An Approximate Convex Optimization Method Based on Time Difference of Arrival for Multi-target Localization by Exterior Approximation

Abstract

The invention discloses a multi-target positioning external impending approximation convex optimization algorithm based on a time difference of arrival. According to the algorithm, first, an original question model is constructed; next, a relaxation method is used to relax the original question model into a convex question to obtain a first external impending approximation algorithm submodel; new proper constraint is constructed according to a positive semi-definite matrix, and then the first external impending approximation algorithm submodel is solved to obtain an integer solution; the obtained integer solution is substituted into a second external impending approximation algorithm submodel, initial rough coordinate values of all targets to be positioned are solved, and the coordinate values are used as starting points to calculate precise positions of all the targets; and then whether an optimal solution is obtained is judged. Through the algorithm, the external impending approximation algorithm is utilized, complicated requirements of existing methods on a layout of a base station and a region where a to-be-detected target is located are avoided, it can be ensured that a global optimal solution is obtained through convergence, and an initial estimation point is not needed.

Description

technical field [0001] The invention belongs to the technical field of positioning based on wireless signals, and in particular relates to a convex optimization method for a multi-target positioning problem, which is applicable to the multi-target positioning problem based on TDOA. Background technique [0002] Wireless positioning technology was first used to locate military targets such as ships and fighter jets during World War II. With the development of science and technology, more and more wireless positioning technology has been widely used in the fields of industry, civil and national defense. Such as emergency rescue response, real-time tracking of dangerous goods, mobile phone positioning, process control. Improving the estimated speed and accuracy of wireless positioning algorithms through mathematical methods has always been a research hotspot in related fields. [0003] Thanks to the development of convex optimization algorithms, efficient convex optimization ...

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Problems solved by technology

Among them, in order to improve the calculation efficiency, algorithms with high convergence speed such as the first-order acceleration algorithm, quasi-Newton method and interior point method are also used in the calculation of the above relaxed problems, but since the problem itself is a non-convex problem, it is difficult to guarantee The algorithm converges to the global optimal solution in practical application

[0004] In particular, for the multi-target positioning problem, because the base station cannot identify which target the signal originates from, the problem is an NP-hard problem. The existing multi-target positioning algorithm can only arrange the base stations reasonably, and then the target to be measured is distributed in a specific range, a global optimal solution can be obtained under the condition of choosing an appropriate initial estimation point

Otherwise, it is only guaranteed to converge to a local optimal solution

And in order to solve the NP-hard problem, the computational complexity increases exponentially with the increase of the number of targets, and it is easy to fall into the local optimal solution

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