# The Development of the Pipe Jacking Guidance Technology
## 4 Prism Method
### Research Status
#### 4.2.2 \"Two Prisms--Inclinometer\" Scheme  
In the three-prism scheme, the coordinates of the head and tail centers of the pipe jacking machine must be calculated according to the position coordinates of the three prisms. If the distance between the three prisms is too close, it will lead to low data accuracy and poor positioning effect. This is not applicable to small-diameter pipe jacking. In addition, during the pipe jacking process, the internal measuring instruments will move with the pipe jacking machine, and the three prisms are installed in a triangle [16]. This will cause the total station to fail in the process of searching for the prisms, making it difficult to aim at the prisms, and the coordinates of the three prisms need to be measured one after another, which has poor real-time performance. Even if the above problems can be improved by using algorithms to predict the coordinates, the essence of the error caused by the three prisms has not changed. Therefore, in order to overcome the shortcomings of this scheme, the \"two prisms + inclinometer\" scheme is proposed. Compared with the three-prism solution, the \"two prisms + inclinometer\" solution reduces the number of prisms to two and adds a dual-axis inclinometer. The dual-axis inclinometer can be used to directly obtain the pitch angle and roll angle, making up for the problem of insufficient solution parameters caused by the lack of a prism.  
The computational principles underlying the \"two prisms + inclinometer\" method are primarily the spatial geometry method and the rotation matrix method. The spatial geometry method is a process of the coordinate solution. According to the spatial geometric relationship of the pipe jacking machine, the angle information provided by the dual-axis inclinometer is used as the spatial angle parameter, and the coordinates of the head center and the tail center of the pipe jacking machine are solved using the coordinates of the prisms. The rotation matrix method utilizes the real-time output of pitch and roll angles from the dual-axis inclinometer to construct a rotation matrix to describe the attitude and determine the spatial position and attitude information. The method has good real-time performance and meets the requirement of real-time orientation. [PERSON] [17] employed a 3D coordinate transformation model with a 7-parameter model and directly incorporated the inclinometer data as observations in the solution. The researcher constructed a joint leveling method for joint data processing and jointly processed two types of observations from the spatial geometry method and the rotation matrix method to take the redundant observations into account. This methodological improvement enhanced the reliability of the system. This method involves the direct introduction of the data obtained from the inclinometer as the Euler angles corresponding to the rotation matrix [18]. The rotation matrix serves to approximate the biaxial inclination data as equivalent to the Euler angles, accounting for modeling errors. [PERSON] [19] addressed this issue by developing a 13-parameter spatial coordinate transformation model, introducing tiltmeter equivalent observations and constructing a model for leveling computation.