Patent ID: 8185261

Claim:
A moveable object comprising: a computer system for determining an attitude of the movable object by determining a transformation matrix from a body coordinate frame of the moveable object to an inertial reference frame for time t N , {right arrow over (U)} N , where the transformation matrix {right arrow over (U)} N is indicative of the attitude of the movable object at time t N , wherein the computer system comprises: at least one processor circuit; and at least one memory circuit in communication with the at least one processor circuit, wherein the at least one memory circuit stores instructions that when executed by the at least one processor circuit, causes the at least one processor circuit to determine the transformation matrix {right arrow over (U)} N by a process that comprises: determining a slew rate vector, {right arrow over (α)}, for time t N for the moveable object, wherein the slew rate vector, {right arrow over (α)}, represents a change in direction of an angular rate vector, {right arrow over (ω)}, for the moveable object over the time interval from t N−1 to t N in the body coordinate frame; determining an update to the transformation matrix for time t N , Δ{right arrow over (U)} N , wherein the update to the transformation matrix Δ{right arrow over (U)} N for time t N is based on a product of first and second matrices, wherein the first matrix is related to a sum of {right arrow over (ω)} and {right arrow over (α)}, and the second matrix is related to −{right arrow over (α)}; and multiplying a transformation matrix for time t N−1 , {right arrow over (U)} N−1 , and the update to the transformation matrix for time t N , Δ{right arrow over (U)} N , to obtain the transformation matrix for time t N , {right arrow over (U)} N .