Tensor Algebra And Subspace-based Method For Parameter Estimation Of Multidimensional Signal

The field of Multidimensional Signal Parameter Estimation is one of the most important research areas in modern signal processing.The problem of multidimensional signal processing has developed very rapidly in recent decades and the development potential in this direction is still very large.The application of multidimensional signal parameter estimation is very broad,such as array signal processing,nuclear magnetic resonance in biomedicine,submarine sonar and wireless communication,etc.The main research of this thesis is the subspace-based algorithm of multidimensional signal parameter estimation under Gaussian white noise,and the main work can be summarized as follows:1.In the second chapter,some classical subspace-based algorithms of parameter estimation are analyzed and summarized,and their advantages and disadvantages are briefly described.2.In Chapter 3,a new algorithm in the presence of non-uniform noise model is proposed for two-dimensional DOA parameter estimation with matrix completion.The principle used in this algorithm is to achieve two-dimensional DOA parameter estimation by combining projection operator and low rank matrix recovery.The specific idea is to first restore the autocorrelation matrix of the first set of data using the principle of low rank matrix recovery,so as to obtain better parameter estimation accuracy of the first set of parameters.And then the second set of data is estimated by the projection operator constructed by the first set of data,and then the second set of data can be very high under the non-uniform noise model after using the projection operator.Simulation results show that the performance of the proposed algorithm using projection operator and low rank matrix recovery is better in the case of low signal-to-noise ratio.3.In the fourth Chapter,a root-music algorithm based on tensor mode-R and unitary projection separation is proposed for parameter estimation of multidimensional sinusoidal signal model.The time complexity of the algorithm through tensor mode-R and Unitary is reduced.The flow of the algorithm is to estimate the parameter information of the first dimension by the tensor mode-R and the unitary principle,and then construct the projection operator to separate the parameter information of the remaining dimensions by using the parameter information of the first dimension.The parameter estimation of the remaining dimensions can also be obtained by using the principles of tensor mode-R and Unitary,and the final matching of multidimensional parameter estimation is implemented.The performance of the proposed algorithm is compared with the IMDF algorithm,the HOSVD algorithm and the Huang algorithm.4.In the fifth chapter,a UPUMA-based projection separation algorithm is proposed,which is an improved algorithm of UPUMA.The algorithm combines the principle of UPUMA and the principle of projection operator.The disadvantage of UPUMA algorithm is that it has poor performance when dealing with multi-component models with multi-dimensional parameter estimation.Combining projection operators can solve this problem.The algorithm first estimates the parameter information of the first dimension through the subspace-based algorithm,and then constructs the projection operator using the parameter information of the first dimension to separate the parameters of the remaining dimensions.By using UPUMA's algorithm principle after projection separation,UPUMA can guarantee the algorithm resolution of multi-component problem of multi-dimensional parameter estimation.In the computer experiment,by comparing with the IMDF algorithm and the HOSVD algorithm,the UPUMA projection separation algorithm has better performance and lower time complexity.5.A final conclusion is given in the sixth Chapter and a possible research direction in the future is also discussed.