Extended Kalman Filtering with Censoring Statistics for Inertial-Only Navigation under GPS Denial

In the field of aircraft navigation, GPS-denied scenarios pose one of the most significant challenges, causing conventional state estimation approaches to be nearly infeasible. While additional sensors can be used to compensate for the absence of GPS data, they often introduce trade-offs such as increased system complexity, weight, power consumption, and cost. To address this issue without additional hardware, we propose a statistically grounded Extended Kalman Filter designed to handle the GPS measurement censorship directly. The proposed framework models measurement censoring as a probabilistic event using Bernoulli-distributed indicators and truncated Gaussian distributions. This formulation allows the filter to explicitly account for the uncertainty introduced by censored measurements and incorporate it into the correction step. Key components include derived expectations and covariance formulations for censored regions, as well as a sequential update structure that ensures numerical stability and minimizes the influence of unobservable states. Validated through flight simulation, the proposed method demonstrates improved estimation accuracy over standard and modified Extended Kalman Filters, underscoring its robustness and applicability to aerospace navigation in degraded sensing environments.