Vehicle Movement Analyses Considering Altitude Based on Modified Digital Elevation Model and Spherical Bilinear Interpolation Model: Evidence from GPS-Equipped Taxi Data in Sanya, Zhengzhou, and Liaoyang

. Aggravating energy shortages and increasing labor costs have become global problems and have garnered special importance in recent years in the transportation sector, especially in taxi markets. Automatic vehicles have a bright future, however, there is an equal amount of skepticism and concern about safety for all the optimism. To unlock the potential of automatic vehicles in intelligent transportation systems, a lot more data and testing are required to promote safety level as far as possible and achieve the organizational aim of reducing accidents to zero tolerance. And it is vital to provide accurate models for vehicle movement analyses. In this study, Modified Digital Elevation (MDE) model and Spherical Bilinear Interpolation (SBI) model were proposed for vehicle movement analyses considering altitude. And the experimental data of 9,990 GPS-enabled taxis in Sanya, Zhengzhou, and Liaoyang were adopted to support comparisons. Measurement results showed that MDE model had over 99% less disparity with direct solution than original model and SBI model could further improve the effects. It indicated that the application of MDE model and SBI model could improve both accuracy and efficiency of vehicle movement analyses and it had a bright future in the field of automatic vehicles. Future directions could be improving models and expanding data.


Introduction
Nowadays, there are plenty of urgent social issues in the transportation research eld. For example, aggravating energy shortages and increasing labor costs have become global problems and have garnered special importance in recent years in the transportation sector, especially in taxi markets. With the worsening situation of energy shortages and labor costs, taxi markets are facing increasing opportunities as well as challenges. It is essential that appropriate counter measures must be taken to suppress or reverse or at least alleviate the worsening situation.
With the rapid progress of self-driving technologies, there are more and more advanced applications involved in intelligent tra c system. For example, automatic vehicles have a bright future. Dubai Roads and Transportation Authority drivers but computers. On March 19 th in 2018, a terrible accident took place in Tempe, Arizona that a 49-year-old woman with a bicycle on the sidewalk was hit to die by an Uber self-driving car at a speed of 65 kilometers per hour. Since then, the willingness of the public to ride in a fully self-driving vehicle fell in a very low level.
To unlock the potential of automatic vehicles in intelligent transportation systems, a lot more data and testing are required to promote safety level as far as possible and achieve the organizational aim of reducing accidents to zero tolerance. And it is vital to provide accurate models for vehicle movement analyses. In this study, modified digital elevation model and spherical bilinear interpolation model were proposed for vehicle movement analyses considering altitude. And GPSenabled taxi data in Sanya, Zhengzhou, and Liaoyang were adopted to support comparisons. e rest of this paper were organized as follows: Section 2 reviewed related works; Section 3 introduced formulas, models, data and tools; Section 4 presented a sample and described results in Sanya, Zhengzhou, and Liaoyang; Section 5 made a discussion; Section 6 summarized main conclusions, contributions and proposed future directions.

Literature Review
In this section, there are several similar problems and some related works till date, including Internet of Vehicles problem (see Section 2.1), data analysis for automatic vehicles (see Section 2.2) and taxi service improving problem (see Section 2.3).

Internet of Vehicles Problem.
e Internet is a popular network technology all over the world and it has continuous developments in recent years. e evolution of network technology has led to a deployment of various access networks as introduced by Piamrat et al. [1]. Internet of ings (IoT) is a novel paradigm that is rapidly gaining ground in the scenario of modern wireless telecommunications as addressed by Atzori et al. [2]. Miorandi et al. proposed an overview of IoT technologies and services [3]. Xu et al. reviewed classical researches of IoT technologies and major applications in industries [4]. Zanella et al. proposed an urban IoT system and explored the application of the IoT paradigm to smart cities, taking Padova of Italy as an example [5].
Intelligent Transportation Systems (ITS) had significant impact on our life as introduced by Wang [6]. Internet of Vehicle (IoV) is one of the revolutions mobilized by IoT as addressed by Kaiwartya et al. [7]. Lu et al. regarded IoV as the next frontier for automotive revolution and the key to the evolution to ITS [8]. Yang et al. proposed an abstract network model of the IoV and presented its applications [9]. However, IoV also posed new challenges to the communication technology [10]. e information security of IoV was a considerable challenge. Singh et al. presented the potential of transforming vehicle communication in terms of efficiency and safety [11]. Chen proposed a trust-based cooperation authentication bit-map routing protocol against insider security threats in wireless ad-hoc networks [12]. Huang et al. proposed a proactive scheme to secure Edge computing-based IoV against RSU hotspot attack [13]. Furthermore, IoV has rapid developments in recent years. Butt et al. presented a scalable Social IoV (SIoV) architecture based on Restful web technology [14]. Chen et al. proposed Cognitive IoV (CIoV) to enhance transportation safety and network security by communication technologies [15]. Vehicular Ad-hoc Networks (VANET) comprise communications among vehicles and infrastructures by wireless local network technologies as addressed by Hartenstein and Laberteaux [16]. With the wide spread of Global Positioning System (GPS) and Geographic Information System (GIS), the participants in VANET could acquire much more information than before. Benefit from that, GPS-Equipped cars could not only acquire their real-time locations, but also road directions.
us, VANET technologies helped improving road safety and providing comfort for passengers [17,18]. In the field of ITS, IoV and VANET technologies created essential conditions for automatic vehicles.

Data Analysis for Automatic Vehicles.
Automatic vehicles are regarded as the future of transportation. It has been a long-lasting dream of robotics researchers and enthusiasts as indicated by Petrovskaya and run [19]. However, safety is the dominant factor in any automatic vehicle control system design as proposed by Shladover et al. [20]. Much more work was required until autonomous vehicles could participate in real-world urban traffic safely and robustly as proposed by Luettel et al. [21]. To ensure the safety of autonomous vehicles, a holistic fleet deployment scheme from interdisciplinary perspectives should be established as proposed by Koopman and Wagner [22]. Wang et al. investigated the acceptance of intelligent driving vehicles in Guangzhou and indicated that consumers focused on not only the developmental prospects but also the technological safety of intelligent driving vehicles [23]. With the rapid progress of IoV and VANET, there is a great deal of technologies involved in data analysis for automatic vehicles, which are described as follows.  [36]. (iii) Big data technologies. In recent years, a significant change in ITS was that much more data were collected from a variety of sources and can be processed into various forms as proposed by Zhang et al. [37]. And numerous advanced multidisciplinary journals began publishing a special issue of big data, for instance, Nature in 2008 [38] and Science in 2011 [39]. To solve big data, several technologies were proposed, including cloud computing, artificial intelligence and blockchain technology. Gubbi

Taxi Service Improving Problem.
Taxi is the main constituent of urban transportation. With the rapid progress of wireless sensor network [47], vehicle markets meet an evolution from intelligent vehicle grid to autonomous, Internetconnected vehicles and vehicular cloud as discussed by Gerla et al. [48]. Automatic taxis have gradually become reality in several advanced regions but not fully promoted yet. Just like every coin has two sides, automatic taxis have advantages and disadvantages. On the one hand, automatic taxis overcome some defects of human drivers, including excessive stress [49], inadequate sleepiness [50], and negative behaviors [51]. On the other hand, automatic taxis need mountains of work to achieve functions and ensure security. Taxi automation is one of the most promising technologies for the future and it is a challenge well worth meeting for taxi companies.
Fast and reliable service that can compete with the single occupancy vehicle was one of the demands of transit users as proposed by El-Geneidy et al. [52]. And it has become significant to provide users with a range of security-related and user-oriented vehicular applications as proposed by Ning et al. [53]. us, it is necessary for taxi companies improve their service to meet the demand of passengers. Yuan et al. proposed a price equilibrium model for taxi market to improve the service level [54]. Song et al. proposed a planning concept from the perspective of supply and demand economic equilibrium to optimize the transportation markets [55]. Dou et al. proposed a heuristic line piloting method that a taxi deviating from the typical route would raise an alert when malfunction took place or even hijacked by criminals [56]. Tang et al. proposed a customer-search model based on route choice behavior analysis to help taxi drivers find next passengers in urban road networks [57]. Although taxi companies and governments have already made great efforts, there are still plenty of service improving problems to be settled.
To unlock the potential of IoV in ITS, in the previous study [58], Gui and Wu measured taxi efficiency based on 2191 GPSequipped taxi data in Sanya and indicated that the application of Motorcade-Sharing model could not only alleviate urban traffic congestion but also optimize urban taxi markets. However, altitude was not considered in that study which might reduce the measurement accuracy and result in lower safety level when altitude is nonnegligible. us, Original Model need improvements.
To sum up, some helpful works have already been done. However, few researches took altitude into consideration and proposed accurate models for vehicle movement analyses. Besides, autonomous vehicles need assigning continuous directives in time while it is difficult for complex algorithms to response immediately under the background of big data.
How much the altitude will affect the vehicle movement analyses? How to simplify complex algorithms of the Direct Solution for automatic vehicles? And how to handle the situation when some data was missing? In the next section, methods and data are involved to explore these questions.

Methods and Materials
In this section, there are several parts of methods and materials. First, an analysis procedure was presented as an overview (see Section 3.1). Second, traditional methods were reviewed, including Direct Solution (see Section 3.2) and Original Model (see Section 3.3). ird, modified models were proposed, including MDE model (see Section 3.4) and SBI model (see Section 3.5).

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comparisons were raised on the basis of results. e notations for variables were in the Appendix (see Appendix A).

Direct Solution.
Direct solution is the traditional approach and it calculates distances in a direct way (see Figure 2). ere are 4 steps in this section. First, in order to describe the location of vehicles in a mathematical way, the Spherical Coordinate System was established in Formula (1).

Analysis Procedure.
To solve this problem, a series of analysis procedure was established (see Figure 1). In terms of data, GPS data without altitude and digital elevation data were collected at the beginning. GPS data with altitude was calculated on the basis of them a erwards (see Section 3.6). And the preciseness of GPS data with altitude was further improved by Spherical Bilinear Interpolation (SBI) Model (see Section 3.5).
In terms of model, three models were adopted for analyzing vehicle movements. ey are direct solution (see Section 3.2), original model (see Section 3.3) and Modi ed Digital Elevation (MDE) model (see Section 3.4) and they have different functions (see Table 1).
Based on Formula (5), the distance between points 1 and 2 under direct solution can be calculated by Formula (7), which was sophisticated to some extent.
ird, spherical coordinates were converted into rectangular coordinates. Based on Formulas (1), (4), the relationship of them can be represented by Formula (6).
Fourth, all the distances were summed up. Supposing that the variable represents total movements of vehicles under Direct Solution and it can be calculated by Formula (8).

Original Model.
Original Model simpli es the square algorithm of Direct Solution by cosine theorems and it calculates distances in a simple way (see Figure 3).
ere are 5 steps in this section. First, the Spherical Coordinate System was established in Formula (1).
Second, the Rectangular Coordinate System was established in Formula (4).
ird, in order to calculate the distance between two locations, the cosine value of the angle between vectors ⇀ 1 and ⇀ 2 was calculated by Formula (9).
Formula (9) can be converted into Formula (10) and the derivation process is in the Appendix part (see Appendix B in the previous study [58]).
Second, the Rectangular Coordinate System was established in Formula (4).
ird, all the unknown altitude values were calculated approximately by Spherical Bilinear Interpolation Model.
Fourth, considering the equation of arc length calculation, the distance between vectors ⇀ 1 and ⇀ 2 was calculated by Formula (11).
In other words, the distance between 1 , 1 , 1 and 2 , 2 , 2 can be calculated approximately by the longitudes and latitudes of them based on GPS data, and the radius of the earth under Original Model.
Fi h, all the distances were summed up. Supposing that the variable represents total movements of vehicles under Original Model and it can be calculated by Formula (13).

Modi ed Digital Elevation Model. MDE adopts Original
Model and SBI Model to improve the preciseness of results and it calculates distances in a comprehensive way (see Figure 4).
ere are 5 steps in this section. First, the Spherical Coordinate System was established in Formula (1).

Journal of Advanced Transportation
Start Input I and T Formula (17) Formula (18) End

Data and Tools
(i) Data Source. e GPS data of taxis in this study was collected from the big data platform, Travel Cloud, which was developed by Ministry of Transport of the People's Republic of China (see Data Availability). It was provided in part by the transportation department of Liaoning Province, in part by Henan Province department of transportation, in part by Sanya Tra c and Transportation Bureau of Hainan Province. Its major data items include anonymous vehicle ID, longitude, latitude and recording time. And the digital elevation data in this study was collected from Google Map. (ii) Data Processing. In terms of GPS data processing, there are 3 steps. First, all the taxi locations were averaged every 60 seconds so as to improve the accuracy of data, that is to say, average locations of those taxis were recorded every 60 seconds entirely. Second, the aw data was removed so as to ensure the integrity of Fi h, all the distances were summed up. Supposing that the variable ὔ represents total movements of vehicles under Modi ed Digital Elevation Model and it can be calculated by Formula (18).

Spherical Bilinear Interpolation Model. Spherical Bilinear
Interpolation (SBI) Model helps improving the preciseness of GPS data with altitude especially when the data of altitudes is not precise enough or missing (see Figure 5). ere are 3 steps in this section. First, nd out 4 vertexes by positional notation based on the spherical coordinate of point . For any point + ℎ, , where ὔ 1 ≤ ≤ ὔ 2 and ὔ 1 ≤ ≤ ὔ 2 , there are 4 points Figure 6). Second, gure out the relationship among the spherical coordinates of 5 points , 1 , 2 , 3 , 4 . Supposing that there are 4 factors 1 , 2 , 3 , 4 satisfying Formula (19).
As a result, the solution of Formula (19) was settled by Formula (20). e derivation process of Formula (20) is in the Appendix (see Appendix B).
Based on Formula (20), Formula (19) can be converted into Formula (21).  point to the right yellow point (see Figure 7). Luhuitou Park was on a hill and the taxi was on the road uphill. It indicated that the altitude of the taxi in the sample would rise from the le yellow point to the right yellow point. In Figure 7, Luhuitou Park was surrounded by South of Sea Road, also known as Nanbianhai Road in Chinese. Furthermore, four red points surrounding yellow points were supplementary points drawn for SBI Model. eir longitudes and latitudes kept only 3 decimal digits. Actual position in Figure 3 can be converted into Schematic diagram (see Figure 8).
In Figure 8 According to the original digital elevation data, the altitude value of points 1 and 2 were 145 (m) and 147 (m) respectively. e taxi altitude in the sample changed approximately 2 (m) from 1 to 2 . Based on SBI Model, the altitude value of points 1 and 2 can be further calculated by Formula (17). And the altitude value of points 1 and 2 adjusted by SBI Model were 145.00 (m) and 147.30 (m) respectively. Based on Formulas (7), (12), (17), the sample results and comparisons of three methods were gured out (see Table 2). e derivation process of Table 2 is in the Appendix (see Appendix D).
In Table 2

Results
In this section, a sample (see Section 4.  Figure 9).
In Figure 9, colors re ected the elevation. e altitudes of blue area were low. e altitudes of green area were medium. e altitudes of yellow area were high.
In the origin data of Sanya, the locations of 2,506 taxis were recorded every 15 seconds from 9:00 a.m. to 9:59 a.m. on Nov. 15 th in 2016, adding up to 766,042 records (see Figure 10).
In Figure 10, taxi positions of Sanya located minutely at a xed monitor where the longitude was in the range of [109.0°, 109.8°] while the latitude was in the range of [18.1°, 18.5°]. A er data processing, there were 2,191 taxis and 131,460 records le in the experimental data. And 107,427 movements of 2,096 taxis were extracted as a result. Based on Formulas (7), (12), (17), the Sanya results and comparisons of three methods were gured out (see Table 3).
In Table 3, Value1 adopted original digital elevation data while Value2 adopted the digital elevation data adjusted by SBI Model. Under Value1, total vehicle movements under Direct Solution was 34, 065, 354.87 (m). e deviation between Original Model and Direct Solution was 6, 650.88 (m) while the deviation between MDE Model and Direct Solution was only missing, it could be further calculated by SBI Model. By contrast, the deviation between Original Model and Direct Solution was 0.013091 (m) while the deviation between MDE Model and Direct Solution was only 0.000001 (m). It further veri ed the advantage of MDE Model even though some data was missing in the sample results and SBI Model was adopted to improve the preciseness of GPS data with altitude.    (7), (12), (17), the Zhengzhou results and comparisons of three methods were gured out (see Table 4).
In Table 4 Model and MDE Model in Sanya was much more obvious than sample. e results in Sanya veri ed that MDE Model had much less disparity with Direct Solution than Original Model. In addition, even if some original digital elevation data of actual positions in Sanya were missing, it could be further calculated by SBI Model. By contrast, the deviation between Original Model and Direct Solution was 664.16 (m) while the deviation between MDE Model and Direct Solution was only 0.15 (m). It further veri ed the advantage of MDE Model even though some data was missing in Sanya and SBI Model was adopted to improve the preciseness of GPS data with altitude.  Figure 11).

Zhengzhou. Zhengzhou is a city in Henan
In Figure 11, colors re ected the elevation. e altitudes of blue area were low. e altitudes of green area were medium. e altitudes of yellow area were high.
In the origin data of Zhengzhou, the locations of 9,703 taxis were recorded every 15 seconds from 14:50 p.m. to 15:38 p.m. on Nov. 15 th in 2016, adding up to 1,048,575 records (see Figure 12).
In Figure 12, taxi positions of Zhengzhou located minutely at a xed monitor where the longitude was in   (7), (12), (17), the Liaoyang results and comparisons of three methods were gured out (see Table 5).
In Figure 13, colors re ected the elevation. e altitudes of blue area were low. e altitudes of green area were medium. e altitudes of yellow area were high.
In the origin data of Liaoyang, the locations of 2,237 taxis were recorded every 30 seconds from 9:59 a.m. to 10:58 a.m. on Aug. 8 th in 2016, adding up to 268,440 records (see Figure 14).
In Figure 14, 3.0. erefore, we adopted v2.2.0 as a result. (iii) In SBI Model, the rst step was to nd out 4 vertexes by positional notation based on the spherical coordinate of point . We tried both 3 decimal digits and 4 decimal digits and found that 3 decimal digits of longitudes and latitudes were su cient for vertexes. (iv) In this research, we de ned that = 6378137.00 (m), which represents the radius of the earth (see Section 3.2). However, the radius of the earth has di erences in di erent places.

Application Prospects.
In the eld of automatic vehicles, vehicle security is always under the spotlight. And elevation changes have a signi cant e ect on the security of automatic vehicles because it is di cult for them to respond as human beings when tra c changes. Most crucially, the speci c calculations used to vehicle movement analyses must be not only accurate but also fast. Otherwise, those automatic vehicles will be in danger, especially when they are running at high speed. us, appropriate counter measures could be taken to suppress or reverse or at least alleviate its limitations. e application prospects had not been contemplated within former sections, including MDE Model and SBI Model, which are described as follows.
(i) MDE Model. In last section, results veri ed that altitude was a key element of vehicle movement analyses, and it indicated that MDE Model was much more accurate than Original Model in terms of vehicle movement analysis (see Section 4.2-4.5). It is technically feasible to send alerts to the automatic vehicles disparity with Direct Solution than Original Model. In addition, even if some original digital elevation data of actual positions in Liaoyang were missing, it could be further calculated by SBI Model. By contrast, the deviation between Original Model and Direct Solution was 142.20 (m) while the deviation between MDE Model and Direct Solution was less than 0.01 (m). It further veri ed the advantage of MDE Model even though some data was missing in Liaoyang and SBI Model was adopted to improve the preciseness of GPS data with altitude. Tables 3-5, the Comprehensive results and comparisons of three methods were gured out (see Table 6). In Table 6, Value1 adopted original digital elevation data while Value2 adopted the digital elevation data adjusted by SBI Model. Under Value1, total deviation between Original Model and Direct Solution was 10,884.72 (m) while total deviation between MDE Model and Direct Solution was only 15.65 (m). e latter is 0.14% that of the former. Under Value2, total deviation between Original Model and Direct Solution was 9,602.32 (m) while total deviation between MDE Model and Direct Solution was only 15.49 (m). e latter is 0.16% that of the former. Comprehensive results veri ed that MDE Model had over 99% less disparity with Direct Solution than Original Model because MDE Model took altitude into consideration but Original Model did not. In other words, MDE Model was much more accurate than Original Model.

Discussion
In this section, several operational details over the course of this research were presented for fellow colleagues and follow-up studies (see Section 5.1). In addition, the authors discussed the application prospects in the eld of automatic vehicles (see Section 5.2).

Operational Details.
Over the course of this research, there were several operational details that had not been contemplated within, including so ware use and data processing, which are described as follows.
(i) During processing original data by Microso Excel 2019, we found that Excel had a processing limit that its maximum capacity was 1,048,576 rows. If original accuracy of vehicle movement analyses. SBI Model was for further improving the preciseness of GPS data with altitude. Given the arguments above mentioned, the major ndings in this article include several contents, which are described as follows. To sum up, the authors discussed that MDE Model and SBI Model have great practical prospects and they are suitable and useful for autonomous vehicles, especially for automatic taxis.

A. Notations for Variables
In Appendix A, notations for variables are presented (see Table 7).

B. Derivation Process of Formula (20)
In Appendix B, a series of formulas are built to nd out the solution of Formula (19) and work out Formula (20). Supposing that the point is the center of the coordinate system and there are two points 1 and 2 (see Figure 15(a)).

C. Checking Process of Formula (21)
In Appendix C, a series of formulas are built to check Formula (21).
Based on Formula (C.1), the polar angle can be calculated by Formula (C.9).
As a result, Formula (20) is available a er checking and ℎ can be calculated by Formula (21) on the basis of Formula (C.24). Table 2 In Appendix D, a series of formulas are built to work out Table 2. It is worth noting that all the and in degree measure should be converted into radian measure by multiplying /180 ∘ before calculating. Now, we calculate the movements. Based on Formulas (7), (12), (21), the vehicle movement ⇀ 1 2 under Direct Solution, Original Model, MDE Model can be calculated respectively by Formulas (29), (30), (31).