Research On Fast Distributed Localization Algorithm Based On Polynomial Root Time Difference Estimation

Distributed multi-station time difference of arrival(TDOA)positioning technique is a kind of passive localization technology.The time delay estimation algorithm,the geometric distribution of receiving stations and the TDOA localization algorithm are the hot spots in recent years.At the same time,the estimation speed of the algorithm is a big problem which is faced by the time delay estimation algorithm and the TDOA localization algorithm.In this paper,two time delay estimation algorithms and one kind of TDOA localization algorithm are proposed to solve the problem of large computational complexity,the influence of the receiving station distribution mode on positioning accuracy is also studied.The main contents of this paper are as follows:First,based on the deep research on the double spectrum delay estimation algorithm,apply the polynomial root method to this method,the root-double spectrum delay estimation algorithm is proposed.The new algorithm only needs to calculate the one-dimensional slice of the three-order cumulants of the receiving signal,then get the cross spectrum function through the one-dimensional fourier transform,and construct a new spectral function containing information delay,finally obtain the time delay value by root of the polynomial of the spectrum function.Simulation results show that the proposed algorithm not only reduces the computational complexity,but also improves the estimation precision.Next,based on the study of the theory of normalized mutual spectrum delay estimation based on MUSIC algorithm,the algorithm of root-normalized mutual spectrum delay estimation is proposed in this paper.The new algorithm avoids the complicated peak searching process by constructing the polynomial method,and obtains the delay value by using the polynomial root.The simulation results show that the algorithm can be used to reduce the computational complexity,and its performance is even better than the original algorithm.Moreover,based on the inductive research on existing classic cloth station,simulates and analysis geometric dilution of precision(GDOP)contour line distribution of three classical receiving stations way.Then,use the cramer-rao lower bound(CRLB)to deduce the conditions to satisfy the optimal distribution of receiving stations,give the optimum sensor array of the three-dimensional positioning,and the three dimensional four optimal embattling mode has carried on the simulation.Finally,after studying the newton iteration method modified by the regularization theory,the three-step modified newton iteration method is proposed in this paper.The new algorithm improves the convergence order by using the three-step iterative,and the hessian matrix is modified by using regularized parameters.Therefore,while ensuring the steady convergence of the iterative method,the estimation speed is improved.Simulation results show that the convergence performance of the algorithm is similar to that of the original algorithm,but the estimation speed is obviously improved.