The Mathematic Models of the Kalman Filtering for Across-Fault Measurement

This paper makes a probe into the application of the Kalman filtering method to the data processing of across-fault measurements.On the basis of statistical regression,the mathematic and stochastic models of filtration are established by combining the regression method with Kalman filtering.In the filtering computation,not only the randomness of fault movements but also the time-dependent variation of environmental effects have been taken into consideration.By use of the adaptive filtering method,an estimation of the dynamic noise variance matrix is obtained through iteration.Models for one measuring line(leveling line or baseline),two measuring lines(both leveling lines or both baselines)and four measuring lines(two leveling lines and two baselines)are derived and established systematically.By means of these models,the data of across-fault measurements can be processed dynamically in real-time to provide the filtered values of height difference between benchmarks or baseline length at different time in