映射内插高精度频率估计

如何精确估计噪声中的正弦信号的频率是雷达、声纳、通信和生物医学工程等许多领域中的—个重要问题.对于高斯白噪声中的单个或能够很好分辨的P个正弦信号,其频率的极大似然估计就是周期图频率估计(PFE),也就是周期图功率谱最大的P个谱峰所对应的频率[1]. 在实际应用中,由于使用FFT等数字技术,对大量位于离散的谱线之间的频率均无法得到精确的频率估计.通常减小估计误差的方法有两种:一种是增加谱线的条数(M),但使计算量显著增加;另一种是利用抛物线内插法(PIFE),对谱峰的位置加以修正.这些方法减小误差的效果仍不明显,其频率估计的均方根误差(RMSE)如图1所示.

High-Accuracy Frequency Estimation by Mapping Interpolation

How to accurately estimate the frequencies of sinusoidal signal in noise is an important topic in sonar, radar, communication, biomedical engineering, and many other fields. For a single sinusoid or P well-resolvable sinusoids the maximum likelihood estimator of the frequencies is periodogram frequency estimator (PFE), i. e., the frequencies corresponding to the P maximum peaks of periodogram [1]. In applications, the frequencies of sinusoids are frequently located between discrete spectral lines. In such cases, when digital techniques such as FFT are used, accuracy frequency estimation can not be obtained. In general, there are two methods to reduce the estimation errors. One is to increase the number of spectral lines (M) at the price of greatly increased computation. The other is to make use of parabolic interpolation frequency estimator (PIFE) to fix the positions of the maximum spectral peaks. Neither method is efficient in reducing the estimation errors. The root-mean-square errors (RMSE) of the frequency estimators are shown in Figure 1. The author analyzes carefully the cause of failure of PIFE to obtain accuracy frequency estimation. The author proposes a new method called MIFE (mapping interpolation frequency estimator). In this method the mapping function which can greatly reduce the estimation errors is first obtained, then interpolation is done utilizing the new sequence after mapping. Thus high-accuracy frequency estimation is achieved. It should be emphasized that MIFE requires only about the same amount of computation as PIFE. Extensive computer simulation and implementation on TMS32010 digital signal processor show the effectiveness of MIFE. Especially in the case of short data the results are more effective. For the data length N=64 points and the number of spectral lines M=64 the RMSE of MIFE is very small as compared to PFE and PIFE (see Fig. 1). When the signal-to-noise ratio is high (SNR>30 dB) the average mean square error (MSE) of MIFE is just under 0.1% of that of PFE. For SNR=5dB the MSE of MIFE is only about 5% of that of PFE (see Table 1).