioning results are becoming more and more high. In the high precision positioning process, the correct calculation of the integer ambiguity is the key factor to ensure the positioning accuracy. This paper is based on the lattice theory in mathematics to the whole week. The main results and innovations of the paper are summarized as follows:
1. in order to obtain the final position results, we need to convert the mixed integer model which includes both the unknown parameters of the real number and the unknown integer parameters into the integer model, and discusses the two transformation processes based on the least square criterion and the Bayesian criterion, and proves that the integer model obtained under the two classes of criteria is the integer model. Coincident.
2. to deal with the LLL descending correlation algorithm using integer Gram Schmidt transform, the transformation process is seriously affected by the rounding error, which leads to the problem of falling correlation failure in high dimension. An integer block orthogonal transform is proposed, and based on this transformation, the LLL drop correlation calculation based on integer block orthogonal transform is designed. Calculation and analysis show that the performance of the new method is greatly improved.
3. the definition, the characteristics and the two famous problems on the lattice are deeply studied. By the analysis of the integer least square model of the ambiguity resolution, the triangular decomposition of the covariance matrix can be used to construct the corresponding lattice of the ambiguity solution, and the problem of the nearest vector on the lattice is solved by the fuzzy degree search. On this basis, the problem is proposed. The method of ambiguity resolution based on lattice is presented.
4. analysis and study of the LLL protocol base and two implementation algorithms. Due to the diversity of GI, the performance of GI will affect the efficiency and success rate of the CVP solution. For the lattice based ambiguity resolution, it is necessary to choose the group which is the most suitable for solving the problem through the lattice specification. Through the analysis of the LLL protocol basis, The principle of the GI protocol, the process and the fundamental goal are mastered, and the implementation of the two LLL protocol bases based on Gram Schmidt transform and Householder transform is studied.
5. an extended LLL protocol base is proposed. The constraint condition of its length specification is higher than the LLL specification, which guarantees the implementation of the length specification within all base vector ranges. In order to realize the E-LLL protocol base, the Householder transformation based on the system rotation is designed first, which can ensure that the base vector can be orthogonal to its orthogonalization before the specification begins. The volume length is arranged from small to large, and the efficiency of the protocol is improved. Secondly, the HE-LLL protocol algorithm is proposed based on this transformation. Under the aid of the rotation transformation of the system, the size specification and length specification of the base vector are processed one by one, and the E-LLL protocol base can be obtained, and the calculated data can be calculated by using the measured data. The HE-LLL algorithm is verified not only to improve the effectiveness of the protocol, but also to improve the efficiency of the protocol.
6. an improved BKZ protocol algorithm is proposed. The BKZ protocol is based on the LLL protocol to block the lattice, which ensures that the base vector in each block can meet the conditions of the KZ specification. The effect and efficiency of the protocol depend on the size of the block. The bigger the block, the better the efficiency and the lower the efficiency, in order to optimize the protocol. Efficiency is improved on the basis of HE-LLL. By using the analysis of measured and simulated data, it is proved that the efficiency of the improved BKZ algorithm is obviously superior to the BKZ protocol base, and its protocol effect is also superior to the HE-LLL specification in theory.
7. the VB-SD and SE-SD algorithms based on the depth first search model are studied, and the effect of the GI protocol process on its search space is analyzed. It is proved that the size specification process of the GI protocol does not improve the search space, but only the length specification will affect the efficiency and success rate of the search, and use the measured data by using the measured data. The analysis in different cases proves the above conclusion.
8. the K-best search algorithm based on HE-LLL protocol is proposed. The search algorithm based on the depth first is less efficient because of the need for complex iterative analysis. The spherical search algorithm based on the breadth first model, represented by the K-best algorithm, has a relatively fixed complexity because it only searches for the K candidate values at a time. However, it is a suboptimal algorithm. In order to meet the precision requirement of ambiguity resolution, two aspects of the quality of GI and the constraint of the search radius are improved. The calculation and analysis are carried out by the measured data. The results show that the proposed method only needs to select the smaller K value to obtain the optimal solution of fuzzy degree and its efficiency. The rate stability does not change greatly with the increase of the dimension, and is suitable for solving the ambiguity of high dimension.
9. Voronoi cell, as a dual convex domain geometric structure, can be used to analyze the related problems on the lattice. Through the analysis of the Voronoi cell corresponding to the vector corresponding to the lattice, the problem of the ambiguity resolution is converted to the problem of solving the corresponding vector of the target vector in the origin of the Voronoi cell. The Voronoi correlation vector is used. To construct the Voronoi cell corresponding to the original point, and on this basis, the fuzzy degree CVP calculation method based on Voronoi cell is designed, and a set of simulated 2 dimensional data is used to analyze the ambiguity resolution process of the algorithm. Based on the constructed Voronoi cell, the reliability of the result is evaluated, and several sets of measured data are selected at the same time. The correctness of the algorithm is verified.
【学位授予单位】：解放军信息工程大学
【学位级别】：博士
【学位授予年份】：2013
【分类号】：P228.4
【参考文献】
相关硕士学位论文 前1条
1 周小平;格基规约在MIMO中的应用研究[D];北京邮电大学;2011年
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