Adaptive LSSVR-based particle filter for UAV cooperative localization with kinematic model uncertainty

Cooperative localization (CL) enables precise and reliable navigation for unmanned aerial vehicles (UAVs) in critical applications. However, in complex environments, the performance of Bayesian filters is often compromised by non-Gaussian measurement noise and kinematic model uncertainty arising from dynamic disturbances, unmodeled nonlinearities, or sensor biases. The model uncertainty induces erroneous prediction steps that lead to trajectory divergence and propagate unreliable state information throughout the formation, thereby compromising global stability. To address these challenges, this paper proposes an adaptive least squares support vector regression particle filter (ALSSVR-PF) that integrates a sample-driven proposal construction with a whitening-based regularization strategy. First, we employ an ALSSVR density estimator with a Huber loss to reconstruct a continuous empirical prior directly from particles. This approach decouples the proposal distribution from potentially inaccurate nominal dynamics while enhancing robustness against particle outliers. Crucially, the algorithm incorporates current observation information into the proposal by adaptively adjusting penalty factors based on the Mahalanobis distance of measurement residuals, thereby mitigating the impact of anomalous measurements and guiding the proposal towards high-likelihood regions. Furthermore, to overcome the inherent sensitivity of kernel-based density estimators to the extreme state scale disparities, the whitening-based regularization normalizes the particle distribution into an isotropic space, where particle diffusion facilitates state exploration and maintains particle diversity. Simulation results in tightly-coupled UAV CL systems demonstrate that the proposed ALSSVR-PF outperforms state-of-the-art approaches, including variants of Kalman filters and particle filters, in terms of accuracy and robustness under conditions of model uncertainty and non-Gaussian noise.