块Toeplitz矩阵低复杂度求逆的卫星导航空时抗干扰算法

摘要

Sample covariance matrix inversion was a basic operation unit in the realization of space-time anti-jamming algorithm,and its computation load grew rapidly with the increasing number of time taps,which directly restricted the application of space-time anti-jamming technique in GNSS (Global Navigation Satellite System)receiver.Aiming at this problem,a space-time anti-jamming algorithm based on block Toeplitz inversion was adopted into anti-jamming processing.By improving the estimation method of the covariance matrix,the algorithm got a sample covariance matrix both in the form of block Toeplitz matrix and Hermite matrix,and then the fast block Toeplitz inversion algorithm was applied to reduce the inversion complexity of covariance matrix of K taps from O[K3 ]to O[K2 ].Theoretical analysis and simulation results show that when comparing with the traditional algorithm under the condition of 4 antenna elements and 15 taps,the anti-jamming performance cost of the proposed algorithm is less than 1 dB,and its computation load reduction is about 2/3 times of the traditional algorithm.%采样协方差矩阵求逆是空时抗干扰算法的基本运算单元，但由于其运算量随时域抽头个数急剧增长，直接限制了空时抗干扰技术在卫星导航接收机中的应用。针对该问题，提出了基于块Toeplitz矩阵快速求逆的空时抗干扰方法。通过采用新的协方差矩阵近似计算方法，使得该矩阵同时为块Toeplitz矩阵与Hermite矩阵，并运用块Toeplitz 矩阵的快速求逆算法，将时域抽头个数为 K的计算复杂度从 O [K3]降至O[K2]。理论分析和仿真结果表明，在阵元数为4、时域抽头为15的典型情况下，相比现有矩阵求逆方法，该算法的抗干扰性能损耗小于1 dB，但计算量可降低约2／3。