Posterior Delay-Hypothesis-Weighted Filtering with Information-Aware Regularization for Multi-UAV Cooperative Localization Under Random Measurement Delays

Multi-UAV cooperative localization is susceptible to random measurement delays, causing a received measurement to correspond to a historical sensing instant rather than the current one. This paper develops a posterior delay-hypothesis-weighted filtering framework that jointly infers the latent measurement-generation time and updates the error-state estimate. A noise-marginalized branch-conditioned likelihood is constructed for each candidate delay hypothesis, and Bayesian inference yields the corresponding posterior delay probabilities. To mitigate excessive reweighting under weak or ambiguous delay evidence, an information-aware regularization mechanism adaptively shrinks the fusion weights toward the communication-side prior. Its correction strength combines branch separability with a posterior-concentration factor, thereby controlling the amount of posterior correction admitted into recursive fusion. The resulting fusion weights preserve the probability simplex and satisfy a bounded-deviation property with respect to the prior, which are established through four analytical propositions. A fixed-lag augmented-state formulation further extends the framework to multi-step delays while retaining the relevant historical state and measurement-noise information. Monte Carlo experiments with 20 independent seeds were conducted for a four-UAV cooperative localization system under five operating scenarios and maximum delay orders N = 1–4. In the nominal Scenario A, the proposed method achieves a 3-D RMSE of 2.82 m at N = 4, compared with 6.67 m for the standard zero-delay filter, corresponding to a reduction of 57.8%. Across the five evaluated scenarios, the proposed method achieves RMSE values of 2.70–7.37 m and reduces the localization error relative to the standard zero-delay filter. The results support the proposed information-aware fusion mechanism and characterize its performance within the evaluated operating range.: