Robust Autocalibration of Triaxial Magnetometers

Abstract

Self-calibration of a magnetometer usually requires controlled magnetic environment as the calibration output can be affected by field distortions from nearby magnetic objects. In this paper, we develop a 2-stage method which can accurately selfcalibrate magnetometer from measurements containing anomalous readings due to local magnetic disturbances. The method proceeds by robustly fitting an ellipsoid to measurement data via L1-norm convex optimization, yielding initial model variables that are less prone to magnetic disruptions. These are then served as a starting point for robust nonlinear least squares optimization, which refines the magnetometer model to minimize sensor estimation errors while suppressing heavy anomalies. Synthetic and real experimental results are provided to demonstrate improved accuracy of the proposed method in presence of outliers. We additionally show empirically that the method is directly applicable to self-calibration of 3-axis accelerometers.

A Unified Method for Robust Self-Calibration of 3-D Field Sensor Arrays

“…Additionally, none of the aforementioned work have explicitly addressed the issue of anomalies during self-calibration, consequently requiring carefully obtained outlier-free measurements for calibration. Recently, improving robustness to outliers has been studied for the case of single 3-axis magnetometer and accelerometer [23], but the work is not directly applicable to an array of multiple sensors.…”

“…To resolve this ambiguity, we propose a canonical form of the array model. Inspired by prior work [23], [25], for each sensor i, we constrain A i to be an upper triangular matrix, K i ∈ R 3×3 , with positive diagonal entries. This effectively fixes Q i as any orthogonal matrix other than Q i = I will violate this constraint.…”

“…In the first stage, we find each constituent sensor's intrinsics (K i , b i ) and the 3D field directions {x (j) i } in its own sensor frame which best explains the corresponding measurements. For this task, we apply the 2-step robust autocalibration method developed in [23] independently for each sensor.…”

“…(Note changing the L 1norm in (7) to L 2 switches to least squares ellipsoid fitting. ) As stated in [23], ( 7) is first formulated as a convex semidefinite program proposed by Calafiore [26], which can then be efficiently solved using the SeDuMi solver [27].…”

“…where ρ : R → R is a robust kernel implemented to lessen the effect of gross outliers. While several choices are available for ρ(•), we opt for the Cauchy loss ρ(s) = log(1 + s/τ 2 ) like in [23], where τ is the kernel width implying the inlier radius.…”