Sensor fusion and magnetic drift estimation in magnetic measurements using Kalman filter for long-duration plasma operations

Abstract This work introduces a novel technique that incorporates the bias contaminating magnetic coil measurements within the model, building upon previous sensor fusion techniques of magnetic coil and Hall sensor (Quercia et al 2022 Nucl. Fusion 62 106032; Arpaia et al 2021 Sensors 22 182). In the pursuit of sustainable thermo-nuclear magnetic fusion, precise and drift-free magnetic field measurements are essential for effective plasma control. Typically, magnetic field measurements for plasma control and diagnosis in magnetic fusion are achieved through inductive coil sensors and integrators, striving for low noise and fast sampling rates. However, these methods are susceptible to drift due to the presence of bias or offset originated from the magnetic coil <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">d</mml:mi> </mml:mrow> </mml:mrow> <mml:mi>B</mml:mi> <mml:mrow> <mml:mo>/</mml:mo> </mml:mrow> <mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">d</mml:mi> </mml:mrow> </mml:mrow> <mml:mi>t</mml:mi> </mml:mrow> </mml:math> measurements and the integrator. To address the drift issue, we employ a Kalman filter approach that considers the time-varying bias as a Wiener or Brownian process, in conjunction with a Hall sensor. This method is applied to synthetic magnetic field data representing Hall sensor measurements with high noise and synthetic <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">d</mml:mi> </mml:mrow> </mml:mrow> <mml:mi>B</mml:mi> <mml:mrow> <mml:mo>/</mml:mo> </mml:mrow> <mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">d</mml:mi> </mml:mrow> </mml:mrow> <mml:mi>t</mml:mi> </mml:mrow> </mml:math> data representing magnetic coil sensor measurements with time-varying bias. While these conditions are more extreme than typical in current fusion diagnostics, they are chosen to rigorously test the robustness of our method. The results demonstrate successful reconstruction of a low-noise, low-bias magnetic field and the time-varying bias, highlighting the method’s reliability in challenging scenarios. The proposed method offers promising applications in achieving long-term, drift-free control of plasma in magnetic fusion experiments, taking us one step closer to the goal of sustainable fusion energy production.