Perturbation analysis of principal component based algorithm in frequency and DOA estimation
Principal component based algorithms have been extensively used in estimating the parameters of harmonics and the localization of radiating sources because of their rela-tively high resolution. In this thesis, we give the statistical performance analysis of the state-variable algorithm applied in fr...
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| Format: | Theses and Dissertations |
| Language: | English |
| Published: |
2009
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| Online Access: | http://hdl.handle.net/10356/19670 |
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| Institution: | Nanyang Technological University |
| Language: | English |
| Summary: | Principal component based algorithms have been extensively used in estimating the parameters of harmonics and the localization of radiating sources because of their rela-tively high resolution. In this thesis, we give the statistical performance analysis of the state-variable algorithm applied in frequency estimation. The analysis is achieved using the second-order Taylor series approximation of the principal singular vectors and val-ues of the data matrix. The first and second order perturbations of the singular vectors are first presented as vector-valued functions of the data, and the perturbations of the parameters related to the frequency estimator are derived via the functional relation-ship. Since the frequency estimator can be approximated by the second-order Taylor series expansion about the noise-free data, the bias and the variance expression of the frequency estimator are obtained without the assumption that the frequency estima-tor is unbiased. The derived theoretical expressions are verified via simulation results under different data matrix dimensions and different signal-to-noise ratios (SNR). |
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