贝叶斯框架下基于凸优化的系统偏差估计方法  

Systematic Biases Estimation Based on Convex Optimization under Bayesian Framework

作　　者：周林[1] 刘先省[1] 方拥军 金勇[1] ZHOU Lin;LIU Xianxing;FANG Yongjun;JIN Yong(Computer and Information Engineering College,Henan University,Kaifeng,475004,China)

机构地区：[1]河南大学计算机与信息工程学院

出　　处：《探测与控制学报》2019年第4期92-97,共6页Journal of Detection & Control

基　　金：国家自然科学基金项目资助(61771006,61701170);河南省高等学校重点研究计划项目资助(19A413006);河南省科技发展计划项目资助(192102210254);河南大学一流学科培育项目资助(2018YLTD04)

摘　　要：针对多传感器协同探测系统中系统偏差呈现出的随机性和突变性,以及估计方法的误差增加、估计鲁棒性较难保证等问题,在贝叶斯估计框架下,提出了基于凸优化的系统偏差估计方法。该方法首先依据最大似然估计准则推导出量测最大似然函数,并将其变形为与状态参数无关的多传感器量测最大似然函数;其次,结合系统偏差投影等式和待估参数范围不等式两类约束条件,将最大似然估计问题转化为具有目标函数、约束函数的凸优化问题;最后,利用拉格朗日乘子方法构造系统偏差二次函数,并在约束条件下利用凸优化技术实现多传感器系统偏差的优化求解。仿真结果表明,相比于同等条件下的其他方法,所提方法提高了估计精度,降低了时间复杂度。Aiming at the stochastic and abruptness of systematic biases in multi-sensors collaborative detection system,and the increase of estimation error and the difficulty of ensuring robustnesss,a novel method of systematic biases estimation was presented based on convex optimization under the Bayesian framework.Firstly,the maximum likelihood function of measurement was derived under the optimum criterion of maximum likelihood.Then,the maximum likelihood function for multi-sensors measurements was given,and it was not concerned with state parameters.Secondly,combining the systematic biases projection equation and the parameter range inequality to be estimated,we translate the matter of maximum likelihood into the convex programming including objective function constraint function.Thirdly,the quadratic function of systematic biases was structured utilizing Lagrange multiplier method,subsequently,some optimization solutions of multi-sensors systematic biases were obtained using convex programming under constrain conditions.Simulation results showed that,comparing to other methods,the proposed algorithm effectively improved estimation precision,and reduced time complexity.

关 键 词：系统偏差估计 配准 凸优化 贝叶斯框架 

分 类 号：TP274[自动化与计算机技术—检测技术与自动化装置]