# Vehicle Speed Estimation and Forecasting Methods Based on Cellular Floating Vehicle Data
## 3 Traffic Information Estimation and Forecasting Methods
### Vehicle Speed Forecasting Method  
For vehicle speed prediction, a BPNN algorithm is considered to predict the future vehicle speed in accordance with the current traffic information (_i.e._, the estimated vehicle speeds from CFVD in Section 3.1). An intelligent transportation system, which includes a cellular network signal retriever (CNSR), traffic information estimation methods and a vehicle speed forecasting method, has been designed and implemented for traffic information estimation and prediction (shown in Figure 4). The ITS can retrieve cellular network signals (e.g., NLU, PLU, HO and CA) via the A interface and the IuCS interface and analyze these signals to estimate traffic information (e.g., traffic flow, traffic density and vehicle speed). Then, the estimated vehicle speed can be adopted as input characteristics into the proposed vehicle speed forecasting method to predict short-term vehicle speed for road user decision.  
In this subsection, the average vehicle speed of road segment \(i\) at cycle \(\psi\) is expressed as \(U_{i}^{\psi}\), and the estimated vehicle speed at cycle \(\psi\) in accordance with Equations (9)-(12) can be expressed as \(u_{i,ha}^{\psi}\), \(u_{i,na}^{\psi}\), \(u_{i,hp}^{\psi}\) and \(u_{i,np}^{\psi}\), respectively. This study collects the values of the current traffic information (_i.e._, \(u_{i,ha}^{\psi}\), \(u_{i,na}^{\psi}\), \(u_{i,hp}^{\psi}\) and \(u_{i,np}^{\psi}\)) as the input characteristics of the neurons in the BPNN to predict the future vehicle speed (_i.e._, \(U_{i}^{\psi+1}\)) (see Figure 5). Therefore, the number of neurons in the input layer is four. There is one hidden layer, and the output value of the predicted vehicle speed \(U_{i}^{\psi+1}\)/ can be obtained by BPNN.  
Figure 4: Intelligent transportation system based on the proposed methods.  
In the training stage, the historical datasets of cellular network signals from CNSR and traffic information from VDs are collected and calculated the amount of NLU, PLU, HO and CA events. Then vehicle speed can be estimated in accordance with the estimated traffic flows by using NLU and HO events and the estimated traffic densities by using PLU and CA events to obtain the values of \(u_{i,hu}^{\text{b}}\), \(u_{i,na}^{\text{b}}\), \(u_{i,hp}^{\text{b}}\) and \(u_{i,np}^{\text{b}}\) at cycle \(\psi\). Moreover, the average vehicle speed \(U_{i}^{\text{b}+\ 1}\) of road segment \(i\) at next cycle (\(\psi+1\)) can be collected by VD. The proposed vehicle speed forecasting method based on BPNN adopts \(u_{i,hu}^{\text{b}}\), \(u_{i,pa}^{\text{b}}\), \(u_{i,hp}^{\text{b}}\) and \(u_{i,np}^{\text{b}}\) as input characteristics and \(U_{i}^{\text{b}+1}\) as the output characteristic to train a neural network.  
In the runtime stage, the real-time estimated vehicle speeds can be obtained by the proposed traffic information estimation methods based on using CFVD. Then, the estimated vehicle speeds (\(u_{i,hu}\), \(u_{i,na}\), \(u_{i,hp}\) and \(u_{i,np}\)) of road segment \(i\) can be adopted into the trained neural network in the training stage to forecast the short-term vehicle speed at the next cycle.