基于压缩感知的高精度地磁基准图构建方法

High-precision geomagnetic reference map construction method based on compressed sensing

地磁基准图的构建是实现地磁匹配导航的基石。针对实测数据量较小时利用插值法构建的地磁基准图精度不理想的问题,将压缩感知理论应用到地磁信息采集中。结合地磁基准图的结构特点设计了以离散余弦变换作为稀疏基、单位矩阵作为观测矩阵,以压缩采样匹配追踪(CoSaMP)算法作为重构算法的基于压缩感知的高精度地磁基准图构建方法,并与三次样条插值、Kriging插值及PSO-Kriging插值法进行对比。实验结果表明:所提方法具有较高的重构精度和稳定性,与性能最好的PSO-Kriging插值法相比,在6.25%采样率下重构地磁基准图,所提方法使得峰值信噪比(PSNR)由66.97 dB提高至74.67 dB,绝对误差由25.47 nT减小至10.26 nT,均方根误差由28.57 nT减小至11.33 nT。

The construction of geomagnetic reference map is the cornerstone of geomagnetic matching navigation.In this paper, the compressed sensing theory is applied to the geomagnetic information acquisition, which aims at solving the problem that the accuracy of the geomagnetic reference map is not satisfactory with the less measured data based on interpolation methods.A high-precision method of geomagnetic reference map construction based on compressed sensing is put forward, taking the structural characteristics of the geomagnetic reference map into consideration. The discrete cosine transform matrix is used as sparse basis, the unit matrix is used as measurement matrix, and the compression sampling matching pursuit(CoSaMP) algorithm is used as the reconstruction method. The experimental results show that the proposedmethod has better reconstruction accuracy and stability compared withthe methods of cubic spline interpolation, Kriging interpolation and PSO-Kriging interpolation. Compared with the PSO-Kriging interpolation method which has the best performance among the three, when geomagnetic reference map is reconstructed at the sampling rate of 6.25%, the proposed method makes the peak signal-to-noise ratio(PSNR) increase from 66.97 dB to 74.67 dB, themeanabsolute error reduce from 25.47 nT to 10.26 nT,and the root mean square error decrease from 28.57 nT to 11.33 nT.