Research On Algebraic Analytic Method For Single Single Platform Range Only Target Localization

Single platform range-only target localization(SPROTL)has the characteristics of simple deployment,low cost,and high localization accuracy.It is widely used in inverse synthetic aperture radar target tracking,underwater autonomous vehicle localization,unmanned aerial vehicle docking,and emitter localization.The challenges of SPROTL result from the observability and nonlinear relationship between range measurements and the target state.This thesis focuses on the analytical solutions of the SPROTL problem.The main results are listed as follows:(1)To reduce the estimation bias when using the multidimensional scaling(MDS)analysis method,this thesis proposes a MDS-constrained total least squares localization algorithm.Firstly,a multidimensional similar pseudo-linear expression is established using range-only measurements.Then,a constrained total least square is proposed to solve the statistical correlation between the column vectors of the pertubation matrix.Next,the constrained total least square is transformed into an unconstrained optimization problem using Lagrange sub multiplication and solved by Newton optimization method.Finally,simulation results show that the proposed algorithm can reduce the estimation bias of the MDS method and improve the localization accuracy.(2)To improve the ill-conditioned problem of the observation matrix of the pseudo-linear equation,this thesis proposes an improved pseudo-linear estimator for moving target localization.The proposed algorithm modifies the nuisance parameters to obtain a new pseudo-linear expression.Then,a weighted least squares optimizaiton method is used to obtain the estimates of the motion parameters.Subsequently,the coupling between the nuisance parameters and the motion parameters of the moving target is analyzed,and the Taylor series is used to compensate the estimation result in order to improve the estimation accuracy.Simulation results show that the algorithm can effectively reduce the condition number of the observation matrix and improve the estimation accuracy of the motion parameters.(3)The improved pseudo-linear estimation algorithm has the problem of performance degradation when the target speed or the measurement variance is too large,this thesis proposes a new separation pseudo-linear estimator.The proposed algorithm separates the motion parameters from the nuisance parameters and obtains a new pseudo-linear expression.Then,the motion parametersare estimated using alternative optimization.Subsequently,the coupling between the nuisance parameters and the motion parameters is analyzed,and the Taylor series is used to compensate for the motion parameters to improve the estimation accuracy.Simulation results show that the proposed algorithm not only effectively reduces the condition number of the observation matrix,but also can obtain accurate estimates of the motion parameters in the cases of large target velocities and measurement variances.