超短基线系统安装校准技术研究
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摘要
本文基于国内的高精度超短基线(USBL)定位系统，研究系统的海上安装校准及声线跟踪定位算法。经过安装校准，可以计算声线的初始掠射角，才能使用声线跟踪进行定位，而没有声线跟踪算法也无法验证校准的准确度、无法保证系统定位精度，因此这两个内容对于USBL是密不可分的。
安装校准的技术核心是它所使用的安装校准观测方程，它的性质决定了校准的流程和工程实现，从而决定了校准结果是否具有一定的稳健性。稳健性包括：首先校准要有结果，即求解不能不收敛；其次因海上操作的成本，单次校准结果要可信任，即校准的一致性和不确定区间要得到保证；最后校准的结果要保持一定的无偏性，以保证定位的精度。因此，本文重点研究了已有观测方程的性质并对其进行改进，给出了最小二乘准则下估计解的形式，讨论了方程解区间唯一性、无偏性和方差的性质。首先校准航迹是影响方程是否收敛(区间唯一性)和校准不确定区间(方差的性质)的重要因素，它需要有一定的尺度并且尽量对称；其次方程需要粗测安装垂直位移偏差来保证收敛，这在理想条件下是不影响其它的估计的；再次影响方程解偏差(估计的准确度)大小的主要因素是水下声线的弯曲，声线弯曲补偿可以对方程进行去偏，而方程的去偏也可视作声线弯曲补偿，因此第一步的校准方程估计平均声速而第二步方程采用去偏形式；最后，由于方程的非线性和海况，具体的数值解法也是影响估计精度和方差的重要因素，而M估计有较好的抗差性及稳健性，因此本文对最小二乘估计和M估计进行了理论研究后，给出了一种基于异常点剔除算法的加权形式，可不必考虑具体的准则函数直接设置观测权。综上所述，改进的观测方程、合理的航迹和合适的数值解法可基本保证校准的稳健性。
对于声线跟踪定位，假设校准合理、测量条件良好，影响定位精度的主要原因是定位算法。定位算法的工程实现通常是使用常梯度或常声速进行分层跟踪，因此分层好坏直接影响算法的精度，显然分层越密算法精度越高，但这个准则对于USBL实时或深海定位是不可接受的。另外，声速剖面的测量质量或变化对于定位精度的影响难以表达，这对于工程实现也是不利的。而本文初步建立了水平定位误差传递模型，它是由误差传递公式经过变化并且仿真生成参数而建立的。根据模型，本文设计了一种可由算法精度要求而对剖面进行分层的自适应方法，它基于自适应辛普森方法，是辛普森方法的逆过程。另外模型对其它工程问题有一定的指导意义，如剖面在定位之前的处理、常声速和常梯度跟踪的区别等。之后本文讨论了温、盐、压的声速剖面测量方法、剖面的平滑算法和拓延算法，最后总结了USBL声线跟踪定位的转换公式与流程的基本，通过实验数据验证了公式和流程的合理性。
最后对实验数据进行统计处理，统计结果表明了航迹、M估计对估计方差有所改善，以及方程去偏补偿后对校准一致性有所改善。校准之后进行定位，可以看到定位的散点图不再有圆半径的“适应性”，使用某半径上数据进行校准，对其他数据定位依然可以较好的收敛，这验证了校准及跟踪定位的正确性。
This paper is based on the domestic high precise USBL (Ultra-Short Baseline) system toresearch the at-sea installation calibration and ray tracing position algorithm. Afterinstall-calibration, the incidence angle can be calculated to use the tracing positioningalgorithm; the ray-tracing positioning scatter picture can test if the calibration is correct,which is the ultimate goal of the system, therefore the two contents for USBL are inseparable.
The core of install-calibration the measurement equation used, as well as the calibrationprocess decided by the equation property and engineering realization, which need the esurientthat the calibration has to have a certain robustness under normal conditions. The robustnessmeans: first the equation must be convergence to obtain a result; secondly single calibrationshould be trusted, which means the uniform and the uncertainty interval must be guaranteed;at last the calibration should be correct, which means the result should be unbiased as far aspossible. Therefore, this paper focuses on the existing observation equations and itsimprovement, which contains the interval uniqueness, the unbiasedness and the nature of thevariance, then the solution form at the least squares rules. At the first, tracks is an importantissue for whether the equation be convergence (interval uniqueness) and the uncertaintyinterval (the nature of the variance), which needs a certain scale and to be symmetry.Secondly the measurement of vertical displacement is needed to ensure the convergence ofequation, and the imprecisement do not affect other estimates under ideal conditions. Then themajor factor of the size of equation partial (estimated accuracy) is underwater acoustic linebending. Because the ray bending compensation can compensate the partial of the equation,the equation compensation do the same, then the practice is that at the first step to estimate theaverage sound velocity and at the second use the partial form. Finally, due to the nonlinearityof the equation and the sea circumstance, the specific numerical solution also influences theestimation precision and variance. While M estimation has better robustness and stability, thispaper presents a weight-form based on outlier eliminating algorithm, which does not need toconsider the specific criterion function but the weight of observation only. To sum up, theimproved observation equation, reasonable tracks and appropriate numerical solution canensure the stability of calibration basically.
For ray tracing positioning, the positioning precision is mainly due to positioningalgorithm at the condition of reasonable calibration and measurement. Positioning projectalgorithm of tracking positioning is constant gradient or constant sound speed delimination, then the rationality of delimination will directly influence the accuracy of the algorithm.Apparently the denser gets the higher accuracy, but the criterion for USBL real-time or deeppositioning is not acceptable. In addition, influences of the measurement quality or changes ofthe sound speed profile are difficult to express, which is negative to engineeringimplementation. So the horizontal positioning error propagation model is established, whichis deduced by the error transfer formula and whose parameters are confirmed by simulation,and the concept of equivalent measurement error of sound velocity profile is given. Accordingthe model, an adaptive slicing algorithm is designed to control truncation error: it bases on theadaptive Simpson method with inversed process. And then the model has some guidingsignificance, such as profile processing before position, the equivalent difference. For the next,the velocity measurement method by temperature, salinity and pressure is studied as well asthe profile smoothing or stretching. At last formulas needed by USBL positioning and thebasic module are summarized, and the correctness is verified by the experimental data.
At the end of the paper, statistical processing of experimental data shows the improvingof the track and the M estimation. Positioning after calibration using smaller circle data, allthe location have good convergence scatter include the bigger one, which means the scatterhas no radius adaptability and verifies the calibration and tracking accuracy.
安装校准的技术核心是它所使用的安装校准观测方程，它的性质决定了校准的流程和工程实现，从而决定了校准结果是否具有一定的稳健性。稳健性包括：首先校准要有结果，即求解不能不收敛；其次因海上操作的成本，单次校准结果要可信任，即校准的一致性和不确定区间要得到保证；最后校准的结果要保持一定的无偏性，以保证定位的精度。因此，本文重点研究了已有观测方程的性质并对其进行改进，给出了最小二乘准则下估计解的形式，讨论了方程解区间唯一性、无偏性和方差的性质。首先校准航迹是影响方程是否收敛(区间唯一性)和校准不确定区间(方差的性质)的重要因素，它需要有一定的尺度并且尽量对称；其次方程需要粗测安装垂直位移偏差来保证收敛，这在理想条件下是不影响其它的估计的；再次影响方程解偏差(估计的准确度)大小的主要因素是水下声线的弯曲，声线弯曲补偿可以对方程进行去偏，而方程的去偏也可视作声线弯曲补偿，因此第一步的校准方程估计平均声速而第二步方程采用去偏形式；最后，由于方程的非线性和海况，具体的数值解法也是影响估计精度和方差的重要因素，而M估计有较好的抗差性及稳健性，因此本文对最小二乘估计和M估计进行了理论研究后，给出了一种基于异常点剔除算法的加权形式，可不必考虑具体的准则函数直接设置观测权。综上所述，改进的观测方程、合理的航迹和合适的数值解法可基本保证校准的稳健性。
对于声线跟踪定位，假设校准合理、测量条件良好，影响定位精度的主要原因是定位算法。定位算法的工程实现通常是使用常梯度或常声速进行分层跟踪，因此分层好坏直接影响算法的精度，显然分层越密算法精度越高，但这个准则对于USBL实时或深海定位是不可接受的。另外，声速剖面的测量质量或变化对于定位精度的影响难以表达，这对于工程实现也是不利的。而本文初步建立了水平定位误差传递模型，它是由误差传递公式经过变化并且仿真生成参数而建立的。根据模型，本文设计了一种可由算法精度要求而对剖面进行分层的自适应方法，它基于自适应辛普森方法，是辛普森方法的逆过程。另外模型对其它工程问题有一定的指导意义，如剖面在定位之前的处理、常声速和常梯度跟踪的区别等。之后本文讨论了温、盐、压的声速剖面测量方法、剖面的平滑算法和拓延算法，最后总结了USBL声线跟踪定位的转换公式与流程的基本，通过实验数据验证了公式和流程的合理性。
最后对实验数据进行统计处理，统计结果表明了航迹、M估计对估计方差有所改善，以及方程去偏补偿后对校准一致性有所改善。校准之后进行定位，可以看到定位的散点图不再有圆半径的“适应性”，使用某半径上数据进行校准，对其他数据定位依然可以较好的收敛，这验证了校准及跟踪定位的正确性。
This paper is based on the domestic high precise USBL (Ultra-Short Baseline) system toresearch the at-sea installation calibration and ray tracing position algorithm. Afterinstall-calibration, the incidence angle can be calculated to use the tracing positioningalgorithm; the ray-tracing positioning scatter picture can test if the calibration is correct,which is the ultimate goal of the system, therefore the two contents for USBL are inseparable.
The core of install-calibration the measurement equation used, as well as the calibrationprocess decided by the equation property and engineering realization, which need the esurientthat the calibration has to have a certain robustness under normal conditions. The robustnessmeans: first the equation must be convergence to obtain a result; secondly single calibrationshould be trusted, which means the uniform and the uncertainty interval must be guaranteed;at last the calibration should be correct, which means the result should be unbiased as far aspossible. Therefore, this paper focuses on the existing observation equations and itsimprovement, which contains the interval uniqueness, the unbiasedness and the nature of thevariance, then the solution form at the least squares rules. At the first, tracks is an importantissue for whether the equation be convergence (interval uniqueness) and the uncertaintyinterval (the nature of the variance), which needs a certain scale and to be symmetry.Secondly the measurement of vertical displacement is needed to ensure the convergence ofequation, and the imprecisement do not affect other estimates under ideal conditions. Then themajor factor of the size of equation partial (estimated accuracy) is underwater acoustic linebending. Because the ray bending compensation can compensate the partial of the equation,the equation compensation do the same, then the practice is that at the first step to estimate theaverage sound velocity and at the second use the partial form. Finally, due to the nonlinearityof the equation and the sea circumstance, the specific numerical solution also influences theestimation precision and variance. While M estimation has better robustness and stability, thispaper presents a weight-form based on outlier eliminating algorithm, which does not need toconsider the specific criterion function but the weight of observation only. To sum up, theimproved observation equation, reasonable tracks and appropriate numerical solution canensure the stability of calibration basically.
For ray tracing positioning, the positioning precision is mainly due to positioningalgorithm at the condition of reasonable calibration and measurement. Positioning projectalgorithm of tracking positioning is constant gradient or constant sound speed delimination, then the rationality of delimination will directly influence the accuracy of the algorithm.Apparently the denser gets the higher accuracy, but the criterion for USBL real-time or deeppositioning is not acceptable. In addition, influences of the measurement quality or changes ofthe sound speed profile are difficult to express, which is negative to engineeringimplementation. So the horizontal positioning error propagation model is established, whichis deduced by the error transfer formula and whose parameters are confirmed by simulation,and the concept of equivalent measurement error of sound velocity profile is given. Accordingthe model, an adaptive slicing algorithm is designed to control truncation error: it bases on theadaptive Simpson method with inversed process. And then the model has some guidingsignificance, such as profile processing before position, the equivalent difference. For the next,the velocity measurement method by temperature, salinity and pressure is studied as well asthe profile smoothing or stretching. At last formulas needed by USBL positioning and thebasic module are summarized, and the correctness is verified by the experimental data.
At the end of the paper, statistical processing of experimental data shows the improvingof the track and the M estimation. Positioning after calibration using smaller circle data, allthe location have good convergence scatter include the bigger one, which means the scatterhas no radius adaptability and verifies the calibration and tracking accuracy.
引文
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