Abstract: A method for determining relative angles and/or trigonometric functions of the relative angles between coupled rigid bodies arranged in a series, where the series includes at least a rigid body coupled to a previous rigid body. The method includes obtaining a gravitational acceleration vector and an angular velocity of the previous rigid body and a gravitational acceleration and an angular velocity of the rigid body. The relative angles and/or trigonometric functions of the relative angles are determined without using absolute angles of the rigid bodies.

Abstract: A method for determining relative angles and/or component relative angles between coupled rigid bodies arranged in a series, where the series includes at least a rigid body coupled to a previous rigid body. The method includes obtaining a gravitational acceleration vector and an angular velocity of the previous rigid body and a gravitational acceleration and an angular velocity of the rigid body. The relative angles and/or component relative angles are determined without using absolute angles of the rigid bodies.

Abstract: A method for determining centripetal accelerations of pivotally coupled rigid bodies arranged in a series, where the series includes a rigid body arranged between a previous rigid body and a next rigid body, includes determining the centripetal acceleration of the next rigid body and the centripetal acceleration at an inertial measurement unit (IMU) coupled to the next rigid body based on measurements and calculated parameters from the rigid body and the next rigid body. The centripetal acceleration of the next rigid body and the centripetal acceleration at the IMU coupled to the next rigid body are determined without using measurements or calculated parameters from the previous rigid body.

Abstract: A method for determining centripetal accelerations of pivotally coupled rigid bodies arranged in a series, where the series includes a rigid body arranged between a previous rigid body and a next rigid body, includes determining the centripetal acceleration of the next rigid body and the centripetal acceleration at an inertial measurement unit (IMU) coupled to the next rigid body based on measurements and calculated parameters from the rigid body and the next rigid body. The centripetal acceleration of the next rigid body and the centripetal acceleration at the IMU coupled to the next rigid body are determined without using measurements or calculated parameters from the previous rigid body.

Abstract: Yaw and center-of-rotation of a platform are determined using a single Global Navigation Satellite System (GNSS) device and an inertial measurement unit (IMU). A measurement center of the GNSS device is disposed on the platform away from the center-of-rotation and arranged in a known spatial relationship with the center-of-rotation. The platform is rotated about the center-of-rotation between a first orientation and a second orientation. The IMU is used to determine a change in pitch, roll, and yaw of the platform between the first orientation and the second orientation. The GNSS device is used to determine a change in position of the measurement center of the GNSS device between the first orientation and the second orientation. The yaw of the platform is determined at the second orientation and the position of the center-of-rotation of the platform is determined in a global coordinate frame.