Frequency estimation using subspace methods
Complex frequency estimation problem plays a significant role in many engineering applications. The estimation process was traditionally achieved by the Eigenvalue Decomposition (EVD) of the spatial correlation matrix of observations. Frequency estimation has fundamental significant and wide relevance for many reasons. First, any arbitrary signal may be modeled as a sum of frequencies. Hence, any signal estimation problem may be expressed in terms of frequency estimation problems. Second, many parameter estimation applications may be mathematically expressed as a frequency estimation problem. In this thesis an improved frequency estimation technique is presented based on the unitary transformation, which was basically applied in the direction of arrival problem. The key idea of the proposed technique is to convert the complex valued autocorrelation, cumulant, or the direct data matrix in Hankel like shape into a real valued data matrix with the same dimension. The resultant real valued matrix will be used to extract the noise and/or the signal subspace instead of the original complex one. It is well known that real manipulations are easier and faster than the complex ones.