Parameters Estimation Of Contaminated Two-dimensional Harmonics And Application Of Quaternion In It

The parameters estimation of harmonics has taken on a more significant rolein modern signal processing. Specially, parameters estimation of two-dimensional(2-D) harmonics has received a lot of attention in recent years and has been appliedin many applications, such as radar, sonar, geophysics, radio communications andmedical imaging.This dissertation studies not only the harmonics' parametersestimation via higher-order statistics, cyclic statistics, but also the application ofquaternion in 2-D harmonics retrieval too. Our research was supported by NatureScience Fund of China (60172032, 60572069) and Special Fund of Doctor's station(2001404, 20050183073)The creative work of this dissertation includes four aspects: 1, whenuncorrelated multiplicative noise was zero-mean or nonzero-mean, parametersestimation methods based on 2-D cyclic statistics were presented. Results showedthat 2-D cyclic statistics was effective in estimating 2-D harmonics' parameters inmultiplicative noise. 2, when 2-D harmonics were contaminated in mutuallycorrelated multiplicative noise, the quadratic power of original observed data wereconstructed. Then, the definite relationship of overlapped items and originalparameters was used to estimate parameters. 3, when noise was colored additivenoise, nonzero-mean or zero-mean white multiplicative noise, the method of matrixextended matrix pencils was expanded to estimate corresponding parameters.Results showed that this method was also effective in rapid estimation andhigh-resolution of frequencies. 4, Put forward a new idea which was different fromtraditional way and introduced quaternion in 2-D harmonics' parametersestimation.This dissertation is divided into eight chapters:In chapter one, we summarized current research state and the significance of2-D harmonics retrieval, showed the development of quaternion in signalprocessing, and presented the main problems in 2-D harmonics retrieval. Finally,we determined our study in this dissertation.In chapter two, we introduced some foundational knowledge which would beused later, such as matrix algebra, high-order cumulant, cyclo-stationary andquaternion.In chapter three, we studied 2-D cyclo-stationary, and used 2-D cyclic mean,2-D cyclic correlation and 2-D cyclic third-order moment to extract signalparameters in zero-mean or nonzero-mean uncorrelated multiplicative noise. Fromsome simulations, we knew that 2-D cyclic mean was useful in parametersestimation when multiplicative noise was nonzero-mean. However, 2-D cyclicmean was invalid when multiplicative noise was zero-mean. 2-D cyclic correlationand 2-D cyclic third-order moment were effective in parameters estimation whenuncorrelated multiplicative noise was zero-mean while the former demanded tolimit the range of paramerts' value and the latter asked the third-order cumulant ofmultiplicative noise to be skrewness.In chapter four, we studied 1-D and 2-D harmonics' parameters estimation inmutually correlated zero-mean multiplicative noise which was uncorrelated withadditive noise. As for 1-D observed data, we defined a special third-order momentof quadratic power of data because we could get original harmonics' parameterswhich were determined by the values resolved with this special third-order moment.Then, we extended this method to the case of two-dimension. We estimated theparameters of one direction of 2-D data at first and used them to estimate theparameters of another direction in order to decrease the computation and memoryburden if we had extended our method directly from one-dimension totwo-dimension.In chapter five, we studied how to expand classic 2-D parameters estimationmethod named matrix extended matrix pencil (MEMP) into the case of coloredadditive noise, zero-mean or nonzero-mean multiplicative white noise. Weexpanded this method because it was known that this method was rapid, highresolution estimation algorithm. When additive noise was colored noise, weconstructed MEMP of correlation function of data. Some simulations illustratedthat this method was very useful. What's more, it was also valid whenmultiplicative white noise was nonzero-mean. When multiplicative white noise waszero-mean, we could construct MEMP of the fourth-order moment to estimateparameters.In chapter six, we studied application of quaternion in 2-D harmonics retrieval.First, we illustrated in detail about the relationship between 2-D real harmonicsmodel, 2-D complex harmonics model and 2-D harmonics model based onquaternion. Then, we presented corresponding algorithm to estimate parameters of2-D harmonics based on quaternion without any noise. Finally, we appliedquaternion in 2-D parameters estimation when additive noise was white or colored.In chapter seven, we applied our idea and corresponding algorithm which waspresented in chapter six to array signal processing. Results showed that our ideaand algorithm also could be used in many other domains, such as parametersestimation of 2-D direction-of-arrival and joint estimation of frequency anddirection-of-arrival.In chapter eight, a brief summary of this dissertation was given. Someproblems and further research aspects were presented.