Frequency-scanning interferometry using a time-varying Kalman filter for dynamic tracking measurements

Frequency scanning interferometry (FSI) with a single external cavity diode laser (ECDL) and time-invariant Kalman filtering is an effective technique for measuring the distance of a dynamic target. However, due to the hysteresis of the piezoelectric ceramic transducer (PZT) actuator in the ECDL, the optical frequency sweeps of the ECDL exhibit different behaviors, depending on whether the frequency is increasing or decreasing. Consequently, the model parameters of Kalman filter appear time varying in each iteration, which produces state estimation errors with time-invariant filtering. To address this, in this paper, a time-varying Kalman filter is proposed to model the instantaneous movement of a target relative to the different optical frequency tuning durations of the ECDL. The combination of the FSI method with the time-varying Kalman filter was theoretically analyzed, and the simulation and experimental results show the proposed method greatly improves the performance of dynamic FSI measurements.