Research On Fast Algorithms Of Multidimensional Parameter Estimation

Two-Dimensional direction-of-arrival(DOA) estimation of multiple signals by using planar arrays with various array geometries plays an important role in many practical applications such as sonar, radar, and communications. Due to the increase in the dimensionality of the 2-D DOA estimation problem, the computational complexity of DOA estimation process is severly affected by the array geometry, and further the pair-matching of the estimated elevation and azimuth angles is usually required, where most conventional pairing algorithms involve 2-D searching and/or nonlinear optimization. Hence this paper focuses on the computational complexity of algorithms and mainly studies the 2-D DOA parameter estimation algorithms based on L-shape array. The main contents are divided into three parts shown as follows:Firstly, we study the signal model of array geometries and the differences between the calculation of delay and phase based on various planar arrays; meanwhile we briefly introduce 1-D DOA algorithms, including MUSIC(Multiple Signal Classification), ESPRIT(Estimate Signal Parameters via Rotational Invariant Techniques), PM(Propagator Method) and MSWF(Multi-Stage Wiener Filter) algorithm. With those simulations compared about the above 1-D DOA estimation algorithms, we analyse the computational complexity of the algorithms and performance of the estimated angles, also point out how to reduce the computational complexity of those algorithms.Secondly, the 2-D DOA parameter estimation algorithms based on L-shape array with narrow-band signals are studied, including the use of auto-correlation matrix of modified PM and CCM-ESPRIT(Cross-Correlation Matrix based on ESPRIT), and JSVD(Joint Singular Value Decomposition) and CODE(Computationally efficient cross-correlation based 2-D DOA Estimation) by using cross-correlation matrix. Then the origin and properties of those algorithms are explained and calculation complexity of each algorithm is analysed. In the same time, we also pay attention to the drawbacks of those algorithms. At last, we propose a fast algorithm of estimating subspace by using MSWF, which conducts the angle estimation based on cross-correlation matrix. Without any spectral peak searching and SVD, the proposed algorithm earns relatively low computational complexity. With the auto pair-mathcing and low computational complexity, the algorithm is conducive to engineering application for its real-time peoformance.Finally, we do research on the estimation of multidimensional parameters for wideband linear frequency modulated(LFM) signal, and estimate the initial frequency and chirp rate of LFM by using the characteristics of LFM signal in fractional Fourier transform(FRFT). At the same time in the special FRFT domain of LFM, which dechirps the LFM signal, we propose those fast algorithms of DOA estimation by using PM and MSWF, those algorithms don’t need EVD(Eigen-Value Decomposition) or SVD. Despite the loss of angle accuracy, the computational complexity of those algorithms is lower than those algorithms which based on EVD.