**1. Introduction**

Quantitative assessment of lower limb kinematics is required in various applications, such as motion analysis, sports science, and rehabilitation. Although opto-electronic motion capture systems are considered the gold standard for this assessment, their widespread use is limited by their restricted area of measurement, their optical limitations due to marker occlusion or reflection, and their cost. Moreover, opto-electronic trackers are generally used in a restricted lab environment, which further limits the exploration of real-life movements and exercises. Wearable sensors, such as inertial measurement units (IMUs), have been developed to overcome these limitations [1], allowing for human motion analysis in unconstrained real-life conditions [2,3].

Although they generally contain a 3D accelerometer, a 3D gyroscope, and an optional 3D magnetometer, an IMU does not measure joint angles perfectly. Joint angles obtained via signal integration typically drift over time [4,5] and their accuracy varies with the joint assessed and the movement complexity [6,7]. While an error under 5◦ is generally accepted for most clinical gait applications [8], the measurement error typically ranges from 5◦ to 18.8◦ depending on the joint and the plane of motion [6]. Another major challenge in IMU-based human motion analysis that the IMUs' local coordinate systems are not aligned with physiologically meaningful axes [9]. Such alignment, required to compute joint angles, can be performed via a "sensor-to-segment" calibration procedure [10].

The first approach to ensure this alignment consists of a rigorous positioning of the sensor in relation to the anatomy [11]. This method assumes that the segmen<sup>t</sup> axes are parallel to the IMU axes, is approximate, and requires user expertise to locate the sensor axes relative to the joint axes for both segments around each joint. The second approach consists of placing an IMU on each segmen<sup>t</sup> and aligning the IMU and joint axes via a set of calibration postures [12] and/or movements around physiological motion axes. The latter functional method [13,14] consists of making the subject stand upright with straight legs for a few seconds to define the vertical axis for each IMU or segment, while the other axes are defined via active or passive movements [13,14]. Since the movements are generally human-controlled, the accuracy of the axes definition essentially relies on the subjects' ability to precisely hold a given posture and on the execution of a given movement [9]. The third approach consists of exploiting the kinematic constraints of the joints and use almost arbitrary movements to perform the sensor-to-segment calibration [9,15]. This method is particularly adapted to single axis joints that can be satisfactorily modelled as a hinge joint like the knee; however, the modeling of spherical joints requires the execution of movements mostly around one axis to identify the joint axes [9], which resemble the functional method.

The IMU-based tracking of lower limb spherical joints, using one of the two aforementioned methods, therefore requires the execution of a functional calibration movement. While the accuracy of the sensor-to-segment calibration is determined by the quality of the functional calibration movement, to our knowledge, it has only been investigated in one study for upper limb motion tracking [16] and no study has compared functional calibration movements for the tracking of lower limb joint angles.

This study aimed to (1) assess the accuracy of di fferent functional calibration methods in order to compute the lower limb joint angles during walking, (2) assess the reproducibility of di fferent functional calibration movements, and (3) compare the accuracy provided by functional calibration movements in di fferent gait movements.

#### **2. Materials and Methods**
