多波束测深系统偏移效应标校及交叉点误差分析

Two indispensable tasks, i.e. the offset coefficient (OC) calibration and the crossover error (CE) analysis before and after the online survey respectively, are concerned. The inconsistencies about the origins and the directions between the navigation and bathmetry modules bring two kinds of OC, i.e. the translational and rotational respectively. Noticing that the navigation measurement as well as the bathmetry one is error-susceptible, the OC calibration should be considered as a total least squares problem rather than the least squares one as in the traditional aproach. The following three subjects are studied concerning this topic. First, a practical but also rather general weighting matrix is introduced; the Lagrangian is constructed and minimized using the first order necessary condition where the rotational OC is obtained through the singular value decomposition of an elaborately constructed matrix. Second, error analysis is performed about the calibrated OC to get the variance-covariance matrix which will be used in calibration measurement design and bathmetric corrections. Third, the effect of the OC calibration error on the bathmetric data is analyzed based on the error propagation law. The aim of the CE analysis often constitute of the estimation of the systemic error and the variance of the random error, the former of which is assumed constant and the latter is used to evaluate the accuracy of the mission. Three subjects are studied concerning this topic. First, the correlations among difference CEs are revealed for the first time and calculated rigorously. Second, the CEs are adjusted based on the least squares network adjustments with correlated measurements to get the estimation of the coefficients. Third, the statistical characteristics of the estimation is analyzed in detail, e.g. the unbiasedness, the consistency, and the minimum-variance.

课题涉及多波束测深作业前的偏移效应标校与作业后的交叉点不符值分析两个重要内容。考虑到测深和导航数据均存在误差，将标校问题构建为总体最小二乘问题。此部分研究包含三个内容：首先，构建加权总体最小二乘问题，根据Lagrange函数最小化的必要条件消去平动偏移参数，利用奇异值分解求解转动偏移参数；其次，对标校的偏移参数进行误差分析，为标校方案设计和测深精度分析奠定基础；最后，分析偏移效应不确定度对测深结果的影响，为任务可行性分析奠定基础。交叉点误差分析包括对系统差误差和随机误差方差σ2的估计。由于没有先验知识以确定更复杂的系统差模型，假定系统差为常值Δ，问题归结为估计Δ、σ2。此部分研究包括三部分内容：首先，将首次指出数据编辑会引入不同交叉点间的相关性，求取相关性为后续平差提供加权矩阵；其次，考虑观测之间的相关性，根据相关观测的平差理论估计Δ、σ2；最后，分析估计值的统计特性，如无偏性、一致性等。

多波束测深系统精密数据处理技术是当今海洋测绘领域研究的热点与难点问题。关于多波束测深系统偏移效应标校及交叉点误差分析等问题仍需要进一步研究解决。本项目根据多波束水深测量的特点，重点开展海洋水深测量数据处理及误差补偿方法研究、海洋潮汐基准分析与计算方法研究、海洋声场特性分析及计算方法研究和海洋地震波波动成分及传播规律分析研究及应用等研究工作，通过理论推导、仿真分析和试验验证等方法，建立多波束测深系统精密数据处理理论和算法体系，设计海洋测绘成果应用系统。研究成果可为我国标准化、规范化获取海底地形数据信息提供理论依据，为研制我国完全自主知识产权的多波束测深系统提供技术支撑, 具有重要的研究价值和明显的军事效益。