The invention provides an extended ellipsoidal set-member filtering method based on a Fourier-Hermite orthogonal polynomial. The extended ellipsoidal set-member filtering method comprises the steps that a model equation of a GNSS/INS combined navigation system is established; uncertainty intervals of system state parameter components in the step k-1 are calculated; Fourier-Hermite series polynomial approximation is conducted on a state equation and an observation equation; an error boundary of the Fourier-Hermite series polynomial approximation is calculated, and an epibolic ellipsoid of Fourier-Hermite series polynomial approximation calculation errors of a nonlinear equation is obtained; a linear ellipsoidal set-member filtering algorithm is used for calculating the ellipsoid boundary ofpredicted state variables, updating a state ellipsoid boundary and calculating a state parameter variable estimation value and an estimation variance matrix. The extended ellipsoidal set-member filtering method utilizes the Fourier-Hermite series polynomial to obtain linear approximation of the nonlinear system model, the calculation accuracy is higher, the computational complexity is reduced, and the computational stability of the extended ellipsoid set-member filtering algorithm is effectively guaranteed.