High-Performance Relative Localization Based on Key-Node Seeking Considering Aerial Drags Using Range and Odometry Measurements

Using an inertial measurement unit and a single ultrawideband radio can provide effective relative localization only if the system observability is guaranteed. To ensure observability, recent studies utilize extended sliding window filter for state augmentation, selecting key-nodes as replacements for continuous states. However, as the velocity measurements are obtained indirectly through preintegration, integrating over key-nodes far apart could lead to velocity divergence. To tackle this issue, this article proposes the reformulated key-node seeking approach considering aerial drag effects, which inherently reflects the dissipative nature and enhances system observability and estimation precision. Considering the potential velocity divergence, aerial drag effect is extended to reformulate the process model and observability matrix. Then, to further eliminate a possible ill-conditioned observability matrix, an index naturally similar to the condition number of the reconstructed matrix is proposed to measure the degree of observability. Furthermore, the key-node selection strategy is developed, selecting the optimal measurements regarding the least ill-conditioned requirement as optimization. Thus, the selected key-nodes can achieve maximum observability within each sliding window. Finally, validated in single-agent, homogeneous, and heterogeneous multiple-agent systems, the proposed method steadily reduces estimation rmse and the condition number compared with the state-of-the-art methods, showing its effectiveness.