Wiener Mixture Filter And Research On Traffic Flow Forecasting Algorithm

The Wiener filter is a classical linear optimal filter, which is interpreted in another view. We point out that when the joint probability density function (PDF) of the observed signal and desired signal is Gaussian, the Wiener filter is a real optimal filter. However, in many cases, the joint PDF does not satisfy this assumption, thus the Wiener filter is a sub-optimal filter. In this paper, we extend the Wiener filter to a mixing form to deal with more cases. Our basic idea is using a Gaussian Mixture Model (GMM) to approximate the joint PDF. Based on this assumption, we present the formulae of the optimal filter, which is the weighted combination of several individual Wiener filters. The weight of each individual Wiener filter varies according to the input signal. We name our proposed filter as Wiener Mixture Filter (WMF). Since GMM has an ability to approximate to an arbitrary PDF, WMF has a wide application.In real-world applications, the parameters in WMF are usually unknown before hand. Fortunately, it can be learned from the training data. Since all the parameters in WMF can be deduced from the parameters in the GMM, instead of learning WMF's parameters directly, we estimate the parameters in the GMM, which can be solved by the EM algorithm. We prove the WMF's error is no larger than the Wiener filter's. However, the WMF's error doesn't have an analytical solution as the Wiener filter's. We propose the sampling technique to estimate the error. We also give some simulations to show the parameters' impact on the improvement over the Wiener filter.Intelligent Transportation Systems (ITS) is an active research field, in which traffic flow forecasting is an important and difficult problem. We apply our proposed model to traffic flow forecasting to demonstrate how our model works and verify its effectiveness. At the same time. our model also can be seen as a new method for traffic flow forecasting. Besides of WMF, we also propose Switching ARIMA Model to describe traffic flow series. Both of these two algorithms are verified with the data from the UTC/SCOOT system in the Traffic Management Bureau of Beijing. The results show that our proposed methods are feasible and effective.