基于Haar小波变换的信号到达时间估计

Arrival time estimation of signals based on Haar wavelets transform

研究了在信号频率、初相、幅度未知条件下,矩形包络复正弦信号的到达时间估计算法。先利用相关检测算法,对信号的起止时间进行粗估计。在检测到信号的条件下,估计出信号频率并将其变换至基带,在一定尺度下对基带信号作Haar小波变换,检测出小波变换模值的峰点位置作为到达时间精估计。给出了小波尺度选取的原则,并推导了到达时间估计的克拉美罗限(CRLB)。计算机仿真表明,信噪比达6 dB时,到达时间估计的均方根误差小于0.8倍的采样间隔,实现了对信号到达时间的精估计。

The problem of estimating time of arrival （TOA） of complex sinusoid with rectangular pulsed envelope is considered. In the absence of a prior knowledge for the signal parameters （amplitude, phase and frequency）, the coarse estimation of the start position and end position by correlation detection is performed at first. Consequently, the received signal is transformed to baseband one with the estimation of the frequency. The start position of the signal can be effectively extracted by locating peak magnitude of the wavelet transformation of the baseband signal. The principles of wavelet scale selection are discussed and the Cramer-Rao low bounds （CRLB） for TOA estimation is derived. The performance of the estimator is investigated through simulations,and the results show that the method is efficient for fine estimation of TOA. For SNR= 6 dB, the root mean square is less than 0.8 times sample interval.