区域无线电定位系统基站的最优几何布局

Optimum design for geometric layout of base stations of local-radio-fixing system

地面基站的几何布局方式是影响区域无线电定位系统定位精度的重要因素,水平几何精度递变因子(HDOP)是衡量地面基站几何布局对系统定位精度影响的基本指标。为求解区域无线电定位系统基站的最优几何布局,给出了区域无线电定位系统HDOP的计算方法,建立了求解区域无线电定位系统地面基站最优几何布局的数学模型;提出了应用惩罚函数对数学模型进行求解的方法,将约束优化问题转化为无约束优化问题;并针对求解过程中目标函数难于求导的问题,提出了采用模拟退火算法进行全局寻优,使求得的结果逼近全局最优解。仿真结果表明,这种结合惩罚函数法和模拟退火算法进行全局寻优的方法,对于区域无线电定位系统求解地面基站的最优布局方案具有工程实用价值。

In Local-Radio-Fixing System, the Layout of Base Stations exerts close influences on the positioning accuracy, and in general, the Horizontal Dilution of Precision （HDOP） was used to measure the influences. In order to obtain the optimum layout of base stations, a feasible algorithm was developed in this paper. Firstly, the method to calculate HDOP in Local-Radio-Fixing System was given, and a math model to solve the problem was presented. Then the Penalty Function method was introduced to the model, which was used to transform Restricted Optimized problem to Unconstrained Optimization problem. Finally, in view of the difficulty in obtaining the differential coefficient of the object function in the model, the Simulated Annealing Algorithm was introduced to search the approximate solution of the model. The simulation results show that the algorithm, which combines the Penalty Function method with the Simulated Annealing Algorithm to search the optimum layout of base stations in Local-Radio-Fixing System, is correct and feasible in engineering application.