In this brief, an approach is presented to design a robust quadrotor attitude estimator when only inertial measurement units (IMUs) sensor data can be available. A two-step procedure is proposed to improve attitude estimation in the presence of IMU biases and measurement noise. In the first step, a smooth sliding mode observer is designed to estimate the roll and pitch angles using accelerometer measurements. The second step enhances the attitude estimation performance in the presence of noise and bias in IMU data by using a complementary nonlinear filter. Experimental results on a quadrotor test bed together with simulation results obtained using a representative nonlinear model are used to highlight the potential and performance of the proposed solution