| Summary: | This thesis comprises two parts. The first part deals with single carrier and multiple-carrier based frequency estimation. The second part is concerned with the application of ultrasound using the proposed estimators and introduces a novel efficient implementation of a subspace tracking technique. In the first part, the problem of single frequency estimation is initially examined, and a hybrid single tone estimator is proposed, comprising both coarse and refined estimates. The coarse estimate of the unknown frequency is obtained using the unweighted linear prediction method, and is used to remove the frequency dependence of the signal-to-noise ratio (SNR) threshold. The SNR threshold is then further reduced via a combination of using an aver aging filter and an outlier removal scheme. Finally, a refined frequency estimate is formed using a weighted phase average technique. The hybrid estimator outperforms other recently developed estimators and is found to be independent of the underlying frequency. A second topic considered in the first part of this thesis is multiple-carrier based frequency estimation. Based on this idea, three novel velocity estimators are proposed by exploiting the velocity dependence of the backscattered carriers using synthetic data, all three proposed estimators are found to exhibit the capability of mitigating the poor high velocity performance of the conventional correlation based techniques and thereby provide usable performance beyond the conventional Nyquist velocity limit. To evaluate these methods statistically, the Cramer-Rao lower bound for the velocity estimation is derived. In the second part, the fundamentals of ultrasound are briefly reviewed. An efficient subspace tracking technique is introduced as a way to implement clutter eigenfilters, greatly reducing the computation complexity as compared to conventional eigenfilters which are based on the evaluation of the block singular value decomposition technique. Finally, the hybrid estimator and the multiple-carrier based velocity estimators proposed in the first part of the thesis are examined with realistic radio frequency data, illustrating the usefulness of these methods in solving practical problems.
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