整体最小二乘法在精同步中的应用

Application of Total Least Squares in Precise Synchronization

摘要:

为了验证整体最小二乘法(TLS,Total Least Squares)比最小二乘法(LS,Least Squares)更适用于精同步,提出了基于整体最小二乘的精同步方法;该方法以PN码基于BPSK调制的同步模型为基础,在接收端得到鉴相曲线后,对鉴相曲线零值点附近的几个固定位置的数据点利用QR分解和奇异值分解的整体最小二乘法拟合出鉴相曲线,求出同步误差;最后通过在Matlab软件上的仿真,得出结论:在噪声环境下,整体最小二乘法在同步中的应用可以得到优于基于普通最小二乘法的同步法的测量精度和稳定性;特别是在信噪比较低的条件下,基于整体最小二乘的精同步测量精度提升了3倍多,同事稳定性提升5倍多。

Abstract:

To verify that the total least-squares method is a better suitable for fine synchronization than the least-squares method, propose the precise synchronization method based on the total least squares. This method is on the base of PN code’s BPSK modulation . After the receiver get the phase curve, to get the data of curve’s several fixed position near the zero point. then using the total least squares based on QR decomposition and singular value decomposition fitting out the phase line, and estimate the synchronization error. According to the result of the simulation in Matlab software, draw the conclusion:under the noise environment, the Total least squares method in the application of synchronous can be better than that of synchronization based on ordinary least squares method on measuring precision and stability. Especially under the condition of low signal noise ratio (SNR), based on the least squares of synchronous measurement precision is improved more than 3 times.and the stability performance is improved more than 5 times.