ACCELEROMETERS have been used extensively in inclinometers to measure tilt and in inertial measurement units (IMUs) to measure acceleration. An inclinometer senses the direction of gravity and uses this information to determine the body tilt. A conventional six degrees-of-freedom IMU uses three accelerometers and three rate gyroscopes to sense a body’s linear acceleration and angular velocity, and integrates these quantities with respect to time to give the instantaneous position and orientation of the body. There have been proposals for all-accelerometer IMU designs for cost-sensitive applications due to the superior performance of low-cost accelerometers relative to low-cost gyros . In many recent low- ( 2 ) inertial sensing applications, such as indoor robotic navigation , motion tracking of handheld devices for microsurgery , and entertainment , accelerometers have doubled as inclinometers to provide redundant orientation information.
With companies like Analog Devices leading the way, low-cost microelectromechanical systems (MEMS)-based accelerometers have gained substantial ground in inertial navigation applications in the past several years, especially in nonmilitary and consumer markets. However, size and cost advantages notwithstanding, the performance of MEMS silicon accelerometers has not reached tactical or navigation grade. Testing of MEMS accelerometers on rolling artillery projectiles shows that they yield an average tracking error of about 0.1 throughout a 28-s test . Though the report claims that such performance is acceptable, double integration of an acceleration error of 0.1 would mean a position error of more than 350 m at the end of the test.
It is because of this notorious integration drift that inertial measurement technology is seldom used alone in high-precision navigation or motion tracking applications. Any seemingly small error in the acceleration measurement would grow quadratically over time in the position measurement after the double integration. Therefore, to employ accelerometers effectively in high-precision tracking applications, it is imperative to obtain a comprehensive model to account for the errors. There have been some efforts to model MEMS capacitive accelerometers using equivalent electrical circuit models that represent the physics of operation. However, the average user may find such models of limited benefit, since more useful parameters by which accelerometers are usually rated, such as scale factor, bias, nonlinearity, cross-axis sensitivity, and misalignment, are missing from these models.
The objective of this paper is to develop error models of low- MEMS accelerometers, by which the sensors can be compensated to improve accuracy. To model the nonlinear deterministic errors, we present a phenomenological modeling method that relates experimental observations to mathematical representations of parameters such as those mentioned above, without requiring complete understanding of the underlying physics. The proposed model thus identified is verified in tilt and motion sensing experiments where the ground truth is known. The limitations of the proposed model are also discussed. While the deterministic error model developed is specific to the make and model of accelerometer tested, the experiments and modeling methodology are general.