Extended Kalman filter-based real-time state estimation of high-temperature superconducting coils

High-temperature superconducting (HTS) coils exhibit complex loss mechanisms under dynamic operating conditions, and their internal state parameters, including dynamic resistance, dynamic inductance, and critical current, are difficult to measure directly. To enable real-time observation of multiple state parameters, an extended Kalman filter (EKF)-based state estimation method is proposed. First, a nonlinear dynamic electromagnetic model of the HTS coil is established. State and observation equations are then formulated for quasi-static and alternating-current (AC) operating conditions, enabling recursive estimation of dynamic resistance, dynamic inductance, critical current, and power-law exponent. Transport-current experiments under multiple operating conditions demonstrate that the proposed method effectively separates resistive and inductive voltage components and accurately estimates the internal coil states. Comparisons with the finite-data-window least-squares method further demonstrate that the EKF achieves a favorable balance between steady-state accuracy and transient tracking performance without relying on a fixed data window. The proposed method provides support for online monitoring and quench warning of HTS coils.