Navigation filter design and comparison for Texas 2 STEP nanosatellite

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.