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We developed a drift-free method to estimate the three-dimensional (3D) displacement of a body part during cyclical motions using body-worn inertial sensors. We performed the Fourier analysis of the stride-by-stride estimates of the linear acceleration, which were obtained by transposing the specific forces measured by the tri-axial accelerometer into the global frame using a quaternion-based orientation estimation algorithm and detecting when each stride began using a gait-segmentation algorithm. The time integration was performed analytically using the Fourier series coefficients; the inverse Fourier series was then taken for reconstructing the displacement over each single stride. The displacement traces were concatenated and spline-interpolated to obtain the entire trace.

Strap-down integration is prone to several errors that tend to grow unbounded over time. These errors are due to the inertial sensors being affected by wideband measurement noise and bias that slowly evolves over time. Usually, sensor fusion methods for determining orientation are employed to mitigate the integration drift of gyroscopes. A wealth of literature is available to explain how to design sensor fusion methods, especially in difficult conditions when one or more of the following conditions recur: the body part is moving quickly, the magnetic environment is disturbed and/or the recording time is long [5]. There is comparatively less literature discussing the problem of doubly-time integrating the estimated linear acceleration to obtain accurate 3D displacement estimates [6].

Abstract:Position sensing with inertial sensors such as accelerometers and gyroscopes usually requires other aided sensors or prior knowledge of motion characteristics to remove position drift resulting from integration of acceleration or velocity so as to obtain accurate position estimation. A method based on analytical integration has previously been developed to obtain accurate position estimate of periodic or quasi-periodic motion from inertial sensors using prior knowledge of the motion but without using aided sensors. In this paper, a new method is proposed which employs linear filtering stage coupled with adaptive filtering stage to remove drift and attenuation. The prior knowledge of the motion the proposed method requires is only approximate band of frequencies of the motion. Existing adaptive filtering methods based on Fourier series such as weighted-frequency Fourier linear combiner (WFLC), and band-limited multiple Fourier linear combiner (BMFLC) are modified to combine with the proposed method. To validate and compare the performance of the proposed method with the method based on analytical integration, simulation study is performed using periodic signals as well as real physiological tremor data, and real-time experiments are conducted using an ADXL-203 accelerometer. Results demonstrate that the performance of the proposed method outperforms the existing analytical integration method.Keywords: inertial sensors; integration drift; periodic motion; phase-shift; Fourier linear combiner

With the aided sensors or sensing systems, Kalman filters (KF) or extended-Kalman filters (EKF) are commonly used to fuse two sources of information: one coming from the inertial sensors, and the other from aided sensors or sensing systems in an attempt to correct for the drift. For example, correction of orientation drift using EKF and a magnetometer as an aided sensor is described in [3,4]. Correction of position and orientation drift using EKF and ultrasonic sensors as aided sensors is presented in [5]. One of the drawbacks of having to rely on aided sensors to correct for the drift is that the accuracy depends on the update rate, availability, and reliability of the aided sensors.

To obtain drift-free position estimates of periodic or quasi-periodic motion using inertial sensors without employing other aided sensors or sensing systems, one possible solution is to employ linear high-pass filtering of drifted position by choosing a cutoff frequency somewhere between the frequencies of low-frequency drift signal and that of the periodic motion which has relatively high frequency. However, linear filtering inherently introduces phase-shift and attenuation [21], resulting in inaccurate position/orientation estimate.

In sub-section 2.1 existing methods for zero-phase estimation of periodic signals are discussed first. It should be clear that the existing methods are not the contribution of this paper, but are described briefly to aid readers clearly understand the proposed method which is the contribution of the paper. In sub-section 2.2, the proposed method of drift-free position estimation using inertial sensors is described. Since the proposed method requires the use of an existing estimation method and its modification is required, modification to the existing methods are proposed and described. It should be noted that analytical integration method for drift-free estimation described in [19] does not account for the acceleration drift and the phase-shift and attenuation that has already been introduced by inherent hardware filters. The proposed method can handle these issues very well.

In this section, the proposed method of drift-free estimation of desired periodic or quasi-periodic signal using one of the algorithms described in the previous section, and compensation for the phase-shift and attenuation introduced by the linear filters is described. The proposed method is described using acceleration as representative inertial sensor output. A block diagram describing the method to obtain the position estimate of desired periodic or quasi-periodic motion which is sensed by an accelerometer is shown in Figure 3.

In inertial human motion capture, a multitude of body segments are equipped with inertial measurement units, consisting of 3D accelerometers, 3D gyroscopes and 3D magnetometers. Relative position and orientation estimates can be obtained using the inertial data together with a biomechanical model. In this work we present an optimization-based solution to magnetometer-free inertial motion capture. It allows for natural inclusion of biomechanical constraints, for handling of nonlinearities and for using all data in obtaining an estimate. As a proof-of-concept we apply our algorithm to a lower body configuration, illustrating that the estimates are drift-free and match the joint angles from an optical reference system.

The term inertial sensor refers to the combination of accelerometers and gyroscopes. These measure the external specific force and the angular velocity, respectively. Integration of their measurements provides information about the sensor's position and orientation. However, the position and orientation estimates obtained by simple integration suffer from drift and are therefore only accurate on a short time scale. In order to improve these estimates, we combine the inertial sensors with additional sensors and models. To combine these different sources of information, also called sensor fusion, we make use of probabilistic models to take the uncertainty of the different sources of information into account. The first contribution of this thesis is a tutorial paper that describes the signal processing foundations underlying position and orientation estimation using inertial sensors.

In this thesis, we consider the problem of estimating position and orientation (6D pose) using inertial sensors (accelerometers and gyroscopes). Inertial sensors provide information about the change in position and orientation at high sampling rates. However, they suffer from integration drift and hence need to be supplemented with additional sensors. To combine information from the inertial sensors with information from other sensors we use probabilistic models, both for sensor fusion and for sensor calibration. 041b061a72