Computer Science – Information Theory
Scientific paper
2012-02-07
Computer Science
Information Theory
37 pages,14 figures
Scientific paper
Multi-frequency interferometry (MFI) is well known as an accurate phase-based measurement scheme. The paper reveals the close relationship between the unambiguous measurement range (UMR), the outlier and the MSE with the frequency pattern in MFI system. We note that the theoretical rigorous UMR of MFI deduced in the literature is usually optimistic for practical application and derive a more practical expression for the UMR. It is found that the least-square (LS) estimator of MFI has a distinguished "double threshold effect". Distinct difference is observed for the MSE in moderate and high SNR region (denoted by MMSE and HMSE respectively). Beside the conventional threshold effect caused by outlier in low-SNR region, another threshold effect occurs during the rapid transition from MMSE to HMSE with increasing SNR. The closed-form expressions for the MMSE, HMSE and CRB are further derived, with HMSE coinciding with CRB. Since the HMSE (or CRB) is insensitive to frequency pattern, we focused on MMSE minimization by proper frequency optimization. We show that a prime-based frequency interval can be exploited for the purpose of both outlier suppression and UMR extension and design a special optimal rearrangement for any set of frequency interval, in the sense of MMSE minimization. An extremely simple frequency design method is finally developed. Simulation and field experiment verified that the proposed scheme considerably outperforms the existing method in UMR as well as MSE performance, especially in the transition from MMSE to HMSE, for Gaussian and non-Gaussian channel.
Qi Wangdong
Wei Li
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