Estimating Movement Smoothness From Inertial Measurement Units

Abstract

Inertial measurement units (IMUs) are increasingly used to estimate movement quality and quantity to the infer the nature of motor behavior. The current literature contains several attempts to estimate movement smoothness using data from IMUs, many of which assume that the translational and rotational kinematics measured by IMUs can be directly used with the smoothness measures spectral arc length (SPARC) and log dimensionless jerk (LDLJ-V). However, there has been no investigation of the validity of these approaches. In this paper, we systematically evaluate the use of these measures on the kinematics measured by IMUs. We show that: (a) SPARC and LDLJ-V are valid measures of smoothness only when used with velocity; (b) SPARC and LDLJ-V applied on translational velocity reconstructed from IMU is highly error prone due to drift caused by integration of reconstruction errors; (c) SPARC can be applied directly on rotational velocities measured by a gyroscope, but LDLJ-V can be error prone. For discrete translational movements, we propose a modified version of the LDLJ-V measure, which can be applied to acceleration data (LDLJ-A). We evaluate the performance of these measures using simulated and experimental data. We demonstrate that the accuracy of LDLJ-A depends on the time profile of IMU orientation reconstruction error. Finally, we provide recommendations for how to appropriately apply these measures in practice under different scenarios, and highlight various factors to be aware of when performing smoothness analysis using IMU data.

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“…need to be considered. For instance, recent work on estimating movement smoothness with IMUs has shown that the SPARC measure cannot be used with acceleration data, even though the SPARC has been shown to be a good measure of movement smoothness when applied on movement velocity (Melendez-Calderon et al, 2021).…”

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“…However, as an IMU measures accelerations, estimating velocity from it would require additional processing and is usually prone to drift (Woodman, 2007). In a recent study, Melendez-Calderon and colleagues suggest that SPARC should not be applied to linear velocities obtained from IMUs, and an alternative definition based on angular velocities may be of interest (Melendez-Calderon et al, 2021). However, techniques to correct drift due to strapdown integration (Woodman, 2007) were not employed in their study, as the authors suggest that it warrants a systematic analysis of the errors introduced in the smoothness estimate (Melendez-Calderon et al, 2021).…”

“…In a recent study, Melendez-Calderon and colleagues suggest that SPARC should not be applied to linear velocities obtained from IMUs, and an alternative definition based on angular velocities may be of interest (Melendez-Calderon et al, 2021). However, techniques to correct drift due to strapdown integration (Woodman, 2007) were not employed in their study, as the authors suggest that it warrants a systematic analysis of the errors introduced in the smoothness estimate (Melendez-Calderon et al, 2021). Therefore, if the errors are accounted for, it should be possible to reliably measure SPARC using corrected linear velocities obtained from IMUs for a standardized pre-defined movement with a clear start and end posture.…”

“…In both cases, they could be confounded by the shape, i.e., the duration and amplitude, of the movement (Hogan and Sternad, 2009). Some proposed smoothness metrics are based on position, and do not truly reflect smoothness per se (Balasubramanian et al, 2015;Melendez-Calderon et al, 2021) as they do not measure the rate of change of position. Furthermore, some metrics are linear transformations of other smoothness metrics, and are therefore proxies of existing metrics.…”

“…The study showed the feasibility of the setup for measuring smoothness of the reaching events using the SPARC metric. In a recent study on persons with stroke, Melendez-Calderon and colleagues (Melendez-Calderon et al, 2021) concluded that IMU based estimation of SPARC is not recommended due to the issue of drift that occurs when processing IMU data. However, they avoided exploring drift correction techniques and state that velocity reconstruction is almost always erroneous due to incorrect orientation correction.…”