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A nonlinear observer is proposed for a strapdown inertial navigation system (SDINS) in-flight alignment problem using an H∞ filter Riccati equation and a freedom parameter. The proposed observer improves the filtering stability, convergence, and performance. The characteristics of the observer are analyzed using a Lyapunov function. Simulation results demonstrate a significant reduction in alignment errors by employing the proposed nonlinear observer. The observer is developed in general such that it can be applied to estimating nonlinear systems other than the SDINS in-flight alignment.