Pose Estimation in the Geometric Algebra G(3,0,1)

Using techniques from geometric algebra, methods for solving attitude determination problems are extended to the problem of simultaneously estimating attitude and location, that is, pose, from direct or indirect measurements of geometric objects including points, lines, and planes. Wahba’s problem is generalized for the solution of initial pose. The multiplicative extended Kalman filter is generalized for the maintenance of pose solutions. Farrankopf’s model for biases in rotation rate sensors is generalized to biases in twist rate measurements. A multiplicative extended Kalman filter for pose in the presence of such biases is developed. The performance of the filter using idealized sensors is tested in a simulation of a simplified problem involving a general screw motion.