%0 Journal Article
%T Experimental and Analytical Studies on Improved Feedforward ML Estimation Based on LS-SVR
%A Xueqian Liu
%A Hongyi Yu
%J Discrete Dynamics in Nature and Society
%D 2013
%I Hindawi Publishing Corporation
%R 10.1155/2013/192021
%X 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. 1. Introduction Maximum likelihood (ML) estimation depends on the asymptotic theory, which means that the statistical characteristics are shown accurately only when the sample size is infinity. However, burst-mode transmissions always bring problems about short data and severe conditions. Therefore, threshold effect is existing. Namely, the mean square error (MSE) of ML estimation can reach Cramer-Rao lower bound (CRLB) if it is higher than a value, or the performance will be deteriorated rapidly. Statistical learning theory (SLT) and structure risk minimization (SRM) rule in it are specialized in small-sample learning [1]. As their concrete implement, support vector machine (SVM) overcomes the over-fitting and local minimum problems currently existing in artificial neural network (ANN). Least squares support vector regression (LS-SVR) has the following improvements: inequality constraint are substituted by equality one; a squared loss function is taken for the error variable. Hence, we introduce LS-SVR to improve ML estimator and take feedforward single-tone sinusoidal frequency estimation for example, in this study. Estimating frequency of a
%U http://www.hindawi.com/journals/ddns/2013/192021/