| 引用本文: | 郭鹏,崔祜涛,张泽旭,徐田来.一种高阶费歇耳信息矩阵分布式求逆方法[J].哈尔滨工业大学学报,2023,55(4):1.DOI:10.11918/202104073 |
| GUO Peng,CUI Hutao,ZHANG Zexu,XU Tianlai.A distributed inversion method for higher-order Fisher information matrices[J].Journal of Harbin Institute of Technology,2023,55(4):1.DOI:10.11918/202104073 |
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| 摘要: |
| 为获得多智能体系统任意耦合型无向网络导航克拉美-罗下界的显示表达式,简化高阶费歇耳信息矩阵求逆过程,提出了一种分布式求逆方法,即矩阵分块对角化求逆方法。首先,针对任意耦合型无向网络导航定位模型,构造了高阶费歇耳信息矩阵,并结合其对称特点及矩阵元素与网络拓扑间的对应关系,将其分解为两个分块对角矩阵的线性组合,它们分别包含所有节点和边的费歇耳信息量。其次,通过两次运用矩阵求逆引理,推导了费歇耳信息矩阵的逆即克拉美-罗下界以及网络节点等价费歇耳信息矩阵的显式表达式；同时引入了迭代过程,将整个求逆过程完全分解为若干个低阶矩阵间的运算,以减小单步运算量。最后,通过数值试验对该算法进行了验证,并与矩阵分块迭代求逆法进行了对比分析。结果表明,两者均具有较高的计算效率和精度,但本算法运算量更小,计算速度更快,从而验证了算法的准确性和有效性。该算法可用于分析任意耦合型无向网络导航定位模型中各节点或边费歇耳信息的融合过程。 |
| 关键词: 多智能体系统 网络导航 信息耦合 费歇耳信息矩阵 分布式算法 |
| DOI：10.11918/202104073 |
| 分类号:V249 |
| 文献标识码:A |
| 基金项目:国家自然科学基金联合基金重点项目(U20B2001) |
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| A distributed inversion method for higher-order Fisher information matrices |
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GUO Peng,CUI Hutao,ZHANG Zexu,XU Tianlai
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(School of Astronautics, Harbin Institute of Technology, Harbin 150001, China)
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| Abstract: |
| To obtain the explicit expression of Cramér-Rao lower bound (CRLB) and simplify the inversion process of higher-order Fisher information matrices (FIM) for undirected network navigation of multi-agent systems (MAS) with arbitrary information coupling, we proposed a distributed inversion method named block diagonalization method. Firstly, a high-order FIM was constructed for the arbitrary coupling undirected network navigation and positioning model, and then on the basis of its symmetry characteristics and the relationship between submatrices and network topology, the FIM was expressed as a linear combination of two block diagonal matrices, which contained the Fisher information of all nodes and edges respectively. Secondly, the matrix inversion lemma was used twice to derive the explicit expression of the inverse of FIM, i.e. CRLB and the equivalent FIM for network nodes. An iterative process was also introduced to decompose the whole inversion process into computations between several lower-order matrices, so as to mitigate the computational burden at every step. Finally, the proposed algorithm was verified by numerical experiments, and compared with the matrix block iterative inversion method. Results show that both methods had high computational efficiency and accuracy, but the computational burden of the proposed method was lower and the computational speed was faster, which verifies its accuracy and effectiveness. This algorithm can be used to analyze the Fisher information fusion process for every node or edge in arbitrary coupling undirected network navigation and positioning model. |
| Key words: multi-agent system network navigation information coupling Fisher information matrix distributed method |
