Multi-target positioning outer approximation nearly convex optimization algorithm on basis of arrival time

Abstract

The invention discloses a multi-target positioning outer approximation nearly convex optimization algorithm on the basis of arrival time. The multi-target positioning outer approximation nearly convex optimization algorithm includes building original problem models; relaxing original problems by the aid of relaxation methods to obtain a mixed integer convex optimization problem model; constructing novel appropriate constraints for semi-positive definite matrixes; solving coordinate values of various to-be-positioned targets by the aid of outer approximation nearness algorithm sub-models, continuous convex optimization problem models and OAA (open application architecture) algorithms. The multi-target positioning outer approximation nearly convex optimization algorithm has the advantages that complicated requirements of existing methods on layout of base stations and regions where the targets are located can be omitted by outer nearness approximation algorithms, and the global optimal solution can be assuredly converged without initial estimation points.

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 algorithm for multi-target positioning problems, which is applicable to multi-target positioning problems based on TOA. 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, dangerous goods tracking, mobile phone positioning, process control. Improving the estimated speed and accuracy of wireless positioning algorithms through mathematical methods has always been a concern of relevant scientific and technical personnel. [0003] Thanks to the development of convex optimization algorithms, efficient convex optimiza...

AI Technical Summary

Problems solved by technology

[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 reasonably arrange the base station, and then the targets are distributed in a specific range. Under the premise, a global optimal solution can be obtained only 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

Images