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Discrete Dynamics in Nature and Society
Volume 2013 (2013), Article ID 192021, 10 pages
Research Article

Experimental and Analytical Studies on Improved Feedforward ML Estimation Based on LS-SVR

1The State Key Laboratory of Complex Electromagnetic Environment Effects on Electronics and Information System, Luoyang 471003, China
2Luoyang Electronic Equipment Test Center of China, Luoyang 471003, China
3Zhengzhou Information Science and Technology Institute, Zhengzhou 450002, China

Received 9 August 2013; Revised 18 October 2013; Accepted 24 October 2013

Academic Editor: Guoliang Wei

Copyright © 2013 Xueqian Liu and Hongyi Yu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Maximum likelihood (ML) algorithm is the most common and effective parameter estimation method. However, when dealing with small sample and low signal-to-noise ratio (SNR), threshold effects are resulted and estimation performance degrades greatly. It is proved that support vector machine (SVM) is suitable for small sample. Consequently, we employ the linear relationship between least squares support vector regression (LS-SVR)’s inputs and outputs and regard LS-SVR process as a time-varying linear filter to increase input SNR of received signals and decrease the threshold value of mean square error (MSE) curve. Furthermore, it is verified that by taking single-tone sinusoidal frequency estimation, for example, and integrating data analysis and experimental validation, if LS-SVR’s parameters are set appropriately, not only can the LS-SVR process ensure the single-tone sinusoid and additive white Gaussian noise (AWGN) channel characteristics of original signals well, but it can also improves the frequency estimation performance. During experimental simulations, LS-SVR process is applied to two common and representative single-tone sinusoidal ML frequency estimation algorithms, the DFT-based frequency-domain periodogram (FDP) and phase-based Kay ones. And the threshold values of their MSE curves are decreased by 0.3 dB and 1.2 dB, respectively, which obviously exhibit the advantage of the proposed algorithm.