# Can IMU Provide an Accurate Vertical Jump Height Estimate?
## 1 Introduction  
The vertical jump (VJ) is a complex task that requires the coordination of multiple joints [1]. It is characterized by a rapid vertical acceleration of the body mass in the shortest possible time interval and was found to be related to common sports activities, such as sprint, acceleration and change of direction speed (CODS) [2, 3, 4]. The VJ is used in the testing of the mechanical characteristics of the lower limb muscles [5], as well as in sport praxis in order to provide an insight into athletes' training status, and thus inform future training focus [6]. The jump modalities that are most widely used in testing are the counter-movement jump (CM) and the squat jump (SQI). The former utilizes the characteristics of the muscle stretch-shortening cycle (SSC) thus more closely resembling a real-world jumping task while the focus of the latter is the isolated concentric phase of muscle action [7, 8, 9]. The jump height (JH) is considered to be an alternative indirect indicator of lower limb explosive capacities [10] which is commonly used as a measure of VJ performance. Although the use of a force plate (FP) is predominant for in-depth analysis of the mechanical characteristics of the lower limb muscles, it also enables the calculation of the JH [11]. However, the use of an FP is mainly constrained to laboratory settings which certainly raises the question of ecological validity in relation to the sport-specific task demands. In addition, an FP is a barely portable, expensive piece of equipment [12] which makes it unsuitable for in-field use. Consequently, the aforementioned device is commonly used as a criterion device for validation of other equipment while the in-field estimation of VJperformance is done using photoelectric cells, contact mats, mobile apps, and more recently, inertial measurement units (IMU) [13; 14]. An inertial measurement unit is an example of a micro-electromechanical sensor system (MEMS) that typically incorporates an accelerometer, gyroscope, and magnetometer [15]. While IMU can provide kinematic and precise temporal data, when combined with a sensor fusion algorithm it can be used for tracking three-dimensional movements [16]. Due to the small size of an individual unit, IMU-based systems merely affect athletes' performance. Their low power consumption allows for a longer autonomy of the device while using a smaller battery which further reduces the overall size of the device while still allowing several hours of measurement. When these features are combined with wireless data transmission and low cost (<100$) such systems can be effectively used for in-field measurement of performance of single or multiple athletes while the acquired data can be shared instantaneously to the coaches and athletes [17]. During the last decade, IMU-based systems have been used for the measurement and evaluation of nearly all types of sports activities [18], including VJ assessments. As different commercial and custom IMU-based systems have been validated in relation to the measurement of VJ height [19; 20], different positioning of the sensor device on the athlete's body has been used. In studies by [12; 14; 21] sensors have been positioned on the lumbar area at the level of vertebrae L5, while a study by [17] used the positioning of the sensor on the athlete's ankles. The majority of the equipment used for in-field VJ height assessment, such as photoelectric cells and jump mats employs the flight time (FT) calculation method for JH calculation [22]. In fact, the FT method has been shown to be valid and reliable [13; 23; 24; 25] and is considered to be the most common way to estimate VJ height [26]. A study by [17] has shown that the same approach can be used for the measurement of JH using IMU. The FT method uses a basic kinematic equation to calculate jump height [27]. It is mainly dependent on accurate detection of the take-off and landing instances.