Direction cosine matrix estimation from vector observations using a matrix kalman filter

This work presents several estimation algorithms of the attitude matrix using vector observations. All the algorithms are state matrix Kalman filters that preserve the natural formulation of the attitude matrix statespace model equations. The filters feature an efficient, though simplified, estimation error covariance computation algorithm. Four different methods are proposed to enforce the orthogonality of the attitude matrix estimate. All the orthogonalization procedures accelerate the estimation convergence. The special case of unbiased gyros was considered when developing these filters. The performance of the different filters are demonstrated through extensive Monte-Carlo simulations. An augmented state matrix mathematical model is also developed, where the augmented state matrix includes the attitude matrix and a vector of constant gyro biases.