A smoothness-constrained updating recursive Kalman filter technique for real-time light-field tomography of 3D flame temperature field

Aiming at the problems of limited projection information, high noise sensitivity, and the inverse problem's ill-condition in the real-time temperature reconstruction of the three-dimensional (3D) dynamic flames, this work proposes a dynamic laminar reconstruction method that integrates light-field imaging with smoothness-constrained updating recursive Kalman filter (SURKF). This work innovatively integrates flame-radiation tensor decomposition and Tikhonov regularization into the Kalman filter (KF), and introduces the recursive least-squares method for online optimization of the state transition matrix. Analysis shows that the average relative errors of SURKF are 3.60 % and 2.60 % under the dynamic triangular and sinusoidal wave forms, respectively, which is 85.7 % more precise than the classical KF. The parameter optimization analysis reveals that the synergistic modulation of the process noise covariance (Q = 10) and the forgetting factor (r = 0.3–0.7) significantly balances the dynamic response and stability. In the low-temperature region (< 1200 K), reconstruction error is two times higher than that in the high-temperature region, but still maintains a relative error within 3 % through the adaptive regularization constraint. The work verifies the effectiveness of the SURKF algorithm in real-time 3D temperature tomography using a light-field camera. It provides a high-precision solution for dynamic combustion monitoring in aero-engine combustion chambers, gas turbines, and other scenarios.