Research of Wiener Filtering and Pre-estimation Theory By Observed Roadway Flows Including Stochastic Disturbance Factors

摘要

In this paper, a new filtering and pre-estimation idea based on observed roadway flows is proposed for mathematical analysis of deviation of observed quantity and true value of observed roadway flows. According to true characters of statistical distribution of roadway flows, the fundamental assumption is established. By theoretical calculation a mathematical model of Gauss-Markov characteristic distribution of traffic flows is established for describing roadway flows. With consideration on synthetic action of all random disturbance factors, the data of roadway flows are amended by normal stochastic process of white noise in analytic demonstration. Based on established mathematical model the research and analysis of related functions and power spectral density of each item of the model expression are conducted according to estimated theory. Using Wiener's theory, the analysis of power spectral density of continuous stationary stochastic process including stochastic items of roadway flows and comprehensive disturbance is conducted. To yield the optimization characteristics of minimum error of linear mean square, according to the different selected parameters, the profound research is conducted. Optimum prediction and optimum filtering analysis based on the different parameters using in Wiener-hopf equation is provided. Linear time invariant system is designed according to different case separately. The result and the process of theoretic analysis show that the conducted research of Wiener filtering and pre-estimation theory using observed roadway flows including stochastic disturbance factor is capable of reflecting the true data of roadway traffic flows, it has important values of theoretic study and practical application. Then the merits and demerits of the theoretic deduce is discussed, some research to be taken in the future is proposed.