In-Orbit Estimation of Magnetometer Biases and Scale Factors via Nonlinear Two-Stage Kalman Filter

The scale factor and bias of the magnetometer must be determined in order to appropriately estimate satellite dynamics and control orientation. The magnetometer scale factor and bias are not constant due to temperature variation and thermal distortion of the structure, which causes a relatively large magnitude error, and these effects must be eliminated to meet the requirements of the mission. This study proposes a nonlinear two-stage Kalman filter (NTSKF)based method for in-orbit calibration of a magnetometer. The magnetometer bias and scale factor error are combined to form the equivalent non-steady bias noise, which is removed from the magnetometer measurements as bias noise. Each iteration of the estimation process has two stages: the first stage uses the Kalman filter to estimate equivalent magnetometer biases as well as three state parameters; the second stage uses the extension of the Kalman filter proposed in this study to estimate three magnetometer biases and three scale factors. If the magnetometer biases and scale factors change insignificantly in the long-time interval, then biases and scale factors can be accepted as constant and estimated using the proposed extension of the Kalman filter under the conditions defined in this work.