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Beyond the Nyquist criterium: The effect of sampling frequency and angular velocity variability on orientation estimation from gyroscope data
Anne Haitjema, Frank J. Wouda, Kim Sunesen, Jasper Reenalda, Bert-Jan F. van Beijnum, Peter H. Veltink
Session: Poster Session 1 (Even numbers)
Session starts: Thursday 26 January, 16:00
Presentation starts: 16:00
Anne Haitjema (University of Twente)
Frank J. Wouda (Movella Technologies BV)
Kim Sunesen (Movella Technologies BV)
Jasper Reenalda (University of Twente)
Bert-Jan F. van Beijnum (University of Twente)
Peter H. Veltink (University of Twente)
Abstract:
Inertial measurement units (IMUs) are frequently used in human movement analysis. A suitable sampling frequency must be chosen for accurate analysis. The Nyquist criterion, which states that the sampling frequency should be at least twice the highest frequency contained in the signal of interest, is often used to ensure accurate representation of continuous-time signals in the discrete-time domain. However, orientation estimation from sampled angular velocity might be subject to additional sources of error. We want to evaluate, both theoretically and empirically, the influence of sampling frequency and multidimensional angular velocity variability on the accuracy of orientation estimation from human angular velocity measurements.
Theoretically, relative orientation can be estimated by integrating the angular velocity according to Bortz [1]. The discrete nature of this calculation can introduce errors. Two potential factors influencing the magnitude of this error are the multidimensionally variable angular velocity, and the timestep chosen in the integral.
For the empirical evaluation, an experiment will be designed in which 10-15 participants will walk and run whilst instrumented with 4 IMUs (sternum, pelvis and tibias) that output raw sensor data at 1000 Hz. An optical motion capture system will be used as a reference. The different sensor locations and movements will be used to evaluate the effect of the variability in multidimensional angular velocity on orientation estimation. The effect of the sampling frequency on orientation estimation will be evaluating by downsampling the data.
Results from a pilot experiment involving walking data collected at 1000 Hz (pelvis and tibia) indicate that decreasing the sampling frequency increases the error in the orientation estimation, even though inspection of the frequency spectrum suggests that the Nyquist criterion is fulfilled. Furthermore, a lower multidimensional variability in the angular velocity seems to lead to a lower absolute error in the orientation estimation. If it is possible to represent a movement around one main rotational axis, then this decreases the error in the orientation estimation [2]. We hypothesize that the estimation error increases when human movements exhibit a greater multidimensional variability in the angular velocity.
This work is partly funded by TKI HTSM and Movella Technologies BV.
References
1. Bortz JE. A new mathematical formulation for strapdown inertial navigation. IEEE Trans Aerosp Electron Syst. 1971 Jan; 7(1): 61-66.
2. Zandbergen MA, Reenalda J, Middelaar RP van, Ferla RI, Buurke JH and Veltink PH. Drift-free 3D orientation and displacement estimation for quasi-cyclical movements using one inertial measurement unit: Application to running. Sensors. 2022 Jan 26; 22: 956.