Improved Data-driven Time-frequency Analysis And Its Application

The theory and application of adaptive time-frequency analysis methods hasbecome very important nowadays. In this thesis, we design a method that initial valuecan be generated automatically in the data-driven time-frequency analysis (DDTFA),and based on the improved method we study the characteristics of white Gaussian noiseand the problem of pseudo range fluctuation in Beidou navigation system. The work ofthe thesis can be summarized as the following three aspects:Firstly, we take the research on adaptive time-frequency analysis methods. In orderto improve the inconvenience of setting initial value in every step of DDTFA, we designa method that initial value can be generated automatically in DDTFA, which provides agreat convenience for a large quantities of decomposition with DDTFA.Secondly, we study the characteristics of white Gaussian noise using DDTFA andestablish a method of assigning statistical significance of information content for IMFcomponents from any noisy data. First we deduce that the product of the energy densityof IMF and its corresponding averaged period is a constant, and that the energy-densityfunction is chi-squared distributed. Furthermore, we derive the energy-density spreadfunction of the IMF components. Through these results, we establish a method ofassigning statistical significance of information content for IMF components from anynoisy data, which has vast importance to practical problems. Finally we compare theresults derived by DDTFA with that by EMD.At last the problem of pseudo range fluctuation in Beidou navigation system isconsidered. We first introduce pseudo range positioning principle and pseudo rangefluctuation, then describe the data in our experiment and process and analyze the data.We decompose the data into IMFs and test the statistical significance of these IMFsusing the method in Chapter4. Furthermore we calculate the averaged period, theaveraged amplitude and the correlation coefficient of these IMFs. Through thesesystematical process and analysis, we have found the slowly varying components andthe fast varying components in the data. Preliminary analysis to them was also presentedin this thesis, which is helpful in investigating the cause of the fluctuation and finding away to eliminate or suppress the fluctuation.