Multidimensional Gross Error Separability Analysis in CPⅢ Network Considering Observation Space Information

The CPⅢ network of high-speed railways is a resection surveying network with free station observation and automatic observation, enabling simultaneous edge and angle measurements. The separability of gross errors between observations is not only related to the design space of the control network but also affected by observation space factors such as automatic observation of the total station. Therefore, the gross error judgment equation (GEJE) was used to obtain the design space correlation of the separability of multidimensional gross errors of observations in the CPⅢ network. By considering the characteristics of automatic observation of total station during data acquisition in the CPⅢ network, the temporal correlation of observations was introduced. The reliability relationship between observations was extended from the traditional consideration of design space effects to the comprehensive evaluation of both design space and observation space effects. The law of multidimensional gross error separability in accordance with the actual measurement of the CPⅢ network was obtained. Then, the Monte Carlo method was used to demonstrate the correctness of the separability of multidimensional gross errors in the CPⅢ network considering the observation space information. The results show that the reliability of CPⅢ observations will be affected by the observation space, which should be considered in the practice of gross error detection. The observations of each edge in the CPⅢ network have gross error detectability and identifiability. At most two gross errors in one edge can be detected and located in the three edges of the same target. If there is no error in the observation station, at most 2⌊n/2⌋ gross errors in ⌊n/2⌋ edges can be detected and located among n edges of one observation station observing n targets.