一种新的实时相关极值匹配算法设计与仿真

Real-time maximum correlation matching algorithm based on approximated local gravity map

对传统相关极值匹配算法局限性进行了分析,并利用二维高斯样条函数张量积方法对局部重力异常离散格网基准图进行逼近以获取该局部基准图的连续解析表达式,在此基础上对相关极值匹配算法进行重新建模并采用拟牛顿BFGS非线性寻优方法对该模型进行解算。考虑到相关极值算法存在实时性差的缺点,采用固定初始序列长度的方式对初始序列采样结构进行改善,推导出了刚性变换中心从序列质心到原点的转换公式,最终完成能够实现单点迭代的基于局部重力异常基准图实时相关极值匹配算法设计,该匹配算法突破了传统离散匹配算法受限于基准图分辨率的局限。最后在2′×2′卫星测高反演重力异常数据基础上进行了两组仿真实验进行对比分析,实验结果表明,在重力测量噪声和初始定位误差较大的情况下,通过该匹配算法获得的匹配定位仍能以较高的精度实时跟踪真实航迹。

The limitations of the normal maximum correlation matching algorithm was analyzed, and the algorithm to approximate the local grid gravity anomaly map with the tensor product of the Gauss spline function was proposed to get the continuous analytic expression of the local gravity anomaly map. Then, the mathematical model of maximum correlation matching algorithm was redesigned based on the continuous analytic expression, and the BFGS method of Quasi-Newton was adopted to solve the non-linear model. With respect to the bad real-time performance of maximum correlation matching algorithm, the way to fix the length of sample sequence was adopted to improve the sampling structure and the conversion formula between two rigidity transformations with different center. Finally, the design of real-time maximum correlation matching algorithm based on the continuous analytic expression of gravity anomaly map was accomplished. The new matching algorithm is no longer restricted in the resolution of gravity anomaly map. Two simulation experiments have been made based on 2＇x2＇ gravity anomaly database from satellite altimetry inversion for the comparative analysis. The simulation results show that the matching results of the new integrated algorithm can track the real positions with high-precision in case of relatively large observation noise and initial position error.