正弦波信号频率估计快速高精度递推算法的研究

A Research of Fast and Accurate Recursive Algorithm for Frequency Estimation of Sinusoid Signal

该文提出了一种正弦波频率估计的频偏校正算法,结合M-Rife算法精度高和频偏校正算法运算量小的特点,研究了一种快速高精度正弦波信号频率估计的递推算法。先对一个较短的截短信号序列用M-Rife算法进行频率初始估计,以此作初始值用频偏校正算法对一个更长的截短信号序列进行估计得到更精确的估计频率,并依此类推,在最后一步递推时,用M-Rife算法得到最终的估计频率。在信号序列较长时,该算法的运算量小于做一次FFT。仿真结果表明,该算法性能稳定,估计方差接近克拉美-罗限(Cramer-Rao Lower Bound,CRLB),与M-Rife算法相仿。该算法便于实时地实现高精度频率估计。

A frequency offset correcting algorithm is presented for frequency estimation of sinusoid signal, and a fast and accurate recursive algorithm for frequency estimation of sinusoid signal is investigated by associating the advantage of high accuracy of the M-Rife algorithm and the advantage of small computational load of the frequency offset correcting algorithm. Firstly, an initial estimation is obtained by the M-Rife algorithm for a truncated signal series which has a few points. Next, with the initial estimation result, a more accurate estimation is obtained by the frequency offset correcting algorithm for a longer truncated signal series. And then, deduce the rest by analogy. Finally, the ultimate estimation is obtained by the M-Rife algorithm for the entire signal series. The computational complexity of the recursive algorithm is lower than that of an FFT operation when the signal series is long. Simulation results show that the performance of this algorithm is stable, and the estimation variance is nearly the same as the M-Rife algorithm, approaching to CRLB（Cramer-Rao Lower Bound）. The algorithm is convenient for realizing real-time frequency estimation accurately.