Discrete-time Kalman filter for heave motion estimation

This paper addresses the problem of estimating the heave motion of a platform using biased measurements of an accelerometer. We develop a general framework wherein convenient and well-known properties of trigonometric functions are exploited to devise a linear system whose state encompasses implicit representations of wave amplitudes and phase shifts, as well as a constant sensor bias. The observability of the system is analyzed, followed naturally by the implementation of a discrete-time linear time-varying Kalman filter with global asymptotic stability guarantees. Our proposed methodology is validated with realistic numerical examples, including an accurate representation of a continuous wave spectrum within an ocean context.