Finite-Interval Robust Coefficient Design for Six-Sample Sculling Compensation in UAV Strapdown INS Velocity Updating

Accurate onboard velocity updating is essential for UAV strapdown inertial navigation, especially under GNSS-degraded and high-dynamic conditions. Instead of relying only on local Taylor-series cancellation as λ → 0 or directly transferring coning compensation coefficients, the proposed method redesigns velocity-specific sculling coefficients over the finite dimensionless interval λ = ΩΔT ∈ [0,1]. A two-stage strategy is developed. Stage I constructs a low-cost proxy error model from the analytical expansion and applies a minimax criterion to generate robust candidate coefficients. Stage II further refines them by minimizing a multi-condition time-domain RMS sculling error. Attitude-transfer coefficients are also tested to assess the transferability of optimized coning coefficients to velocity sculling compensation. Under a stringent single-frequency sculling protocol, the velocity-specific Stage-II coefficients reduce the global RMS and worst-case errors by 12.57% and 14.20%, respectively, compared with the classical six-sample coefficients. Under constant specific-force bias, constant angular-rate bias, and double-frequency sculling, the reductions remain 10.62–12.44% and 12.29–16.17%. Ablation and reproducibility checks show that the main gain comes from Stage-II time-domain RMS refinement and remains stable under grid, reference-integration, and base-index variations.