Research On Frequency Estimator For A Noisy Real Sinusoid

Parameter estimation of a tone in noise is important in many fields such as radar, sonar,communications, speech signal processing, biomedical engineering, control and measurement.Frequency is the most important parameter and the most essential feature, so its estimation isa classic issue in the field of signal processing. In many practical engineering applications, thesignal samples have real values, such as voice signals. However, fequency estimation ofa real sinusoid is more difficult relatively than the complex one, for the formerincludes "negative frequency" in the spectrum, and the phase of its correlation affects theaccuracy of frequency estimation. So that, the method of frequency estimationfor the complex sinusoid can not be directly applied to the real one, especially for thetime-domain algorithms. White Gaussian noise is a common noise in the nature, so thefrequency estimation of the real sinusoid embedded in white Gaussian noise hasbeen received extensive attention.The method of the frequency estimation can be divided into two categories: based ontime-domain and transform domain, such as frequency-domain. For the methods based onfrequency-domain, they have advantages in the estimation performance, but they arecomputationally demanding. While, the methods based on time-domain are relativelysimple, and they are especially suitable for applications where the real-time estimation isrequired. The mean square error is often used as a measure of inaccuracy for the frequencyestimation, and there is an ideal theoretic bound named Cramer Rao Bound (CRB), whichdepends on the length of signal and SNR. For the short sequence, efficient time-domainestimators which approach the CRB and have less computation demanding as well are the keypoint in the study of frequency estimation. Since the sample correlation sequence has thesame frequency as the original signal, but with less noise effect, this dissertation has madedeep research on the correlation-based estimator and the major contributions are as thefollowing:(1)A closed-form expanded correlation method for real sinusoid frequency estimation isproposed and the effects of White Gaussian noise on the performance is derived, so that aclosed-form theoretical performances bound is abtained. Since the sample correlationsequence has the same frequency as the original signal, a few correlation coefficients can beexploited to estimate the frequency qulickly but the performance is inefficient. To improvethe estimation formance, many researchers proposed a lot of modified correlations andmultiple-stage correlaton, however, the former is not very effective and the latter increases the amount of computation. We take the performance and complexity into consideration andpropose an expanded correlation method. The mothod makes full use of the multiplecorrelaition lags and extends the idea of a coarse search and a fine search of frequencyestimation in the frequency-domain to the time-domain. Firstly, the modified covariance(MC) method based on multiple correlation lags is applied to provide a coarse frequencyestimate. Then, a closed-form adjustment term based on a least square cost function is derivedto get the fine frequency estimate. Simulation results show that the performance of theproposed algorithm, when compared with several existing closed-form time-domainestimators, is closer to the Cramer-Rao Bound (CRB) at0dB. Moreover, the proposed methodhas lower computation complexity than other autocorrelation-based approaches, which alsouse multiple autocorrelation lags. The research productions are published in Signal Processing,etc.(2)An real single-tone frequency estimator based on phase compensation of multiplecorrelation lags is proposed. For the limited-length single sinusoid, its correlation has anon-zero phase, which is always neglected for correlaton-based methods. So we propose touse Taylor series to expand the correlation at the coarse estimated frequency to exploitmultiple correlation information and take the phase of the correlation into consideration. Theselection of multiple correlation lags is discussed deeply by experiments. Simulation resultsshow that this new method outperforms the Pisarenko harmonic decomposer stimator.Moreover, when compared with other existing considerable computational estimator, themean square frequency error of the proposed method is closer to the CRB for certain SNRrange, especially when the signal length is very short. The research productions are publishedin IEICE Transactions, etc.(3)A modified PHD method based on windowed correlation sequence is investigated.The PHD method only utilizes correlation lags1and2to estimate the frequency. It has beenproved using higher correlation lags can improve the estimtation performance but leads tofrequency ambiguity and edge frequency. So, we research on a method, which exploiteshigher correlation lags and can improve performance with avoiding frequency ambiguity andedge frequency. In addition, the noise effect on the correlation concentrates around lag0,and the correlation with higher lag is inaccurate for its computation involves less availablesamples, thus we consider adding a rectangle window to the correlaton. Based on thewindowed correlation sequence, an adjustment term is derived to add to the coase frequency,which is obtained by PHD method with higher correlation lags. Theoretical analysis showsthat the algorithm can approach the CRB, and it gives guidance on how to select a windowed correlation sequence. Simulation experiments illustrate the performance of our proposedmethod is generally superior to the PHD and other correlation-based methods, and it can solvethe problem about frequency ambiguity and edge frequency. The research productions arepublished in Chinese Electronic Journal, etc.