The primary goal for this work is to establish a three-axis spacecraft attitude estimator suitable for coarse attitude estimation and control during low accuracy spacecraft operational modes. An innovative algorithm for spacecraft attitude and angular velocity estimation is developed based on a new Kalman filtering approach applied to magnetometer measurements only and named as hybrid Kalman filtering. The new approach alleviates many problems encountered with the standard extended Kalman filter. It also estimates spacecraft attitude and attitude rate taking into account various sources of errors related to measurement and process noise. The filter could start with initial attitude and rate estimation errors as large as 180o and 0.03 o/s respectively and still be able to converge to a (3-σ) attitude and rate estimation errors of 0.8o and 0.0017 o/s respectively. The new approach could be expanded to deal with other vector measurements besides the earth's magnetic field as well.