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A generalized algorithm for spacecraft three-axis attitude and rate estimation is presented. The filter concept presented here is quite general and applicable to a wide range of sensor systems. The structure of the filter is built using spacecraft nonlinear dynamics in the presence of momentum exchange devices. Then quaternion kinematics are augmented with spacecraft dynamics to represent the filter process dynamics. Magnetometer measurements and their corresponding time derivatives are utilized to represent the filter measurement model. The filter is designed to suit spacecraft in low-Earth orbits, so the aerodynamic drag in addition to spacecraft magnetic residuals are included as disturbance torques to the process dynamics. To test the filter EgyptSat-1 is used as a real test case where a magnetometer and fiber-optic gyros are used for attitude and rate determination. A Monte-Carlo simulation is then applied to study the performance of the proposed filter with initial attitude and angular velocity sampled from a uniform distribution, each axis respectively. The filter shows the capability of estimating the attitude within 5 deg and rate on the order of 0.03 deg/s in each axis.