# Vehicle Speed Estimation and Forecasting Methods Based on Cellular Floating Vehicle Data

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## Abstract

**:**

## 1. Introduction

## 2. Literature Review

#### 2.1. Cellular Networks

#### 2.1.1. System Components

#### 2.1.2. Mobility Management

#### Idle Mode

- (1)
- Normal location updating: NLU is performed when a new location area is entered (European Telecommunications Standards Institute (ETSI), 1995).
- (2)
- Periodic location updating: PLU is performed at the expiration of the timer (ETSI, 1995).
- (3)
- International Mobile Subscriber Identity (IMSI) attach: IMSI attach is performed when the MS is turned on [16].

#### Radio Resource Connected Mode

#### 2.2. Traffic Information Estimation Methods

#### 2.2.1. Location Services

#### 2.2.2. Signal Statistics

#### 2.2.3. Summary

#### 2.3. Traffic Information Forecasting Methods

## 3. Traffic Information Estimation and Forecasting Methods

#### 3.1. Traffic Information Estimation Methods

**Table 1.**The definition of notation. PLU, periodic location update; HO, handover; CA, all arrival; NLU, normal location update.

Parameter | Description |
---|---|

Q (car/h) | The practical traffic flow |

K (car/km) | The practical traffic density |

U (km/h) | The practical vehicle speed |

τ (h/call) | The call inter-arrival time |

λ (call/h) | The call arrival rate |

t (h/call) | The call holding time |

1/μ (h/call) | The mean call holding time |

x (km) | The time x is between the preceding call arrival and entering the target road |

l_{i} (km) | The length of road segment covered by Cell_{i} |

b (h) | The cycle time of PLU |

${h}_{i}$ (event/h) | The amount of HOs of road segment covered by Cell_{i} |

${a}_{i}$ (event/h) | The amount of CAs of road segment covered by Cell_{i} |

${p}_{i}$ (event/h) | The amount of PLUs of road segment covered by Cell_{i} |

${q}_{i,h}$ (car/h) | The estimated traffic flow by using ${h}_{i}$ |

${q}_{i,n}$ (car/h) | The estimated traffic flow by using NLU events |

${k}_{i,a}$ (car/km) | The estimated traffic density by using ${a}_{i}$ |

${k}_{i,p}$ (car/km) | The estimated traffic density by using ${p}_{i}$ |

${u}_{i,ha}$ (km/h) | The estimated vehicle speed by using ${q}_{i,h}$ and ${k}_{i,a}$ |

${u}_{i,na}$ (km/h) | The estimated vehicle speed by using ${q}_{i,n}$ and ${k}_{i,a}$ |

${u}_{i,hp}$ (km/h) | The estimated vehicle speed by using ${q}_{i,h}$ and ${k}_{i,p}$ |

${u}_{i,np}$ (km/h) | The estimated vehicle speed by using ${q}_{i,n}$ and ${k}_{i,p}$ |

${U}_{i}^{\mathsf{\psi}}$ (km/h) | The practical vehicle speed of road segment i at cycle $\mathsf{\psi}$ |

${U}_{i}^{\mathsf{\psi}+1}$ (km/h) | The practical vehicle speed of road segment i at cycle $\left(\mathsf{\psi}+1\right)$ |

${U}_{i}^{\mathsf{\psi}+1}\text{'}$ (km/h) | The predicted vehicle speed of road segment i at cycle $\left(\mathsf{\psi}+1\right)$ |

${u}_{i,ha}^{\mathsf{\psi}}$ (km/h) | The estimated vehicle speed of ${u}_{i,ha}$ at cycle $\mathsf{\psi}$ |

${u}_{i,na}^{\mathsf{\psi}}$ (km/h) | The estimated vehicle speed of ${u}_{i,na}$ at cycle $\mathsf{\psi}$ |

${u}_{i,hp}^{\mathsf{\psi}}$ (km/h) | The estimated vehicle speed of ${u}_{i,hp}$ at cycle $\mathsf{\psi}$ |

${u}_{i,np}^{\mathsf{\psi}}$ (km/h) | The estimated vehicle speed of ${u}_{i,np}$ at cycle $\mathsf{\psi}$ |

#### 3.1.1. Traffic Flow Estimation

_{i}) and the amount of NLUs (q

_{i,n}) to estimate traffic flow (Q

_{i}) on the road segment covered by Cell

_{i}.

#### Traffic Flow Estimation by Using HO Events

_{i}. The MS in a car performs the call set-up at time t

_{0}(in Figure 1a,b); then, the MS goes into the handover area of the coverage of Cell

_{i−1}and Cell

_{i}at time t

_{1}(in Figure 1a,b), and the base station controller (BSC) or radio network controller (RNC) will allocate an available channel for the communicating MS. At this moment, if Cell

_{i}has a free channel, the connection between the MS and Cell

_{i}will be established successfully. The process is called a handover from Cell

_{i−1}to Cell

_{i}.

**Figure 1.**(

**a**) The scenario diagram for vehicle movement and the handover on the road; (

**b**) the timing diagram for the handover on the road segment covered by Celli. BSC, base station controller; RNC, radio network controller.

_{i}, and the traffic flow is Q

_{i}. Furthermore, the length of road segment covered by Celli is l

_{i}. Let the variable x be the time difference between t

_{0}and t

_{1}, and l

_{i}/U

_{i}denotes the time difference between t

_{1}and t

_{2}. The handover procedure will be performed when the call holding time (t) is larger than x. Thereby, the amount of handover (h

_{i}) on the road segment covered by Cell

_{i}can be expressed as Equation (2), and this study can estimate traffic flow (${q}_{i,h}$) by using Equation (3), which is the traffic flow multiplied by the number of HO events.

#### Traffic Flow Estimation by Using NLU Events

_{i}is ${Q}_{i}$ and one MS is in each car (shown in Figure 2) [24]. Therefore, the estimated traffic flow ${q}_{i,n}$ (i.e., the number of NLU events) on the road segment covered by Cell

_{i}can be calculated as Equation (4), which is the traffic flow multiplied by the number of NLU events.

#### 3.1.2. Traffic Density Estimation

_{i}) and the amount of periodic location updates (PLUs) (p

_{i}) to estimate traffic density (K

_{i}) on the road segment covered by Cell

_{i}.

#### Traffic Density Estimation by Using CA events

_{i}. The MS in a car moving along the road performs the first call at time t

_{0}(in Figure 3a,b) and enters the coverage area of Cell

_{i}at time t

_{1}(in Figure 3a,b). The MS performs another call at time t

_{2}(in Figure 3a,b) before leaving Cell

_{i}(time t

_{3}in Figure 3a,b), and the call performed by the MS is called a call arrival in Cell

_{i}.

**Figure 3.**(

**a**) The scenario diagram for vehicle movement and call arrivals on the road; (

**b**) the timing diagram for call arrivals on the road segment covered by Celli.

_{i}, and the average speed of cars is U

_{i}. Therefore, l

_{i}/U

_{i}denotes the time difference between t

_{1}and t

_{3}. This study analyzes the amount of call arrivals (a

_{i}) that occur between t

_{1}and t

_{3}on the road segment covered by Cell

_{i}. The amount of call arrivals can be expressed as Equation (5), and Equation (6) indicates that this study can derive estimated traffic density (${k}_{i,a}$) from the amount of call arrivals.

#### Traffic Density Estimation by Using PLU Events

_{i}according to the number of PLU events. This model had been proven in [24,38], and this study summarizes the assumptions in this model as follows.

- •
- The actual vehicle density ${K}_{i}$ and traffic speed ${U}_{i}$ can be obtained from VD on the road. Furthermore, the length of a road segment covered by the cell is $l$.
- •
- The call arrival rate to a cell is $\mathsf{\lambda}$, and the call arrival process is assumed to be a Poisson process.
- •
- The cycle time of PLU is $b$, and the number of PLU events is ${p}_{i}$.

#### 3.1.3. Vehicle Speed Estimation

_{i,h}), the estimated traffic flow by using NLU events (q

_{i,n}), the estimated traffic density by using CA events (k

_{i,a}) and the estimated traffic density by using PLU events (k

_{i,p}). Based on Section 3.1.1 and Section 3.1.2, the estimated vehicle speeds ${u}_{i,ha}$, ${u}_{i,na}$, ${u}_{i,hp}$ and ${u}_{i,np}$ can be expressed as Equations (9)–(12). For instance, the estimated vehicle speed ${u}_{i,ha}$ can be obtained by using q

_{i,h}and k

_{i,a}; the estimated vehicle speed ${u}_{i,na}$ can be obtained by using q

_{i,n}and k

_{i,a}; the estimated vehicle speed ${u}_{i,hp}$ can be obtained by using q

_{i,h}and k

_{i,p}; the estimated vehicle speed ${u}_{i,np}$ can be obtained by using q

_{i,n}and k

_{i,p}.

#### 3.2. Vehicle Speed Forecasting Method

## 4. Experimental Results and Analyses

#### 4.1. Experimental Environments

**Figure 7.**The distribution of cells, location areas and vehicle detectors (VDs) in the simulation experiments.

#### 4.2. The Evaluation of Traffic Information Estimation Methods

#### 4.2.1. The Evaluation of Traffic Flow Estimation

_{i}are collected as CFVD to generate ${q}_{i,h}$ and ${q}_{i,n}$. NLU is only performed with MS entering new LA, so the estimated traffic flows are consistence in the same LA in the proposed approach. For instance, the amount of HOs in Cell

_{1}(${h}_{1}$) was 126 at 8 a.m. and 9 a.m., so the traffic flow of the first road segment (${q}_{1,h}$) could be estimated as 7560 car/h by utilizing Equation (3) and MS communication behaviors (e.g., the expected value ($1/\mathsf{\mu}$) of call holding time is 1 min/call). Furthermore, because 6672 NLUs in Cell

_{1}were performed at 8 a.m. and 9 a.m., the traffic flow of the first road segment (${q}_{1,n}$) could be estimated as 6672 car/h according to Equation (4). This study calculated the accuracies of traffic flow estimation as $1-\frac{\left|{Q}_{i}-{q}_{i,h}\right|}{{Q}_{i}}$ and $1-\frac{\left|{Q}_{i}-{q}_{i,n}\right|}{{Q}_{i}}$. Table 2 shows that the average accuracies of traffic flow estimation of the first road segment between 8 a.m. and 22 p.m. are 89% for the amount of HOs and 100% for the amount of NLUs. As shown in Table 3, the comparison of the traffic flow estimation comparisons between ${q}_{1,h}$ and ${q}_{i,n}$ indicates that the amount of NLUs is more suitable for traffic flow estimation than the amount of HOs.

Time | Q_{1} | The Amount of HOs | The Amount of NLUs | ${\mathit{q}}_{\mathbf{1}\mathbf{,}\mathit{h}}$ | ${\mathit{q}}_{\mathbf{1}\mathbf{,}\mathit{n}}$ | $\mathbf{1}\mathbf{-}\frac{\mathbf{\left|}{\mathit{Q}}_{\mathbf{1}}\mathbf{-}{\mathit{q}}_{\mathbf{1}\mathbf{,}\mathit{h}}\mathbf{\right|}}{{\mathit{Q}}_{\mathbf{1}}}$ | $\mathbf{1}\mathbf{-}\frac{\mathbf{\left|}{\mathit{Q}}_{\mathbf{1}}\mathbf{-}{\mathit{q}}_{\mathbf{1}\mathbf{,}\mathit{n}}\mathbf{\right|}}{{\mathit{Q}}_{\mathbf{1}}}$ |
---|---|---|---|---|---|---|---|

8 | 6672 | 126 | 6672 | 7560 | 6672 | 87% | 100% |

9 | 6200 | 112 | 6200 | 6720 | 6200 | 92% | 100% |

10 | 5435 | 92 | 5435 | 5520 | 5435 | 98% | 100% |

11 | 5663 | 80 | 5663 | 4800 | 5663 | 85% | 100% |

12 | 5532 | 90 | 5532 | 5400 | 5532 | 98% | 100% |

13 | 5265 | 90 | 5265 | 5400 | 5265 | 97% | 100% |

14 | 5546 | 90 | 5546 | 5400 | 5546 | 97% | 100% |

15 | 6368 | 88 | 6368 | 5280 | 6368 | 83% | 100% |

16 | 5762 | 78 | 5762 | 4680 | 5762 | 81% | 100% |

17 | 6101 | 124 | 6101 | 7440 | 6101 | 78% | 100% |

18 | 6122 | 104 | 6122 | 6240 | 6122 | 98% | 100% |

19 | 5378 | 74 | 5378 | 4440 | 5378 | 83% | 100% |

20 | 4667 | 72 | 4667 | 4320 | 4667 | 93% | 100% |

21 | 4625 | 64 | 4625 | 3840 | 4625 | 83% | 100% |

22 | 4312 | 60 | 4312 | 3600 | 4312 | 83% | 100% |

Mean | 89% | 100% |

Cell | $\mathbf{1}\mathbf{-}\frac{\mathbf{\left|}{\mathit{Q}}_{\mathit{i}}\mathbf{-}{\mathit{q}}_{\mathit{i}\mathbf{,}\mathit{h}}\mathbf{\right|}}{{\mathit{Q}}_{\mathit{i}}}$ | $\mathbf{1}\mathbf{-}\frac{\mathbf{\left|}{\mathit{Q}}_{\mathit{i}}\mathbf{-}{\mathit{q}}_{\mathit{i}\mathbf{,}\mathit{n}}\mathbf{\right|}}{{\mathit{Q}}_{\mathit{i}}}$ |
---|---|---|

Cell_{1} | 89% | 100% |

Cell_{2} | 76% | 100% |

Cell_{3} | 77% | 100% |

Cell_{4} | 78% | 100% |

Cell_{5} | 70% | 100% |

Cell_{6} | 67% | 99% |

Cell_{7} | 68% | 100% |

Cell_{8} | 70% | 100% |

Cell_{9} | 72% | 100% |

Mean | 74% | 100% |

#### 4.2.2. The Evaluation of Traffic Density Estimation

_{i}are collected as CFVD to generate ${k}_{i,a}$ and ${k}_{i,p}$. For instance, the amount of CAs in Cell

_{1}(${a}_{1}$) was 97 at 8 a.m., so the traffic density of the first road segment (${k}_{1,a}$) could be estimated as 97 car/km by Equation (6) and MS communication behaviors (e.g., the expected value ($1/\mathsf{\lambda}$) of the call inter-arrival time is 1 h/call). Furthermore, because 126 PLUs were performed in Cell

_{1}at 8 a.m., the traffic density of the first road segment (${k}_{1,p}$) could be estimated as 128 car/h in accordance with Equation (8) and MS communication behaviors (e.g., call inter-arrival time). This study calculated the accuracies of traffic density estimation as $1-\frac{\left|{K}_{i}-{k}_{i,a}\right|}{{K}_{i}}$ and $1-\frac{\left|{K}_{i}-{k}_{i,p}\right|}{{K}_{i}}$. Table 4 shows that the average accuracies of traffic density estimation of the first road segment between 8 a.m. and 22 p.m. are 91% for the amount of CAs and 81% for the amount of PLUs. As shown in Table 5, the results of the traffic density estimation between ${k}_{i,a}$ and ${k}_{i,p}$ indicate that the amount of CAs is more suitable for traffic density estimation than the amount of PLUs.

Time | K_{1} | The Amount of CAs | The Amount of PLUs | ${\mathit{k}}_{\mathbf{1}\mathbf{,}\mathit{a}}$ | ${\mathit{k}}_{\mathbf{1}\mathbf{,}\mathit{p}}$ | $\mathbf{1}\mathbf{-}\frac{\mathbf{\left|}{\mathit{K}}_{\mathbf{1}}\mathbf{-}{\mathit{k}}_{\mathbf{1}\mathbf{,}\mathit{a}}\mathbf{\right|}}{{\mathit{K}}_{\mathbf{1}}}$ | $\mathbf{1}\mathbf{-}\frac{\mathbf{\left|}{\mathit{K}}_{\mathbf{1}}\mathbf{-}{\mathit{k}}_{\mathbf{1}\mathbf{,}\mathit{p}}\mathbf{\right|}}{{\mathit{K}}_{\mathbf{1}}}$ |
---|---|---|---|---|---|---|---|

8 | 97 | 97 | 126 | 97 | 128 | 99% | 67% |

9 | 88 | 86 | 112 | 86 | 103 | 97% | 83% |

10 | 77 | 71 | 92 | 71 | 81 | 93% | 95% |

11 | 69 | 62 | 80 | 62 | 74 | 90% | 92% |

12 | 67 | 69 | 90 | 69 | 58 | 96% | 87% |

13 | 63 | 69 | 90 | 69 | 70 | 91% | 89% |

14 | 67 | 69 | 90 | 69 | 74 | 97% | 89% |

15 | 78 | 68 | 88 | 68 | 99 | 87% | 72% |

16 | 70 | 60 | 78 | 60 | 85 | 86% | 78% |

17 | 87 | 96 | 124 | 96 | 105 | 89% | 78% |

18 | 87 | 80 | 104 | 80 | 105 | 92% | 79% |

19 | 76 | 57 | 74 | 57 | 97 | 75% | 72% |

20 | 56 | 55 | 72 | 55 | 60 | 99% | 92% |

21 | 55 | 49 | 64 | 49 | 70 | 89% | 73% |

22 | 51 | 46 | 60 | 46 | 64 | 90% | 75% |

Mean | 91% | 81% |

Cell | $\mathbf{1}\mathbf{-}\frac{\mathbf{\left|}{\mathit{K}}_{\mathit{i}}\mathbf{-}{\mathit{k}}_{\mathit{i}\mathbf{,}\mathit{a}}\mathbf{\right|}}{{\mathit{K}}_{\mathit{i}}}$ | $\mathbf{1}\mathbf{-}\frac{\mathbf{\left|}{\mathit{K}}_{\mathit{i}}\mathbf{-}{\mathit{k}}_{\mathit{i}\mathbf{,}\mathit{p}}\mathbf{\right|}}{{\mathit{K}}_{\mathit{i}}}$ |
---|---|---|

Cell_{1} | 91% | 81% |

Cell_{2} | 88% | 75% |

Cell_{3} | 90% | 70% |

Cell_{4} | 86% | 86% |

Cell_{5} | 84% | 75% |

Cell_{6} | 88% | 73% |

Cell_{7} | 86% | 76% |

Cell_{8} | 87% | 84% |

Cell_{9} | 84% | 73% |

Mean | 87% | 77% |

#### 4.2.3. The Evaluation of Vehicle Speed Estimation

_{i,h}) Equation (3), the estimated traffic flow by using NLU events (q

_{i,n}) Equation (4), the estimated traffic density by using CA events (k

_{i,a}) and the estimated traffic density by using PLU events (k

_{i,p}) by Equations (9)–(12). For instance, the average vehicle speed of the first road segment ${u}_{1,ha}$ can be estimated as 78 km/h (i.e., ${u}_{1,ha}={q}_{1,h}/{k}_{1,a}$) at 8 a.m. in accordance with the estimated traffic flow by using HO events (i.e., q

_{1,h}= 7560 car/h) and the estimated traffic density by using CA events (i.e., k

_{1,a}= 97 car/km). This study calculated the accuracies of traffic density estimation as $1-\frac{\left|{U}_{i}-{u}_{i,ha}\right|}{{U}_{i}}$, $1-\frac{\left|{U}_{i}-{u}_{i,na}\right|}{{U}_{i}}$, $1-\frac{\left|{U}_{i}-{u}_{i,hp}\right|}{{U}_{i}}$ and $1-\frac{\left|{U}_{i}-{u}_{i,np}\right|}{{U}_{i}}$. In accordance with the results in Section 4.2.1 and Section 4.2.2, Table 6 shows that the average accuracies of vehicle speed estimation of the first road segment between 8 a.m. and 22 p.m. are 92%, 90%, 81% and 85% for the estimated vehicle speeds ${u}_{i,ha}$, ${u}_{i,na}$, ${u}_{i,hp}$ and ${u}_{i,np}$, respectively. As shown in Table 7, the results of the vehicle speed estimation show that the estimated traffic flow based on the amount of NLUs and estimated traffic density based on the amount of CAs can obtain the highest accuracy of vehicle speed estimation.

Time | U_{1} | ${\mathit{u}}_{\mathbf{1}\mathbf{,}\mathit{h}\mathit{a}}$ | ${\mathit{u}}_{\mathbf{1}\mathbf{,}\mathit{n}\mathit{a}}$ | ${\mathit{u}}_{\mathbf{1}\mathbf{,}\mathit{h}\mathit{p}}$ | ${\mathit{u}}_{\mathbf{1}\mathbf{,}\mathit{n}\mathit{p}}$ | $\mathbf{1}\mathbf{-}\frac{\mathbf{\left|}{\mathit{U}}_{\mathbf{1}}\mathbf{-}{\mathit{u}}_{\mathbf{1}\mathbf{,}\mathit{h}\mathit{a}}\mathbf{\right|}}{{\mathit{U}}_{\mathbf{1}}}$ | $\mathbf{1}\mathbf{-}\frac{\mathbf{\left|}{\mathit{U}}_{\mathbf{1}}\mathbf{-}{\mathit{u}}_{\mathbf{1}\mathbf{,}\mathit{n}\mathit{a}}\mathbf{\right|}}{{\mathit{U}}_{\mathbf{1}}}$ | $\mathbf{1}\mathbf{-}\frac{\mathbf{\left|}{\mathit{U}}_{\mathbf{1}}\mathbf{-}{\mathit{u}}_{\mathbf{1}\mathbf{,}\mathit{h}\mathit{p}}\mathbf{\right|}}{{\mathit{U}}_{\mathbf{1}}}$ | $\mathbf{1}\mathbf{-}\frac{\mathbf{\left|}{\mathit{U}}_{\mathbf{1}}\mathbf{-}{\mathit{u}}_{\mathbf{1}\mathbf{,}\mathit{n}\mathit{p}}\mathbf{\right|}}{{\mathit{U}}_{\mathbf{1}}}$ |
---|---|---|---|---|---|---|---|---|---|

8 | 69 | 78 | 69 | 59 | 52 | 87% | 99% | 85% | 75% |

9 | 70 | 78 | 72 | 65 | 60 | 89% | 97% | 93% | 86% |

10 | 71 | 78 | 77 | 69 | 67 | 90% | 92% | 97% | 95% |

11 | 83 | 77 | 91 | 65 | 76 | 94% | 89% | 78% | 92% |

12 | 83 | 78 | 80 | 93 | 96 | 94% | 96% | 88% | 85% |

13 | 83 | 78 | 76 | 77 | 75 | 94% | 92% | 92% | 90% |

14 | 83 | 78 | 80 | 73 | 75 | 94% | 97% | 88% | 90% |

15 | 82 | 78 | 94 | 53 | 64 | 95% | 86% | 65% | 78% |

16 | 83 | 78 | 96 | 55 | 68 | 94% | 84% | 67% | 82% |

17 | 70 | 78 | 64 | 71 | 58 | 90% | 90% | 100% | 82% |

18 | 70 | 78 | 77 | 59 | 58 | 89% | 91% | 84% | 83% |

19 | 71 | 78 | 94 | 46 | 55 | 90% | 67% | 65% | 78% |

20 | 84 | 79 | 85 | 72 | 78 | 94% | 99% | 86% | 93% |

21 | 84 | 78 | 94 | 55 | 66 | 93% | 87% | 65% | 79% |

22 | 84 | 78 | 94 | 56 | 67 | 93% | 89% | 67% | 80% |

Mean | 92% | 90% | 81% | 85% |

Cell | $\mathbf{1}\mathbf{-}\frac{\mathbf{\left|}{\mathit{U}}_{\mathit{i}}\mathbf{-}{\mathit{u}}_{\mathit{i}\mathbf{,}\mathit{h}\mathit{a}}\mathbf{\right|}}{{\mathit{U}}_{\mathit{i}}}$ | $\mathbf{1}\mathbf{-}\frac{\mathbf{\left|}{\mathit{U}}_{\mathit{i}}\mathbf{-}{\mathit{u}}_{\mathit{i}\mathbf{,}\mathit{n}\mathit{a}}\mathbf{\right|}}{{\mathit{U}}_{\mathit{i}}}$ | $\mathbf{1}\mathbf{-}\frac{\mathbf{\left|}{\mathit{U}}_{\mathit{i}}\mathbf{-}{\mathit{u}}_{\mathit{i}\mathbf{,}\mathit{h}\mathit{p}}\mathbf{\right|}}{{\mathit{U}}_{\mathit{i}}}$ | $\mathbf{1}\mathbf{-}\frac{\mathbf{\left|}{\mathit{U}}_{\mathit{i}}\mathbf{-}{\mathit{u}}_{\mathit{i}\mathbf{,}\mathit{n}\mathit{p}}\mathbf{\right|}}{{\mathit{U}}_{\mathit{i}}}$ |
---|---|---|---|---|

Cell_{1} | 92% | 90% | 81% | 85% |

Cell_{2} | 80% | 86% | 62% | 81% |

Cell_{3} | 75% | 90% | 62% | 79% |

Cell_{4} | 86% | 83% | 72% | 88% |

Cell_{5} | 76% | 81% | 59% | 80% |

Cell_{6} | 73% | 85% | 55% | 80% |

Cell_{7} | 76% | 84% | 57% | 82% |

Cell_{8} | 72% | 85% | 64% | 86% |

Cell_{9} | 78% | 80% | 56% | 78% |

Mean | 79% | 85% | 63% | 82% |

#### 4.3. The Evaluation of Vehicle Speed Forecasting Method

**Table 8.**The accuracies of vehicle speed forecasting of the road segment covered by Cell

_{1}. LR, logistic regression.

Time | ${\mathit{U}}_{\mathit{i}}^{\mathit{\psi}\mathbf{+}\mathbf{1}}$ | Forecasted Vehicle Speed of LR | Forecasted Vehicle Speed of BPNN | The Accuracy of LR | The Accuracy of BPNN |
---|---|---|---|---|---|

8 | 70 | 76 | 69 | 92.32% | 98.90% |

9 | 71 | 78 | 73 | 90.05% | 96.32% |

10 | 83 | 79 | 77 | 95.95% | 93.26% |

11 | 83 | 83 | 81 | 99.78% | 97.30% |

12 | 83 | 85 | 86 | 98.40% | 96.86% |

13 | 83 | 80 | 80 | 96.60% | 96.74% |

14 | 82 | 80 | 80 | 97.89% | 98.18% |

15 | 83 | 81 | 78 | 97.89% | 93.95% |

16 | 70 | 82 | 79 | 83.16% | 87.91% |

17 | 70 | 72 | 73 | 97.73% | 96.19% |

18 | 71 | 74 | 75 | 95.30% | 93.91% |

19 | 84 | 79 | 81 | 94.50% | 96.52% |

20 | 84 | 79 | 80 | 94.54% | 95.47% |

21 | 84 | 80 | 84 | 94.75% | 99.93% |

22 | 85 | 79 | 86 | 93.47% | 98.76% |

Mean | 94.82% | 96.01% |

Cell | The Accuracy of LR | The Accuracy of BPNN |
---|---|---|

Cell_{1} | 94.82% | 96.01% |

Cell_{2} | 93.76% | 96.29% |

Cell_{3} | 93.42% | 95.24% |

Cell_{4} | 92.39% | 94.03% |

Cell_{5} | 93.25% | 94.72% |

Cell_{6} | 93.59% | 97.35% |

Cell_{7} | 92.26% | 95.74% |

Cell_{8} | 93.73% | 95.19% |

Cell_{9} | 93.84% | 96.88% |

Mean | 93.45% | 95.72% |

## 5. Conclusions and Future Work

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**MDPI and ACS Style**

Lai, W.-K.; Kuo, T.-H.; Chen, C.-H.
Vehicle Speed Estimation and Forecasting Methods Based on Cellular Floating Vehicle Data. *Appl. Sci.* **2016**, *6*, 47.
https://doi.org/10.3390/app6020047

**AMA Style**

Lai W-K, Kuo T-H, Chen C-H.
Vehicle Speed Estimation and Forecasting Methods Based on Cellular Floating Vehicle Data. *Applied Sciences*. 2016; 6(2):47.
https://doi.org/10.3390/app6020047

**Chicago/Turabian Style**

Lai, Wei-Kuang, Ting-Huan Kuo, and Chi-Hua Chen.
2016. "Vehicle Speed Estimation and Forecasting Methods Based on Cellular Floating Vehicle Data" *Applied Sciences* 6, no. 2: 47.
https://doi.org/10.3390/app6020047