## 1 Introduction  
A radio telescope is a scientific instrumentation for observing the electromagnetic signals from the universe. As shown in Figure 1, most large-aperture radio telescopes, though not all, choose an alidade-supported antenna, which consists of an alidade, a reflector, an azimuth axis, an elevation axis, wheels on the track, and other components. By driving azimuth and elevation mechanisms to rotate around the azimuth axis and the elevation axis separately, the antenna reflector can be pointed at the astronomical  
Figure 1: The components of a radio telescope. source to be observed. If there is a deviation between the commanded position of the antenna and the actual position of the astronomical source, then the radio telescope has an antenna pointing error, as shown in Figure 2. Pointing error has two components: elevation error and azimuth error (or cross-elevation error). In order to ensure the sensitivity and resolution of radio telescopes, it is desirable that the antenna pointing error should not exceed \(1/10\) of the beam width (half power beam width, HPBW) [1], which brings strict requirements for radio signal observation above the centimeter wavelength band. For example, when operating at 100 GHz, a pointing accuracy of \(1^{\prime\prime}\) is reasonable. From the perspective of antenna components, a major source of pointing errors is the antenna alidade [2; 3; 4]. The alidade is the foundation of the antenna, an important part of the antenna azimuth and elevation motion mechanism since it plays a significant role in ensuring perfect orthogonality between the azimuth axis and the elevation axis of the antenna. The pointing errors caused by the alidade are mainly caused by two reasons: one is the real-time change in the environmental load, such as temperature gradients [5; 6; 7; 8], and the other is by the track unevenness [9; 10; 11]. When there are temperature gradients on the alidade due to solar irradiation, or unevenness on the track, the alidade will deform and tilt, resulting in non-orthogonality of the axis system, and further pointing error. Some experimental and simulation studies prove the pointing error caused by solar radiation and orbital unevenness account for a large part of the antenna's overall pointing error. One way to obtain the overall pointing errors of a radio telescope is to use astronomical measurement [12; 13; 14], such as the cross-scan method which measures the deviation between the center of the signal peak and the antenna instruction position by scanning the radio source in two orthogonal directions and performing a multi-point Gaussian fitting. However, performing an astronomical measurement needs to suspend the scheduled astronomical observation and arrange a specific period of time, which brings a loss of effective observing time. Moreover, astronomical measurement is sensitive, which makes the measurement results of one period not instructive for observation in other periods when the external environmental conditions change. For the above two reasons, it is impossible to achieve real-time pointing error measurement without interrupting planned observation using astronomical methods. Therefore, it is necessary to explore a pointing error measurement method that can be carried out under all weather conditions and parallel to scheduled astronomical observations. The biaxial inclinometer is a high-precision inclination sensor that simultaneously measures the small inclinations of its x- and y-axis. The horizontal plane of an inclinometer is a fluid surface that remains horizontal irrespective of the inclination of the sensor so that the angle of inclination corresponds to the angle between the surface of the fluid and the base of the sensor. Some commercial inclinometers can reach a resolution of 0.001 mrad, or 0.2 arcseconds [15]. The ability of an inclinometer to measure small inclinations makes it suitable for tilt measurement of antenna alidade, by which the pointing error resulting from the tilt of the alidade can be inferred.