Quantification of Mars entry trajectory uncertainty: Dynamic adaptive error band modeling and multi-scenario performance evaluation

Robust uncertainty quantification during the Entry phase of Mars Entry, Descent, and Landing (EDL) is critical for high-precision landing. Current EDL trajectory error assessments rely on discrete-time state errors, lacking a holistic metric for continuous trajectory uncertainty. This study develops a trajectory error band model by integrating Dynamic Adaptive Covariance Interpolation (DACI) with geometric error band modeling. This model addresses the construction of continuous trajectory error bands under sparse sampling of state error covariances. To generate a continuous covariance sequence from sparse data, the proposed DACI method adapts the adjacent covariance matrices of the vehicle's state error. This is achieved by fusing temporal linear interpolation and state-deviation adjustments to ensure that the time-varying covariance inherits the initial error characteristics while adapting to the trajectory dynamics. The geometric error band model constructs two-dimensional or three-dimensional (2D/3D) uncertainty boundaries using the trajectory's positional error covariances. For 2D error band construction, it extracts extreme points on positional error ellipses with maximum orthogonal distance to the trajectory's local tangent, forming a conservative boundary of extremum curves and endpoint semi-ellipses. For 3D error band construction, a plane is constructed using extreme points projected from three orthogonal planes onto the positional error ellipsoid. The intersecting ellipse of this plane with the positional error ellipsoid defines the local positional error boundary, which creates a spatial envelope composed of mid-segment curved cylinders and endpoint semi-ellipsoids. This model generates Potential Path Areas (PPAs) that conservatively bound trajectory uncertainties in both planar and spatial contexts. Simulations validate the proposed DACI error band model's robustness performance under both low and high disturbance conditions, achieving a Monte Carlo sample hit rate of over 99%, with a coverage of over 99.90% and a redundancy of less than 1.4% when compared to the reference error band. The model's efficiency under sparse sampling supports Mars EDL mission planning and real-time risk management.