一种凸组合技术优化的高斯和容积卡尔曼滤波算法  

An Optimized Gaussian Sum Cubature Kalman Filter Algorithm byConvex Combination Technology

作　　者：戴卿 万茹 吴涛 樊智辉 DAI Qing;WAN Ru;WU Tao;FAN Zhihui(School of Urban Construction,Luoyang Polytechnic,Luoyang 471000,China;Institute of Geo-spatial Information,Information Engineering University,Zhengzhou 450052,China;National Engineering Research Center for Surveying and Mapping Technology,Beijing 100036,China;School of Mathematics and Statistic,Henan University of Science and Technology,Luoyang 471023,China)

机构地区：[1]洛阳职业技术学院城建学院,河南洛阳471000 [2]信息工程大学地理空间信息学院,郑州450052 [3]国家测绘工程技术研究中心,北京100036 [4]河南科技大学数学与统计学院,河南洛阳471023

出　　处：《西安航空学院学报》2025年第1期1-7,共7页Journal of Xi’an Aeronautical Institute

基　　金：河南省科技攻关项目(242102241067);河南省高等学校重点科研项目(24A420003);河南省职业技术教育学会研究课题(2024-ZJXH-14)。

摘　　要：高斯和容积卡尔曼滤波在非高斯模型高斯化过程中会产生大量的高斯分量,通过采用高斯分量融合方法可减弱其对滤波性能造成的不利影响,但现有的方法常采用单一融合基准或策略难以全面准确地衡量需融合的高斯分量,为此,提出了一种凸组合技术优化的高斯和容积卡尔曼滤波算法。该算法在容积卡尔曼滤波的基础上综合考虑了马氏距离和信息散度下高斯分量融合方法的原理差异与性能互补。具体而言,算法先分别基于两种距离度量进行高斯分量融合,以优化融合策略的合理性;随后,以这两种距离度量独立输出的融合结果为基础,再进行加权融合。实验结果表明,本文所提算法在不以损失计算效率为代价的前提下,其估计精度较单一距离度量的高斯和容积卡尔曼滤波有显著提升,且在不同非高斯场景下能表现较好的稳定性,具有一定的工程应用前景。In the Gaussianization process of non-Gaussian models,Gaussian sum cubature Kalman filter(GSCKF)can generate a large number of Gaussian components,and the adverse effects on filtering performance can be mitigated by employing Gaussian component fusion methods.However,existing methods often adopt a single fusion criterion or strategy,making it difficult to comprehensively and accurately assess the Gaussian components that need to be fused.To address this issue,a GSCKF algorithm optimized by convex combination technology is proposed.Based on the GSCKF,this algorithm comprehensively considers the theoretical differences and performance complementary of Gaussian component fusion algorithms under Mahalanobis distance and information divergence on the basis of cubature Kalman filter.Initially,Gaussian component fusion is performed based on these two-distance metrics to optimize the fusion strategy;then,a weighted fusion is conducted based on the merged terms independently output by the two-distance metrics.Experimental results show that the proposed algorithm significantly improves estimation accuracy compared with the Gaussian and cubature Kalman filter based on a single distance metric without sacrificing computational efficiency,and exhibits stable effectiveness and robustness across various non-Gaussian scenarios,indicating its potential for engineering applications.

关 键 词：高斯和滤波 容积卡尔曼滤波 凸组合技术 组合导航算法 

分 类 号：TN95[电子电信—信号与信息处理] P228[电子电信—信息与通信工程]