Genetic algorithm-based method for optimizing sequential inverse covariance fusion order

Multi-source information fusion is a key technique in multi-robot cooperative localization, unmanned system navigation, and distributed perception because robots can improve localization accuracy by exchanging and fusing local state estimates obtained from different sensing and communication links. In practical distributed cooperative localization systems, however, local estimates are often affected by unknown cross-correlations caused by shared historical observations, repeated communication, and intermediate information propagation. Under such conditions, conventional fusion methods based on independence assumptions may underestimate the covariance and even yield inconsistent estimations. Inverse covariance intersection (ICI) is effective in ensuring consistent fusion without explicit computation of unknown cross-correlations. However, in sequential ICI fusion, the final result depends not only on the fusion rule itself but also on the order in which local estimates are introduced into the fusion process. This order sensitivity may lead to different covariance contraction results and localization performance, even when the same local estimates are used. To address this problem, this study investigates the order sensitivity of sequential ICI fusion and proposes a fusion-order optimization method based on a genetic algorithm.

First, the update characteristics of the sequential ICI fusion operator are analyzed from the perspective of pairwise recursive fusion. Because the ICI update contains nonlinear matrix inversion of covariance convex combinations, the sequential fusion operator generally does not satisfy commutativity or associativity, theoretically accounting for the different intermediate covariance evolution paths and, consequently, the different final fusion results obtained with different fusion orders. On this basis, the fusion-order selection problem is formulated as a permutation-based combinatorial optimization problem with the objective of minimizing the trace of the final fused covariance matrix. A genetic algorithm is introduced to perform a global search in the permutation space. In the proposed method, each chromosome represents a valid fusion order, the fitness of each chromosome is evaluated by executing the complete sequential ICI fusion process and computing the trace of the final covariance matrix, tournament selection is used to retain competitive individuals, and order crossover and swap mutation are implemented to preserve permutation feasibility and enhance search diversity. A one-dimensional search is embedded in each pairwise ICI fusion step to optimize the fusion weight, enabling the outer-layer genetic algorithm to optimize the fusion order while the inner-layer search refines the local fusion parameter. To validate the proposed method, two types of experiments are designed. The first is a static fusion-order analysis, in which several local state estimates with different directional uncertainty characteristics are constructed to simulate multi-source pose estimates that may occur in cooperative localization, and all feasible fusion orders are enumerated to study the influence of different orders on the covariance trace and error ellipse distribution. The second is a dynamic multi-robot cooperative localization simulation experiment, in which a five-robot cooperative localization environment with heterogeneous observation noise is established, and different order strategies, including fixed order, heuristic order, and genetic-algorithm-optimized order, are compared. In this experiment, the time-varying localization RMSE curve and the full-time average RMSE are used as performance indices.

Sequential ICI fusion is inherently order-sensitive, and changing only the order of the local estimates can produce evident differences in the final covariance trace and fused error ellipse. The proposed genetic algorithm consistently obtains better fusion-order solutions than heuristic rules based on only a single factor, such as precision or relative distance, because it can more effectively exploit the directional characteristics and complementary uncertainty structures of local estimates. In the dynamic cooperative localization simulation, the proposed method maintains lower localization errors for most of the simulation, shows smaller fluctuations after convergence, and achieves the best full-time average RMSE among all tested strategies.

These results indicate that reasonable optimization of the sequential ICI fusion order can effectively reduce fusion uncertainty, improve localization accuracy, and enhance the stability of multi-robot cooperative localization systems. Therefore, the proposed method provides a practical framework for fusion-order optimization in distributed information fusion systems and facilitates the experimental evaluation of sequential fusion strategies in cooperative localization applications.