## 3 Method for Improving the Pointing Error
### Systematic Errors Model  
Due to the influence of machining, installation, and other factors, the telescope contains systematic errors. The error sources include the non-verticality of the horizontal and vertical axes, non-orthogonality of the visual and horizontal axes, and bending of the mirror tube and displacement of the optical axis. For ground telescopes, the research on absolute pointing accuracy correction method is relatively mature [29; 30]. But at present there is no good method to complete the high precision systematic error calibration on the mobile platform.  
We take the installation error model and systematic error model into consideration, and get the following expression, as shown in Equation (11):  
\[\left\{\begin{array}{l}\Delta\mathrm{A_{c_{i}}}=\hat{\mathrm{A_{c_{i}}}}- \mathrm{A_{c_{i}}}=f(\mathrm{A_{c_{i}}},\mathrm{E_{c_{i}}})+\varepsilon_{i}, \mathrm{i}=1,2\ldots,\mathrm{n}\\ \Delta\mathrm{E_{c_{i}}}=\hat{\mathrm{E_{c_{i}}}}-\mathrm{E_{c_{i}}}=g( \mathrm{A_{c_{i}}},\mathrm{E_{c_{i}}})+\tau_{i},\mathrm{i}=1,2\ldots,\mathrm{ n}\end{array}\right. \tag{11}\]  
where, \(\left(\hat{\mathrm{A_{c_{i}}}},\hat{\mathrm{E_{c_{i}}}}\right)\) can be obtained from the equation \(\hat{\Lambda}=\hat{\Psi}t*\xi t*\Lambda\), \(\left(\Delta\mathrm{A_{c_{i}}},\Delta\mathrm{E_{c_{i}}}\right)\) are the observation error; \(f(\mathrm{A_{c_{i}}},\mathrm{E_{c_{i}}})\) and \(g(\mathrm{A_{c_{i}}},\mathrm{E_{c_{i}}})\) represent the approximate functions with the pointing angles \(\left(\mathrm{A_{c_{i}}},\mathrm{E_{c_{i}}}\right)\) as unknowns, that is, the systematic error correction model; \(\varepsilon_{i}\) and \(\tau_{i}\) are residual errors.  
According to Figure 2, the zero position of the azimuth encoder is no longer aligned with due North, but with the zero position of the fore-and-aft line. Therefore, we consider the deck coordinate system as the reference when designing the error model.  
The expression for the mount model [31] is shown in Equation (12):  
\[\left\{\begin{array}{l}\Delta\mathrm{A}_{\mathrm{c_{i}}}=f(\mathrm{A}_{ \mathrm{c_{i}}},\mathrm{E}_{\mathrm{c_{i}}})+\varepsilon_{i}=\sum_{j=1}^{m} \mathrm{d}_{j}\mathrm{Y}_{j}(\mathrm{A}_{\mathrm{c_{i}}},\mathrm{E}_{\mathrm{c_ {i}}})+\varepsilon_{i},\mathrm{i}=1,2\ldots,\mathrm{n}\\ \Delta\mathrm{E}_{\mathrm{c_{i}}}=g(\mathrm{A}_{\mathrm{c_{i}}},\mathrm{E}_{ \mathrm{c_{i}}})+\tau_{i}=\sum_{j=1}^{m}\mathrm{d}_{j}\mathrm{I}_{j}(\mathrm{ A}_{\mathrm{c_{i}}},\mathrm{E}_{\mathrm{c_{i}}})+\tau_{i},\mathrm{i}=1,2\ldots, \mathrm{n}\end{array}\right. \tag{12}\]  
where \(\mathrm{d}_{j},\mathrm{j}=1,2,\ldots,\mathrm{m}\) are the model coefficients for the m terms; \(\mathrm{Y}_{j}(\mathrm{A}_{\mathrm{c_{i}}},\mathrm{E}_{\mathrm{c_{i}}})\) represents the function in azimuth residual of the azimuth, \(\mathrm{A}_{\mathrm{c_{i}}}\) and elevation \(\mathrm{E}_{\mathrm{c_{i}}}\) of star i, i = 1, 2, \(\ldots,\mathrm{n}\); \(\mathrm{\Gamma}_{j}(\mathrm{A}_{\mathrm{c_{i}}},\mathrm{E}_{\mathrm{c_{i}}})\) represents the function in elevation residual of the azimuth, \(\mathrm{A}_{\mathrm{c_{i}}}\) and elevation \(\mathrm{E}_{\mathrm{c_{i}}}\) of star i, i = 1, 2, \(\ldots,\mathrm{n}\). The ATP mount model is presented in Table 2.