| Popis: |
The gross errors reflected in the corresponding closure errors of conditional equations obtained by L1-norm estimation are more significant than those in LS residuals, and thereby, the former estimation is helpful for the gross error detection and location. Unfortunately, there is a kind of observations which have the ability to detect and locate gross errors, no matter how large the gross error is, but it cannot be accurately located in L1-norm estimation. For convenience of discussion, such observation is called as Robustness Failpoint in L1-norm estimation, RFP-L1 for short. Obviously, only to meet such a premise, the results of gross error detection based on L1-norm estimation can be accurate and reliable, i.e., it is ensured that there is no RFP-L1 in the surveying system, or whether the RFP-L1 contains gross error can be judged accurately. And in this process, the accurate identification of RFP-L1 is the basis for solving the problem. From conditional equation, the calculation formula of influence coefficient which reflect the extent of the influence of gross error on corresponding closure errors of conditional equations is derived, and the distinguish relation of judging whether an observation is RFP-L1 or not according to the value of least influence coefficient is formulated. Furthermore, the numerical characteristic of design matrix that might contain RFP-L1 is explored. And at the end, a method of identifying RFP-L1 is put forward. The simulation results show that the least influence coefficient reflects the influence of gross errors on the objective function of L1-norm estimation, and the least influence coefficient of normal observation and RFP-L1 have a significant regularity equal to one and less than one respectively. In addition, it can be concluded that there is no RFP-L1 in the surveying system with design matrix containing only±1 and 0. |
