Using low-cost sensors in miniature aerial vehicles such as a quadrotor requires a design of a robust-filtering system in order to compensate for noises and biases. Moreover, the coupling dynamics characteristic between the angular movements and the translational movements leads to deviations in the quadrotor's path due to the presence of biases in measurements. The estimations of quadrotor angles are calculated according to the tilt in the gravitational vector represented in body coordinate. However, the accelerometer readings are affected by non-gravitational forces such as blade flapping and drag forces that affect the estimations. Accordingly, failure to compensate for these forces leads to linear velocity drift, especially when the GPS signal is lost. Therefore, this work aims to design a filtration system, using complementary filters, that provides robust and accurate estimates of a quadrotor's attitude, position, and velocity. In addition, the estimation system can compensate the velocity drift in the lateral directions through new acceleration model. The effectiveness of the presented system has been verified and compared with the traditional complementary filters through several flight tests. The proposed estimation system shows superiority over traditional ones, and it shows its effectiveness in reducing lateral speed drift, especially when GPS signal is lost.