This paper presents an algorithm for calibrating strapdown magnetometers in the magnetic field domain. In contrast to the traditional method of compass swinging, which computes a series of heading correction parameters and, thus, is limited to use with two-axis systems, this algorithm estimates magnetometer output errors directly. Therefore, this new algorithm can be used to calibrate a full three-axis magnetometer triad. The calibration algorithm uses an iterated, batch least squares estimator which is initialized using a novel two-step nonlinear estimator. The algorithm is simulated to validate convergence characteristics and further validated on experimental data collected using a magnetometer triad.It is shown that the post calibration residuals are small and result in a system with heading errors on the order of 1 to 2 degrees.

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Attitude determination systems that use inexpensive sensors and are based on computationally ecient and robust algorithms are indispensable for realtime vehicle navigation, guidance and control applications. This paper describes an attitude determination system that is based on two v ector measurements of non-zero, non-colinear vectors. The algorithm is based on a quaternion formulation of Wahba's problem, whereby t h e error quaternion (q e ) becomes the observed state and can be cast into a standard linear measurement equation. Using the earth's magnetic eld and gravity as the two measured quantities, a low-cost attitude determination system is proposed. An iterated least-squares solution to the attitude determination problem is tested on simulated static cases, and shown to be globally convergent. A time-varying Kalman lter implementation of the same formulation is tested on simulated data and experimental data from a maneuvering aircraft.The time varying Kalman Filter implementation of this algorithm is exercised on simulated and real data collected from an inexpensive triad of accelerometers and magnetometers. The accelerometers in conjucnction with the derivative of GPS velocity provided a measure of the gravitation eld vector and the magnetometers measured the earth's magnetic eld vector. Tracking errors on experimental data are shown to be less than 1 degree mean and standard deviation of approximately 11 degrees in yaw, and 3 degrees in pitch and roll. Best case performance of the system during maneuvering is shown to improve standard deviations to approximately 3 degrees in yaw, and 1.5 degrees in pitch and roll.