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Master Thesis Code
by Simon Moser
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this function estimates accelerometer calibration parameters More...
Go to the source code of this file.
Functions | |
| function | jumpEstimateCalibrationParameters (in data, in zeroVelocity, in options) |
this function estimates accelerometer calibration parameters
this function estimates accelerometer calibration parameters (sensitivity and bias) using zero velocity ranges. The function uses data coming from a 6 axis calibration sequence (rotating a cube on a flat surface) or from a 12 axis calibration sequence (rotating a dodecahedron on a flat surface). The function uses a least squares optimization to estimate the calibration parameters. The function also estimates the gyroscope bias.
| data | - struct as defined in jumpCheckData, the data must contain zero movement sequences where only one axis is aligned with gravity and the other two axes are perpendicular to gravity. The data must contain at least six different sequences, i.e. every side must lay towards the ground at least once. The order of the sequences is not important. |
| zeroVelocity | - logical vector indicating zero velocity ranges |
| options | - the available options are:
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| params | - struct containing the estimated calibration parameters for the accelerometer and high g sensor. The struct has the following fields:
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The calibration parameters are estimated using the following error models.
For the six faces case:
The accelerometer measurements are modeled as:
\[ \begin{align*} a_x^\text{(meas)} &= s_{x}^\text{(a)} \cdot a_x^\text{(true)} + b_{x}^\text{(a)} + \varepsilon_{ax} \\ a_y^\text{(meas)} &= s_{y}^\text{(a)} \cdot a_y^\text{(true)} + b_{y}^\text{(a)} + \varepsilon_{ay} \\ a_z^\text{(meas)} &= s_{z}^\text{(a)} \cdot a_z^\text{(true)} + b_{z}^\text{(a)} + \varepsilon_{az} \\ \end{align*} \]
where \( \varepsilon \) is the residual error.
The return value for the sensitivity is a \( 1 \times 3 \) vector containing the sensitivities in the following order: \( s_{x}^\text{(a)} \), \( s_{y}^\text{(a)} \), \( s_{z}^\text{(a)} \). The return value for the bias is a \( 1 \times 3 \) vector containing the biases in the following order: \(b_{x}^\text{(a)} \), \(b_{y}^\text{(a)} \), \(b_{z}^\text{(a)} \).
The gyroscope measurements are modeled as:
\[ \begin{align*} \omega_x^\text{(meas)} &= \omega_x^\text{(true)} + b_{x}^{(\omega)} + \varepsilon_{\omega x} \\ \omega_y^\text{(meas)} &= \omega_y^\text{(true)} + b_{y}^{(\omega)} + \varepsilon_{\omega y} \\ \omega_z^\text{(meas)} &= \omega_z^\text{(true)} + b_{z}^{(\omega)} + \varepsilon_{\omega z} \\ \end{align*} \]
The return value for the bias is a \( 1 \times 3 \) vector containing the biases in the following order: \(b_{x}^{(\omega)} \), \(b_{y}^{(\omega)} \), \(b_{z}^{(\omega)} \).
For the twelve faces case:
The accelerometer measurements are modeled as:
\[ \begin{align*} a_x^\text{(meas)} &= s_{x}^{(a)} a_{x} + s_{xy}^{(a)} a_{y} + s_{xz}^{(a)} a_{z} + b_x^{(a)} + \varepsilon_{ax} \\[3mm] a_y^\text{(meas)} &= s_{yx}^{(a)} a_{x} + s_{y}^{(a)} a_{y} + s_{yz}^{(a)} a_{z} + b_y^{(a)} + \varepsilon_{ay} \\[3mm] a_z^\text{(meas)} &= s_{zx}^{(a)} a_{x} + s_{zy}^{(a)} a_{y} + s_{z}^{(a)} a_{z} + b_z^{(a)} + \varepsilon_{az}, \end{align*}, \]
where the returned sensitivity matrix is
\[ \mathbf{s}_a = \begin{bmatrix} s_{xx}^{(a)} & s_{xy}^{(a)} & s_{xz}^{(a)} \\ s_{yx}^{(a)} & s_{yy}^{(a)} & s_{yz}^{(a)} \\ s_{zx}^{(a)} & s_{zy}^{(a)} & s_{zz}^{(a)} \end{bmatrix} \]
and the returned bias vector is identical to the six faces case.
The gyroscope measurements are modeled identically to the six faces case.
Definition in file jumpEstimateCalibrationParameters.m.
| function jumpEstimateCalibrationParameters | ( | in | data, |
| in | zeroVelocity, | ||
| in | options ) |