Demonstration of static atomic gravimetry using Kalman filter

The measurement precision of the static atomic gravimetry is limited by white Gaussian noise in short term, which costs previous works an inevitable integration to reach the precision demanded. Here, we propose a statistical model based on the quantum projection noise and apply the Kalman filter to the waveform estimation in static atomic gravimetry. With the white Gaussian noise significantly removed by the the Kalman-filter formalism, the measurement noise of the gravimetry is reshaped in short term and shows $\tau^{1/2}$ feature that corresponds to random walk. During 200 hours of static measurement of gravity, the atomic gravimeter using Kalman filter demonstrates a sensitivity as good as 0.6 $\rm{nm/s^2}/\sqrt{\rm{s}}$, and highlights a precision of 1.7 $\rm{nm/s^2}$ at the measuring time of a single sample. The measurement noise achieved is also lower than the quantum projection limit below $\sim$ 30 s.