To address the degradation of accuracy in inertial-magnetometer integrated attitude estimation caused by linear acceleration (LA) and ferromagnetic disturbance (FD), this paper proposes an adaptive estimation algorithm based on the Minimum Bounding Sphere (MBS). The LA and FD components are modeled as first-order Gauss-Markov processes, and a parallel Kalman filter structure is employed to separate these disturbance components. The MBS algorithm is utilized to compute the radius of the minimum bounding sphere enclosing the measured data from the accelerometer and magnetometer in real time. This radius serves as a geometric indicator reflecting the intensity of composite interference. A mapping function is then established between this indicator and the process noise covariance of the disturbance state, enabling online adaptive adjustment of the covariance. The measurement data purified by disturbance separation are subsequently fed into a Multiplicative Extended Kalman Filter (MEKF) for attitude computation. Experimental results demonstrate that the proposed method achieves higher estimation accuracy compared to existing approaches under disturbance.