## 2 Data Processing  
For the strong motion station \(r\) at the epoch \(k\), the accelerometer measurement \(a_{r,k}\) can be expressed as:  
\[a_{r,k}=\vec{a}_{r,k}+b_{r,k}+\varepsilon_{a}\,\mathcal{E}_{a}\sim N(0,Q_{a}) \tag{1}\]where, \(\tilde{a}_{r,k}\) is the true acceleration; \(b_{r,k}\) is the acceleration bias which is estimated as a slowly time-varying parameter, \(\varepsilon_{a}\) is the noise-like random error with variance \(Q_{a}\). In loosely-integrated procedures, the GPS phase and pseudorange data are first analyzed to estimate station displacements by using either relative network positioning or precise point positioning. The GPS-derived displacement at the station \(r\) and epoch \(k\) can be expressed as:  
\[x_{r,k}=\tilde{x}_{r,k}+\varepsilon_{x}\,\varepsilon_{x}\sim N(0,Q_{x}) \tag{2}\]  
where, \(\varepsilon_{x}\sim N(0,Q_{x})\) is the GPS position noise. The GPS displacement Equation (2) is combined with the accelerometer Equation (1) for the measurement update of the Kalman filter. The state vector \(X_{k}\) can be expressed as:  
\[X_{r,k}= \begin{pmatrix}x_{r,k}\\ v_{r,k}\\ a_{r,k}\end{pmatrix}  \tag{3}\]  
\[ \begin{pmatrix}x_{r,k}\\ v_{r,k}\\ a_{r,k}\end{pmatrix} = \begin{pmatrix}1&\tau&\tau^{2}\ /\ 2\\ 0&1&\tau\\ 0&0&1\end{pmatrix}\begin{pmatrix}x_{r,k-1}\\ v_{r,k-1}\\ a_{r,k-1}\end{pmatrix}  \tag{4}\]  
where, \(x_{r,k}\) is the coordinate, \(v_{r,k}\) is the velocity and \(a_{r,k}\) is the acceleration; \(\tau\) is the accelerometer sampling interval; the transition Equation (4) is used for time update of the Kalman filter. The accelerometer data can be applied as strict constraints on the position variation between epochs and therefore improves GPS ambiguity resolution and outlier identification. Here, we apply the tightly-coupled integration Kalman filter to analyze raw GPS phase and pseudorange observations and raw strong motion data. The linearized equations for raw carrier phase and pseudo-range observations can be expressed as follows [20,21]:  
\[l_{r,j}^{s}=-u_{r}^{s}\cdot x_{r}+m_{r}^{s}\cdot Z_{r}-t^{s}+t_{r}+\lambda_{j} (b_{r,j}-b_{j}^{s})-I_{r,j}^{s}+\lambda_{j}N_{r,j}^{s}+\varepsilon_{r,j}^{s} \tag{5}\]  
\[p_{r,j}^{s}=-u_{r}^{s}\cdot x_{r}+m_{r}^{s}\cdot Z_{r}-t^{s}+t_{r}+c(d_{r,j}+d _{j}^{s})+I_{r,j}^{s}+e_{r,j}^{s} \tag{6}\]  
where, \(l_{r,j}^{s}\), \(p_{r,j}^{s}\) denote \"observed minus computed\" phase and code observables from satellite \(s\) to receiver \(r\) at frequency \(j\); \(u_{r}^{s}\) is the unit direction vector from receiver to satellite; \(x_{r}\) denotes the vector of the receiver position; \(Z_{r}\) denotes tropospheric zenith wet delay; \(m_{r}^{s}\) is the wet part of global mapping function; \(t^{s}\) and \(t_{r}\) are the clock errors of satellite and receiver respectively; \(\lambda_{j}\) is the wavelength of the \(j\) frequency; \(b_{r,j}\) is the receiver-dependent uncalibrated phase delay at the \(j\) frequency; \(b_{j}^{s}\) is satellite-dependent uncalibrated phase delay; \(d_{r,j}\) is the code bias of the receiver; \(d_{j}^{s}\) is the code bias of satellite; \(\Gamma_{r,j}\) is ionospheric delay on the path at the \(j\) frequency; \(N_{r,i}\) is the integer phase ambiguity; \(e_{r,i}^{s}\) is the pseudo-range measurement noise; \(\varepsilon_{r,i}^{s}\) is measurement noise of carrier phase. Integer ambiguity fixing in PPP requires not only precise satellite orbit and high-rate satellite clock corrections but also uncalibrated phase delay (UPD) [22].