Model-inertial deep fusion navigation and impact point uncertainty quantification for rocket sub-stages under prolonged GNSS outages

Abstract

During atmospheric re-entry of rocket sub-stages, GNSS signals may be lost for extended periods due to plasma sheath and attitude occlusion. In such scenarios, the integrated navigation system degrades to pure inertial navigation, and position errors grow cubically over time, making conventional filtering and prediction methods ineffective. This paper presents a deep fusion navigation algorithm based on the unscented Kalman filter (UKF) that tightly couples a three-degree-of-freedom re-entry dynamic model with an inertial navigation system. The dynamic model serves as a virtual observation source, providing physically plausible position and velocity constraints to suppress the inertial error divergence. Model error parameters, including aerodynamic coefficient deviation and atmospheric density scale factor, are augmented into the state vector and estimated online to adapt the model to actual flight conditions. To address the residual uncertainty in the navigation solution, a Monte Carlo simulation framework using Latin hypercube sampling is established to quantify the impact of point dispersion. Results from a 120-second complete GNSS outage simulation with a tactical-grade IMU show that the proposed method reduces the positioning error from tens of kilometers to tens of meters, and the resulting 95% confidence ellipse of the impact point encompasses the true impact point with a probability close to 95%.