## 2 Methodology
### GNSS/INS Tightly Coupled Positioning Model  
GNSS/INS integrated navigation system adopts Extended Kalman Filter (EKF) for system fusion to realize high-precision navigation and positioning by effectively detecting and rejecting Multipath/NLOS signals in complex urban areas. In vehicle navigation, due to the strong reliability and highly real-time performance of the pseudorange/INS system, this paper employs the integrated positioning solution of GNSS double-differenced pseudorange (DGNSS) and INS observation. The system state model depends on the INS error model and the description of the inertial sensor system error. The INS error equation based on the psi angle is adopted in this paper [43]. \[\delta\mathbf{r}^{n}= -\mathbf{\omega}_{en}^{n}\times\delta\mathbf{r}^{n}+\delta\mathbf{\psi}^{n} \tag{7}\] \[\delta\mathbf{v}^{n}= -(2\mathbf{\omega}_{ie}^{n}+\mathbf{\omega}_{en}^{n})\times\delta\mathbf{v}^{ n}-\mathbf{\psi}^{n}\times\mathbf{f}^{n}+\delta\mathbf{g}^{n}+\mathbf{C}_{b}^{n}\delta\mathbf{f}_{ ib}^{b}\] (8) \[\dot{\mathbf{\psi}}^{n}= -(\mathbf{\omega}_{ie}^{n}+\mathbf{\omega}_{en}^{n})\times\mathbf{v}^{n}-\mathbf{ C}_{b}^{n}\delta\mathbf{\omega}_{ib}^{b} \tag{9}\]  
where \(\delta\mathbf{r}^{n}\), \(\delta\mathbf{v}^{n}\), and \(\delta\mathbf{\psi}^{n}\) indicate position error, velocity error, and attitude angle error, respectively; \(\mathbf{C}_{b}^{n}\) is the rotation matrix from the body frame (\(b\)-frame) to the navigation frame (\(n\)-frame); \(\delta\mathbf{f}_{ib}^{b}\) and \(\delta\mathbf{\omega}_{ib}^{b}\) are the accelerometer and gyroscope error vector in the \(b\)-frame, separately; In addition, the specific force vector measured by the accelerometer, the rotation velocity of the earth, and the transfer rate are represented by \(\mathbf{f}^{n}\), \(\mathbf{\omega}_{ie}^{n}\), and \(\mathbf{\omega}_{en}^{n}\), respectively. The accelerometer error and gyroscope error are the main factors affecting the accuracy of GNSS/INS tightly coupled system, and the bias errors are modeled by a random walk process. Their specific forms can be expressed as:  
\[ \begin{cases}\dot{\mathbf{b}}_{a}=w_{ba}\\ \dot{\mathbf{b}}_{g}=w_{bg}\end{cases}  \tag{10}\]  
where \(\mathbf{b}_{a}\) is bias of the accelerometer; \(\mathbf{b}_{g}\) is the bias of the gyroscope; \(w_{ba}\) and \(w_{bg}\) express the corresponding random white noise. The equation of the state of the system is as follows:  
\[\dot{\mathbf{X}}_{ins}=\mathbf{F}\cdot\mathbf{X}_{ins}+\mathbf{G}\cdot\mathbf{W} \tag{11}\]  
where \(\mathbf{F}\) is the state transition matrix; \(\mathbf{G}\) and \(\mathbf{W}\) represent the dynamic noise matrix and the noise vector; \(\mathbf{X}_{ins}\) is the state parameter, \(\mathbf{X}_{ins}\)\(=(\delta r,\delta v,\delta\mathbf{\psi},\mathbf{bg},ba)_{15\times 1}\). Based on the INS error model, \(\mathbf{G}\) and \(\mathbf{W}\) are optimized and presented as follows:  
\[\mathbf{F}= \begin{bmatrix}F_{rr}&F_{rv}&\mathbf{0}&\mathbf{0}&\mathbf{0}\\ F_{vr}&F_{rv}&f^{*}\times&\mathbf{0}&\mathbf{C}^{n}_{b}\\ F_{qr}&F_{r\psi}&-\left(\omega^{n}_{ic}+\omega^{n}_{en}\right)\times&-C^{n}_{ b}&\mathbf{0}\\ \mathbf{0}&\mathbf{0}&\mathbf{0}&\mathbf{0}&\mathbf{0}\\ \mathbf{0}&\mathbf{0}&\mathbf{0}&\mathbf{0}&\mathbf{0}\end{bmatrix} ,\mathbf{G}= \begin{bmatrix}\mathbf{0}& \mathbf{0}&\mathbf{0}&\mathbf{0}\\ \mathbf{0}&\mathbf{C}^{n}_{b}&\mathbf{0}&\mathbf{0}&\mathbf{0}\\ -C^{n}_{b}&\mathbf{0}&\mathbf{0}&\mathbf{0}&\mathbf{0}\\ \mathbf{0}&\mathbf{0}&\mathbf{0}&\mathbf{0}&\mathbf{1}\\ \end{bmatrix}  \tag{12}\]  
where \(\mathbf{I}\) indicates the unit matrix; \(F_{rr}\) and \(F_{rv}\) represent state coefficients of position; \(\mathbf{F}_{vr}\) and \(F_{rv}\) represent coefficients of velocity; \(\mathbf{F}_{\psi r}\) and \(\mathbf{F}_{r\psi}\) represent coefficients of attitude. The specific derivation of the above symbols can be found in [33].