CN113686336A - A method for improving underwater navigation accuracy based on iterative optimal loop points based on grid topology - Google Patents
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Abstract
Description
技术领域technical field
本发明属于水下导航学、海洋测绘学等交叉技术领域,尤其涉及一种基于格网拓扑结构迭代最佳环域点提高水下导航精度方法。The invention belongs to the cross technical fields of underwater navigation, oceanographic mapping and the like, and in particular relates to a method for improving underwater navigation accuracy based on iterative optimal ring domain points based on a grid topology structure.
背景技术Background technique
惯性导航系统(Inertial Navigation System,INS)是实现水下潜器自主导航的核心导航系统,具有短时高精度定位特性,但惯性元器件的固有误差和定位解算的多次积分等却导致INS误差随时间累积发散而难以满足潜器长航时高精度的定位目标,因此,INS需要进行定期校准以保持导航精度。Inertial Navigation System (INS) is the core navigation system to realize autonomous navigation of underwater submersibles. It has the characteristics of short-term high-precision positioning, but the inherent errors of inertial components and the multiple integration of positioning solutions lead to INS. The error accumulates and diverges with time, and it is difficult to meet the high-precision positioning target of the long-running submersible. Therefore, the INS needs to be calibrated regularly to maintain the navigation accuracy.
作为地球固有地理属性之一的重力场信息不易受气候、海浪等不确定环境影响并表现出长时间相对稳定性,故重力场信息适合被用于辅助导航,目前重力辅助导航系统作为水下辅助INS导航的一项重要技术并已成为国内外学者研究的国际热点议题。As one of the inherent geographical attributes of the earth, gravity field information is not easily affected by uncertain environments such as climate and ocean waves, and exhibits long-term relative stability. Therefore, gravity field information is suitable to be used for auxiliary navigation. At present, gravity-assisted navigation systems are used as underwater aids. INS navigation is an important technology and has become an international hot topic of research by scholars at home and abroad.
匹配算法是重力辅助惯导系统的核心,目前常见的重力匹配算法主要包括桑迪亚惯性地形辅助导航算法SITAN、迭代最近等值线点算法ICCP和地形轮廓匹配算法TERCOM。相较而言,TERCOM算法以计算简单、对初始误差不敏感、鲁棒性强、定位精度较高等优点而得到学者的广泛关注和研究。The matching algorithm is the core of the gravity-assisted inertial navigation system. At present, the common gravity matching algorithms mainly include the Sandia inertial terrain-assisted navigation algorithm SITAN, the iterative nearest contour point algorithm ICCP and the terrain contour matching algorithm TERCOM. In comparison, the TERCOM algorithm has received extensive attention and research by scholars for its advantages of simple calculation, insensitivity to initial error, strong robustness, and high positioning accuracy.
在提高TERCOM算法匹配精度方面,Liu等提出一种由坐标变换、误匹配检测和卡尔曼滤波相组合的新型INS/TERCOM系统优化结构,并研究其分散式与自适应联邦滤波信息融合算法的匹配性能;Yan等通过整合TERCOM和ICCP而提出一种新的匹配算法,以TERCOM得到初始位置并以ICCP进行精确定位;Yuan等以TERCOM/ICCP算法融合Kalman滤波而提出组合水下辅助导航算法,同时精确匹配精度采用滑动窗口以提高算法效率;Wang等基于TERCOM算法而提出旋转拼接型重力匹配算法;Tong等以二维高斯基函数对局部重力基准图逼近且以拟牛顿BFGS非线性寻优方法解算相关极值匹配模型而提出基于局部重力图逼近的组合匹配算法,同时以TERCOM的粗匹配和以差分法的实测数据预处理来提高算法的匹配精度;Zhao等将TERCOM算法与粒子滤波相组合而提出一种新的地形辅助导航算法以增强BITANII算法的定位精度;Wei等基于加权递减迭代而提出一种相关SITAN算法以解决初始误差和线性误差问题,同时将TERCOM用于算法的相关性处理过程;Zhang等为解决TERCOM算法易受高程测量误差、地形相似性等影响的误匹配问题而提出一种相关面内多参照点联合概率误匹配在线判断准则;Wang等在海斗数据支持下通过TERCOM算法实现地球海洋最深处的无声纳定位;Zhang等利用TERCOM算法仿真分析得出潜器航速、测深精度、初始位置偏差、水下地形特征、数字地图分辨率等主要因素对匹配精度的影响规律。在改善TERCOM算法匹配效率和可靠性方面,Han等融合最短路径算法和新相关分析算法而构建一种改进TERCOM算法,同时通过空间顺序约束和决策准则限制整合机制而提出一种误匹配诊断方法下的新匹配算法,以提高TERCOM的可靠性和匹配精度;刘现鹏等以INS输出的速度和航向信息追踪潜器航迹而提出一种基于航迹线追踪的TERPM定位算法;李钊伟等基于粗-细匹配策略而提出一种新型分层邻域阈值搜索法以改善TERCOM算法逐点遍历搜索的匹配效率;Li等通过球面几何的最短弧原则和空-海环境下姿态控制理论相耦合而提出一种新的基于测地线方法以缩小匹配区域尺度并改善算法的匹配效率;Zhang等以TERCOM为线匹配算法以几何相似性进行面匹配而提出线面组合的水下地形匹配算法,以提高算法的稳健性与定位精度。In improving the matching accuracy of the TERCOM algorithm, Liu et al. proposed a novel INS/TERCOM system optimization structure combining coordinate transformation, mismatch detection and Kalman filtering, and studied the matching of its decentralized and adaptive federated filtering information fusion algorithms performance; Yan et al. proposed a new matching algorithm by integrating TERCOM and ICCP, using TERCOM to obtain the initial position and using ICCP for precise positioning; Yuan et al. proposed a combined underwater assisted navigation algorithm by combining the TERCOM/ICCP algorithm with Kalman filtering, and at the same time The exact matching accuracy uses a sliding window to improve the efficiency of the algorithm; Wang et al. proposed a rotation-splicing gravity matching algorithm based on the TERCOM algorithm; Tong et al. approximated the local gravity reference map with a two-dimensional Gaussian function and solved it with a quasi-Newtonian BFGS nonlinear optimization method. A combined matching algorithm based on local gravity map approximation was proposed by calculating the relevant extreme value matching model. At the same time, the matching accuracy of the algorithm was improved by the rough matching of TERCOM and the preprocessing of measured data by the difference method; Zhao et al. combined the TERCOM algorithm with particle filtering. A new terrain-aided navigation algorithm was proposed to enhance the positioning accuracy of the BITANII algorithm; Wei et al. proposed a correlation SITAN algorithm based on weighted decreasing iteration to solve the initial error and linear error problems, and used TERCOM for the correlation processing of the algorithm. Process; Zhang et al. proposed an online judgment criterion for joint probability mismatch of multiple reference points in the correlation plane to solve the mismatch problem that the TERCOM algorithm is susceptible to elevation measurement errors, terrain similarity, etc.; Wang et al. The TERCOM algorithm realizes sonar-free positioning in the deepest part of the earth's oceans; Zhang et al. used the TERCOM algorithm to simulate and analyze the influence of the main factors such as the speed of the submersible, the sounding accuracy, the initial position deviation, the characteristics of the underwater terrain, and the resolution of the digital map on the matching accuracy. law. In terms of improving the matching efficiency and reliability of the TERCOM algorithm, Han et al. integrated the shortest path algorithm and the new correlation analysis algorithm to construct an improved TERCOM algorithm. At the same time, they proposed a mismatch diagnosis method through the spatial order constraint and the decision criterion constraint integration mechanism. To improve the reliability and matching accuracy of TERCOM; Liu Xianpeng et al. tracked the track of the submersible with the speed and heading information output by INS and proposed a TERPM positioning algorithm based on track line tracking; Li Zhaowei et al. proposed a new hierarchical neighborhood threshold search method to improve the matching efficiency of the point-by-point traversal search of the TERCOM algorithm; Li et al. proposed a method by coupling the shortest arc principle of spherical geometry and attitude control theory in air-sea environment The new geodesic-based method can reduce the size of the matching area and improve the matching efficiency of the algorithm; Zhang et al. used TERCOM as the line matching algorithm to perform surface matching with geometric similarity and proposed a line-surface combination underwater terrain matching algorithm to improve the algorithm. Robustness and positioning accuracy.
综上所述,大部分学者主要围绕TERCOM的应用和提高水下潜器导航性能展开研究,而鲜有关于改变TERCOM匹配格网拓扑结构方面的研究工作。但囿于传统TERCOM算法不依赖于航迹起点位置信息而仅以航迹终点处INS误差3倍作为半边长张成方型格网匹配点阵,并遍历搜索以确定水下潜器位置的最佳匹配定位,但该种搜索机制运算量大而易导致算法匹配效率低;此外,TERCOM算法难以有效处理观测噪声和过程噪声且对惯导航段的角度误差敏感等缺点,因此,需要进一步探讨不同于TERRCOM匹配格网拓扑结构的设计问题。To sum up, most scholars mainly focus on the application of TERCOM and the improvement of the navigation performance of underwater submersibles, and there is little research work on changing the topology of TERCOM matching grid. However, due to the fact that the traditional TERCOM algorithm does not rely on the position information of the starting point of the track, it only uses 3 times the INS error at the end of the track as the half length to form a square grid matching lattice, and traverse the search to determine the best match for the position of the underwater vehicle However, this search mechanism has a large amount of computation and is easy to lead to low matching efficiency of the algorithm; in addition, the TERCOM algorithm is difficult to effectively deal with observation noise and process noise, and is sensitive to the angle error of the inertial navigation segment. The design problem of matching grid topology.
发明内容SUMMARY OF THE INVENTION
本发明的技术解决问题:克服现有技术的不足,提供一种基于格网拓扑结构迭代最佳环域点提高水下导航精度方法和系统,旨在提高水下潜器重力辅助导航的匹配精度。The technical solution of the present invention is to overcome the deficiencies of the prior art, and to provide a method and system for improving the accuracy of underwater navigation based on iterative optimal loop points based on grid topology, aiming to improve the matching accuracy of gravity-assisted navigation of underwater submersibles. .
为了解决上述技术问题,本发明公开了一种基于格网拓扑结构迭代最佳环域点提高水下导航精度方法,包括:In order to solve the above technical problems, the present invention discloses a method for improving underwater navigation accuracy based on iterative optimal ring domain points based on grid topology structure, including:
通过航迹起点小环域格网匹配定位策略,得到水下潜器航迹起点的最佳匹配位置;The optimal matching position of the track starting point of the underwater vehicle is obtained through the grid matching and positioning strategy of the small ring area of the track starting point;
根据水下潜器航迹起点的最佳匹配位置,通过航迹终点变角度三层环域匹配定位策略,生成大环域待匹配格网点;According to the best matching position of the starting point of the track of the underwater vehicle, the grid points to be matched in the large ring area are generated through the variable angle three-layer ring field matching and positioning strategy at the end point of the track;
迭代计算大环域待匹配格网点的匹配效能评价指标,并按最优原则获得大环域范围内水下潜器航迹终点的最佳匹配位置,以实现水下潜器航迹终点的有效匹配定位,进而修正INS系统控制参数并辅助完成水下潜器长航时长航距的航行目标。Iteratively calculate the matching efficiency evaluation index of the grid points to be matched in the large ring domain, and obtain the best matching position of the end point of the track of the underwater vehicle within the scope of the large ring domain according to the optimal principle, so as to realize the effective performance of the end point of the track of the underwater vehicle. Matching and positioning, and then correcting the control parameters of the INS system and assisting the completion of the long-duration and long-distance navigation goal of the underwater submersible.
在上述基于格网拓扑结构迭代最佳环域点提高水下导航精度方法中,航迹起点小环域格网匹配定位策略的构建流程如下:In the above-mentioned method of improving underwater navigation accuracy based on iterative optimal loop points based on grid topology, the construction process of the small loop grid matching positioning strategy at the starting point of the track is as follows:
获取某段水下潜器航行按采样时间间隔Δt的INS航迹输出惯导序列{S1,S2,…,SL};其中,L表示INS航迹的采样序列长度,S1、S2、…、SL表示惯导序列中的各航迹点;Obtain the INS track output inertial navigation sequence {S 1 , S 2 ,..., S L } of the INS track of a certain submersible voyage according to the sampling time interval Δt; where L represents the sampling sequence length of the INS track, S 1 , S 2 , ..., SL represents each track point in the inertial navigation sequence;
从{S1,S2,…,SL}中提取得到各航迹点对应的位置坐标和实测重力值,构建得到位置坐标序列{(x1,y1),(x2,y2),…,(xL,yL)}和水下潜器实测重力值序列{g1,g2,…,gL};From {S 1 , S 2 ,…,S L }, the position coordinates and measured gravity values corresponding to each track point are extracted, and the position coordinate sequence {(x 1 , y 1 ), (x 2 , y 2 ) is constructed and obtained ,…,(x L ,y L )} and the underwater vehicle’s measured gravity value sequence {g 1 ,g 2 ,…,g L };
以惯导序列中的航迹起点S1的位置坐标(x1,y1)为中心,以3σ0作为最大外延的搜索边界半径,构建得到小环域;其中,σ0表示采样间隔为Δt时的惯导漂移误差的标准差;Taking the position coordinates (x 1 , y 1 ) of the track starting point S 1 in the inertial navigation sequence as the center, and taking 3σ 0 as the maximum extension search boundary radius, a small ring domain is constructed; among them, σ 0 indicates that the sampling interval is Δt The standard deviation of the inertial navigation drift error when ;
根据北偏东旋转角度θ0和环半径比例均分系数λ,确定小环域内的待匹配格点的总数目和位置坐标,构建得到小环域待匹配格网点集。According to the north-easterly rotation angle θ 0 and the ring radius proportional sharing coefficient λ, the total number and position coordinates of the grid points to be matched in the small ring domain are determined, and the set of grid points to be matched in the small ring domain is constructed.
在上述基于格网拓扑结构迭代最佳环域点提高水下导航精度方法中,小环域内各待匹配格网点的位置坐标的计算公式如下:In the above method for improving underwater navigation accuracy based on iterative optimal ring domain points based on grid topology, the position coordinates of each grid point to be matched in the small ring domain The calculation formula is as follows:
其中,和分别表示第i个小环上第j个格点的横纵坐标,ri表示小环域内第i个环的半径,βj表示小环域各环上第j个格点的旋转角度。in, and respectively represent the abscissa and vertical coordinates of the jth grid point on the ith ringlet, ri represents the radius of the ith ring in the ringlet domain, and βj represents the rotation angle of the jth grid point on each ring of the ringlet.
在上述基于格网拓扑结构迭代最佳环域点提高水下导航精度方法中,In the above method to improve underwater navigation accuracy based on iterative optimal loop points based on grid topology,
ri=3σ0λir i =3σ 0 λi
βj=j·θ0 β j =j·θ 0
其中,i=1,2,…,且i的最大值且j的最大值 Among them, i=1,2,..., and the maximum value of i and the maximum value of j
在上述基于格网拓扑结构迭代最佳环域点提高水下导航精度方法中,通过航迹起点小环域格网匹配定位策略,得到水下潜器航迹起点的最佳匹配位置,包括:In the above method of improving underwater navigation accuracy based on iterative optimal loop points based on grid topology, the optimal matching position of the track starting point of the underwater vehicle is obtained through the grid matching and positioning strategy of the small loop starting point of the track, including:
将航迹起点S1的位置坐标(x1,y1)和小环域内各待匹配格网点的位置坐标作为航迹起点真实位置的待匹配点集;The position coordinates (x 1 , y 1 ) of the track starting point S 1 and the position coordinates of the grid points to be matched in the small ring domain The set of points to be matched as the true position of the track start point;
逐点将航迹起点真实位置的待匹配点集映射到重力基准图上,并按最近重力基准格点处的重力值作为待匹配点重力值,得到(x1,y1)对应的理论重力值和对应的理论重力值 Map the set of points to be matched at the real position of the track starting point to the gravity reference map point by point, and take the gravity value at the nearest gravity reference grid point as the gravity value of the point to be matched, and obtain the theoretical gravity corresponding to (x 1 , y 1 ) value and The corresponding theoretical gravity value
其中,C表示重力基准图的格网分辨率,mapt(·,·)表示重力基准图按格点位置的重力值矩阵,[·]表示四舍五入取整;Among them, C represents the grid resolution of the gravity reference map, mapt(·,·) represents the gravity value matrix of the gravity reference map according to the grid position, and [·] represents the rounding;
按重力偏差绝对值最小化原则,得到水下潜器航迹起点的最佳匹配位置 According to the principle of minimizing the absolute value of gravity deviation, the best matching position of the starting point of the track of the underwater vehicle is obtained
其中,当i=0、j=0时,即为x1、即为y1。Among them, when i=0, j=0, is x 1 , That is y 1 .
在上述基于格网拓扑结构迭代最佳环域点提高水下导航精度方法中,航迹终点变角度三层环域匹配定位策略的构建流程如下:In the above-mentioned method for improving underwater navigation accuracy based on iterative optimal loop points based on grid topology, the construction process of the three-layer loop matching positioning strategy with variable angle at the end of the track is as follows:
根据惯导序列中的航迹起点S1的位置坐标(x1,y1)和航迹终点SL的位置坐标(xL,yL),确定得到水下潜器航行的航向信息和航距信息:According to the position coordinates (x 1 , y 1 ) of the track starting point S 1 and the position coordinates (x L , y L ) of the track end point S L in the inertial navigation sequence, it is determined to obtain the heading information and navigation of the underwater vehicle. Distance information:
其中,dINS表示以h∈[0,+∞)范数刻画惯导航迹起-终点间的距离度量,设h=2,即计算欧氏距离;αINS表示以坐标系的横坐标为正方向的航向弧度角;Among them, d INS represents the distance metric between the start and end points of the inertial navigation track with the h∈[0, +∞) norm, and set h=2, that is, calculate the Euclidean distance; α INS represents the abscissa of the coordinate system as a positive The heading radian angle of the direction;
根据以及水下潜器航行的航向信息和航距信息,估算得到大环域的中心位置坐标(xO,yO):according to As well as the heading information and distance information of the underwater vehicle navigation, the center position coordinates (x O , y O ) of the large ring domain are estimated:
以(xO,yO)为中心,以Rmax作为最大外延的搜索边界半径,构建得到覆盖航迹真实终点的变角度三层拓扑结构环型格网点区域,记作大环域;Taking (x O , y O ) as the center, and taking R max as the maximum extension search boundary radius, a variable-angle three-layer topology ring grid point area covering the true end point of the track is constructed, which is denoted as a large ring area;
以重力基准图的格网分辨率C作为大环域各环跨度间隔,得到大环域的总环数 Taking the grid resolution C of the gravity reference map as the span interval of each ring in the large ring, the total number of rings in the large ring is obtained
将重力基准图的格网分辨率C与中间环的半径之比作为大环域内各格点生成的基准角按“内倍外半”原则,确定大环域内层环上相邻格点间的跨度角为外层环上相邻格点间的跨度角为并结合总环数M,构建得到大环域待匹配格网点集;其中,大环域待匹配格网点集为变角度三环层格点拓扑结构。Compare the grid resolution C of the gravity datum map with the middle ring The ratio of the radii of , as the reference angle generated by each grid point in the large ring domain According to the principle of "inner double outer half", the span angle between adjacent lattice points on the inner ring of the large ring domain is determined as The span angle between adjacent lattice points on the outer ring is Combined with the total number of rings M, the set of grid points to be matched in the large ring domain is constructed; among them, the set of grid points to be matched in the large ring domain is a variable-angle three-ring layer grid point topology.
在上述基于格网拓扑结构迭代最佳环域点提高水下导航精度方法中,大环域待匹配格网点的生成方式如下:In the above-mentioned method for improving underwater navigation accuracy based on iterative optimal loop points based on grid topology, the grid points to be matched in the large loop are generated as follows:
将1σ-EPMP、2σ-EPMP、3σ-EPMP三种机制下大环域的总环数分别记作其中,σ表示惯导累积漂移误差标准差;The total number of rings in the macrocyclic domain under the three mechanisms of 1σ-EPMP, 2σ-EPMP and 3σ-EPMP is denoted as Among them, σ represents the standard deviation of the inertial navigation accumulated drift error;
对分别进行修正,得到修正后的三种机制下的大环域的总环数M′1、M′2、M′3:right Corrected respectively, to obtain the total ring numbers M′ 1 , M′ 2 , M′ 3 of the macroring domain under the three modified mechanisms:
其中,ξ=1,2,3,分别对应1σ-EPMP机制、2σ-EPMP机制、3σ-EPMP机制;Among them, ξ=1, 2, 3, corresponding to 1σ-EPMP mechanism, 2σ-EPMP mechanism, and 3σ-EPMP mechanism respectively;
根据修正后的三种机制下的大环域的总环数M1′、M2′、M3′,得到三种机制下大环域各环的半径R1,j、R2,j、R3,j:According to the total ring numbers M 1 ′, M 2 ′ and M 3 ′ of the macrocyclic domain under the three modified mechanisms, the radii R 1,j , R 2,j , R 3,j :
Rξ,ζ=ζC,ζ=1,2,…,M′ξ···(6)R ξ,ζ =ζC,ζ=1,2,...,M' ξ ...(6)
其中,Rξ,ζ表示第ξ种机制下的大环域的第ζ环的半径;Among them, R ξ,ζ represents the radius of the ζth ring of the macrocyclic domain under the ξth mechanism;
根据修正后的三种机制下的大环域的总环数M′1、M′2、M′3,得到三种机制下大环域的中间环半径 According to the revised total ring numbers M′ 1 , M′ 2 , M′ 3 of the macrocyclic domain under the three mechanisms, the intermediate ring radius of the macrocyclic domain under the three mechanisms is obtained
根据三种机制下大环域的中间环半径得到三种机制下大环域内各格点生成的基准角 According to the middle ring radius of the macrocyclic domain under the three mechanisms Obtain the reference angle generated by each lattice point in the large ring domain under the three mechanisms
根据(5)~(8),得到不同机制下的大环域待匹配格网点。According to (5)-(8), the grid points to be matched in the macroring domain under different mechanisms are obtained.
在上述基于格网拓扑结构迭代最佳环域点提高水下导航精度方法中,In the above method to improve underwater navigation accuracy based on iterative optimal loop points based on grid topology,
1σ-EPMP机制下大环域的内-中-外环层上各待匹配格网点的位置坐标的计算公式如下:The position coordinates of each grid point to be matched on the inner-middle-outer ring layer of the large ring domain under the 1σ-EPMP mechanism The calculation formula is as follows:
2σ-EPMP机制下大环域的内-中-外环层上各待匹配格网点的位置坐标的计算公式如下:The position coordinates of each grid point to be matched on the inner-middle-outer ring layer of the large ring domain under the 2σ-EPMP mechanism The calculation formula is as follows:
3σ-EPMP机制下大环域的内-中-外环层上各待匹配格网点的位置坐标的计算公式如下:The position coordinates of each grid point to be matched on the inner-middle-outer ring layer of the macroring domain under the 3σ-EPMP mechanism The calculation formula is as follows:
在上述基于格网拓扑结构迭代最佳环域点提高水下导航精度方法中,迭代计算大环域待匹配格网点的匹配效能评价指标,并按最优原则获得大环域范围内水下潜器航迹终点的最佳匹配位置,包括:In the above method of improving underwater navigation accuracy based on iterative optimal loop points based on grid topology, iteratively calculates the matching efficiency evaluation index of grid points to be matched in the large loop, and obtains the underwater diving within the large loop according to the optimal principle. The best matching position of the end point of the track of the aircraft, including:
确定第ξ种机制下大环域的内-中-外环层上的待匹配格网点的总数目Nξ;Determine the total number N ξ of grid points to be matched on the inner-middle-outer ring layer of the macroring domain under the ξth mechanism;
将第ξ种机制下大环域的第r个待匹配格网点作为待评估航迹终点,记作点其中,r∈{1,2,…,Nξ};Take the rth grid point to be matched in the large ring domain under the ξth mechanism as the end point of the track to be evaluated, denoted as a point where, r∈{1,2,…, Nξ };
将点在重力基准图中对应的位置(xr,yr)与重力基准图的格网分辨率C相比,并按四舍五入原则得到重力基准图上最近邻于点的格网点baseL;will point The corresponding position (x r , y r ) in the gravity reference map is compared with the grid resolution C of the gravity reference map, and the nearest adjacent point on the gravity reference map is obtained according to the rounding principle. The grid point base L of ;
将格网点baseL对应的重力值作为点重力值的近似;Set the gravity value corresponding to the grid point base L as a point Approximation of gravity value;
根据格网点baseL在重力基准图上的位置坐标、水下潜器航行的航速和航向,提取得到点对应的重力图航迹序列及对应的最近邻重力序列 According to the position coordinates of the grid point base L on the gravity reference map, the speed and heading of the underwater vehicle, the points are extracted. Corresponding gravity map track sequence and the corresponding nearest neighbor gravity sequence
将与水下潜器实测重力值序列{g1,g2,…,gL}进行对比,并计算匹配效能评价指标,记作MSDr;Will Compare with the actual gravity value sequence {g 1 ,g 2 ,...,g L } of the underwater vehicle, and calculate the matching efficiency evaluation index, denoted as MSD r ;
依次计算得到第ξ种机制下大环域的内-中-外环层上的各待匹配格网点的匹配效能评价指标,得到第ξ种机制下大环域的内-中-外环层上的所有待匹配格网点的匹配效能评价指标集和{MSDr|r=1,2,…,Nζ};Calculate the matching efficiency evaluation index of each grid point to be matched on the inner-middle-outer ring layer of the macroring domain under the ξth mechanism in turn, and obtain the inner-middle-outer ring layer of the macroring domain under the ξth mechanism. The matching performance evaluation index set and {MSD r |r=1,2,...,N ζ } of all grid points to be matched of ;
基于{MSDr|r=1,2,…,Nζ},按最优原则筛选得到大环域范围内水下潜器航迹终点的最佳匹配位置 Based on {MSD r |r=1,2,…,N ζ }, the best matching position of the end point of the track of the underwater vehicle in the large ring domain is obtained by filtering according to the optimal principle.
相应的,本发明还公开了一种基于格网拓扑结构迭代最佳环域点提高水下导航精度系统,包括:Correspondingly, the present invention also discloses a system for improving underwater navigation accuracy based on iterative optimal ring domain points based on grid topology structure, including:
解算模块,用于通过航迹起点小环域格网匹配定位策略,得到水下潜器航迹起点的最佳匹配位置;The solving module is used to obtain the best matching position of the starting point of the track of the underwater vehicle by matching the positioning strategy with the small ring grid at the starting point of the track;
生成模块,用于根据水下潜器航迹起点的最佳匹配位置,通过航迹终点变角度三层环域匹配定位策略,生成大环域待匹配格网点;The generation module is used to generate the grid points to be matched in the large ring area according to the best matching position of the starting point of the track of the underwater vehicle, through the variable angle three-layer ring matching and positioning strategy at the end point of the track;
迭代确定模块,用于迭代计算大环域待匹配格网点的匹配效能评价指标,并按最优原则获得大环域范围内水下潜器航迹终点的最佳匹配位置,以实现水下潜器航迹终点的有效匹配定位,进而修正INS系统控制参数并辅助完成水下潜器长航时长航距的航行目标。The iterative determination module is used to iteratively calculate the matching efficiency evaluation index of the grid points to be matched in the large ring area, and obtain the best matching position of the end point of the track of the underwater vehicle within the large ring area according to the optimal principle, so as to realize underwater diving. It can effectively match and locate the end point of the track of the underwater vehicle, and then correct the control parameters of the INS system and assist in the completion of the long-duration and long-distance navigation goal of the underwater submersible.
本发明具有以下优点:The present invention has the following advantages:
为突破传统重力匹配算法固有格网结构的限制并改善水下重力匹配导航精度,本发明提出一种新型格网拓扑结构迭代最佳环域点法(IOAP),其原理如下:首先,根据惯导起点位置和漂移误差及旋转角等构建航迹起点的小环域格网的匹配定位策略,通过小环域格网匹配点的匹配比较,得到航迹起点的最佳匹配定位并增强算法对初始位置误差的不敏感性;其次,利用航迹起点最佳匹配位置,再结合惯导航向航距信息、累积漂移误差等构造航迹终点变角度三层环域的匹配定位机制,以生成环型拓扑结构的环域匹配点;最后,迭代计算环域匹配点的匹配指标并按最优原则获得环域范围内航迹终点的最佳匹配位置。In order to break through the limitation of the inherent grid structure of the traditional gravity matching algorithm and improve the navigation accuracy of underwater gravity matching, the present invention proposes a new iterative optimal loop point method (IOAP) for the grid topology structure. The matching and positioning strategy of the small ring grid of the track starting point is constructed by guiding the starting point position, drift error and rotation angle. Through the matching comparison of the matching points of the small ring grid, the best matching positioning of the track starting point is obtained and the algorithm is enhanced. The insensitivity of the initial position error; secondly, using the best matching position of the starting point of the track, combined with the inertial navigation distance information, accumulated drift error, etc. Finally, iteratively calculates the matching index of the matching points in the loop domain and obtains the best matching position of the track end point within the loop domain according to the optimal principle.
综合考虑匹配精度统计指标、平均匹配时间和匹配成功率等作为匹配优劣的分析依据,验证了本发明所述的方法在不同惯导累积误差倍数或基准角环半径下的匹配性能差异性及其良好鲁棒性。Considering the statistical indicators of matching accuracy, average matching time and matching success rate, etc. as the analysis basis for matching quality, it verifies the matching performance difference of the method described in the present invention under different inertial navigation cumulative error multiples or reference angle ring radii. Its good robustness.
此为,通过对不同区域起点且终点落于不同重力区间的航迹进行重力匹配测试比较,证明了:本发明所述的方法具有匹配精度高、不同重力区段定位适用性强等优点,其平均匹配精度和最差匹配精度分别相对于TERCOM算法最高提升了40.39%和72.16%。This is, by comparing the gravity matching test of the tracks with the starting points and ending points in different gravity zones in different regions, it is proved that the method of the present invention has the advantages of high matching accuracy and strong positioning applicability in different gravity zones. Compared with the TERCOM algorithm, the average matching accuracy and worst matching accuracy are improved by 40.39% and 72.16% respectively.
附图说明Description of drawings
图1是本发明实施例中一种基于格网拓扑结构迭代最佳环域点提高水下导航精度方法的步骤流程图;1 is a flow chart of the steps of a method for improving underwater navigation accuracy based on iterative optimal ring domain points based on grid topology structure in an embodiment of the present invention;
图2是本发明实施例中一种基于SPMP策略的小环域待匹配点分布示意;2 is a schematic diagram of the distribution of points to be matched in a small ring domain based on an SPMP strategy in an embodiment of the present invention;
图3是本发明实施例中一种基于EPMP策略的大环域待匹配点分布示意;3 is a schematic diagram of the distribution of points to be matched in a large ring domain based on an EPMP strategy in an embodiment of the present invention;
图4是本发明实施例中一种研究区域卫星遥感及局部放大区域的重力异常分布示意;其中,4(a)为卫星遥感图,4(b)为重力异常基准图;4 is a schematic diagram of the distribution of gravity anomalies in a study area satellite remote sensing and a local enlarged area in the embodiment of the present invention; wherein, 4(a) is a satellite remote sensing map, and 4(b) is a gravity anomaly reference map;
图5是本发明实施例中一种不同σ准则下重力匹配算法的匹配测试效果对比示意图;其中,5(a)为TERCOM算法,5(b)为1σ-IOAP算法,5(c)为2σ-IOAP算法,5(d)为3σ-IOAP算法;5 is a schematic diagram of a comparison of the matching test effects of gravity matching algorithms under different σ criteria in an embodiment of the present invention; wherein, 5(a) is the TERCOM algorithm, 5(b) is the 1σ-IOAP algorithm, and 5(c) is the 2σ algorithm -IOAP algorithm, 5(d) is 3σ-IOAP algorithm;
图6是本发明实施例中一种不同定位精度下4种算法成功匹配概率的柱状对比图;Fig. 6 is a bar graph comparison of the successful matching probabilities of four algorithms under a different positioning accuracy in an embodiment of the present invention;
图7是本发明实施例中一种TERCOM算法匹配位置与真实位置对比及其格网点的类别划分示意图;其中,7(a)为TERCOM算法100次测试,7(b)为TERCOM算法匹配位置点分类;7 is a schematic diagram of the comparison between the matching position of a TERCOM algorithm and the real position and the classification of grid points in an embodiment of the present invention; wherein, 7(a) is 100 tests of the TERCOM algorithm, and 7(b) is the matching position point of the TERCOM algorithm Classification;
图8是本发明实施例中一种不同σ-IOAP算法的匹配位置与真实位置对比示意图;其中,8(a)为1σ-IOAP算法100次测试,8(b)为2σ-IOAP算法100次测试,8(c)为3σ-IOAP算法100次测试;FIG. 8 is a schematic diagram of comparing the matching position and the real position of a different σ-IOAP algorithm in an embodiment of the present invention; wherein, 8(a) is 100 tests of the 1σ-IOAP algorithm, and 8(b) is 100 times of the 2σ-IOAP algorithm Test, 8(c) is 100 tests of 3σ-IOAP algorithm;
图9是本发明实施例中一种不同环半径基准角下IOAP算法的匹配效果对比示意图;其中,9(a)为TERCOM算法,9(b)为1-IOAP算法,9(c)为1.5-IOAP算法,9(d)为2-IOAP算法,9(e)为2.5-IOAP算法;9 is a schematic diagram of the comparison of the matching effects of the IOAP algorithm under a different ring radius reference angle in an embodiment of the present invention; wherein, 9(a) is the TERCOM algorithm, 9(b) is the 1-IOAP algorithm, and 9(c) is 1.5 -IOAP algorithm, 9(d) is 2-IOAP algorithm, 9(e) is 2.5-IOAP algorithm;
图10是本发明实施例中一种不同环半径基准角下IOAP算法匹配成功概率的柱状对比图;Fig. 10 is a columnar comparison chart of the IOAP algorithm matching success probability under a kind of different ring radius reference angles in the embodiment of the present invention;
图11是本发明实施例中一种不同航迹起点下算法匹配定位效果的对比示意图;其中,11(a)为TERCOM算法(航迹起点A),11(b)为TERCOM算法(航迹起点B),11(c)为TERCOM算法(航迹起点C),11(d)为1.5-IOAP算法(航迹起点A),11(e)为1.5-IOAP算法(航迹起点B),11(f)为1.5-IOAP算法(航迹起点C)。11 is a schematic diagram of the comparison of the matching and positioning effects of algorithms under different track starting points in the embodiment of the present invention; wherein, 11(a) is the TERCOM algorithm (track starting point A), and 11(b) is the TERCOM algorithm (track starting point A) B), 11(c) is TERCOM algorithm (track starting point C), 11(d) is 1.5-IOAP algorithm (track starting point A), 11(e) is 1.5-IOAP algorithm (track starting point B), 11 (f) is the 1.5-IOAP algorithm (track start point C).
具体实施方式Detailed ways
为使本发明的目的、技术方案和优点更加清楚,下面将结合附图对本发明公开的实施方式作进一步详细描述。In order to make the objectives, technical solutions and advantages of the present invention clearer, the embodiments disclosed in the present invention will be described in further detail below with reference to the accompanying drawings.
本发明基于TERCOM算法匹配点阵的结构布局以及INS系统的漂移误差特性,提出了一种基于格网拓扑结构迭代最佳环域点提高水下导航精度方法,简称IOAP算法,其实现原理如下:为降低IOAP算法对初始误差的敏感性,以惯导起点位置为中心并以一定漂移误差和旋转角张成小环域匹配格点,构建环型拓扑结构的航迹起点小环域匹配定位策略,并按重力偏差绝对值最小化原则得到起点最优匹配位置;根据航迹起点的最佳匹配位置,再结合惯导航向航距信息得到大环域匹配格网的中心位置,再基于惯导累积漂移误差等以确定大环域匹配格网环数,并按中间环半径的格点基准偏转角和“内倍外半”原则,得到匹配格网点环形分布的拓扑结构,并构建航迹终点变角度三层环域的匹配定位策略,通过格网点提取重力图序列再与实测重力序列间计算均方差并匹配比较,按均方差最小化原则得到航迹终点的最佳匹配位置。Based on the TERCOM algorithm matching the structure layout of the lattice and the drift error characteristics of the INS system, the present invention proposes a method for improving the underwater navigation accuracy based on the iterative optimal loop points based on the grid topology structure, which is referred to as the IOAP algorithm, and its realization principle is as follows: In order to reduce the sensitivity of the IOAP algorithm to the initial error, the starting point position of the inertial navigation system is taken as the center, and a small ring field matching lattice is formed with a certain drift error and rotation angle, and a small ring field matching and positioning strategy of the track start point of the ring topology is constructed. , and obtain the optimal matching position of the starting point according to the principle of minimizing the absolute value of the gravity deviation; according to the optimal matching position of the starting point of the track, combined with the information of the inertial navigation direction, the center position of the matching grid in the large ring domain is obtained, and then based on the inertial navigation Accumulate drift error, etc. to determine the number of matching grid rings in the large ring domain, and according to the grid point deflection angle of the intermediate ring radius and the principle of "inside double outer half", obtain the topology structure matching the annular distribution of grid points, and construct the track end point The matching and positioning strategy of the variable-angle three-layer ring domain is to extract the gravity map sequence through grid points, and then calculate the mean square error between the measured gravity sequence and the measured gravity series, and then match and compare, and obtain the best matching position of the end of the track according to the principle of minimizing the mean square error.
如图1,在本实施例中,该基于格网拓扑结构迭代最佳环域点提高水下导航精度方法,包括:As shown in Figure 1, in this embodiment, the method for improving underwater navigation accuracy based on iterative optimal ring domain points based on grid topology structure includes:
步骤101,通过航迹起点小环域格网匹配定位策略,得到水下潜器航迹起点的最佳匹配位置。
在本实施例中,考虑到SITAN和ICCP等重力匹配算法对初始误差的相对敏感性问题,同时为一定程度上改善IOAP算法对重力匹配初始误差的不敏感性(鲁棒性),构建了航迹起点小环域格网匹配定位策略/机制(Matching Positioning strategy of thetracking Starting Point in small ring domain,SPMP)。其中,SPMP策略以惯导指示水下潜器位置为中心并以一定的漂移误差和旋转角度张成一个小型依概率覆盖航迹真实起点位置的待匹配的小环形拓扑结构格网点区域(记为小环域),再通过待匹配点重力匹配评价指标的最优原则以确定出航迹起点的最佳匹配位置。In this embodiment, considering the relative sensitivity of gravity matching algorithms such as SITAN and ICCP to the initial error, and at the same time to improve the insensitivity (robustness) of the IOAP algorithm to the initial error of gravity matching to a certain extent, a navigation system is constructed. Matching Positioning strategy of the tracking Starting Point in small ring domain (SPMP). Among them, the SPMP strategy takes the position of the underwater vehicle indicated by the inertial navigation as the center, and uses a certain drift error and rotation angle to form a small annular topology grid point area to be matched that covers the true starting point position of the track according to the probability (denoted as Small ring domain), and then determine the best matching position of the starting point of the track through the optimal principle of the gravity matching evaluation index of the point to be matched.
优选的,航迹起点小环域格网匹配定位策略的构建流程可以如下:Preferably, the construction process of the small ring domain grid matching positioning strategy at the starting point of the track may be as follows:
获取某段水下潜器航行按采样时间间隔Δt的INS航迹输出惯导序列{S1,S2,…,SL};从{S1,S2,…,SL}中提取得到各航迹点对应的位置坐标和实测重力值,构建得到位置坐标序列{(x1,y1),(x2,y2),…,(xL,yL)}和水下潜器实测重力值序列{g1,g2,…,gL}。其中,L表示INS航迹的采样序列长度,S1、S2、…、SL表示惯导序列中的各航迹点。Obtain the inertial navigation sequence {S 1 ,S 2 ,…,S L } of the INS track output by the sampling time interval Δt of a certain underwater vehicle navigation; extracted from {S 1 ,S 2 ,…,S L } The position coordinates and the measured gravity value corresponding to each track point are constructed to obtain the position coordinate sequence {(x 1 , y 1 ), (x 2 , y 2 ),...,(x L , y L )} and the submersible Sequence of measured gravity values {g 1 ,g 2 ,…,g L }. Among them, L represents the sampling sequence length of the INS track, and S 1 , S 2 , ..., SL represent each track point in the inertial navigation sequence.
则,SPMP策略下,以惯导序列中的航迹起点S1的位置坐标(x1,y1)为中心,以3σ0作为最大外延的搜索边界半径,确定小环域。进一步的,根据北偏东旋转角度θ0和环半径比例均分系数λ,可以确定小环域内的待匹配格点的总数目和位置坐标,进而构建得到小环域待匹配格网点集。其中,σ0表示采样间隔为Δt时的惯导漂移误差的标准差。例如,当θ0=45、λ=1/3时,SPMP策略所张成的小环域待匹配格网点集的分布如图2所示。Then, under the SPMP strategy, take the position coordinates (x 1 , y 1 ) of the track starting point S 1 in the inertial navigation sequence as the center, and take 3σ 0 as the maximum extension search boundary radius to determine the small ring domain. Further, according to the north easterly rotation angle θ 0 and the ring radius proportional sharing coefficient λ, the total number and position coordinates of the grid points to be matched in the small ring domain can be determined, and then the set of grid points to be matched in the small ring domain can be constructed. Among them, σ 0 represents the standard deviation of the inertial navigation drift error when the sampling interval is Δt. For example, when θ 0 =45 and λ = 1/3, the distribution of the grid point set to be matched in the small ring domain stretched by the SPMP strategy is shown in FIG. 2 .
进一步的,根据上述参变量的设置情况,可得小环域内各待匹配格网点的位置坐标的计算公式如下:Further, according to the setting of the above parameters, the position coordinates of each grid point to be matched in the small ring domain can be obtained. The calculation formula is as follows:
其中,和分别表示第i个小环上第j个格点的横纵坐标;ri表示小环域内第i个环的半径,ri=3σ0λi;βj表示小环域各环上第j个格点的旋转角度,βj=j·θ0;i=1,2,…,且i的最大值且j的最大值 in, and respectively represent the abscissa and vertical coordinates of the jth lattice point on the ith ringlet; ri represents the radius of the ith ring in the ringlet domain, ri = 3σ 0 λi; β j represents the jth ring on each ring of the ringlet domain Rotation angle of lattice point, β j =j·θ 0 ; i=1,2,..., and the maximum value of i and the maximum value of j
则,水下潜器航迹起点的最佳匹配位置的确定流程可以如下:Then, the process of determining the best matching position of the starting point of the track of the underwater vehicle can be as follows:
将航迹起点S1的位置坐标(x1,y1)和小环域内各待匹配格网点的位置坐标作为航迹起点真实位置的待匹配点集;逐点将航迹起点真实位置的待匹配点集映射到重力基准图上,并按最近重力基准格点处的重力值作为待匹配点重力值,得到(x1,y1)对应的理论重力值和对应的理论重力值 The position coordinates (x 1 , y 1 ) of the track starting point S 1 and the position coordinates of the grid points to be matched in the small ring domain The set of points to be matched as the real position of the starting point of the track; the set of points to be matched at the real position of the starting point of the track is mapped to the gravity reference map point by point, and the gravity value at the nearest gravity reference grid point is used as the gravity value of the point to be matched, Get the theoretical gravity value corresponding to (x 1 , y 1 ) and The corresponding theoretical gravity value
为确定水下潜器航迹起点的最佳匹配位置,可按重力偏差绝对值最小化原则,得到水下潜器航迹起点的最佳匹配位置 In order to determine the best matching position of the starting point of the track of the underwater vehicle, the best matching position of the starting point of the track of the underwater vehicle can be obtained according to the principle of minimizing the absolute value of the gravity deviation.
其中,C表示重力基准图的格网分辨率,mapt(·,·)表示重力基准图按格点位置的重力值矩阵,[·]表示四舍五入取整;当i=0、j=0时,即为x1、即为y1。Among them, C represents the grid resolution of the gravity reference map, mapt(·,·) represents the gravity value matrix of the gravity reference map according to the grid point position, [·] represents the rounding; when i=0, j=0, is x 1 , That is y 1 .
需要说明的是,小范围多格点进行重力基准图映射时可能会出现多模态现象,本实施例按第一个重力偏差绝对值最小格点予以匹配,当然也可按随机选择机制得到航迹起点的最佳匹配,本实施例对此不作限制。It should be noted that the multi-modal phenomenon may occur when the gravity reference map is mapped to a small range of multi-grid points. In this embodiment, the first grid point with the smallest absolute value of the gravity deviation is matched. Of course, the navigation can also be obtained according to the random selection mechanism. The best matching of the starting point of the trace is not limited in this embodiment.
由上可见,SPMP策略可依概率实现水下潜器航迹起点的有效匹配定位,并弱化IOAP算法对初始误差的敏感性,同时为下一步基于惯导航向航距信息引导的航迹终点位置匹配定位提供航迹起点的位置信息基础。It can be seen from the above that the SPMP strategy can realize the effective matching and positioning of the starting point of the track of the underwater vehicle according to the probability, and weaken the sensitivity of the IOAP algorithm to the initial error. Matching positioning provides the basis for the location information of the origin of the track.
步骤102,根据水下潜器航迹起点的最佳匹配位置,通过航迹终点变角度三层环域匹配定位策略,生成大环域待匹配格网点。In
在本实施例中,考虑到惯导航迹序列蕴藏着较好的短时高精度航向和航距信息,结合SPMP策略所得的航迹起点最佳匹配位置可进一步推得航迹终点待匹配域的中心位置O;再基于惯导系统的漂移误差统计特性而构建新的待匹配格网点环形分布的拓扑结构及其匹配定位策略(航迹终点变角度三层环域匹配定位策略/机制,MatchingPositioning mechanism of the tracking Ending Point in three-layer loopdomain,EPMP),EPMP策略以惯导累积漂移误差标准差σ、重力基准图的格网分辨率C和中间环的半径三者间的相对关系,得到环形覆盖区域的最大环数和匹配格网点间的偏转角并张成一个大的依概率覆盖航迹真实终点位置的待匹配的变角度三层拓扑结构环型格网点区域,记为大环域;再按各格网点坐标位置提取出匹配航迹的重力图序列再与水下潜器的真实重力序列比对并按评价指标最优原则确定出航迹终点的最佳匹配位置。In this embodiment, considering that the inertial navigation track sequence contains better short-term high-precision heading and distance information, the best matching position of the track starting point obtained by combining the SPMP strategy The center position O of the track end point to be matched can be further deduced; then based on the drift error statistical characteristics of the inertial navigation system, a new topology structure of the grid points to be matched is constructed and its matching positioning strategy (track end point variable angle three) is constructed. Layer loop domain matching positioning strategy/mechanism, MatchingPositioning mechanism of the tracking Ending Point in three-layer loopdomain, EPMP), EPMP strategy is based on the inertial navigation cumulative drift error standard deviation σ, the grid resolution C of the gravity reference map and the intermediate loop The relative relationship between the three radii, the maximum number of loops in the annular coverage area and the deflection angle between the matching grid points are obtained, and a large variable-angle three-layer topology to be matched covering the true end position of the track according to probability is formed. The grid point area is recorded as a large ring area; then the gravity map sequence matching the track is extracted according to the coordinate position of each grid point, and then compared with the real gravity sequence of the underwater vehicle, and the end point of the track is determined according to the principle of optimal evaluation index. Best match location.
优选的,航迹终点变角度三层环域匹配定位策略的构建流程可以如下:Preferably, the construction process of the variable-angle three-layer ring domain matching positioning strategy at the track end point may be as follows:
根据惯导序列中的航迹起点S1的位置坐标(x1,y1)和航迹终点SL的位置坐标(xL,yL),确定得到水下潜器航行的航向信息和航距信息:According to the position coordinates (x 1 , y 1 ) of the track starting point S 1 and the position coordinates (x L , y L ) of the track end point S L in the inertial navigation sequence, it is determined to obtain the heading information and navigation of the underwater vehicle. Distance information:
其中,dINS表示以h∈[0,+∞)范数刻画惯导航迹起-终点间的距离度量,设h=2,即计算欧氏距离;αINS表示以坐标系的横坐标为正方向的航向弧度角。Among them, d INS represents the distance metric between the start and end points of the inertial navigation track with the h∈[0, +∞) norm, and set h=2, that is, calculate the Euclidean distance; α INS represents the abscissa of the coordinate system as a positive The heading angle in radians of the direction.
然后,根据以及水下潜器航行的航向信息和航距信息,估算得到大环域的中心位置坐标(xO,yO):Then, according to As well as the heading information and distance information of the underwater vehicle navigation, the center position coordinates (x O , y O ) of the large ring domain are estimated:
则,EPMP策略下,以(xO,yO)为中心,以Rmax作为最大外延的搜索边界半径,构建得到覆盖航迹真实终点的变角度三层拓扑结构环型格网点区域,记作大环域。同时,以重力基准图的格网分辨率C作为大环域各环跨度间隔,得到大环域的总环数 Then, under the EPMP strategy, with (x O , y O ) as the center and R max as the maximum extension search boundary radius, a variable-angle three-layer topology ring grid point area covering the true end point of the track is constructed, denoted as Large ring domain. At the same time, the grid resolution C of the gravity reference map is used as the span interval of each ring in the large ring, and the total number of rings in the large ring is obtained.
在此基础上,再给定大环域的各环上相邻格点间的偏转角度,即可张成一待匹配格网点集。若选择与SPMP策略相同的方式来确定大环域的各环上相邻格点间的偏转角度,大环域等偏转角度会保持各环相等量的格点,则会导致SPMP策略所张成的格网出现“内密外稀”现象,即内层环格点间隔过小而外侧环格点间隔则过大。故而,针对大环域,本发明实施例提出了一种新型的确定相邻格点间的偏转角度的方式,即变角度三环层格点拓扑结构:以重力基准图的格网分辨率C与中间环的半径之比作为大环域内各格点生成的基准角按“内倍外半”原则,确定大环域内层环上相邻格点间的跨度角为外层环上相邻格点间的跨度角为并结合总环数M,构建得到大环域待匹配格网点集,为一变角度三环层格点拓扑结构。例如,当M=9时,EPMP策略所张成的大环域待匹配格网点集的分布如图3所示。On this basis, given the deflection angle between adjacent grid points on each ring of the large ring domain, a set of grid points to be matched can be formed. If you choose the same method as the SPMP strategy to determine the deflection angle between adjacent lattice points on each ring of the large ring domain, the deflection angle of the large ring domain will keep the same amount of grid points on each ring, which will lead to the expansion of the SPMP strategy. There is a phenomenon of “inner dense and outer sparse” in the grid of , that is, the interval between the inner ring grid points is too small and the outer ring grid point interval is too large. Therefore, for the large ring domain, the embodiment of the present invention proposes a new method for determining the deflection angle between adjacent grid points, that is, the variable-angle three-ring layer grid point topology: the grid resolution C of the gravity reference map is used. with middle ring The ratio of the radii of , as the reference angle generated by each grid point in the large ring domain According to the principle of "inner double outer half", the span angle between adjacent lattice points on the inner ring of the large ring domain is determined as The span angle between adjacent lattice points on the outer ring is Combined with the total number of rings M, the set of grid points to be matched in the large ring domain is constructed, which is a variable-angle three-ring layer grid point topology. For example, when When M=9, the distribution of the grid point set to be matched in the large ring domain formed by the EPMP strategy is shown in Fig. 3 .
在本实施例中,考虑到自然条件下正态分布对任意系统误差的良好适用性及3σ准则99.73%的高概率覆盖特性,同时为后续测验不同σ(σ,表示惯导累积漂移误差标准差)原则下EPMP策略的水下重力匹配效能差异性,则根据不同σ原则分别构建了基于1σ-EPMP、2σ-EPMP、3σ-EPMP机制的三种IOAP算法,简记为1σ-IOAP、2σ-IOAP、3σ-IOAP。其中,采用ξ=1,2,3来表示1σ-EPMP、2σ-EPMP、3σ-EPMP三种机制,即,ξ=1,表示1σ-EPMP机制;ξ=2,表示2σ-EPMP机制;ξ=3,表示3σ-EPMP机制。In this embodiment, considering the good applicability of normal distribution to any systematic error under natural conditions and the high probability coverage of 99.73% of the 3σ criterion, at the same time, different σ(σ) is used for the subsequent tests, indicating the standard deviation of the inertial navigation cumulative drift error. ) principle, three IOAP algorithms based on 1σ-EPMP, 2σ-EPMP, and 3σ-EPMP mechanisms are constructed according to different σ principles, which are abbreviated as 1σ-IOAP, 2σ- IOAP, 3σ-IOAP. Among them, ξ=1, 2, 3 are used to represent the three mechanisms of 1σ-EPMP, 2σ-EPMP and 3σ-EPMP, that is, ξ=1, representing the 1σ-EPMP mechanism; ξ=2, representing the 2σ-EPMP mechanism; ξ =3, indicating the 3σ-EPMP mechanism.
则可以按照如下新方式构建EPMP策略:Then the EPMP policy can be constructed in the following new way:
将1σ-EPMP、2σ-EPMP、3σ-EPMP三种机制下大环域的总环数分别记作 The total number of rings in the macrocyclic domain under the three mechanisms of 1σ-EPMP, 2σ-EPMP and 3σ-EPMP is denoted as
考虑到不同σ原则下大环域总环数未必为3倍数,同时为进一步增强EPMP策略大环域格点对水下潜器真实位置的良好覆盖效果,可按如下公式对分别进行修正,得到修正后的三种机制下的大环域的总环数M1′、M2′、M3′,以便于后续对大环域的内中外三环层的划分:Considering that the total number of loops in the large loop is not necessarily a multiple of 3 under different σ principles, and at the same time to further enhance the good coverage effect of the EPMP strategy on the real position of the submersible by the large loop grid, the following formula can be used to calculate: Correction is made respectively to obtain the total number of rings M 1 ′, M 2 ′ and M 3 ′ of the macrocyclic domain under the revised three mechanisms, so as to facilitate the subsequent division of the inner, middle and outer three-ring layers of the macrocyclic domain:
则,根据修正后的三种机制下的大环域的总环数M1′、M2′、M3′,可以得到三种机制下大环域各环的半径R1,j、R2,j、R3,j,以及三种机制下大环域的中间环半径 Then, according to the total number of rings M 1 ′, M 2 ′ and M 3 ′ of the macrocyclic domain under the revised three mechanisms, the radii R 1,j , R 2 of each ring of the macrocyclic domain under the three mechanisms can be obtained ,j , R 3,j , and the intermediate ring radius of the macroring domain under the three mechanisms
Rξ,ζ=ζC,ζ=1,2,…,M′ξ···(6)R ξ,ζ =ζC,ζ=1,2,...,M' ξ ...(6)
其中,Rξ,ζ表示第ξ种机制下的大环域的第ζ环的半径。where R ξ,ζ denotes the radius of the ζth ring of the macrocyclic domain under the ξth mechanism.
进而,可以得到三种机制下大环域内各格点生成的基准角 Furthermore, the reference angles generated by each lattice point in the macrocyclic domain under the three mechanisms can be obtained
最后,根据(5)~(8),得到不同机制下的大环域待匹配格网点。其中,各机制下的大环域待匹配格网点的计算式如下:Finally, according to (5)-(8), the grid points to be matched in the macroring domain under different mechanisms are obtained. Among them, the calculation formula of the grid points to be matched in the large ring domain under each mechanism is as follows:
1σ-EPMP机制下大环域的内-中-外环层上各待匹配格网点的位置坐标的计算式为:The position coordinates of each grid point to be matched on the inner-middle-outer ring layer of the large ring domain under the 1σ-EPMP mechanism The calculation formula is:
2σ-EPMP机制下大环域的内-中-外环层上各待匹配格网点的位置坐标的计算式为:The position coordinates of each grid point to be matched on the inner-middle-outer ring layer of the large ring domain under the 2σ-EPMP mechanism The calculation formula is:
3σ-EPMP机制下大环域的内-中-外环层上各待匹配格网点的位置坐标的的计算式为:The position coordinates of each grid point to be matched on the inner-middle-outer ring layer of the macroring domain under the 3σ-EPMP mechanism The calculation formula is:
步骤103,迭代计算大环域待匹配格网点的匹配效能评价指标,并按最优原则获得大环域范围内水下潜器航迹终点的最佳匹配位置,以实现水下潜器航迹终点的有效匹配定位,进而修正INS系统控制参数并辅助完成水下潜器长航时长航距的航行目标。
在本实施例中,考虑到重力基准图中格网分辨率处重力值的较高准确性而插值法推算的重力值未必能真实反映匹配点处的实际重力,因此,可以采用类似于传统TERCOM算法的匹配过程,以确定EPMP大环域待匹配点集中水下潜器终点的最佳匹配定位。In this embodiment, considering the high accuracy of the gravity value at the grid resolution in the gravity reference map, the gravity value calculated by the interpolation method may not truly reflect the actual gravity at the matching point. The matching process of the algorithm is to determine the best matching positioning of the end point of the underwater vehicle in the set of points to be matched in the EPMP large ring.
优选的,一种可行的迭代计算大环域待匹配格网点的匹配效能评价指标,并按最优原则获得大环域范围内水下潜器航迹终点的最佳匹配位置的方式如下:Preferably, a feasible way to iteratively calculate the matching efficiency evaluation index of the grid points to be matched in the large ring area, and obtain the best matching position of the end point of the track of the underwater vehicle in the large ring area according to the optimal principle is as follows:
确定第ξ种机制下大环域的内-中-外环层上的待匹配格网点的总数目Nξ。Determine the total number N ξ of grid points to be matched on the inner-middle-outer ring layer of the macroring domain under the ξth mechanism.
将第ξ种机制下大环域的第r(r∈{1,2,…,Nξ})个待匹配格网点作为待评估航迹终点,记作点将点在重力基准图中对应的位置(xr,yr)与重力基准图的格网分辨率C相比,并按四舍五入原则得到重力基准图上最近邻于点的格网点baseL。将格网点baseL对应的重力值作为点重力值的近似;根据格网点baseL在重力基准图上的位置坐标、水下潜器航行的航速和航向,提取得到点对应的重力图航迹序列及对应的最近邻重力序列将与水下潜器实测重力值序列{g1,g2,…,gL}进行对比,并计算匹配效能评价指标,记作MSDr。其中,需要说明的是,在计算匹配效能评价指标时,可以选择任意一种适当效能评价指标进行计算匹配,本实施例中是以均方差MSD为例进行的说明。Take the r (r∈{1,2,…,N ξ })th grid point to be matched in the large ring domain under the ξth mechanism as the end point of the track to be evaluated, denoted as a point will point The corresponding position (x r , y r ) in the gravity reference map is compared with the grid resolution C of the gravity reference map, and the nearest adjacent point on the gravity reference map is obtained according to the rounding principle. The grid point base L . Set the gravity value corresponding to the grid point base L as a point The approximation of the gravity value; according to the position coordinates of the grid point base L on the gravity reference map, the speed and course of the underwater vehicle, the points are extracted and obtained. Corresponding gravity map track sequence and the corresponding nearest neighbor gravity sequence Will Compare with the measured gravity value sequence {g 1 ,g 2 ,...,g L } of the submersible, and calculate the matching efficiency evaluation index, denoted as MSD r . It should be noted that, when calculating the matching efficiency evaluation index, any appropriate efficiency evaluation index may be selected for calculation and matching. In this embodiment, the mean square error MSD is used as an example for description.
按照上述第r个待匹配格网点的计算过程,可以依次计算得到第ξ种机制下大环域的内-中-外环层上的各待匹配格网点的匹配效能评价指标,得到第ξ种机制下大环域的内-中-外环层上的所有待匹配格网点的匹配效能评价指标集和{MSDr|r=1,2,…,Nζ}。According to the above calculation process of the rth grid point to be matched, the matching efficiency evaluation index of each grid point to be matched on the inner-middle-outer ring layer of the large ring domain under the ξth mechanism can be calculated in turn, and the ξth mechanism can be obtained. The matching performance evaluation index set of all grid points to be matched on the inner-middle-outer ring layer of the large ring domain under the mechanism is {MSD r |r=1,2,...,N ζ }.
最后,基于{MSDr|r=1,2,…,Nζ},按最优原则筛选得到大环域范围内水下潜器航迹终点的最佳匹配位置 Finally, based on {MSD r |r=1,2,...,N ζ }, the best matching position of the end point of the track of the underwater vehicle within the large ring domain is obtained by filtering according to the optimal principle.
综上,通过上述步骤101~103,实现了水下潜器终点的有效匹配定位,将得到的水下潜器航迹终点的最佳匹配位置作为水下潜器航迹终点,以修正INS系统控制参数,并辅助完成水下潜器长航时长航距的航行目标。In summary, through the
在上述实施例的基础上,下面对上述实施例所述的基于格网拓扑结构迭代最佳环域点提高水下导航精度方法进行验证。On the basis of the above embodiment, the method for improving the underwater navigation accuracy based on the iterative optimal loop domain point based on the grid topology structure described in the above embodiment is verified below.
为验证该IOAP算法在水下潜器重力导航应用中的有效性和优越性,共设计3组测试:In order to verify the effectiveness and superiority of the IOAP algorithm in the application of underwater vehicle gravity navigation, a total of 3 sets of tests are designed:
测试1,验证不同σ准则下IOAP算法的匹配性能差异;Test 1, to verify the matching performance difference of the IOAP algorithm under different σ criteria;
测试2,以不同环半径下的基准角验证其对算法匹配性能的不同影响;Test 2, verify the different influences on the algorithm matching performance with reference angles under different ring radii;
测试3,以不同区域航迹起点验证所提IOAP算法对水下重力匹配导航的良好适用性。In Test 3, the good applicability of the proposed IOAP algorithm to underwater gravity matching navigation is verified with the starting points of different regional tracks.
实例数据源自加利福尼亚大学圣迭戈分校网站(http://topex.ucsd.edu/),其分辨率为1′×1′的重力异常数据。如图4(a)所示,本发明选取南海地区重力异常数据进行研究,其数据经纬度取值范围为(经度113°E–115°E,纬度10°N–12°N)。本发明通过双线性插值法将重力异常基准数据转换成100m×100m的格网分辨率重力数据,如图4(b)所示,该区域重力异常最大值为130.57mGal,最小值为-33.53mGal,平均值为15.43mGal。The example data is derived from the website of the University of California, San Diego (http://topex.ucsd.edu/), and its resolution is 1′×1′ gravity anomaly data. As shown in Fig. 4(a), the present invention selects the gravity anomaly data in the South China Sea for research, and the longitude and latitude of the data ranges from (113°E–115°E longitude, 10°N–12°N latitude). The present invention converts the gravity anomaly reference data into 100m×100m grid resolution gravity data through the bilinear interpolation method, as shown in Figure 4(b), the maximum gravity anomaly in this area is 130.57mGal, and the minimum value is -33.53 mGal, with an average of 15.43 mGal.
(1)不同σ准则下IOAP算法的匹配性能差异性验证(1) The matching performance difference verification of IOAP algorithm under different σ criteria
模拟样本区块内重力异常格网分辨率为100m×100m、加速度计常值零偏10-3m/s2(惯导均方根误差服从正态分布)、航速10m/s1、航向北偏东70°、初始位置误差0m、速度误差0.04m/s1、航向误差0.05°、重力仪实时测量数据为真实航迹在重力异常数据库中的采样值叠加标准差为1mGal的随机噪声,采样点数目110个、采样周期20s。其中,本发明定义匹配定位精度为l,则匹配位置与真实位置的绝对值之差在闭区间[0,l]内即为有效匹配,故可得N次实验测试下算法的有效匹配次数n和算法的匹配成功率同时记录N次测试匹配定位精度的平均值(mean)、标准差(std)和最差值(max)以及航迹平均匹配时间T(不含环境配置时间)作为重力匹配算法性能评价指标。The resolution of the gravity anomaly grid in the simulated sample block is 100m×100m, the accelerometer constant zero bias is 10 -3 m/s 2 (the root mean square error of the inertial navigation follows a normal distribution), the speed is 10m/s 1 , and the heading north 70° east, initial position error 0m, velocity error 0.04m/s 1 , heading error 0.05°, the real-time measurement data of the gravimeter is the sampling value of the real track in the gravity anomaly database superimposed with random noise with a standard deviation of 1mGal. The number of points is 110, and the sampling period is 20s. Among them, the present invention defines the matching positioning accuracy as 1, then the difference between the absolute value of the matching position and the real position is an effective matching within the closed interval [0, 1], so the effective matching times n of the algorithm under N experimental tests can be obtained. and the matching success rate of the algorithm At the same time, the mean (mean), standard deviation (std) and worst value (max) of the matching positioning accuracy of N tests and the average track matching time T (excluding the environmental configuration time) were recorded as the performance evaluation indicators of the gravity matching algorithm.
为测试分析不同σ准则的IOAP算法在水下潜器重力匹配导航中的应用性能,以1σ-IOAP、2σ-IOAP和3σ-IOAP算法进行100次独立实验,同时以TERCOM算法作为对比算法,以重力基准图格网点坐标(1400,1500)作为水下潜器航行的模拟起点,则直观匹配定位精度对比效果如图5所示。In order to test and analyze the application performance of IOAP algorithms with different σ criteria in gravity matching navigation of underwater vehicles, 100 independent experiments were conducted with 1σ-IOAP, 2σ-IOAP and 3σ-IOAP algorithms, and the TERCOM algorithm was used as a comparison algorithm. The grid point coordinates (1400, 1500) of the gravity reference map are used as the simulation starting point of the underwater submersible navigation, and the comparison effect of intuitive matching and positioning accuracy is shown in Figure 5.
不同σ作用下IOAP算法的匹配定位性能有所差异,以3σ-IOAP算法的匹配效果表现最为优异且显著优于传统TERCOM算法。在T指标上,1σ-IOAP算法虽然平均运行时间最小但匹配效果较差而难以有效应用于实际水下潜器的导航;2σ-IOAP算法平均运行时间约是TERCOM算法的一半、平均匹配精度小于1个格网分辨率,且在定位精度l=100条件下其匹配概率也优于TERCOM算法(88%>82%),表明2σ-IOAP算法在匹配效率和匹配精度的双目标条件下具有一定的实际导航应用价值,可根据实际导航需求适定性选择该重力导航机制;3σ-IOAP算法则与TERCOM的T指标相差不大,而在匹配精度的mean值、std值和max值以及匹配成功概率等指标上均优于TERCOM算法及其他算法的大部分指标值,充分表明所提IOAP算法在水下潜器重力辅助导航的较好匹配性能和良好潜在实用价值。The matching and positioning performance of the IOAP algorithm under different σ effects is different, and the matching effect of the 3σ-IOAP algorithm is the best and significantly better than the traditional TERCOM algorithm. On the T index, although the average running time of the 1σ-IOAP algorithm is the smallest, the matching effect is poor and it is difficult to be effectively applied to the navigation of actual underwater vehicles; the average running time of the 2σ-IOAP algorithm is about half of that of the TERCOM algorithm, and the average matching accuracy is less than 1 grid resolution, and its matching probability is also better than that of the TERCOM algorithm (88%>82%) under the condition of positioning accuracy l=100, indicating that the 2σ-IOAP algorithm has certain matching efficiency and matching accuracy under the dual target condition. According to the actual navigation application value, the gravity navigation mechanism can be appropriately selected according to the actual navigation requirements; the 3σ-IOAP algorithm is not much different from the T index of TERCOM, and the mean value, std value and max value of the matching accuracy and the matching success probability are not different. It is better than most of the index values of TERCOM algorithm and other algorithms in terms of indicators, which fully shows that the proposed IOAP algorithm has better matching performance and good potential practical value in gravity-assisted navigation of underwater vehicles.
为进一步分析不同定位精度L约束条件下4种算法的成功匹配效果差异,分别以l为20、40、60、80、100和的约束条件下统计100次测试的成功匹配概率对比结果的直观对比柱状图,如图6所示。In order to further analyze the difference of the successful matching effect of the four algorithms under the constraint condition of different positioning accuracy L, take l as 20, 40, 60, 80, 100 and The intuitive comparison histogram of the comparison results of the successful matching probability of the statistics for 100 tests under the constraint conditions is shown in Figure 6.
不同定位精度约束下不同σ-IOAP算法的成功匹配概率差异明显,且3种σ-IOAP算法在l≤40时已有一定次数的成功匹配但TERCOM却均匹配失效;综合分析不同定位精度l下算法的成功匹配概率,以3σ-IOAP算法的匹配性能表现最好、2σ-IOAP次之且优于传统TERCOM算法,但1σ-IOAP算法定位精度约束下则弱于TERCOM;图6则进一步直观展示了3σ-IOAP算法优异的成功匹配性能,上述结论仍有效验证了所提3σ-IOAP算法在水下重力匹配导航中的优异性能。The successful matching probabilities of different σ-IOAP algorithms under different positioning accuracy constraints are significantly different, and the three σ-IOAP algorithms have a certain number of successful matching when l≤40, but all TERCOM matching fails; comprehensive analysis of different positioning accuracy l For the successful matching probability of the algorithm, the matching performance of the 3σ-IOAP algorithm is the best, followed by the 2σ-IOAP algorithm, which is better than the traditional TERCOM algorithm, but the 1σ-IOAP algorithm is weaker than the TERCOM algorithm under the constraint of positioning accuracy; Figure 6 shows it further intuitively. The excellent and successful matching performance of the 3σ-IOAP algorithm is shown, and the above conclusions still effectively verify the excellent performance of the proposed 3σ-IOAP algorithm in underwater gravity matching navigation.
为进一步探究并剖析3σ-IOAP算法优异于TERCOM及其他σ-IOAP算法匹配效率和精度的原因,绘制TERCOM算法匹配位置与水下潜器实际位置的散点对比示意如图7所示(以惯导位置作为图像坐标原点以保证100次测试结果均可绘制在同一幅图像)。In order to further explore and analyze the reasons why the 3σ-IOAP algorithm is superior to TERCOM and other σ-IOAP algorithms in terms of matching efficiency and accuracy, the scatter comparison between the matching position of the TERCOM algorithm and the actual position of the underwater vehicle is drawn as shown in Figure 7 (in the usual way. The guide position is used as the origin of the image coordinates to ensure that 100 test results can be drawn on the same image).
由图7(a)分析可知,TERCOM算法100次测试的水下潜器实际位置几乎均位于惯导位置的3σ误差格网范围内(图7(a)中虚线圆外侧的实线框),同时所有位置点也几乎均位于以惯导位置为中心的3σ圆环边界虚线内部(图7(a)中内切实线框的虚线圆),即在一定程度上表明TERCOM算法矩形格网待匹配点存在一定量的小概率被匹配点,见图7(b)中实线框与虚线圆间的点,即这些3σ圆环外侧点虽被匹配概率较小但却明显影响着TERCOM的匹配效率,因此,删除3σ环域外匹配点的重力匹配算法可在不显著影响算法匹配精度的同时可有效改善其匹配效率,这也从侧面有效佐证了本发明基于环域拓扑结构设计格网点匹配机制的可行性和有效性。From the analysis in Figure 7(a), it can be seen that the actual positions of the underwater vehicles tested by the TERCOM algorithm for 100 times are almost all within the 3σ error grid range of the inertial navigation position (the solid line frame outside the dotted circle in Figure 7(a)), At the same time, all the position points are almost all located inside the dashed line of the 3σ ring boundary centered on the inertial navigation position (the dashed circle of the inner solid line frame in Figure 7(a)), which indicates to a certain extent that the rectangular grid of the TERCOM algorithm needs to be matched. There are a certain number of points to be matched with a small probability, as shown in Figure 7(b), the points between the solid line box and the dotted circle, that is, the points outside the 3σ circle have a small probability of being matched, but they obviously affect the matching efficiency of TERCOM. , therefore, the gravity matching algorithm that deletes the matching points outside the 3σ ring domain can effectively improve the matching efficiency without significantly affecting the matching accuracy of the algorithm. Feasibility and effectiveness.
为进一步剖析3σ-IOAP算法优异于其他σ-IOAP匹配精度的原因,绘制不同σ-IOAP算法100次测试的匹配效果示意如图8所示。由图8分析可知,基于不同σ环域的IOAP算法对水下潜器真实位置的覆盖匹配效果有所差异:3σ-IOAP算法以大环域格点覆盖性实现了水下潜器的高精度匹配定位;而2σ-IOAP和1σ-IOAP仅实现了大环域内真实位置的良好匹配,但对域外真实位置的最优匹配往往只是散布于其边界环上、难以寻得更优的匹配位置而影响了算法的匹配精度,进而在一定程度上解释了不同σ-IOAP算法成功匹配概率的差异及其3σ-IOAP算法的良好匹配精度,表明3σ-IOAP算法在水下潜器重力匹配导航中的重要潜在应用价值。In order to further analyze the reason why the 3σ-IOAP algorithm is superior to other σ-IOAP matching accuracy, a schematic diagram of the matching effect of different σ-IOAP algorithms for 100 tests is shown in Figure 8. From the analysis in Figure 8, it can be seen that the IOAP algorithms based on different σ ring domains have different coverage and matching effects on the real position of the underwater vehicle: the 3σ-IOAP algorithm realizes the high precision of the underwater vehicle with the grid coverage of the large ring domain. Matching positioning; while 2σ-IOAP and 1σ-IOAP only achieve good matching of real positions in the large ring domain, but the optimal matching of real positions outside the domain is often only scattered on its boundary ring, and it is difficult to find better matching positions. It affects the matching accuracy of the algorithm, and then explains the difference in the successful matching probability of different σ-IOAP algorithms and the good matching accuracy of the 3σ-IOAP algorithm to a certain extent. important potential application value.
(2)不同环半径基准角下IOAP算法匹配性能的影响差异性验证(2) Differential verification of the impact of the matching performance of the IOAP algorithm under different ring radius reference angles
为进一步探究基于不同环半径R所定基准角对3σ-IOAP算法匹配性能的影响效果,分别以3σ-IOAP算法的内环层最大环半径R1=RM/3、“内中”环层中间环半径中间环层最大环半径R2=R2M/3、“中外”环层中间环半径来确定3σ-IOAP算法的基准角并张成变角度三环层待匹配格点集,相应算法分别记为1-IOAP、1.5-IOAP(即2.1节的3σ-IOAP)、2-IOAP和2.5-IOAP算法。根据式(6)分析可知,环半径R越大则3σ-IOAP算法的大环域基准角越小,生成的待匹配格网点总数目N越多,故理论上1-IOAP算法的匹配效率最快而2.5-IOAP算法的执行最慢。In order to further explore the reference angle based on different ring radii R The effect on the matching performance of the 3σ-IOAP algorithm is based on the maximum ring radius R 1 = RM/3 of the inner ring layer of the 3σ-IOAP algorithm, and the middle ring radius of the “inner middle” ring layer. The maximum ring radius of the middle ring layer R 2 =R 2M/3 , the middle ring radius of the “intermediate” ring layer to determine the reference angle of the 3σ-IOAP algorithm And the grid points to be matched in the variable-angle three-ring layer are denoted as 1-IOAP, 1.5-IOAP (ie 3σ-IOAP in Section 2.1), 2-IOAP and 2.5-IOAP algorithms respectively. According to the analysis of formula (6), it can be seen that the larger the ring radius R is, the larger the reference angle of the large ring domain of the 3σ-IOAP algorithm is. The smaller the value, the more the total number N of grid points to be matched will be generated. Therefore, in theory, the matching efficiency of the 1-IOAP algorithm is the fastest and the execution of the 2.5-IOAP algorithm is the slowest.
模拟样本区块、航迹起点格网坐标等参数设置均同上(1),100次独立测试的算法匹配定位统计结果分别如图9和图10所示。3σ-IOAP算法的匹配精度和成功概率几乎均随基准角环半径R的增大呈现匹配效果改善的特点,且以2.5-IOAP性能最优、2-IOAP次之,1-IOAP匹配效果相对较差但在6/7指标上仍优于TERCTOM算法,表明基于不同环半径的基准角会影响3σ-IOAP算法的匹配性能;而根据T指标分析可知,不同环半径基准角的IOAP算法随环半径R增大而表现出“匹配效率降低”的现象,且该结果与其理论分析结论相一致,表明不同环半径基准角对应的待匹配格网点总量不同并导致算法匹配效率的差异。因此,在实际水下潜器导航应用中,可根据具体匹配目标需求以适定性选择合适的环半径R所对应的3σ-IOAP算法并完成特定航行匹配任务,说明本发明所提的3σ-IOAP算法在水下重力匹配导航中具有较高算法鲁棒性和良好应用价值。The parameter settings such as the simulated sample block and the grid coordinates of the track starting point are the same as above (1). The algorithm matching and positioning statistical results of 100 independent tests are shown in Figure 9 and Figure 10 respectively. The matching accuracy and success probability of the 3σ-IOAP algorithm almost show the improvement of the matching effect with the increase of the reference angle ring radius R, and the performance of 2.5-IOAP is the best, followed by 2-IOAP, and the matching effect of 1-IOAP is relatively better. It is worse but still better than the TERCTOM algorithm in 6/7 indicators, indicating that the reference angles based on different ring radii will affect the matching performance of the 3σ-IOAP algorithm. The increase of R shows the phenomenon of "decrease of matching efficiency", and this result is consistent with its theoretical analysis conclusion, indicating that the total number of grid points to be matched corresponding to different ring radius reference angles is different, which leads to the difference of matching efficiency of the algorithm. Therefore, in the actual underwater vehicle navigation application, the 3σ-IOAP algorithm corresponding to the appropriate ring radius R can be appropriately selected according to the specific matching target requirements, and the specific navigation matching task can be completed, illustrating the 3σ-IOAP proposed in the present invention. The algorithm has high algorithm robustness and good application value in underwater gravity matching navigation.
2.5-IOAP算法的匹配精度和不同尺度下匹配成功概率几乎均优越于其他IOAP算法和TERCOM算法,但其匹配T指标值最高且几乎为TERCOM匹配时间的2倍,故在匹配效率要求不高且更重视匹配精度的水下导航情境下,2.5-IOAP算法不失为重力匹配算法的最佳选择;而在匹配效率和匹配精度双目标要求情境下,1-IOAP算法则是重力匹配算法的最佳选择,因此,进一步佐证了3σ-IOAP算法具有较好的水下重力匹配导航鲁棒性。此外,1.5-IOAP算法(即2.1节的3σ-IOAP算法)在匹配效率和匹配精度间表现出较好的折中效果,同时考虑到其与TERCOM算法的匹配效率相差不大,故下节按1.5-IOAP算法进一步测试以验证其在不同起点下的良好匹配性能。2.5- The matching accuracy and matching success probability of the IOAP algorithm at different scales are almost superior to other IOAP algorithms and TERCOM algorithms, but its matching T index value is the highest and almost twice the matching time of TERCOM, so the matching efficiency requirements are not high and Under the situation of underwater navigation that pays more attention to matching accuracy, the 2.5-IOAP algorithm is the best choice for the gravity matching algorithm; while in the situation where matching efficiency and matching accuracy are required for dual targets, the 1-IOAP algorithm is the best choice for the gravity matching algorithm. , therefore, it further proves that the 3σ-IOAP algorithm has good underwater gravity matching navigation robustness. In addition, the 1.5-IOAP algorithm (that is, the 3σ-IOAP algorithm in Section 2.1) shows a good compromise between matching efficiency and matching accuracy, and considering that its matching efficiency is not much different from the TERCOM algorithm, the next section is based on The 1.5-IOAP algorithm is further tested to verify its good matching performance under different starting points.
(3)不同区域航迹起点下IOAP算法的良好匹配性能验证(3) Verification of good matching performance of IOAP algorithm under different regional track starting points
为进一步验证1.5-IOAP算法在水下潜器匹配导航中的良好匹配适用性,本发明以区域格网坐标A(1660,1410)、B(1550,740)和C(1400,350)分别作为水下潜器航迹起点的位置。在匹配效率(T指标)相差不大的前提下,1.5-IOAP算法在平均匹配精度(mean)、匹配精度标准差(std)和最差匹配精度(max)等4项指标上均显著优于传统TERCOM算法;与TERCOM相比较,3种情境下1.5-IOAP的最差匹配精度分别相对提高了47.24%、63.96%和72.16%,而平均匹配精度则相对提高20.37%、40.39%和13.88%,表明本发明所提IOAP算法具有较高的匹配精度和多次测试良好的同步寻优性能;同时在不同成功匹配尺度l下,本发明算法相较于TERCOM算法表现出相对更为优异的匹配成功概率,特别是匹配精度小于40时1.5-IOAP算法仍一定概率实现水下潜器位置的成功匹配,有效验证了所提IOAP算法在不同区域起点条件下对水下重力匹配导航的良好匹配适用性。In order to further verify the good matching applicability of the 1.5-IOAP algorithm in the matching and navigation of underwater vehicles, the present invention uses the regional grid coordinates A (1660, 1410), B (1550, 740) and C (1400, 350) as The location of the start of the submersible track. On the premise that the matching efficiency (T index) is not much different, the 1.5-IOAP algorithm is significantly better than the average matching accuracy (mean), the standard deviation of the matching accuracy (std) and the worst matching accuracy (max). Traditional TERCOM algorithm; compared with TERCOM, the worst matching accuracy of 1.5-IOAP in the three scenarios is relatively improved by 47.24%, 63.96% and 72.16%, while the average matching accuracy is relatively improved by 20.37%, 40.39% and 13.88%, It shows that the IOAP algorithm proposed in the present invention has high matching accuracy and good synchronous optimization performance in multiple tests; at the same time, under different successful matching scales l, the algorithm of the present invention shows relatively better matching success than the TERCOM algorithm. Probability, especially when the matching accuracy is less than 40, the 1.5-IOAP algorithm still has a certain probability to successfully match the position of the underwater submersible, which effectively verifies the good matching applicability of the proposed IOAP algorithm for underwater gravity matching navigation under the conditions of different starting points. .
为直观展示1.5-IOAP算法和TERCOM算法在3个测试位置下的匹配效果差异,绘制100次测试中最差匹配定位对比示意,如图11所示。由图11分析可知,在不同区域航迹起点下水下重力匹配定位中,1.5-IOAP算法相较于TERCOM算法具有更高的匹配定位精度,同时这3条航迹终点落于不同的重力区间段内,在一定程度上有效验证了所提IOAP算法在不同重力区段均具有较好的匹配适应性,进一步有效佐证了本发明基于新型格网拓扑结构的迭代最佳环域点算法在提高水下潜器重力匹配精度的有效性和可靠性。In order to visually show the difference in matching effect between the 1.5-IOAP algorithm and the TERCOM algorithm under three test positions, a comparison diagram of the worst matching positioning in 100 tests is drawn, as shown in Figure 11. From the analysis in Figure 11, it can be seen that in the underwater gravity matching positioning under the starting points of the tracks in different regions, the 1.5-IOAP algorithm has higher matching positioning accuracy than the TERCOM algorithm, and the end points of the three tracks fall in different gravity intervals. To a certain extent, it effectively verifies that the proposed IOAP algorithm has good matching adaptability in different gravity sections, and further effectively proves that the iterative optimal ring domain point algorithm based on the new grid topology structure of the present invention can improve the water quality. Validity and reliability of submersible gravity matching accuracy.
在上述实施例的基础上,本发明还公开了一种基于格网拓扑结构迭代最佳环域点提高水下导航精度系统,包括:解算模块,用于通过航迹起点小环域格网匹配定位策略,得到水下潜器航迹起点的最佳匹配位置;生成模块,用于根据水下潜器航迹起点的最佳匹配位置,通过航迹终点变角度三层环域匹配定位策略,生成大环域待匹配格网点;迭代确定模块,用于迭代计算大环域待匹配格网点的匹配效能评价指标,并按最优原则获得大环域范围内水下潜器航迹终点的最佳匹配位置,以实现水下潜器航迹终点的有效匹配定位,进而修正INS系统控制参数并辅助完成水下潜器长航时长航距的航行目标。On the basis of the above-mentioned embodiment, the present invention also discloses a system for improving underwater navigation accuracy based on iterative optimal ring domain points based on grid topology structure, comprising: a solving module for passing a small ring domain grid at the track starting point Match the positioning strategy to obtain the best matching position of the starting point of the track of the underwater vehicle; the generation module is used to match the positioning strategy through the three-layer ring domain of the track end point according to the best matching position of the starting point of the track of the underwater vehicle. , generate the grid points to be matched in the large ring domain; the iterative determination module is used to iteratively calculate the matching efficiency evaluation index of the grid points to be matched in the large ring area, and obtain the end point of the track of the underwater vehicle within the large ring area according to the optimal principle. The best matching position is to realize the effective matching and positioning of the end point of the track of the underwater submersible, and then correct the control parameters of the INS system and assist in the completion of the long-duration and long-distance navigation of the underwater submersible.
对于系统实施例而言,由于其与方法实施例相对应,所以描述的比较简单,相关之处参见方法实施例部分的说明即可。As for the system embodiment, since it corresponds to the method embodiment, the description is relatively simple, and for related parts, please refer to the description of the method embodiment part.
本发明虽然已以较佳实施例公开如上,但其并不是用来限定本发明,任何本领域技术人员在不脱离本发明的精神和范围内,都可以利用上述揭示的方法和技术内容对本发明技术方案做出可能的变动和修改,因此,凡是未脱离本发明技术方案的内容,依据本发明的技术实质对以上实施例所作的任何简单修改、等同变化及修饰,均属于本发明技术方案的保护范围。Although the present invention has been disclosed above with preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art can use the methods and technical contents disclosed above to improve the present invention without departing from the spirit and scope of the present invention. The technical solutions are subject to possible changes and modifications. Therefore, any simple modifications, equivalent changes and modifications made to the above embodiments according to the technical essence of the present invention without departing from the content of the technical solutions of the present invention belong to the technical solutions of the present invention. protected range.
本发明说明书中未作详细描述的内容属于本领域专业技术人员的公知技术。Contents that are not described in detail in the specification of the present invention belong to the well-known technology of those skilled in the art.
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