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This paper presents an approach to estimate the attitude of skis for an entire ski jump using wearable, MEMS-based, low-cost Inertial Measurement Units (IMUs). First of all, a kinematic attitude model based on rigid-body dynamics and a sensor error model considering bias and scale factor error are established. Then, an extended Rauch-Tung-Striebel (RTS) smoother is used to combine measurement data provided by both gyroscope and magnetometer to achieve an attitude estimation. Moreover, parameters for the bias and scale factor error in the sensor error model and the initial attitude are determined via a maximum-likelihood principle based parameter estimation algorithm. By implementing this approach, an attitude estimation of skis is achieved without further sensor calibration. Finally, results based on both the simulated reference data and the real experimental measurement data are presented, which proves the practicability and the validity of the proposed approach.

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To satisfy an increasing demand to reconstruct an athlete’s motion for performance analysis, this paper proposes a new method for reconstructing the position and velocity in the context of ski jumping trajectories. Therefore, state-of-the-art wearable sensors, including an inertial measurement unit, a magnetometer, and a GPS logger are used. The method employs an extended Rauch-Tung-Striebel smoother with state constraints to estimate state information offline from recorded raw measurements. In comparison to the classic inertial navigation system and GPS integration solution, the proposed method includes additional geometric shape information of the ski jumping hill, which are modeled as soft constraints and embedded into the estimation framework to improve the position and velocity estimation accuracy. Results for both simulated measurement data and real measurement data demonstrate the effectiveness of the proposed method. Moreover, a comparison between jump lengths obtained from the proposed method and video recordings shows the relative root-mean-square error of the reconstructed jump length is below 1.5 m depicting the accuracy of the algorithm.