An efficient orientation filter for inertial and inertial/magnetic sensor arrays. Madgwick, S. O. Technical Report
abstract   bibtex   
This report presents a novel orientation filter applicable to IMUs consisting of tri-axis gyroscopes and accelerometers, and MARG sensor arrays that also include tri-axis magnetometers. The MARG implementation incorporates magnetic distortion and gyroscope bias drift compensation. The filter uses a quaternion representation, allowing accelerometer and magnetometer data to be used in an analytically derived and optimised gradient-descent algorithm to compute the direction of the gyroscope measurement error as a quaternion derivative. The benefits of the filter include: (1) computationally inexpensive; requiring 109 (IMU) or 277 (MARG) scalar arithmetic operations each filter update, (2) effective at low sampling rates; e.g. 10 Hz, and (3) contains 1 (IMU) or 2 (MARG) adjustable parameters defined by observable system characteristics. Performance was evaluated empirically using a commercially available orientation sensor and reference measurements of orientation obtained using an optical measurement system. A simple calibration method is presented for the use of the optical measurement equipment in this application. Performance was also benchmarked against the propriety Kalman-based algorithm of orientation sensor. Results indicate the filter achieves levels of accuracy exceeding that of the Kalman-based algorithm; \textless 0.6◦ static RMS error, \textless 0.8◦ dynamic RMS error. The implications of the low computational load and ability to operate at low sampling rates open new opportunities for the use of IMU and MARG sensor arrays in real-time applications of limited power or processing resources or applications that demand extremely high sampling rates.
@techreport{sebastian_o.h._madgwick_efficient_nodate,
	type = {internal},
	title = {An efficient orientation filter for inertial and inertial/magnetic sensor arrays},
	abstract = {This report presents a novel orientation filter applicable to IMUs consisting of
tri-axis gyroscopes and accelerometers, and MARG sensor arrays that also include
tri-axis magnetometers. The MARG implementation incorporates magnetic distortion
and gyroscope bias drift compensation. The filter uses a quaternion representation,
allowing accelerometer and magnetometer data to be used in an analytically derived
and optimised gradient-descent algorithm to compute the direction of the gyroscope
measurement error as a quaternion derivative. The benefits of the filter include: (1)
computationally inexpensive; requiring 109 (IMU) or 277 (MARG) scalar arithmetic
operations each filter update, (2) effective at low sampling rates; e.g. 10 Hz, and (3)
contains 1 (IMU) or 2 (MARG) adjustable parameters defined by observable system
characteristics. Performance was evaluated empirically using a commercially available
orientation sensor and reference measurements of orientation obtained using an optical
measurement system. A simple calibration method is presented for the use of the
optical measurement equipment in this application. Performance was also benchmarked
against the propriety Kalman-based algorithm of orientation sensor. Results indicate
the filter achieves levels of accuracy exceeding that of the Kalman-based algorithm;
{\textless} 0.6◦ static RMS error, {\textless} 0.8◦ dynamic RMS error. The implications of the low
computational load and ability to operate at low sampling rates open new opportunities
for the use of IMU and MARG sensor arrays in real-time applications of limited power
or processing resources or applications that demand extremely high sampling rates.},
	author = {Sebastian O.H. Madgwick}
}

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