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Abstract:
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A Discrete Extended Kalman Filter has been designed to process measurements from a magnetometer , sun sensor , IMU , and GPS receiver to provide the relative position , velocity , attitude , and gyro bias of a chaser spacecraft relative to a target spacecraft . An Extended Kalman Filter with Uncompensated Bias has also been developed for the implementation of well known biases and errors that are not directly observable . A detailed explanation of the algorithms , models , and derivations that go into both filters is presented . With this simulation and specific sensor selection the position of the chaser spacecraft relative to the target can be estimated to within about 5 m , the velocity to within .1 m /s , and the attitude to within 2 degrees for both filters . If a thrust is applied to the IMU measurements , it takes about 1 .5 minutes to get a good position estimate , using the Extended Kalman Filter with Uncompensated Bias . The error settles almost immediately using the general Extended Kalman Filter . These filters have been designed for and can be implemented on almost any small , low cost , low power satellite with this inexpensive set of sensors . |