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Smooth IMU Acceleration

Description

가공되지 않은 IMU 가속도에는 noise가 존재하며, 분석에 그대로 활용하면 오차를 발생시킬 수 있다. 따라서 해당 데이터를 먼저 10Hz로 down-sampling(10개씩 평균 계산)하여 noise가 적은 부드러운 데이터로 만든다. 그 결과를 smooth IMU acceleration이라 한다.

Formal Definition

The IMU accelerations

\mathbf{a}^{\mathsf{IMU}} = (a_x^{\mathsf{IMU}}, a_y^{\mathsf{IMU}}, a_z^{\mathsf{IMU}}) : \mathbb{T}[\lambda^{\mathsf{IMU}}] \rightarrow \mathbb{R}^3

are smoothed by averaging every

m^{\mathsf{IMU}} = \Delta t / \lambda^{\mathsf{IMU}} \ (\in \mathbb{N})

consecutive data points. This results in the smooth IMU accelerations

\mathbf{\bar{a}}^{\mathsf{IMU}} = (\bar{a}_x^{\mathsf{IMU}}, \bar{a}_y^{\mathsf{IMU}}, \bar{a}_z^{\mathsf{IMU}}) : \mathbb{T}[\Delta t] \rightarrow \mathbb{R}^3

such that

\mathbf{\bar{a}}^{\mathsf{IMU}}(P,t) = (\bar{a}^{\mathsf{IMU}}_x(P,t), \bar{a}^{\mathsf{IMU}}_y(P,t), \bar{a}^{\mathsf{IMU}}_z(P,t)) := \frac{1}{m^{\mathsf{IMU}}} \sum_{i=0}^{m^{\mathsf{IMU}}-1} \mathbf{\bar{a}}^{\mathsf{IMU}} (P,t-i\lambda^{\mathsf{IMU}})

Parameter Setting

•

[1.8.3] [1.9.2] λIMU=0.01 s\lambda^{\mathsf{IMU}} = 0.01\,\text{s}λIMU=0.01s and Δt=0.1 s\Delta t = 0.1\,\text{s}Δt=0.1s, i.e., mIMU=10m^{\mathsf{IMU}} = 10mIMU=10.
(Raw IMU accelerations are down-sampled by 10 Hz.)

•

[1.9.0] λIMU=0.01 s\lambda^{\mathsf{IMU}} = 0.01\,\text{s}λIMU=0.01s and Δt=0.5 s\Delta t = 0.5\,\text{s}Δt=0.5s, i.e., mIMU=50m^{\mathsf{IMU}} = 50mIMU=50.
(Raw IMU accelerations are down-sampled by 2 Hz.)