New reliability measure for dynamic surveying systems and its applications in dynamic system quality control

The important difference between a static surveying system (SSS) and a dynamic surveying system (DSS) is the inclusion of the state equations, besides the observation equations, in DSS models. The state equations reflect the operating characteristics of a DSS. Therefore, the reliability measures of a DSS should ideally be able to describe the ability of the system for the detection and identification of blunders (gross errors) in both of the state and the observation models. In this paper, the redundancy numbers and their distribution in DSS are employed as the reliability measures of DSS models. It is proved through both theoretical derivations and numerical examples, (1) that both the observations and the predicted state parameters contribute to the redundancy, hence to the reliability of a DSS; (2) that the amount of the redundancy contribution depends on many factors, including the state transition matrix, the number of state parameters, the state noise, the observation matrix, the number and type of observations, the observation noise and the data sampling rate; and (3) that the sum of the redundancy numbers of a DSS equals the number of observations in a DSS. The concept of internal and external reliability is also extended from SSS to DSS.