基于稀疏傅里叶变换的TDOA时延估计方法

TDOA Time Delay Estimation Method Based on Sparse Fourier Transform

在基于到达时间差(TDOA)的无源定位研究中,利用互相关算法估计站间时延被广泛采用.相关算法计算量较大,算法复杂度为O(N^2).随着研究深入,有学者提出了基于傅里叶变换的互相关算法,由于使用快速傅里叶变换(FFT)算法,处理速度得到较大提升,算法复杂度由平方级降低至亚线性级,即O(N·log N).在一些实时性较强的环境,当采样点数较大时,传统FFT算法仍很难满足要求.本文借鉴稀疏傅里叶变换(SFT)算法,引入稀疏信号的映射和重构思想,优化互相关计算过程,以进一步提高时延估计的速度,改进算法的算法复杂度为O(N),从亚线性级降低至线性级.实测数据表明,测量精度满足工程应用的要求,可为实时性较高的无源时差定位提供技术参考.

In the study of passive locat ion based on the Time Di f ference of Arrival （TDOA）, the cross-correlation algorithm has been widely used to estimate time delay. The computational com-plexity of cross-correlation algorithm is large, and the algorithm complexity is 0（NZ）. With fur-ther research, some scholars have proposed a cross-correlation algorithm based on Fourier trans-form. By using the FFT algorithm,the processing speed has been greatly improved and the algo-rithm complexity reduced to 0（N ？ log N） ,from square level down to sub-linear level. In some re-al-time occasions, especially when the sampling point is quite large,the traditional FFT algorithm is still difficult to meet the requirements. By introducing the mapping and reconstruction of sparse signals,the calculation of cross-correlation is optimized by using the Sparse Fourier Transform （SFT） algorithm, which can further improve the speed of time delay estimation. The algorithm complexity reduces to O（N） , from sub- linear level down to linear level. The mea sure d da ta shows that accuracy can meet the requirement of engineering application,and it provides a technical ref-erence for real-time passive TDOA location.