Clock Error Modeling Based On The Theory Of Semi-parametric Regression Model

The semi-parametric model of a statistical model is developed in the eighties of the lastcentury, it introduces a non-parametric component, provides a new method to estimate the modelerror; but it also contains the parameters component, taking into account the parameters of themodel and non-parametric model has the advantage. Theory of semi-parametric regression modelapplied to the modeling and prediction of the atomic clock of great significance. National timeservice center (National Time Service Center, NTSC) is responsible to establish and maintain ourcountry’s standard time UTC (NTSC), and independent of the atom when the TA (NTSC), keepthe clock standard time-frequency signals to produce and maintain the basis. The establishmentof the semi-parametric clock model prediction clock difference helps to improve the accuracy ofthe modeling, thus improving the precision and stability of time scales. At the same time, reliableatomic clock operating parameters and the accurate prediction of clock error is the basis ofsatellite navigation and positioning to achieve high-precision real-time navigation.After the stability of time reference system, the analysis and processing of various types oftime and frequency data on the work is one of the most important elements of punctuality. Usingall kinds of mathematical and statistical in analyzing and processing scientific data of frequencyand time, and developing analytical methods applied to comprehensive measurement of theatomic clock data are all have great significance to the maintenance of a stable time scale.The basic theories and methods from the semi-parametric model, this paper studied thecharacteristics of the application of the semi-parametric model, discussed semi-parametric naturefrom the perspective of data smoothing, and discussed the semi-parameter theory for the clockerror modeling and prediction of clock errorsrelated issues. The main contents include:(1) Discussed the theory and methods of estimation of the semi-parametric regressionmodel, analyzed the penalized least squares method for solving features, studied on the methodsof determing regular matrix R and the smoothing factor α, gotten some key features ofsemi-parametric applications from using a simulation example.(2) From the point of data smoothing, analyzed the nature of the semi-parametricregression model. Pointed out that the method based on the natural-like strip is use to determinethe matrix R and gotten the parameter estimates in the penalized least squares method. In fact,it’s the promotion of the natural spline smoothed data. Also pointed out that the data processingof Vondrak smoothing method is the observed values of the unknown function which usedpiecewise linear interpolation smoothing, that the essence of Vondrak data smoothing is based onthe non-parametric piecewise linear interpolation fitting. Binding data fit the actual, first proposed the concept of the Vondrak cluster smooth data. This is a summary of the Vondrak filterconcept and promotion.(3) Clock error modeling and prediction methods. This paper systematically summarizedseveral common clock error prediction models, including polynomial, gray model, regressionand Kalman filtering model. Comparatived and analyzed the characteristics of the respectiveforecast, focused on the Kalman filtering method, in particular, article focused discussion on theKalman method. Based on semi-parametric theory applied to the clock error modeling andprediction, discussed the three different theoretical modeling and prediction of the specificapplication of semi-parametric methods. Semi-parametric model can weaken the system error,when clock error in the complex system errors, the accuracy of the modeling and forecasting willbe better improved of using semi-parametric.Finally, briefly summarizes the work done and the next job prospect.