  This paper concerns the problem of attitude determination and estimation. The
early applications considered algebraic methods of attitude determination.
Attitude determination algorithms were supplanted by the Gaussian attitude
estimation filters (which continue to be widely used in commercial
applications). However, the sensitivity of the Gaussian attitude filter to the
measurement noise prompted the introduction of the nonlinear attitude filters
which account for the nonlinear nature of the attitude dynamics problem and
allow for a simpler filter derivation. This paper presents a survey of several
types of attitude determination and estimation algorithms. Each category is
detailed and illustrated with literature examples in both continuous and
discrete form. A comparison between these algorithms is demonstrated in terms
of transient and steady-state error through simulation results. The comparison
is supplemented by statistical analysis of the error-related mean, infinity
norm, and standard deviation of each algorithm in the steady-state. Keywords:
Comparative Study, Attitude, Determination, Estimation, Filter, Adaptive
Filter, Gaussian Filter, Nonlinear Filter, Overview, Review, Rodrigues Vector,
Special Orthogonal Group, Unit-quaternion, Angle-axis, Determinstic,
Stochastic, Continuous, Discrete, Multiplicative extended kalman filter, KF,
EKF, MEKF, white noise, colored noise.
