Fig. 1. Estimation of time-varying parameter

Fig. 2. Schematic of adaptive time-varying phase estimation method via weak measurement^[49]

Fig. 3. Adaptive optical phase estimation using time-symmetric quantum smoothing^[50]. (a) Signal and local oscillator generation; (b) adaptive phase estimation; (c) no-adaptive phase estimation; (d) experimental and theoretical variance ${\sigma }^{\mathrm{2}}$ of filtered non-adaptive (DH) and adaptive phase (AP); (e) experimental and theoretical variance ${\sigma }^{\mathrm{2}}$ of smoothed DH and AP

Fig. 4. Conceptual diagram and results for waveform estimation^[57]. (a) Concept of waveform estimation with n₁ samplings and n₂ independent or correlated quantum resources; (b) statistical error; (c) deterministic error; (d) total error

Fig. 5. Atomic sensor based on Kalman filtering^[59].(a) Time-varying signal estimation based on atomic sensor; (b) applied waveform (input) along with the corresponding measured photocurrent (output) and the recovered waveform (KF estimation); (c) spectrograms of input, output, and KF estimation

Fig. 6. Schematic of magnetic field estimation^[60]

Fig. 7. Real-time sensing of magnetic fields based on a NV center prepared in a CPT setting^[61]