This paper proposes a novel robust attitude estimation algorithm for a small unmanned aerial vehicle (UAV) in the absence of GPS measurements. A synthetic sideslip angle (SSA) measurement formulated for use under the zero-angle assumption is newly proposed for a UAV without angle-of-attack (AOA)/SSA sensors to enhance the state estimation performance during a GPS outage. In addition, the nongravitational acceleration is estimated using the proposed Kalman filter and is then subtracted from the raw acceleration to yield a reliable gravity estimate. Then, a fuzzy-logic-aided adaptive measurement covariance matching algorithm is devised to adaptively reduce the weight given to disturbed acceleration and magnetic field measurements in the attitude estimation, yielding the fuzzy adaptive error-state Kalman filter (FAESKF) algorithm. Experimental flight results demonstrate that the proposed FAESKF algorithm achieves a remarkable improvement in attitude estimation compared to the conventional algorithm.