# Research Progress of Dynamic Measurement Technology of Atom Gravimeter
## 2 Dynamic Measuring Principle and Device of Atom Gravimeter
### Dynamic Measurement Principle of Atom Gravimeter
#### 2.2.1 Coarse-Fine Combination  
The scheme of ONERA is the Coarse-fine combination, and the specific process is as follows. Within a measurement period, the atom gravimeter obtains the population \(P(t)\), and the possible gravity value is obtained by reverse solving Equation (2):  
\[g_{\text{at}}(t,s,n)=\frac{s\times\arccos\left[2\frac{P_{0}-P(t)}{C}\right]+2 \pi\times n}{k_{\text{eff}}T^{2}}+\frac{2\pi\alpha}{k_{\text{eff}}}. \tag{3}\]  
However, for a measured population, there are multiple possible gravity values corresponding to it, where \(s=\pm 1\), and \(n\) is an integer, which represents the multi-valued property of the measurement. In the case of little fluctuation in environmental factors such as temperature, the changes in parameters \(P_{0}\) and \(C\) are relatively small [42; 43]. Generally, these parameters are either obtained by fringe fitting in static measurement, set as fixed values in dynamic measurement, or estimated by the average value and standard deviation of the output signal of the atom gravimeter [6]. The chirp rate \(\alpha\) is determined by  
\[\alpha=\pm 1\bigg{(}k_{\text{eff}}\times g_{\text{prev}}+\frac{\text{rd}(2 \pi)}{T^{2}}\bigg{)}, \tag{4}\]  
where \(g_{\text{prev}}\) is the result of the previous measurement period, and the sign of \(\alpha\) is changed alternately with the measurement period to eliminate some systematic errors [35; 36].  
While the sampling rate of the accelerometer is usually higher, the gravity sequence \(g_{\text{acc}}(tt)\) can be obtained with the same period, which is convolved with the sensitivity function of the atom gravimeter \(h(tt)\) to obtain a rough estimate of gravity within the measurement period:  
\[g_{\text{acc}}(t)=\int_{-T}^{T}g_{\text{acc}}(t_{\pi}+tt)h(tt)\text{d}tt, \tag{5}\]  
\[h(tt)=\left\{\begin{array}{l}\frac{T+tt}{T^{2}},-T\leq tt\leq 0\\ \frac{T-tt}{T^{2}},0\leq t\prime\leq T\end{array},\right. \tag{6}\]  
where \(t_{\pi}\) represents the time corresponding to the \(\pi\) pulse. Find the closest \(g_{\text{at}}(t,s,n)\) to the value, and \(n\) and \(s\) in Equation (3) can be determined. Then the multi-value of the atom gravimeter output can be eliminated and a definite value \(g_{\text{at}}(t)\) can be obtained. The data processing flow of the coarse-fine combination is shown in Figure 4.  
The dynamic range corresponding to one fringe period of the atom gravimeter can be calculated by Equation (2) as \(2\pi/k_{\text{eff}}T^{2}\), and for a gravimeter \(T=15\) ms, it is only about 170 mGal. However, the general accelerometer is above 1 g, and some can even reach hundreds of g. Therefore, when the accuracy of the accelerometer is better than \(2\pi/k_{\text{eff}}T^{2}\), the coarse-fine combination has a good effect. While solving the multi-valued problem, this scheme can improve the dynamic range of the atom gravimeter to be comparable to that of the accelerometer [11; 22; 44; 45; 46; 47; 48].  
In this scheme, the vibration noise is mainly filtered by offline low-pass filtering of the output data, so it is more suitable for scenarios such as gravity map mapping and resource exploration that do not require high real-time performance.  
Figure 4: Flow chart of coarse–fine combination data processing.