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This paper presents a novel three single-axis accelerometer configuration for measuring relative acceleration in a moving reference frame without knowledge of motion or orientation of the moving frame itself. Also presented is an extended Kalman filter (EKF) that combines this relative acceleration measurement with a linear-position measurement for state estimation. The motivation for this approach is the need for high-quality linear-state estimation in pneumatic cylinder control, but potential applications of this approach are much broader, including mobile robots and general relative linear-state sensing. When applied to a pneumatic cylinder, this method eliminates the need for kinematic knowledge of the cylinder base and allows state estimation to be implemented at the cylinder level without regard to the external motion of the robot. Experimental tests were performed to compare the presented reference-frame-independent EKF method to a standard kinematically dependent end-effector EKF. When kinematic knowledge of the end effector is known, both standard and presented methods perform well as expected. However, removing kinematic knowledge of the local reference frame adversely affects the performance of a standard kinematically dependent EKF, but does not affect the performance of the presented method as it does not depend on such global kinematic knowledge. Experimental results also show that the addition of a direct relative velocity measurement does not significantly improve performance over the presented method.