Study On Theories And Methods Of Multidimensional Parameter Estimation For Array Signal

Multidimensional parameter estimation for signals is an important research direction of array signal processing, which is used to measure or locate the signal sources through the joint estimation of multiple parameters. Relatively, multidimensional parameter estimation is more appropriate for practical application environment, which attracts great amount of research.Recently it has attracted scientists'attention that solve the problems of signal processing from enginevalue decomposing method. Using the signal's linear model, we can deposed the problem of nonlinear estimation to two simple aspects: one is the problem of linear model parameter estimation, the other is nonlinear process which is the process to collect the needed messages(frequency, attenuation factor, DOA) from the estimation model parameters. The two aspects are very important for the whole parameter estimation. The reliability of first step depends on the estimation scheme of model parameter, and the reliability of second step depends on the sensibility of model parameter.During the research of signal processing, linear model multinomial is often used, but state-space description of linear model may be another choice .It is appropriate for solving of some signal processing problems. It can more easily expose the nature of the problems than other models such as AR, MA and ARMA model, because the state-space model possesses invariant structure which if being properly made use of can ultimately improve the performance of DOA estimation, and again, the structure property provides new way and new ideal for signal processing. In addition, the well-known subspace methods based on AR, MA and ARMA models can also be totally summarized as the special cases of the methods based on state-space model.As a helpful complementarity of traditional linear system identification methods, subspace identification methods has received extensive attention. This class of methods colligates the ideas of system theory, linear algebra and statistics. Its characteristic is to identify the system state-space model directly from the input and output data, so it is greatly suit for multi-variable system identification. The core of subspace identification methods is to obtain the broad sense observability matrix, then find the system state-space model through the broad sense observability matrix.The multidimensional parameter estimation which is usually researched involves 2-D angle, frequency and 2-D polarizing angle. Multidimensional parameter estimation develops from the unidimensional parameter (DOA) estimation. Most early methods formed from the extention of unidimensional parameter estimation, which didn't make the best of multidimensional parameter message array signal carried. Therefor, those methods have the problem such as large computation complexity and difficulty for parameters pairing.In this paper, we take advantage of the second order and high order statistical properties, and combine the theories and methods of array signal processing, matrix analysis, state-space model and subspace identification. We research the key problem of multidimensional parameter estimation of far-field narrow-band signal sources, and analyze the computation complexity, parameter pairing and measurement accuracy. The main research result is:(1)We analyze the mathematical model of DOA and frequency jointestimation, and establish the mathematical model based on state-space model. The system matrix and observability matrix of state-space model separately involve the frequency and DOA message that we need. Then we use subspace identification method to get the estimation of the extended observability matrix, and get the estimation of system matrix and observability matrix from the extended observability matrix. At last, we get the estimations of frequency and DOA from the system matrix and observability matrix. The method has high computation speed and estimation accuracy, and can pair the parameters automatically.(2)Under the foundation of the research above, we research the improved algorithm to restrain the noise. We construct third order cumulant by using auxiliary matrix, and get the estimations of system matrices from the extended observability matrix. At last, we get the estimations of frequency and DOA from the system matrix and observability matrix. We use third order cumulant to restrain the Gaussian colored noise in this method, which extend the application range of the method.(3)We research the DOA and frequency joint estimation based on forth order cumulant. Under the background of Gaussian colored noise, using forth order cumulant can get higher estimation accuracy. Forth order cumulant also has the feature of extending the array, which can reduce the demand of the array structure. But most forth order cumulant estimation methods only use eigenvalue from the eigenvalue decomposition of the forth order cumulant, which need multiple eigenvalue decompositions and parameter pairing computation. The method we present in this paper only use one time eigenvalue decomposition, and estimate the DOA and frequency using eigenvalues and eigenvectors. The method has lower computation complexity and can pair the parameters automatically.(4) Under the foundation of the research above, we research the 2-D angle and frequency joint estimation based on forth order cumulant. We research the structure and feature of L type array, and establish the mathematical model of 2-D angle and frequency joint estimation based on L type array. We use L type array to lower the estimation dimension, and transform the 3-D estimation into one 2-D estimation and one unidimensional estimation. The method make best of the eigenvalues and eigenvector from the eigenvalue decomposition of the forth order cumulant, which only need once eigenvalue decomposition. The method has lower computation complexity and can pair the parameters automatically.