A Triaxial Accelerometer Calibration Method Using a Mathematical Model

This paper presents a new triaxial accelerometer calibration method using a mathematical model of six calibration parameters: three gain factors and three biases. The fundamental principle of the proposed calibration method is that the sum of the triaxial accelerometer outputs is equal to the gravity vector when the accelerometer is stationary. The proposed method requires the triaxial accelerometer to be placed in six different tilt angles to estimate the six calibration parameters. Since the mathematical model of the calibration parameters is nonlinear, an iterative method is used. The results are verified via simulations by comparing the estimated gain factors and biases with the true gain factors and biases. The simulation results confirm that the proposed method is applicable in extreme cases where the gain factor is 1000 V/(m/s(2)) and the bias is +/-100 V, as well as the cases where the gain factor is 0.001 V/(m/s(2)) and the bias is 0 V. The proposed calibration method is also experimentally tested with two different triaxial accelerometers, and the results are validated using a mechanical inclinometer. The experimental results show that the proposed method can accurately estimate gain factors and biases even when the initial guesses are not close to the true values. In addition, the proposed method has a low computational cost because the calculation is simple, and the iterative method usually converges within three iteration steps. The error sources of the experiments are discussed in this paper.

本文提出了一种新的三轴加速度计校准方法，该方法使用包含六个校准参数（三个增益因子和三个偏差）的数学模型。所提出的校准方法的基本原理是，当加速度计静止时，三轴加速度计输出的总和等于重力矢量。该方法要求将三轴加速度计放置在六个不同的倾斜角度以估计六个校准参数。由于校准参数的数学模型是非线性的，所以使用了一种迭代方法。通过将估计的增益因子和偏差与真实的增益因子和偏差进行比较的模拟来验证结果。模拟结果证实，所提出的方法适用于增益因子为1000 V/(m/s²)且偏差为±100 V的极端情况，以及增益因子为0.001 V/(m/s²)且偏差为0 V的情况。所提出的校准方法还使用两个不同的三轴加速度计进行了实验测试，并使用机械倾角仪对结果进行了验证。实验结果表明，即使初始猜测值与真实值相差较大，所提出的方法也能准确估计增益因子和偏差。此外，由于计算简单，且迭代方法通常在三个迭代步骤内收敛，所以该方法计算成本较低。本文还讨论了实验的误差来源。