Robust ellipsoid fitting method based on optimization of a novel nonlinear cost function in navigation systems

Low-cost sensors based on micro-electro-mechanical systems (MEMS) are typically used for attitude determination in navigation systems especially magnetometer which is used for heading determination. The measured value of the MEMS magnetometer is subjected to different kinds of error such as random noise, constant bias, non-orthogonality, scale factor deviation and more importantly hard iron and soft iron effects. Therefore, in order to reach more accurate measurement, high-precision calibration is needed. One of the most common methods for calibrating MEMS magnetic sensors is least squares ellipsoid fitting. But, the common least squares ellipsoid fitting method can be inefficient for real-time applications in the presence of colored noise and outliers. In this paper, a modified ellipsoid fitting method is proposed in which a nonlinear optimization is developed to minimize a novel cost function. In the cost function of the proposed robust method, the effect of outliers and noise is considered and the standard deviation of the data is kept minimum. Finally, the efficiency of the new algorithms is demonstrated through the experimental results.