足印探测法是星载激光测高仪真实性校验的常用方法,而激光足印的中心提取是足印探测法的关键技术之一。针对受到大气湍流的影响的激光足印信号,提出一种基于Levenberg-Marquard(LM)算法的激光足印中心提取方法,以椭圆高斯函数为目标函数模型,通过椭圆高斯特征参数更新和迭代,以目标函数与观察值的残差作为判据,从而实现对特定参数即激光足印中心的提取。采用前40项泽尼克多项式模拟大气湍流作为激光足印在大气传输过程中的噪声,利用仿真数据对算法的提取精度和稳定性进行验证,实验结果表明,本文算法比传统的中心定位方法有着更高的定位精度并且相对稳定,假设激光足印探测器的布设间距为4 m,本文算法比其他传统算法的提取精度至少优于0.5 m。
The footprint detection method is a common method for the authenticity verification of the spaceborne laser altimeter,and the central extraction of the laser footprint is one of the key technologies of the footprint detection method. A laser footprint center extraction method based on the Levenberg-Marquard (LM) algorithm is proposed for the laser footprint signal affected by atmospheric turbulence. The elliptical Gaussian function is used as the objective function model,and the elliptical Gaussian characteristic parameters are updated and iterated. The residual of the objective function and the observed value is used as a criterion to achieve extraction of a specific parameter which includes a laser footprint center. The first 40 Zernike polynomials are used to simulate the atmospheric turbulence as the noise of the laser footprint in the atmospheric transmission process and the simulation data is used to verify the extraction accuracy and stability of the algorithm. The experimental results show that the proposed algorithm has higher positioning accuracy and is more stable than the traditional central positioning method. Assuming that the laser footprint detector is arranged at a distance of 4 m,the proposed algorithm is better than other traditional algorithms with an extraction accuracy of at least 0.5 m.