Single/Multiple Station Localization Method Research In Unified Near-far-field Model And Ill-conditioned Matrix Situation

Obtaining the source position is significant in both military and civilian fields.The localization methods based on intermediate parameters have been well studied in the past few decades so that it gained a great number of achievements.The closed-form solution attracts much interest since it is low computation-complexity and well-performed,which satisfies the requirements of real-time and high accuracy in many application scenarios.Traditional localization methods are developed in Cartesian,where the geometric condition is assumed non-ill-conditioned and the priori knowledge whether the source is in the near-field or far-field is known.The researchers now realize that many state-of-the-art localization methods are infeasible under some exceptional sensor-source deployments,in which the Cartesian-based approaches suffer the ill-conditioned problem.Two of the special cases present in the scenarios with a single station and unknown source range,respectively.In mono station locating,the matrix in the measurement equation is close to singular since the baseline is limited.To handle this problem,on the one hand,the new algorithm shall be developed to reduce the perturbation due to the illness.On the other hand,increasing the equivalent baseline is an effective way.The other problem is the thresholding effect,the rapid performance losing that happens when the source moves from the near-field into the far-field.Previous research presents the modified polar representation(MPR)to unify the localization for near source and bearing finding for far source into one framework.However,the state-of-the-art approaches are computationally prohibitive without guarantee of convergence.The unified model and single station localization are the breakthrough and compensation of the location studies,which are the technological frontier and research hotspot in the world.This thesis focuses on the closed-form localization approaches using only one station and in the unified model based on MPR.The main contents include theoretical analysis,algorithm development and simulation verification,listed as follow:1.Several ill-conditioned problems existing in the multiple sensors localization systems are discussed.In terms of the derivation of hybrid Bhattacharyya-Barankin bound(HBBB),the thresholding effect of the near-field model in Cartesian is verified mathematically when increasing the source range.2.Using the thinking of inverse synthetic aperture radar(ISAR)is able to increase the equivalent baseline,where the corresponding Cram′er-Rao Lower Bound(CRLB)is derived.Since common weighted total least squares(WTLS)can’t suppress the perturbation effectively,this thesis proposes a bias reduction(BR)algorithm and a Newton-Gauss iterative implementation for maximum likelihood estimator(MLE).The new algorithms alleviate the ill-conditioned problem,which estimates the source position and velocity accurately and reliably.3.The CRLB of TDOA localization in the unified model is derived.Two closedform solutions for MPR-based TDOA localization are proposed: successive unconstrained minimization(SUM)solution and general trust region subproblem(GTRS)solution.They overcome the thresholding effect in Cartesian.The equation is approximately pseudo-linear in small noise region,which results the closed-form solution in MPR.4.The proposed SUM and GTRS have much higher bias than the MLE.To improve the bias performance,this thesis proposes two bias reduction methods in closed-form:direct deviation refinement(DDR)and constrained deviation refinement,which lower the bias close to the MLE level.5.The more realistic model with sensor position errors is considered.Besides the CRLB in this situation,two methods,called weighted error compensation(WEC)and unconstrained successive calibration(USC),are developed to alleviate the performance degradation due to the sensor uncertainty.6.The CRLB is extended to the AOA and hybrid AOA-TDOA case to evaluate the optimal performance.An eigendecomposition-based algebraic approach,constrained eigenspace-based solution(CES),is developed for the AOA only case.When the measurement vector contains TDOA information,the solutions extend the SUM and GTRS approaches to the AOA-TDOA case directly.It fills in the blank that there is no algebraic/closed-form solution in MPR using AOA and TDOA measurements.The feasibility and accuracy of the proposed algorithms in this thesis are validated through both theoretical analysis and numerical simulations.Both analytical and emulational results show that the proposed algorithms in this thesis achieve CRLB performance under the small noise conditions,while the modified methods improve the MSE performance and bias performance noticeably.