Abstract
Nonlinear exponential trend model is linearized into the linear model, then linearized model parameters are regarded as the state vector containing the dynamic noise to erect Kalman filter model based on exponential trend model to predict the deformation of the rock landslide. Deformation observation values of the landslide are regarded as a time series to erect AR(1) model, then model parameters of AR(1) model are regarded as the state vector containing the dynamic noise to erect Kalman filter model based on AR(1) model to predict the deformation of the rock landslide. The deformation of the landslide is regarded as the function of the time, then Taylor series is used to determine the functional relationship between the deformation of the landslide and the time, and Taylor series is spread to erect Kalman filter model based on Taylor series to predict the deformation of the earthy landslide. The deformation of landslides relates to many factors, the rainfall and the temperature influence the deformation of landslides specially, thus Kalman filter model based on multiple factors is erect to predict the deformation of the earthy landslide on the basis of Taylor series. Numerical examples show that the fitting errors and the forecast errors of the four Kalman filter models are little.
Highlights
The landslide is a common natural disaster, and the disaster caused by the landslide harms the production and the life of people, and greatly destroys the natural resource and the natural environment[1,2,3]
This paper establishes four Kalman filter models, i.e. Kalman filter model based on exponential trend model, Kalman filter model based on AR(1) model, Kalman filter model based on the time factor and Taylor series, Kalman filter model based on multiple factors and Taylor series, and these models are used to forecast the deformation of some landslides
The example of the calculation about Kalman filter model based on exponential trend model
Summary
The landslide is a common natural disaster, and the disaster caused by the landslide harms the production and the life of people, and greatly destroys the natural resource and the natural environment[1,2,3]. The filter means that the best estimator is obtained by means of processing observation data containing errors. Our aim is to obtain the estimated value of the unknown parameter by means of the observation value containing errors. Kalman filter equations are obtained by means of the maximum posterior estimation or the minimum variance estimation, and it uses the previous eatimated value or the recent observation value to estimate the current value. Kalman filter estimates the new state estimator on the basis of the state estimator and the observation value at the current time, and can process massive repeated observation data www.nature.com/scientificreports quikly, and can combine the parameter estimation with the forecast[39], it is used widely in many applications, such as navigation, target trcking, control and data processing[39,40,41,42,43]. Numerical examples show that the fitting effect and forecast effect of these models are good
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