Adaptive Kernel Density Soft-Gating for Robust GNSS/INS Georeferencing of Highly Dynamic Remote-Sensing Platforms Under Measurement Outliers

GNSS measurement outliers degrade positioning accuracy in integrated global navigation satellite system/inertial navigation system (GNSS/INS) georeferencing for highly dynamic remote-sensing platforms. This study presents an adaptive kernel density robust Kalman filter (KDE-RKF) for attenuating anomalous observations through continuous measurement weighting. The method estimates the distribution of normalized innovation energies using a sliding-window logarithmic Gaussian kernel density estimator with adaptive bandwidth selection. Local density estimates determine channel-specific soft-gating weights that scale the effective measurement covariance. Performance was evaluated through 100 Monte Carlo runs per scenario covering isolated outliers, attitude-related bursts, terminal multipath, and simulated jamming. At 15% isolated-outlier contamination, KDE-RKF achieved a three-dimensional position root mean square error of 38.4m, compared with 87.3m for the extended Kalman filter. Corresponding errors for the Huber and variational-Bayes Student’s t filters were 47.2 and 44.3m, respectively. Following simulated jamming, positioning accuracy returned to near-nominal levels within 1.8s. Each GNSS update required 0.312ms on the simulation platform. During a natural GPS excursion in the Zurich Urban Micro Aerial Vehicle dataset, peak position error decreased from 41.63 to 28.97m. These results support density-based soft-gating for reducing positioning errors under the evaluated GNSS degradation conditions.