Real-time estimation of roll angles by magnetometer based on two-step adaptive Kalman filter

Abstract

The geomagnetic field vector information is critical to the navigation and positioning in the magnetic measurement of satellites, ships, and aircraft, however, suffers from the internal inherent error and the internal error interfering magnetic fields. Most real-time geomagnetic correction algorithms based on the specific ellipsoid fitting typically lead to the difficulty in real-time acquisition of the attitude roll angle of the projectile and the estimation accuracy. Herein, we propose a novel real-time estimation algorithm based on Magnetometer measurement involved two-step adaptive Kalman filter. The first-step adaptive Kalman filter algorithm is proposed for online error compensation of the magnetometer by using the error model and ellipsoid model of the magnetometer. The robust estimation theory is proposed to apply to the first-step adaptive Kalman filtering for ellipsoid fitting. The capability of preprocessing data and the adaptive observation vector's covariance matrix enable the real-time separation and correction of outliers. In addition, a vector-dot product invariant method is proposed to estimate the 12 coefficients in the magnetometer error model, solving the problem that the traditional method cannot ultimately determine the coefficients of the error matrix. Furthermore, the second-step adaptive Kalman is utilized to adaptively real-time estimate the roll angle. In particular, the results of the simulations and experiments show that the algorithm's parameters tend to be stable, beginning since 3 s for the data collection; and the accuracy range of the roll angle is boost to between ±0.4°. Moreover, the error parameters of the magnetometer are fully calibrated, and the estimation accuracy of roll angle is improved by 1/2 with regard to that of conventional methods. The results demonstrate the capability of compensating for the random magnetic field error caused by the motor. The results show that the two-step adaptive Kalman filter algorithm can reduce the estimation error of roll angle and could be extended to practical engineering applications.