Overview and prospect of key technologies for underwater gravity-aided inertial navigation
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摘要:
水下高精度自主导航是海洋探索与开发的关键核心技术。惯性导航系统(INS)的定位误差随航行时间累积发散，需要外部信息辅助修正。地球重力场作为地球固有属性，兼具稳定性、自主性与无源性，是理想的信息源，由此发展而来的重力辅助惯性导航技术具有重要的研究价值。在分析系统基本原理与技术架构的基础上，围绕重力基准图构建、重力场适配性分析、重力匹配算法、航迹规划四大关键技术，系统梳理了多源数据融合、网格化插值、特征评估与适配区提取、序列相关匹配、非线性滤波、智能路径优化等主流方法的研究进展，深入剖析了当前技术发展中尚未解决的共性问题。针对现阶段研究存在的技术瓶颈展望未来研究发展方向，旨在为后续构建高精度、高可靠性和高自主性的水下重力辅助惯性导航系统(GAINS)提供理论参考与技术指引。
Abstract:Underwater high-precision autonomous navigation is a core enabling technology for ocean exploration and development. The positional error of an inertial navigation system (INS) builds up and diverges with time, requiring outside data to be corrected. As an inherent property of the Earth, the gravity field offers stability, autonomy, and passivity, making it an ideal information source. Consequently, gravity-aided inertial navigation technology holds significant research value. This paper systematically reviews the research progress of four important technologies: trajectory planning, gravity matching algorithms, gravity reference map construction, and gravity field adaptability analysis. It is based on an analysis of the system’s technical architecture and fundamental principles. Mainstream methods, such as multi-source data fusion, gridded interpolation, feature evaluation and matching area extraction, sequential correlation matching, nonlinear filtering, and intelligent path optimization, are comprehensively summarized. Furthermore, common unresolved issues in current technological development are thoroughly examined. Finally, in view of the technical bottlenecks at this stage, future research directions are discussed, aiming to provide theoretical references and technical guidance for the subsequent development of a high-precision, high-reliability, and high-autonomy underwater gravity-aided inertial navigation system (GAINS).
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图 3 重力基准图构建核心技术及主要方法
Figure 3. Core technologies and main methods for constructing gravity reference maps
图 4 重力场适配性分析关键技术及主要方法
Figure 4. Key technologies and main methods for gravity field adaptability analysis
图 5 重力匹配算法分类及主要方法
Figure 5. Classification and main methods of gravity matching algorithms
图 6 航迹规划算法发展阶段及主要方法
Figure 6. Development stages and main methods of route planning algorithms
表 1 不同插值算法性能对比
Table 1. Comparison of performance of different interpolation algorithms
插值算法 优势 劣势 IDW插值算法 原理简单，易于编程实现；计算效率高，适合大规模数据 对权重系数敏感，主观性强；易产生“牛眼”效应，结果不够平滑；无法估计插值误差 改进Shepard算法 继承IDW简单性，同时减少“牛眼”效应；通过半径搜索或权重修正，提高了局部拟合精度；计算量低于Kriging等统计方法 对搜索半径、拟合度等参数敏感；对数据边界区域的处理效果较差；不提供误差估计 Kriging插值算法 提供最优无偏估计，可给出插值误差；充分利用数据空间相关性，理论严密；可结合各向异性、趋势项等复杂模型 计算复杂，耗时长；需拟合变异函数，参数选择敏感；数据非平稳时效果下降 RBF插值算法 精确插值，光滑性好；适合不规则分布数据，灵活性高；多种核函数可选适应不同场特征 计算量大，速度慢；对核函数和光滑因子敏感；边缘区域误差较大 格林函数样条插值算法 物理意义明确；插值结果二阶光滑，适合连续物理场；可融合边界条件，自然处理数据稀疏区 格林函数构造复杂，涉及奇异性处理；大规模计算困难；对测量噪声敏感，易过拟合 曲线/曲面拟合法 整体拟合，趋势表达清晰，抑制噪声；参数少，模型稳定，易于解释；计算量小，适合大范围趋势提取 局部细节描述能力弱，易平滑掉真实重力异常；阶次选择主观，低阶欠拟合，高阶易振荡 
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表 2 典型重力场方向性特征参数对比分析
Table 2. Comparison and analysis of classical directional characteristic parameters
方向性特征参数 适用场景 优点 缺点 计算复杂度 各向同性系数[119] 评估区域整体的方向敏感程度，判断适配区是否在各方向上均适用；适用于适配区的初筛与方向性定性评估 首次将方向性定量纳入适配性评估；系数接近1时表明区域方向适应性好；理论基础严密，具有明确的物理意义 仅反映方向一致性，无法度量重力变化强度，需与其他特征联合使用；计算涉及频域变换，较为复杂 O(nlog2n)
（n为滑动窗口总数量）重力异常和向量差[120] 识别区域重力变化的主导方向；适合作为航迹规划中方向选择的参考依据；在重力变化各向异性明显的区域效果突出 可获取方向上的匹配度，克服标量参数无法反映方向性的局限；模值设计基于圆概率误差与3σ准则，理论依据充分 在重力变化剧烈但方向相互抵消的区域，模值可能偏小；矢量和方向对窗口形状敏感 O(n) 方向匹配率[121] 评估区域在多方向上的综合适配能力；适合需要全面评估区域各方向匹配性能的场景，尤其是航向不确定时的适配区选取 多方向梯度特征提取全面；CNN分类避免了主观阈值设定；实现方向适配性的定量评估 灰度级量化参数和方向数选择主观；特征计算涉及图像变换，复杂度较高 O(ndSL2)
（dS为Sobel算子的方向数量，L为灰度量化级数）曲率方向特征[122] 兼顾区域重力变化幅度与方向一致性的综合评估；适合对适配区进行方向鲁棒性筛选 曲率特征直接反映曲面几何特性，物理意义清晰；配合K-means聚类与形态学闭运算，兼顾区域连通性 需计算主曲率与高斯曲率，对重力数据平滑性敏感；方向一致性指标仅基于主曲率方向，未覆盖所有航向 O(nW2)
（W为滑动窗口边长）重力剖面相似性[123] 评估沿特定航向的匹配可行性，直接反映轨迹序列的独特性，适配于航迹规划中航向优选 直接反映沿航向的重力序列独特性，对匹配算法的实际效果预测更准确 剖面长度参数与权重参数需人工设定，对结果敏感 O(nW3) 方向梯度集中度[123] 评估特定航行方向上的重力变化强度与一致性，识别重力场方向性各向异性的区域 可量化任意给定航向的适配性；正交方向负相关特性可验证特征合理性 需针对每个航向单独计算，计算量随方向数量线性增长；Prewitt算子的方向分辨率有限 O(ndPW2)
（dP为Prewitt算子的方向
数量）
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表 3 典型多算法融合的匹配算法对比分析
Table 3. Comparison and analysis of representative multi-algorithm fusion matching algorithms
多算法融合 匹配精度 实时性 参数敏感性 适用场景 TERCOM+EKF[184] 匹配精度依赖重力测量误差，1×10−5 m/s2的重力测量误差的平均定位误差为674.128 m，5×10−5 m/s2的重力测量误差的平均定位误差为 4379.98 m基于EKF的递推估计，可实时工作 对重力场粗糙度、初始误差、线性化误差及重力仪噪声均敏感 适用于中等粗糙度区域、重力仪精度较高和实时性要求较高的场景 TERCOM+ICCP[186] TERCOM出现明显误匹配且ICCP匹配结果较好时，平均定位误差由 1998.308 m降至870.44 m批处理算法，实时性较差 对TERCOM初始匹配质量和ICCP匹配精度敏感 适用于修正TERCOM误匹配的实时性要求不高的场景 PF+EKF[187] 全程平均定位误差达620.42 m；适配区的均方根误差：东向为281.504 m，北向为272.244 m 并行计算增加负载，但满足实时要求 依赖预计算阈值，但决策树自动选择方法降低调参难度 适用于各类重力场；存在较大测量噪声的长航时、连续水下导航场景 ICCP+BP神经网络[191] 与ICCP一致（未量化位置误差，仅提升计算速度） 相较于ICCP，迭代次数降82%，时间降低81% 对网络结构、学习率等超参数敏感，但文章未进行相关分析 适用于实时性要求高、计算资源受限的嵌入式平台 PF+PSO算法[195] 横穿等高线轨迹的平均定位误差为 1140.832 m，平行于等高线轨迹的平均定位误差为594.492 m采用滑动窗口递推，满足实时导航需求 缓解了标准PSO算法对初始参数敏感的固有缺陷，但依赖数字重力图的精度和重力仪实测数据的质量 适用于长航时重力辅助惯性导航场景，但不适用于重力场变化平缓或背景图分辨率与精度不足的区域 引入K近邻算法[196] 平均定位误差均小于800.064 m 每匹配点平均耗时5.87 s，可满足实时导航需求 对K值、搜索半径敏感，但抗噪性优于平均平方差相关算法 适用于存在较大测量噪声或重力场变化较平缓等困难条件的长航时、大航程航行任务
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表 4 三类重力匹配算法的性能对比与适用场景
Table 4. Comparison of performance and suitable applications of three types of gravity matching algorithms
对比维度 序列匹配 实时滤波 多算法融合 实时性 属于批处理方法，需累积一定航迹长度后才能完成匹配，实时性较差 可逐点实时输出定位结果，实时性较好 实时性中等，通常包含批处理与递推两阶段，计算延迟较高 初始误差容忍度 TERCOM对初始误差不敏感；ICCP在惯导初始误差较大时，容易陷入局部最优解 对初始误差容忍度较低 对初始误差容忍度较高，常通过粗匹配阶段压制大初始误差 重力特征敏感性 对重力图分辨率和精度敏感，平坦区易误匹配 在平坦区易发散，易导致误匹配 相对鲁棒，可通过多算法互补缓解平坦区失配问题 重力测量噪声鲁棒性 对噪声较敏感，但长序列可在一定程度上抑制噪声影响 当重力测量噪声较大时，滤波过程极有可能发散 较好，多源信息融合可抑制噪声干扰 计算复杂度 计算量与搜索范围相关，会随搜索范围增大急剧增加 SITAN低，PF中等，PMF高（随网格分辨率指数增长） 高，需同时运行多个算法 适用场景 重力特征明显、初始位置误差大、对实时性要求不高的长航程任务 实时性要求高、机动航行、实时修正、初始误差较小的场景 高精度要求、允许较高计算资源、需兼顾大初始误差与复杂噪声的环境
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