Development of computationally efficient and accurate frequency estimation algorithms
Student thesis: Master's Thesis
In this thesis, new algorithms are developed for real sinusoid frequency estimation. The proposed frequency estimators are based on the techniques of least squares (LS), weighted least squares (WLS) and structured total least squares (STLS), respectively. The LS-based frequency estimator, namely, modified Pisarenko harmonic de-composition (MPHD) method is an improvement of Pisarenko harmonic decomposition (PHD) method. Unlike PHD, the MPHD method is unbiased and its variance is lower than that of PHD when the signal-to-noise ratio (SNR) is sufficiently high. Although the MPHD method is unbiased, it cannot provide optimal estimation performance. Motivated by the suboptimality of LS approach, two frequency estimators are developed based on WLS with monic and unit-norm constraints. It is proved theoretically and experimentally that the proposed estimators can attain Cramer-Rao lower bound (CRLB) when the data length is long enough and/or the SNR is sufficiently high. On the other hand, four frequency estimators based on the idea of STLS approach are developed. Compared with the existing STLS method, the proposed estimators have the advantages of more computationally efficient the requiring no user-defined parameters. The proposed approach which has comparable performance of the maximum likelihood (ML) estimator is unbiased, consistent and efficient. Apart from algorithm development, the variances of the proposed frequency estimation algorithms have also been derived and verified by computer simulations.
- Computer algorithms