【摘要】：隨著衛(wèi)星導(dǎo)航系統(tǒng)的建設(shè)和發(fā)展，衛(wèi)星定位技術(shù)的應(yīng)用領(lǐng)域不斷擴(kuò)大，用戶對定位結(jié)果的精度和可靠性的要求也越來越高。高精度的定位過程中，整周模糊度的正確解算是保證定位精度的關(guān)鍵因素，本文基于數(shù)學(xué)中的格理論對整周模糊度的估計(jì)方法進(jìn)行了研究，論文的主要成果和創(chuàng)新點(diǎn)概括如下： 1.為了獲得最終的位置結(jié)果，需要首先將既包含實(shí)數(shù)未知參數(shù)又包含整數(shù)未知參數(shù)的混合整數(shù)模型轉(zhuǎn)化為整數(shù)模型進(jìn)行解算，討論了基于最小二乘準(zhǔn)則和基于Bayesian準(zhǔn)則的兩種轉(zhuǎn)換過程，并且證明了兩類準(zhǔn)則下轉(zhuǎn)換得到的整數(shù)模型是一致的。 2.針對LLL降相關(guān)算法利用整數(shù)Gram Schmidt變換進(jìn)行處理，變換過程受取整舍入誤差的影響嚴(yán)重，而導(dǎo)致高維情況下出現(xiàn)降相關(guān)失敗的問題，提出了一種整數(shù)分塊正交變換法，并且基于這種變換設(shè)計(jì)了基于整數(shù)分塊正交變換的LLL降相關(guān)算法。通過計(jì)算分析，證明了新方法的降相關(guān)性能有了很大的提高。 3.深入研究了格的定義，特點(diǎn)以及格上的兩個著名難題，通過對模糊度解算的整數(shù)最小二乘模型的分析，對協(xié)方差矩陣進(jìn)行三角分解即可構(gòu)造出模糊度解算對應(yīng)的格，而模糊度搜索固定的問題等價于格上的最近向量問題，在此基礎(chǔ)上，提出了基于格的模糊度解算方法。 4.分析研究了LLL規(guī)約基及兩種實(shí)現(xiàn)算法。由于格基具有多樣性，格基性能的好壞將會影響到格上CVP解算的效率和成功率，對于基于格的模糊度解算來說，需要通過格基規(guī)約的方式選擇出最適合問題解算的那組基。通過對LLL規(guī)約基的分析，掌握了格基規(guī)約的原理、過程與根本目標(biāo)，同時對基于Gram Schmidt變換和基于Householder變換的兩種LLL規(guī)約基的實(shí)現(xiàn)方法進(jìn)行研究。 5.提出了一種擴(kuò)展的LLL規(guī)約基，其長度規(guī)約的約束條件要高于LLL規(guī)約，可保證在所有的基向量范圍內(nèi)實(shí)現(xiàn)長度規(guī)約。為了實(shí)現(xiàn)E-LLL規(guī)約基，，首先設(shè)計(jì)了基于系統(tǒng)旋轉(zhuǎn)的Householder變換，其可在規(guī)約開始之前就保證基向量能夠按照其正交化向量長度由小到大的順序排列，從而提高規(guī)約的效率，其次基于這種變換方式提出了HE-LLL規(guī)約算法，該方法在系統(tǒng)旋轉(zhuǎn)變換的輔助下，對基向量逐一進(jìn)行大小規(guī)約和長度規(guī)約處理，最終可保證獲得E-LLL規(guī)約基。通過利用實(shí)測數(shù)據(jù)進(jìn)行計(jì)算，驗(yàn)證了HE-LLL算法不僅提高規(guī)約效果，而且提高了規(guī)約的效率。 6.提出了一種改進(jìn)的BKZ規(guī)約算法，BKZ規(guī)約是在LLL規(guī)約的基礎(chǔ)上對格基進(jìn)行進(jìn)行分塊處理，保證每個分塊中的基向量能夠滿足KZ規(guī)約的條件，其規(guī)約的效果和效率取決于分塊的大小，分塊越大則效果越好同時效率也越低，為了優(yōu)化規(guī)約的效率，基于HE-LLL進(jìn)行了改進(jìn)，通過利用實(shí)測和模擬數(shù)據(jù)的分析，驗(yàn)證了改進(jìn)的BKZ算法的計(jì)算效率要明顯優(yōu)于BKZ規(guī)約基，同時其規(guī)約效果在理論上也優(yōu)于HE-LLL規(guī)約。 7.研究了基于深度優(yōu)先搜索模式的VB-SD和SE-SD算法，并且對格基規(guī)約過程對其搜索空間的影響進(jìn)行了分析，證明了格基規(guī)約的大小規(guī)約過程并不能改善搜索空間，而只有長度規(guī)約才會對搜索的效率和成功率產(chǎn)生影響，通過利用實(shí)測數(shù)據(jù)在不同情況下的分析證明了以上結(jié)論。 8.提出了基于HE-LLL規(guī)約的K-best搜索算法，基于深度優(yōu)先的搜索算法由于需要進(jìn)行復(fù)雜的迭代分析，在高維情況下效率較低，以K-best算法為代表的基于廣度優(yōu)先模式的球形搜索算法由于每次只搜索k個候選值，所以具有比較固定的復(fù)雜度，但是這導(dǎo)致了它是一種次優(yōu)的算法。為了滿足模糊度解算的精度要求，在格基質(zhì)量和搜索半徑約束兩個方面進(jìn)行了改進(jìn)，利用實(shí)測數(shù)據(jù)進(jìn)行了計(jì)算分析，結(jié)果表明本文提出的方法只需選取較小的k值即可獲得模糊度的最優(yōu)解，并且其效率穩(wěn)定不會隨著維數(shù)的增加而產(chǎn)生很大的變化，適用于高維的模糊度解算。 9. Voronoi cell作為一種具有對偶性質(zhì)的凸域幾何結(jié)構(gòu)，可用來對格上相關(guān)問題進(jìn)行分析研究。通過對格上向量對應(yīng)的Voronoi cell的分析，將模糊度CVP求解的問題轉(zhuǎn)化為求解目標(biāo)向量在原點(diǎn)的Voronoi cell中對應(yīng)向量的問題。利用Voronoi相關(guān)向量來構(gòu)造原點(diǎn)對應(yīng)的Voronoi cell，并且在此基礎(chǔ)上設(shè)計(jì)了基于Voronoi cell的模糊度CVP解算方法，利用一組模擬的2維數(shù)據(jù)，對算法的模糊度解算過程進(jìn)行了分析，基于其構(gòu)造的Voronoi cell對結(jié)果的可靠性進(jìn)行評價，同時選取幾組實(shí)測數(shù)據(jù)進(jìn)一步驗(yàn)證了算法的正確性。
[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.
【學(xué)位授予單位】：解放軍信息工程大學(xué)
【學(xué)位級別】：博士
【學(xué)位授予年份】：2013
【分類號】：P228.4

【參考文獻(xiàn)】

相關(guān)碩士學(xué)位論文 前1條

1 周小平;格基規(guī)約在MIMO中的應(yīng)用研究[D];北京郵電大學(xué);2011年

本文編號：2150729