Filtering Method of Monitoring Levelling Networks

A monitoring levelling network can be described by a linear dynamic system which consists of state equations with a random initial state vector and process noise vectors as well as observation equations: to which the Kalman filtering technique is applied for the estimate of the state vectors.As compared with the conventional dynamic adjustments,this method is more general and effective.A Kalman filter requires an exact knowledge of the process noise covariance matrix D_w and the measurement noise covarance matrix D_e.In a number of practical situations,D_w and D_e are either unknown or known only approximately.Here we consider the case in which the true values of D_w and D_e are unknown but each internal structure is known.The noise sequence W_k and ε_k are assumed to be white.Hence we give an improved approach to optimal filtering which summarizes the system and its statistical models with a few unknown parameters into a variance compoment model of the linear system.According to this model,the optimal estimates of the state vectors and the statistical parameters can be obtained simultaneously.In this paper the MINQUE formula for the variance components of two models both with and without process noise are given.The theoretical analysis shows that this approach is not only an effective adaptive filtering,but also has the functions of limiting model errors and enhancing the stability of filtering,while the Kalmam filtering is only a special case.As an example,a repeated levelling network is analysed.The results show the feasiblity and effectiveness of the approach.