System and method for determining appropriate curve warning signs

Abstract

An exemplary embodiment of the present disclosure provides a method for improving curve markings, the method comprising: receiving data from a plurality of user devices disposed within each of the vehicles as the respective vehicles travel along one or more roads that include one or more curves; determining, based at least in part on the data, desired curve markings to be displayed at the one or more curves; and displaying a list of desired curve markings to be displayed at the one or more curves.

Description

[Technical Field]

[0001] (CROSS-REFERENCE TO RELATED APPLICATIONS) This application claims the benefit of U.S. Provisional Application No. 63 / 369,811, filed July 29, 2022, which is incorporated by reference in its entirety as if fully set forth below.

[0002] (Government License Rights) This invention was made with government support under Contract No. PI#0016839 awarded by the National Cooperative Highway Research Program. The government has certain rights in this invention.

[0003] (Technical field) Various embodiments of the present disclosure generally relate to systems and methods for determining appropriate markings along a curve in a road. [Background technology]

[0004] Although curves represent only a small portion of the road network (5% of highway miles), a disproportionate number of serious vehicle accidents (25% of fatalities) occur on horizontal curves. When friction is insufficient to counteract the lateral forces experienced by a vehicle traveling on a curve, the vehicle skids off the road (ROR). Because the ultimate goal is to reduce serious vehicle accidents on curves, this is a high-priority issue of significant interest to transportation agencies across the United States. According to interviews with state Department of Transportation (DOT) engineers, this issue is complicated because in-service curve characteristics, including superelevation, can change over time with repaving, which provides new pavement. Therefore, understanding in-service curve characteristics is essential to improving curve safety. In-service curve characteristics, such as curve radius, superelevation, and ball-bank indicator (BBI) angle, are crucial for establishing appropriate curve speed recommendations and for evaluating and analyzing curve safety. The BBI measurement is one of the key curve safety indicators specified in the Manual of Uniform Traffic Control Devices (MUTCD) (2009), and is a composite index that includes curvature, superelevation, side friction condition, and driving speed.

[0005] However, obtaining such detailed information about roadway characteristics of curves at the road network level during their service life can be extremely challenging for transportation agencies. For example, state transportation agencies, such as the Georgia Department of Transportation (GDOT), use electronic devices (manufactured by Rieker Inc.) to collect BBI measurements in the field. For each curve being evaluated, GDOT engineers drive each curve more than twice at increasing speeds, measuring the BBI on each drive, to determine the appropriate recommended speed for the curve. This process typically requires two workers (one to drive the vehicle and the other to record the BBI), which is labor-intensive, time-consuming, and costly. Once representative BBI values are determined for each curve, along with the appropriate recommended speed, countermeasures (e.g., setting recommended speeds at the beginning of the curve, applying high-friction surface treatments (HFST) or other treatments) can be implemented based on an analysis of potential safety improvements, completion of a benefit-cost analysis, and a determination of funding availability.

[0006] In summary, current transportation agency practice involves collecting curve characteristic information at the roadway network level using specialized devices operated by designated engineers to assess the safety status of curves. This practice is generally laborious, time-consuming, and costly. Because current practices and methods are time-consuming, labor-intensive, and cost-intensive, completing a curve safety assessment for 100% of state-managed roads typically takes one to two years. For local (county or city) transportation agencies with limited resources, the process of completing a roadway network curve safety assessment can be even longer. As a result, curve sections requiring safety improvements are often not identified until an accident occurs. The long intervals between curve safety assessments make it difficult for transportation agencies to proactively identify problems and implement timely improvements to curve safety. The limitations of current practices and methods significantly hinder transportation agencies' ability to reduce the disproportionate number of fatal accidents at curves. The problems with current practices significantly hinder transportation agencies' ability to proactively implement safety improvements to reduce the number of accidents at roadway curves. Therefore, there is an urgent need to develop improved methods that enable transportation agencies to conduct network-level curve safety assessments in a cost-effective, safe, and timely manner. Because transportation agencies often have limited funds and budgets that must be spent prudently, innovative, cost-effective methods are needed to enable transportation agencies to implement more policies with less money. Summary of the Invention

[0007] An exemplary embodiment of the present disclosure provides a method for improving curve markings, comprising: receiving data from a plurality of user devices disposed within each of the vehicles as the respective vehicles travel along one or more roads having one or more curves, the data collected by the user devices, determining, based at least in part on the data, desired curve markings to be displayed at the one or more curves, and displaying a list of the desired curve markings to be displayed at the one or more curves.

[0008] In any of the embodiments disclosed herein, the data may indicate a speed of the user device.

[0009] In any of the embodiments disclosed herein, the data may indicate a GPS location of the user device.

[0010] In any of the embodiments disclosed herein, the data may include IMU data of the user device.

[0011] In any of the embodiments disclosed herein, the IMU data may include accelerometer data of the user device.

[0012] In any of the embodiments disclosed herein, the IMU data may include gyroscope data of the user device.

[0013] In any of the embodiments disclosed herein, the IMU data may include magnetometer data of the user device.

[0014] In any of the embodiments disclosed herein, the data may include video data of the one or more roads.

[0015] In any of the embodiments disclosed herein, the method may further comprise determining a position of the one or more curve portions based at least in part on the data.

[0016] In any of the embodiments disclosed herein, determining the positions of the one or more curve segments may include determining a curve start point of the one or more curve segments.

[0017] In any of the embodiments disclosed herein, determining the positions of the one or more curve segments may include determining curve endpoints of the one or more curve segments.

[0018] In any of the embodiments disclosed herein, determining the desired curve markings to be displayed at the one or more curve segments may include determining a curve radius for the one or more curve segments.

[0019] In any of the embodiments disclosed herein, the curve radius may be based at least in part on GPS data and / or road centerline data within the data obtained from the plurality of user devices.

[0020] In any of the embodiments disclosed herein, determining the desired curve markings to be displayed on the one or more curve segments may include determining a deviation angle of the one or more curve segments.

[0021] In any of the embodiments disclosed herein, the deviation angle may be based at least in part on GPS data and / or road centerline data within the data obtained from the plurality of user devices.

[0022] In any of the embodiments disclosed herein, determining the desired curve markings to be displayed at the one or more curve portions may include determining a superelevation of the one or more curve portions.

[0023] In any of the embodiments disclosed herein, the superelevation may be based at least in part on speed data in the data obtained from the plurality of user devices, as well as a path radius and BBI determined based at least in part on the data obtained from the plurality of user devices.

[0024] In any of the embodiments disclosed herein, determining the desired curve markings to be displayed at the one or more curve sections may include determining a recommended speed for the one or more curve sections.

[0025] In any of the embodiments disclosed herein, the determination of the recommended speed at the one or more curve sections may be based at least in part on a curve radius and superelevation of the one or more curve sections.

[0026] In any of the embodiments disclosed herein, the curve radius and the superelevation of the one or more curve portions may be determined based at least in part on the data obtained from the plurality of user devices.

[0027] In any of the embodiments disclosed herein, the recommended rate is calculated according to the formula:

number

[0028] In any of the embodiments disclosed herein, the method may further include determining one or more movement characteristics of the vehicle traveling along one or more roads based at least in part on the data.

[0029] In any of the embodiments disclosed herein, the one or more movement characteristics may include a path radius taken by the vehicle when traveling along the one or more curved portions.

[0030] In any of the embodiments disclosed herein, the path radius may be based at least in part on velocity data and IMU data in the data obtained from multiple user devices.

[0031] In any of the embodiments disclosed herein, the one or more movement characteristics may include a ball bank indicator (BBI) of the vehicle when traveling along the one or more curves.

[0032] In any of the embodiments disclosed herein, the BBI may be based at least in part on IMU data in the data obtained from multiple user devices.

[0033] In any of the embodiments disclosed herein, the BBI has the formula:

number

[0034] In any of the embodiments disclosed herein, displaying the list of desired curve signs to be displayed on the one or more curve segments may include displaying a list of coordinates each corresponding to a geographic location and a desired sign for each of the coordinates.

[0035] In any of the embodiments disclosed herein, displaying the list of desired curve marks to be displayed at the one or more curve sections may include displaying a map including the one or more curve sections and the desired curve marks to be displayed at the one or more curve sections.

[0036] In any of the embodiments disclosed herein, the plurality of user devices may be smartphones.

[0037] In any of the embodiments disclosed herein, the plurality of user devices may be tablets.

[0038] In any of the embodiments disclosed herein, the method may further comprise determining existing markers currently displayed on the one or more curve segments based at least in part on the data.

[0039] In any of the embodiments disclosed herein, the method may further include comparing the existing markings currently displayed on the one or more curve segments with the desired curve markings to be displayed on the one or more curve segments.

[0040] In any of the embodiments disclosed herein, the method may further include matching the existing markings currently displayed on the one or more curve segments to the desired curve markings to be displayed on the one or more curve segments by generating a list of markings to be displayed on the one or more curve segments based at least in part on the comparison.

[0041] In any of the embodiments disclosed herein, the method may further comprise displaying the list of markers to be displayed on the one or more curve portions.

[0042] In any of the embodiments disclosed herein, displaying the list of signs to be displayed at the one or more curve portions may include displaying a list of coordinates each corresponding to a geographic location and a desired sign for each of the coordinates.

[0043] In any of the embodiments disclosed herein, displaying the list of signs to be displayed at the one or more curves may include displaying a map including the one or more curves and the signs to be displayed at the one or more curves.

[0044] Another embodiment of the present disclosure provides a method for calculating a recommended driving speed for a curved portion of a road, the method comprising: receiving data from a user device disposed within a vehicle as the vehicle travels along a road including a curved portion, the user device collecting data from the user device while the vehicle is traveling along the curved portion of the road, determining a recommended driving speed for the curved portion of the road based at least in part on the data, and generating an output indicative of the recommended driving speed for the curved portion of the road.

[0045] Another embodiment of the present disclosure provides a system for improving curb markings, which may include one or more processors, which may be individually and / or collectively configured to execute code that causes the system to implement any of the methods or portions of methods disclosed herein.

[0046] These and other aspects of the present disclosure are described below in the Detailed Description and accompanying drawings. Other aspects and features of the embodiments will become apparent to those skilled in the art upon review of the following description of certain exemplary embodiments in conjunction with the drawings. While features of the present disclosure may be described with reference to particular embodiments and drawings, all embodiments of the present disclosure may include one or more of the features described herein. Furthermore, while one or more embodiments may be described as having certain advantageous features, one or more of such features may also be used with various embodiments described herein. Similarly, while exemplary embodiments may be described below as device, system, or method embodiments, it should be understood that such exemplary embodiments may be implemented in various devices, systems, and methods of the present disclosure. [Brief explanation of the drawings]

[0047] The following detailed description of certain embodiments of the present disclosure will be better understood when read in conjunction with the accompanying drawings. For the purpose of illustrating the disclosure, certain embodiments are shown in the drawings. It should be understood, however, that the disclosure is not limited to the precise arrangements and instrumentalities of the embodiments shown in the drawings.

[0048] [Figure 1] FIG. 1 is a schematic diagram of a system for improving curb markings, according to some embodiments of the present disclosure.

[0049] [Figure 2] FIG. 2 is a flowchart illustrating a data collection and calculation method according to some embodiments of the present disclosure.

[0050] [Figure 3] FIG. 3 is an illustration of a coordinate system of an IMU of a mobile device, according to some embodiments of the present disclosure.

[0051] [Figure 4] FIG. 4 is an explanatory diagram of time series data registration in data tables with different sampling frequencies according to some embodiments of the present disclosure.

[0052] [Figure 5] FIG. 5 is an explanatory diagram of the difference between the path radius and the curve radius due to lateral movement within a lane.

[0053] [Figure 6] FIG. 6 is an illustration of the interaction between BBI, superelevation, lateral acceleration, and vehicle body roll.

[0054] [Figure 7] Figure 7 is a chart of road centerlines with curves extracted.

[0055] [Figure 8] Figure 8 is a chart of the azimuth angles from which the curves were extracted.

[0056] [Figure 9] FIG. 9 is a chart illustrating the relationship between calculated BBI and side friction angle on the NCAT test track where superelevation was measured manually, according to some embodiments of the present disclosure.

[0057] [Figure 10] FIG. 10 shows the locations on the NCAT test track where superelevation was manually measured.

[0058] [Figure 11A] FIG. 11A is a chart of uncalibrated superelevation error at different speeds as measured with a GoPro, according to some embodiments of the present disclosure. [Figure 11B] FIG. 11B is a chart of uncalibrated superelevation error at different speeds measured by a first smartphone, according to some embodiments of the present disclosure. [Figure 11C] FIG. 11C is a chart of uncalibrated superelevation error at different speeds measured with a second smartphone, according to some embodiments of the present disclosure.

[0059] [Figure 12] FIG. 12 is a chart of uncalibrated superelevation RMSE according to some embodiments of the present disclosure.

[0060] [Figure 13] FIG. 13 is an illustration of a driving route with different driving behaviors according to some embodiments of the present disclosure.

[0061] [Figure 14A] 14A-14B are charts of superelevation calculated using path radius (FIG. 14A) versus curve radius (FIG. 14B) for "good driving," according to some embodiments of the present disclosure. [Figure 14B]FIG. 14B is a chart of superelevation calculated using path radius (FIG. 14A) versus curve radius (FIG. 14B) for "good driving," according to some embodiments of the present disclosure.

[0062] [Figure 15] FIG. 15 is a chart of superelevation calculated as a route radius for "bad driving" according to some embodiments of the present disclosure.

[0063] [Figure 16A] FIG. 16A is a chart illustrating the performance difference between different methods of path radius estimation, according to some embodiments of the present disclosure. [Figure 16B] FIG. 16B is a chart illustrating the performance difference between different methods of path radius estimation, according to some embodiments of the present disclosure.

[0064] [Figure 17A] FIG. 17A is a chart showing the relationship between measured BBI angle and side friction angle for a GoPro, according to some embodiments of the present disclosure. [Figure 17B] FIG. 17B is a chart illustrating the relationship between measured BBI angle and side friction angle for a first smartphone, according to some embodiments of the present disclosure. [Figure 17C] FIG. 17C is a chart illustrating the relationship between measured BBI angle and side friction angle for a second smartphone, according to some embodiments of the present disclosure.

[0065] [Figure 18A] FIG. 18A is a chart showing calibrated superelevation error at different speeds for a GoPro, according to some embodiments of the present disclosure. [Figure 18B] FIG. 18B is a chart showing calibrated superelevation error at different speeds for a first smartphone, according to some embodiments of the present disclosure. [Figure 18C]FIG. 18C is a chart showing calibrated superelevation error at different speeds for a second smartphone, according to some embodiments of the present disclosure.

[0066] [Figure 19] FIG. 19 is a chart showing calibrated superelevation RMSE according to some embodiments of the present disclosure.

[0067] [Figure 20A] FIG. 20A is a chart showing linear regression between measured and expected BBI angles using different devices for a GoPro, according to some embodiments of the present disclosure. [Figure 20B] FIG. 20B is a chart showing a linear regression between measured and expected BBI angles using different devices for a first smartphone, according to some embodiments of the present disclosure. [Figure 20C] FIG. 20C is a chart showing a linear regression between measured and expected BBI angles using a different device for a second smartphone, according to some embodiments of the present disclosure. [Figure 20D] FIG. 20D is a chart showing linear regression between measured and predicted BBI angles using different devices for a Rieker device, according to some embodiments of the present disclosure.

[0068] [Figure 21] FIG. 21 is a map showing Georgia Highway 17 and the curves selected for use in testing some embodiments of the present disclosure.

[0069] [Figure 22] FIG. 22 illustrates a computing device that may be used with some embodiments of the present disclosure. DETAILED DESCRIPTION OF THE INVENTION

[0070] To facilitate an understanding of the principles and features of the present disclosure, various exemplary embodiments are described below. The components, steps, and materials described below as making up various elements of the embodiments disclosed herein are intended to be exemplary and not limiting. Many suitable components, steps, and materials that perform the same or similar functions as the components, steps, and materials described herein are intended to be encompassed within the scope of the present disclosure. Such other components, steps, and materials not described herein include, but are not limited to, similar components or steps developed after the development of the embodiments disclosed herein.

[0071] With the advancement of sensor technology, it has become possible to collect sensor data and vehicle motion parameters (e.g., vehicle speed, lateral acceleration, roll angle, etc.) using low-cost mobile devices (e.g., smartphones, tablet PCs, GoPro cameras, etc.) that typically integrate various sensors (e.g., GPS sensors, accelerometers, magnetometers, gyroscopes). These sensor data and vehicle motion parameters can be used to calculate curve feature information such as radius, superelevation, and BBI value for road network-level curve safety assessment.

[0072] Disclosed herein is an improved curve safety assessment and calculation method using low-cost mobile devices. The method uses in-house, crowdsourced, low-cost mobile devices and data analysis from multiple trips to timely identify problematic road curves requiring safety improvements. The goal of the disclosed method is to reduce the current disproportionate number of fatal accidents on road curves. In-house, crowdsourced, low-cost mobile devices can be used to collect sensor data on the road while engineers perform other tasks, thereby reducing engineers' time on the road and minimizing their exposure to dangerous curve sections.

[0073] 1 is a schematic diagram of an exemplary system for optimizing curve markings according to some embodiments of the present disclosure. The systems and methods disclosed herein provide an in-house, crowdsourced data collection and computation framework by leveraging an agency's existing fleet and traffic engineers. This framework allows for data collection (e.g., GPS data, acceleration, gyroscope data, image data, etc.) from multiple trips using low-cost mobile user devices (e.g., smartphones and / or tablet PCs). In fact, this methodology allows traffic engineers to collect data while performing other tasks.

[0074] As noted above, the long intervals between curve safety inspections (typically annual or biennial) can make it difficult for transportation agencies to take proactive measures to improve curve safety in a timely manner. However, the systems and methods disclosed herein can provide a low-cost means for transportation agencies to perform preliminary network-level curve safety screening on a daily or weekly schedule. Once road sections needing curve safety improvement are identified, detailed curve safety assessments can be performed on the identified target sections. This allows transportation agencies to focus their time and attention on the target road curve sections needing improvement rather than sections that do not need improvement. This can result in significant time and cost savings for transportation agencies. By providing such proactive and targeted attention on a daily, weekly, or monthly basis, rather than annually or biennially, the quality and timeliness of curve safety inspections and proactive improvements are significantly improved. The systems and methods disclosed herein are intended to improve upon current network-level curve safety assessment methods, which are costly, laborious, time-consuming, and often dangerous. The disclosed systems and methods can provide transportation agencies with the means to proactively reduce fatalities in the most cost-effective and timely manner.

[0075] The innovative features of the method of the present invention allow for the creative use of low-cost mobile devices within an agency and through crowdsourcing to optimize data collection efforts. The disclosed method allows for roadway data to be collected using agency vehicles while employees perform other daily tasks. In this way, survey frequency is expected to increase from annual to at least weekly. Because agency vehicles travel the same roads multiple times, data can be collected for a single curve section from different drivers on multiple trips at different times. This data can then be analyzed to eliminate bias that would occur if data were collected from only a single trip. Crowdsourcing data collected from fleets and employees within a single transportation agency, i.e., within the agency, ensures data quality.

[0076] Currently, there are no crowdsourced, low-cost mobile applications that can productively and cost-effectively collect and analyze data (collected from multiple trips by different drivers) for assessing road curve safety at the road network level, and perform BBI calculations, superelevation calculations, and recommended speed determinations. The proposed method, which uses a novel in-house, crowdsourced data collection and computation framework, leverages a) existing low-cost mobile user devices (e.g., smartphones, tablet PCs, GoPro cameras, etc.) to collect multiple trip sensor data, such as GPS data and IMU data, and b) the agency's existing fleet and traffic engineers, who can collect data while simultaneously performing other tasks. The data collection and computation framework of the method disclosed herein consists of six modules, described in more detail below: 1) movement data collection, 2) movement data registration and processing, 3) driving kinematics calculation, 4) curve shape calculation, 5) recommended speed calculation, and 6) curve warning sign design. The detailed data collection and computation framework is shown below.

[0077] An exemplary cost-effective method is described that utilizes low-cost mobile user devices and leverages an agency's existing vehicle fleet. The method can accurately and robustly collect and calculate in-service superelevation, BBI values, and recommended speed limits. The proposed method also overcomes current technical challenges related to different driving speeds and behaviors that are expected when engineers simultaneously collect data while performing other daily tasks. The exemplary method is built on the data collection and calculation framework shown in Figure 2.

[0078] An exemplary embodiment of the present disclosure provides a method for improving curve markings. The method may include receiving data from a plurality of user devices. The user devices may be many different user devices, including, but not limited to, smartphones, tablets, GoPros, etc. Data may be collected by user devices located within each of the vehicles as the vehicles travel along one or more roads. For example, data may be received from a first device within a first vehicle and data may be received from a second device within a second vehicle. In some embodiments, each vehicle may include multiple user devices. In particular, the user devices may collect certain information as the vehicles travel along a curved portion of a road.

[0079] Data collected by the user device can be transmitted to a remote computer for further processing. In some embodiments, the data can be transmitted in real time as the data is collected by the user device. In some embodiments, the data can be stored locally on the user device and later transmitted to a remote device (e.g., a cloud-based server). The remote device (e.g., a server) can analyze the data collected from the user device.

[0080] The data collected by the user device may be many different types of data. In some embodiments, the data may be GPS data associated with the user device over a period of time. In some embodiments, the data may indicate the velocity of the user device. In some embodiments, the data may be inertial measurement unit ("IMU") data, including, but not limited to, accelerometer data, gyroscope data, and / or magnetometer data. In some embodiments, the data may include video data. For example, the user device may be equipped with a camera, and the user device may collect video data as the vehicle travels down a road. The video data may include video of the road and video of existing signs along the road.

[0081] The method may further include determining, based at least in part on the data, desired curve markings to be displayed at one or more curve portions. The desired curve markings may be, for example, marks indicating a recommended speed around the curve portion or other marks instructing a driver about the curve portion of the road.

[0082] In any of the embodiments, the method may further comprise determining a location of a curve in the road, which may comprise determining a curve start point (where the curve begins when approached from a particular direction) and / or a curve end point (where the curve ends when approached from a particular direction).

[0083] In some embodiments, determining a desired curve marking to be displayed on a curve in a road may include analyzing data received from a user device to calculate various parameters related to the curve. Exemplary methods for using the data to determine these various characteristics are described below. For example, a curve radius for a particular curve may be determined. In some embodiments, the curve radius may be determined using GPS data and / or road centerline data (which may also be obtained from camera data or map data). In some embodiments, a deviation angle for the curve may be determined. The deviation angle may be determined using GPS data and / or road centerline data.

[0084] An important characteristic of a curve that can be determined by the methods of the present disclosure is the superelevation of the curve, which can be determined using speed data from the user device as well as the path radius and BBI (both of which can be determined using data from the user device).

[0085] As noted above, determining a desirable curve marking may include determining a recommended speed for the curve, which may be determined using the curve radius and the superelevation of the curve, both of which may be determined from data from the user device.

[0086] Determining the desired curve markings may further include determining one or more motion characteristics of the vehicle. In some embodiments, the motion characteristic may be a path radius taken by the vehicle when navigating the curve. In some embodiments, the path radius may be determined using speed data and IMU data in the data acquired from the multiple user devices. In some embodiments, the motion characteristic may include a ball bank indicator (also referred to as ball bank indicator angle) ("BBI") when navigating the curve. The BBI may be determined using IMU data from the user devices.

[0087] The method may further include generating an output indicative of the desired curve marking once the desired curve marking is determined. For example, in some embodiments, the output may be a display of the desired curve marking to be displayed at the curve. In some embodiments, the display may be a list of desired curve markings to be displayed at the curve. The list may include a list of coordinates each corresponding to a geographic location and a desired marking for each of the coordinates. In some embodiments, the display may include a map showing the curve and the desired curve marking to be displayed at the curve. In some embodiments, the output may be a command indicating that a particular marking should be displayed. In some embodiments, the command may also include a location where the particular marking should be displayed.

[0088] It may also be important to determine whether existing signs on the curve match the desired sign. Thus, in some embodiments, the method may further include determining existing signs currently displayed on the curve. In some embodiments, the existing signs may be determined by analyzing video data from a user device that indicates the existing signs. Determining the existing signs may include determining both the location and sign type of the existing signs.

[0089] In some embodiments, the method may further include comparing existing markings currently displayed at the curve with desired curve markings to be displayed at the curve. In some embodiments, the method may further include matching existing markings currently displayed at the curve with desired curve markings to be displayed at the curve by generating a list of markings to be displayed at the curve based on the comparison. In some embodiments, the method may further include generating an output (e.g., a display) of the list of markings to be displayed at the curve. In some embodiments, the list may include a list of coordinates each corresponding to a geographic location and a desired marking for each of the coordinates.

[0090] In addition to the methods described above, some embodiments of the present disclosure provide a system for improving curb markings. The system may include one or more processors. The processors may individually and / or collectively implement one or more steps of the methods disclosed herein. For example, in some embodiments, a first processor may configure one or more steps of the method, and a second processor may perform one or more other steps of the method. In some embodiments, the first and second processors may collectively perform one or more steps of the method. In some embodiments, the one or more processors may be part of a computing device.

[0091] FIG. 22 illustrates an exemplary computing device that can be used to implement the methods (or one or more steps of the methods) disclosed herein. As will be appreciated by those skilled in the art, computing device 220 may be configured to implement all or some of the features described in connection with methods 1000 and 1100. As shown, computing device 220 may include a processor 222, input / output ("I / O") devices 224, and memory 230 including an operating system ("OS") 232 and programs 236. In certain exemplary implementations, computing device 220 may be a single server or may be configured as a distributed computing system including multiple servers or computers that cooperate to perform one or more processes and functions related to the disclosed embodiments. In some embodiments, computing device 220 may be one or more servers in a serverless or scaled server system. In some embodiments, computing device 220 may further include a peripheral interface, a transceiver, a mobile network interface in communication with processor 222, a bus configured to facilitate communication between various components of computing device 220, and a power supply configured to provide power to one or more components of computing device 220.

[0092] For example, a peripheral interface may include hardware, firmware, and / or software that enables communication with various peripheral devices, such as media drives (e.g., magnetic disk, solid state, or optical disk drives), other processing devices, or other input sources used in connection with the disclosed technology. In some embodiments, a peripheral interface may include a serial port, a parallel port, a general-purpose input / output (GPIO) port, a game port, a universal serial bus (USB), a micro USB port, a high-definition multimedia interface (HDMI) port, a video port, an audio port, Bluetooth, TMThe communication interface may include a port, a near field communication (NFC) port, another similar communication interface, or any combination thereof.

[0093] In some embodiments, the transceiver may be configured to communicate with compatible devices and ID tags when they are within a predetermined range. The transceiver may be configured to communicate with any of a variety of technologies, including radio frequency identification (RFID), near field communication (NFC), Bluetooth TM , low power consumption Bluetooth TM (BLE), WiFi TM , ZigBee TM , Ambient Backscatter (ABC) protocol, or similar technologies.

[0094] The mobile network interface may provide access to a cellular network, the Internet, or other wide-area or local-area networks. In some embodiments, the mobile network interface may include hardware, firmware, and / or software that enables the processor 222 to communicate with other devices over wired or wireless networks, whether local or wide-area, and whether private or public, as known in the art. The power source may be configured to provide an appropriate alternating current (AC) or direct current (DC) to operate the components.

[0095] Processor 222 may include one or more, or a combination of, a microprocessor, a microcontroller, a digital signal processor, a coprocessor, etc., capable of executing stored instructions and operating on stored data. Memory 230, in some implementations, may include one or more suitable types of memory (e.g., volatile or non-volatile memory, random access memory (RAM), read-only memory (ROM), programmable read-only memory (PROM), erasable programmable read-only memory (EPROM), electrically erasable programmable read-only memory (EEPROM), magnetic disk, optical disk, floppy disk, hard disk, removable cartridge, flash memory, redundant array of independent disks (RAID), etc.) for storing files containing an operating system, application programs (including, for example, a web browser application, a widget or gadget engine, and other applications as appropriate), executable instructions, and data. In one embodiment, the processing techniques described herein may be implemented as a combination of executable instructions and data stored in memory 230.

[0096] Processor 222 is an Intel TM Pentium TM Family or AMD TM Turion TMThe processor 222 may be one or more known processing devices, including, but not limited to, a microprocessor of the same family. The processor 222 may include a single core or a multi-core processor that simultaneously performs parallel processing. For example, the processor 222 may be a single-core processor configured with virtual processing technology. In particular embodiments, the processor 222 may use logical processors to simultaneously execute and control multiple processes. The processor 222 may implement virtual machine technology or other similar known technology to provide the ability to execute, control, operate, manipulate, store, etc., multiple software processes, applications, programs, etc. Additionally, the processor 222 may include multiple processors, each configured to implement one or more features / steps of the disclosed technology. Those skilled in the art will appreciate that other types of processor configurations that provide the functionality disclosed herein may be implemented.

[0097] According to certain exemplary implementations of the disclosed technology, computing device 220 may include one or more storage devices configured to store information used by processor 222 (or other components) to perform certain functions related to the disclosed embodiments. In one example, computing device 220 may include memory 230 containing instructions that enable processor 222 to execute one or more applications, such as server applications, network communication processes, and any other type of application or software known to be available on computer systems. Alternatively, instructions, application programs, etc. may be stored on external storage devices or available from memory over a network. The one or more storage devices may be volatile or nonvolatile, magnetic, semiconductor, tape, optical, removable, non-removable, or other types of storage or tangible computer-readable media.

[0098] In one embodiment, computing device 220 may include memory 230 containing instructions that, when executed by processor 222, perform one or more processes consistent with the functionality disclosed herein. Methods, systems, and articles of manufacture consistent with the disclosed embodiments are not limited to separate programs or computers configured to perform dedicated tasks. For example, computing device 220 may include memory 230 that may include one or more programs 236 for performing one or more functions of the disclosed embodiments.

[0099] The processor 222 may execute one or more programs located remotely from the computing device 220. For example, the computing device 220 may access one or more remote programs that, when executed, perform functions related to the disclosed embodiments.

[0100] Memory 230 may include one or more memory devices that store data and instructions used to implement one or more features of the disclosed embodiments. Memory 230 may also include a memory controller device (e.g., a server, etc.) or one or more software-controlled databases, such as a document management system, Microsoft TM SQL database, SharePoint TM Database, Oracle TM Database, Sybase TMThe memory 230 may include any combination of a database, a software repository 102, a software program 202, or other relational or non-relational databases. The memory 230 may include software components that, when executed by the processor 222, perform one or more processes consistent with disclosed embodiments. In some examples, the memory 230 may include a database 234 configured to store various data described herein. For example, the database 234 may be configured to store data generated by the software repository 102 or repository intent model 104, such as synopses of computer instructions stored in the software repository 102, input received from a user (e.g., responses to questions or edits made to synopses), or other data that may be used to train the repository intent model 104.

[0101] Computing device 220 may also be communicatively connected to one or more memory devices (e.g., databases), either locally or over a network. The remote memory devices may be configured to store information and may be accessed and / or managed by computing device 220. By way of example, remote memory devices may include document management systems, Microsoft TM SQL database, SharePoint TM Database, Oracle TM Database, Sybase TM The database may be a database, or other relational or non-relational database, however, systems and methods consistent with disclosed embodiments are not limited to these separate databases, or even to using databases.

[0102] Computing device 220 may also include one or more I / O devices 224, which may include one or more user interfaces 226, for receiving signals or input from the device and for providing signals or output to one or more devices that enable data to be received and / or transmitted by computing device 220. For example, computing device 220 may include interface components that can provide an interface to one or more input devices, such as one or more keyboards, mouse devices, touch panels, trackpads, trackballs, scroll wheels, digital cameras, microphones, sensors, etc., that enable computing device 220 to receive data from a user.

[0103] In exemplary embodiments of the disclosed technology, computing device 220 may include any number of hardware and / or software applications executing to facilitate any of its operations. One or more I / O interfaces may be utilized to receive or collect data and / or user instructions from a wide variety of input devices. Received data may be processed by one or more computer processors and / or stored in one or more memory devices, as desired in various implementations of the disclosed technology.

[0104] Although computing device 220 has been described as one form for implementing the techniques described herein, other functionally equivalent techniques may be employed. For example, some or all of the functionality implemented via executable instructions may be implemented using firmware and / or hardware devices, such as application specific integrated circuits (ASICs), programmable logic arrays, state machines, etc. Furthermore, other implementations of computing device 220 may include more or fewer components than those described.

[0105] The following describes various portions of the above-described method in more detail. However, the following discussion provides exemplary embodiments of the present disclosure and should not be construed as limiting the scope of the present disclosure. The following framework is discussed in the context of specific "modules." As used herein, the term "module" is intended to be broadly interpreted and can refer to one or more pieces of software, one or more processors, a collection of method steps, etc. Figure 2 shows six modules: a movement data collection module, a movement data registration and processing module, a driving kinematics calculation module, a curve shape calculation module, a recommended speed calculation module, and a curve warning sign design module.

[0106] Module 1 can collect vehicle speed, global positioning system (GPS), and inertial measurement unit (IMU) data using a mobile device (e.g., smartphone, tablet, GoPro, etc.). The collected data can be registered and processed in Module 2. Module 3 can calculate data items related to driver inputs and vehicle-road interaction (driving kinematics data). This data can include the path radius and BBI angle of the driving trajectory during data collection. After the driving kinematics data is processed, Module 4 calculates curve shape data. While data collected by the mobile device itself (when the vehicle roll rate is unknown) is sufficient to estimate the road superelevation, in some embodiments, better results can be achieved if the vehicle roll rate, a characteristic related to the vehicle's suspension, can be used to calibrate the superelevation results. Furthermore, to determine the curve radius and curve deviation angle, a curve centerline can be used as an external data input for calculating these data items. As shown in Module 5, obtaining the curve shape data allows for the calculation of recommended speeds and speed differentials (using the posted speed limit as an external data input). Finally, Module 6 can use the calculated data results from the previous modules to provide a curve warning sign design that provides appropriate warning sign selection and placement. Disclosed below is an exemplary method for using data collected by a mobile device to calculate the data items in Modules 1 through 5 to support MUTCD curve warning sign design. Also described below is a novel calibration method for estimating vehicle roll rate to correct superelevation calculations to account for the effects of vehicle body roll.

[0107] Module 1: Mobile Data Collection

[0108] A mobile application, referred to herein as "AllGather," was developed to collect and store GPS trajectory, vehicle speed, IMU data, and on-board camera view movement data during data collection.

[0109] Vehicle speed, GPS trajectory, and IMU data can be saved in CSV format and used in computational frameworks. IMU data collected from a mobile device can include three-axis (XYZ) readings from the accelerometer, gyroscope, and magnetometer. This data can be used to describe the vehicle's motion while driving. Therefore, it can be used to calculate driving kinematics data such as the driving path radius and BBI angle. The three-axis readings of the IMU data can be coordinated using the mobile device's local reference frame, as shown in Figure 3. Vehicle speed, GPS, and IMU data can be acquired and recorded using recommended Android library functions. The accelerometer and magnetometer can measure linear acceleration and magnetic field strength along each of the three axes, and the gyroscope can measure angular velocity around each axis. Because the axes use the mobile device's local reference frame, they may not change depending on the smartphone's orientation. Therefore, to describe vehicle motion using IMU data from a mobile device, it may be desirable to fix the mobile device to the vehicle to keep the mobile device's local reference frame aligned with the vehicle.

[0110] The mobile device's camera can be used to record video during data collection, including road image data that helps visualize the condition of curves and data collection status. Additionally, the collected video logs can be used to detect and inventory existing traffic signs and other roadside assets such as guardrails and retaining walls. The camera data collected using the AllGather application can be saved in various video formats, including MPEG4 video format.

[0111] Data collected by the various mobile devices may be transmitted to a remote location (such as a server) where it may undergo various further processing and utilization steps, as disclosed below.

[0112] Module 2: Movement Data Registration

[0113] Data registration is the procedure of aligning two or more data tables generated by different sensors or devices so that they share the same index column. For temporal data registration, the index column may be a timestamp, and for spatial data registration, the index column may be a GPS location or a linear reference distance on a road centerline. This section describes exemplary methods for temporally registering data collected by different sensors in a single data collection run and spatially registering data collected in multiple data collection runs.

[0114] Time data registration

[0115] During data collection for a single trip, mobile data collection can record readings from different sensors (GPS and IMU). Even if the sensors share the same system clock, different sensors may have different sampling rates, which may require time data registration. For example, a typical Android device may report GPS data at a sampling frequency of 1 Hz, while IMU data may update at a higher frequency (e.g., 10 Hz). As a result, data tables may have different lengths for the same time period. Therefore, to obtain correlated IMU data at each GPS location, and vice versa, both data tables can be resampled with the same sampling frequency and a common timestamp.

[0116] Figure 4 shows how two data tables can be registered to share the same timestamp. First, the two data tables are joined using an outer join operation to create a supertable with a single timestamp column containing timestamps from both the raw data from device A and the raw data from device B. In the resulting consolidated data table, missing data (corresponding to timestamps that appear in only one of the input tables) is created using linear interpolation. Finally, the consolidated data table can be resampled at a fixed frequency (e.g., 2 Hz) using averaged values to generate the registered data table.

[0117] Spatial data registration

[0118] In data collection across multiple runs, the data collected on each run can be registered using temporal registration, but the data may not share a common timestamp across runs. Therefore, spatial data registration can be used to enable data aggregation, comparison, and analysis across multiple runs. The goal of spatial registration is to consolidate data tables so that the resulting tables have a common GPS or spatial index column.

[0119] The process of spatial data registration can be very similar to that of temporal registration. The difference is that spatial information can be used as a common index. There are two types of spatial information that can be used as a spatial index: GPS and linear reference distance. The advantage of using GPS as a spatial index is that GPS data is easily available from collected data and no preprocessing is required. To calculate the linear reference distance, it may be necessary to project the GPS point onto the road centerline before calculating the linear reference distance. However, because curve segments can be defined using the linear reference distances of PC and PT points in the curve inventory data, using linear reference distance can be convenient for querying data related to a specific curve. Apart from the difference in what is used as the common index, the spatial data registration procedure can be basically the same as that of temporal data registration.

[0120] Module 3: Calculating driving kinematics data

[0121] Kinematic data items included in the computational framework can include path radius and BBI angle. It is worth noting that in the exemplary computational framework shown in FIG. 2 , there are two types of radius data: path radius and curve radius. In some embodiments, radius estimation can be a key step in the computational framework, and understanding the difference between path radius and curve radius can be important because they are not used interchangeably to calculate curve superelevation and determine appropriate curve recommendation behavior. When negotiating a curve, a vehicle moves laterally within its lane, so the curvature of the vehicle's path may differ from the curve's shape radius. As shown in FIG. 5 , an experienced driver may use lateral movement within the lane to "straighten" a curve so that the path curvature (the inverse of the radius) is less than the curvature of the curve's centerline. Similarly, an inexperienced driver or a driver who "jerks" the steering wheel and makes poor turns may temporarily cause the path curvature to be greater than the curvature of the curve's centerline. Therefore, in this specification, "path radius" reflects the driving trajectory, while "curve radius" reflects the curved road shape. As a technical challenge, the current practice of using curve radius can poorly represent the actual path radius of a vehicle trajectory, introducing errors into the superelevation calculation and increasing sensitivity to driving behavior. Therefore, in some embodiments, the path radius can be calculated based on the actual vehicle trajectory to enable more accurate superelevation calculations.

[0122] Path Radius Estimation Using Vehicle Speed and Angular Velocity

[0123] As shown in Figure 5, the path radius is highly dependent on steering input from the driver and can easily change from moment to moment. Therefore, it is desirable for path radius measurements to reflect the vehicle's movement at a specific moment. A GPS trajectory may not reflect the vehicle's overall movement to some extent for estimating the path radius. However, considering that at least three GPS points are mathematically required to estimate the path radius, i.e., the results are based on a period rather than an instance, and that if too few points are used, the radius results may be numerically unstable due to GPS accuracy, GPS points may not be the optimal data for estimating the path radius. However, the IMU sensor on a smartphone can be used to capture vehicle fluctuations. This specification proposes a method for determining the path radius at any time during vehicle movement using IMU data and GPS data collected by a mobile device, assuming the vehicle is not spinning (oversteering) on the road.

[0124] Curve driving kinematics

[0125] This section briefly describes curve kinematics, which is the basis for calculating BBI and superelevation using the BBI angle. To explain curve kinematics, this section primarily refers to Appendix A of "Development of Guidelines for Establishing Effective Curve Advisory Speeds," by Bonneson et al., FHWA / TX-07 / 0-5439 1, Texas Department of Transportation, Austin, Texas, 2007.

[0126] The ball bank indicator angle (BBI angle) represents the movement of the ball measured in degrees of deflection; this reading indicates the combined effects of superelevation, lateral (centripetal) acceleration, and vehicle body roll. Figure 6 shows the relationship between the BBI angle (α) and lateral acceleration (m(V)). 2 / R), superelevation (φ), and vehicle body roll (ρ).

[0127] The relationship shown in FIG. 6 is valid for any timestamp as long as the vehicle is traveling on a curve, and can be expressed by Equation 1.

number

[0128] From Figure 6, we can see that the angle θ is caused by the centripetal acceleration, the superelevation causes part of the acceleration, and the remaining part is caused by side friction between the tire and the pavement. The angle φ represents the superelevation angle, so the side friction angle (f) is calculated as the difference between the lateral acceleration angle and the superelevation angle (θ - φ). r ) can be defined. Therefore, the relationship in Equation 2 can be derived.

number

[0129] Also, from Figure 6, the BBI angle (α) is related to the side friction angle (f r ) is found to be closely related to

number

[0130] Vehicle body roll is caused by lateral loads acting on the vehicle. The amount of body roll under the same lateral load is highly dependent on the vehicle's suspension characteristics. Previous research has shown that there is a certain roll rate between the side friction angle and the body roll angle. This relationship is shown in Equation 4, where k = vehicle roll rate (rad / rad).

number

[0131] Subsequently, the relationship between the BBI angle and the lateral friction angle is expressed as Equation 5.

number

[0132] Then, by substituting the side friction angle of Equation 5 into Equation 2, Equation 6 is derived.

number

[0133] It is worth noting that assuming the vehicle roll rate is equal to zero when it is not available is the same as assuming no body roll when the vehicle turns, and estimating the side friction angle from the BBI angle using this assumption may result in an exaggerated side friction angle. The error amount from this assumption has a positive linear relationship with the BBI angle, so the error amount increases as the BBI angle increases.

[0134] Equation 6 shows that if the vehicle speed, path radius, and superelevation are known, the side friction angle can be calculated and has a (1 + k) relationship to the BBI angle. If the vehicle roll rate is also known, the expected BBI angle can be calculated and verified from the mobile device's BBI angle.

[0135] BBI angle calculation

[0136] If you understand curve kinematics, you will know that the BBI angle can be the angle between the vertical of the vehicle chassis and the net acceleration (including gravity) experienced by the vehicle. Therefore, the BBI angle can be calculated by dividing two items in the motion data: the vertical vector of the vehicle chassis TIFF2025527214000010.tif5151 and net acceleration vector TIFF2025527214000011.tif5151. The chassis normal vector represents the direction of the net acceleration vector, and if they are parallel the BBI reading will be "zero", hence referred to herein as the "zero vector".

[0137] To obtain the "zero vector," the data collection device can first be secured to the vehicle chassis (e.g., attached to the windshield using a suction cup holder or other means of securing the user device to the car) with the camera facing forward. In some embodiments, a better reading can be obtained if the vehicle remains stationary on level ground for the first few seconds of the data collection run. During the stationary phase, the direction of gravity can be measured by the accelerometer and used as the "zero vector."

[0138] Once the "zero vector" is obtained, the accelerometer can continuously measure the acceleration experienced by the vehicle, and the acceleration component perpendicular to the vehicle's direction of travel can be used to calculate the BBI angle.

[0139] Module 4: Calculating Curve Shape Data

[0140] This section provides examples of how to calculate curve shape data. The curve radius and deviation angle can be calculated from road centerline or GPS data, and the curve superelevation can be calculated from IMU data.

[0141] Determining curve radius and deviation angle

[0142] In some embodiments, the curve radius and curve deviation angle of a road can be determined by fitting a circle to the geometry of the road centerline or GPS trajectory, which can consist of three main steps: step 1—smoothing the centerline or trajectory data; step 2—locating the curve beginning point (“PC”) and curve ending point (“PT”) and estimating the deviation angle; and step 3—estimating the radius.

[0143] Step 1 can consist of removing outliers from the raw centerline and GPS data. This is because identifying PCs and PTs can be highly dependent on orientation changes that can be calculated by rolling consecutive points along the data. In some embodiments, the polynomial approximation with exponential kernel (PAEK) method can be used, a smoothing algorithm developed by ESRI in ArcGIS software that provides a robust line smoothing function. This function was developed based on the algorithm defined by Bodansky et al., "Smoothing and compression of lines obtained by raster-to-vector conversion," in International Workshop on Graphics Recognition, pp. 256-265. Springer, Berlin, Heidelberg, 2001.

[0144] Step 2 may consist of identifying PC and PT based on heading change. A vehicle's heading change begins at PC and ends at PT. The heading change can be calculated as the difference in heading angle between consecutive points. Figure 7 shows the curve-extracted centerline data for State Route 2 (SR-2), and Figure 8 shows the corresponding curve-extracted heading angles.

[0145] Step 3 may consist of fitting a circle between PC and PT to estimate the radius of each extracted curve. In some embodiments, the Kasa method can be used (Kasa, I., "A Circle Fitting Procedure and Its Error Analysis," IEEE Transactions on Instrumentation and Measurement IM-25, no. 1 (1976): 8-14. https: / / doi.org / 10.1109 / TIM.1976.6312298). This is a widely used least-squares circular geometric fitting method based on finding the minimum distance from a given point to the fitted geometric feature.

[0146] Determining the superelevation of a curve

[0147] From Equation 6, the superelevation calculation is derived as Equation 7. The relationship in Equation 7 can be based on any instance of the vehicle being in motion. Therefore, a timestamp (R p (t i )) can be used.

number

[0148] If the BBI reading indicates that the "ball of steel" is swinging towards the outside of the curve, a positive BBI angle may have a positive sign, and if the "ball of steel" is swinging towards the inside of the curve, a negative sign may be used.

[0149] Calibration method for vehicle roll rate estimation

[0150] As shown in Equation 7, the superelevation of a curve can be determined using vehicle speed, path radius, BBI angle, and vehicle roll rate. Vehicle speed, path radius, and BBI angle can be obtained directly or calculated from collected travel data. Vehicle roll rate (k) may not be directly measurable with a mobile device. As discussed in the section on curve driving kinematics above, assuming k = 0 may still produce reasonable superelevation results, but the superelevation error may increase continuously with increasing side friction angle. Therefore, as driving speed increases, superelevation results may become increasingly underestimated. Because driving speeds and trajectories are not always smooth, this technical challenge may hinder the use of low-cost smart mobile devices and the utilization of existing vehicle fleets (while engineers are performing their daily tasks).

[0151] Although vehicle roll rate can be measured mechanically, it may be impractical to require all data collection of vehicle roll rate to be done mechanically. Therefore, two calibration methods are described herein that use mobile data collection to estimate vehicle roll rate without mechanical testing. The first method can utilize known measurements of superelevation, while the second method can utilize data collection from multiple runs of the same curve at different driving speeds, but may not utilize known superelevation.

[0152] Calibration using a curve with known superelevation

[0153] The lateral friction angle (f r ) can be determined using the known vehicle speed, path radius, and superelevation. The resulting side friction angle (f r ) can have a (1+k) relationship to the measured BBI angle. Therefore, if the superelevation is known, the side rub angle can be calculated using the known superelevation for the location where the BBI angle data was measured, and the side rub angle and BBI angle can have a linear relationship with a slope equal to (1+k).

[0154] Figure 9 shows an example of the results of testing conducted at the National Center of Asphalt Technology (NCAT) test track. Superelevation was measured manually every 100 ft on increasing radius sections and every 200 ft on constant radius sections. The measured superelevation was combined with collected travel data to calculate side friction angle, which was found to have a good linear relationship with a slope of 1.093 and a roll rate of 0.093 rad / rad for the data collection vehicle. Detailed results using this calibration method are provided in the following section on validation.

[0155] Calibration using curves with unknown superelevation

[0156] Manually measuring the superelevation of a curve may be impractical for agencies without external access to closed facilities. Therefore, a calibration method is disclosed herein that does not require superelevation measurements. Data collection can be performed on multiple runs at different speeds on the same curve where the superelevation is unknown. This method is effective because the superelevation of the same curve does not change between runs. While the true superelevation is unknown, if the vehicle roll rate is correctly estimated, the calculated superelevation will be similar between runs at different speeds.

[0157] The data shown in Figure 9 was collected at five different speeds in 5 MPH increments. Using the same data but without measured superelevation, this calibration method is able to find a best fit vehicle roll rate equal to 0.095 rad / rad, similar to the roll rate of 0.093 found using the "known superelevation" method. A detailed analysis of this calibration method is provided in the following section on validation.

[0158] Module 5: Determining Recommended Speeds

[0159] As described below, according to various embodiments of the present disclosure, recommended speeds for curves can be determined based on data collection from a single trip or multiple trips.

[0160] Determine recommended speed by collecting data from a single run

[0161] Accurately calculating the recommended curve speed is crucial to driver safety because it determines the type and placement of warning signs. If the calculated recommended speed is too high, the driver may not be prepared for a sharp curve. If the calculated recommended speed is too low, the driver may lose confidence in the curve warning signs and begin to ignore them, ultimately putting themselves at risk. Equation 8 shows an example calculation for determining the recommended curve speed. In this calculation, the route radius (R p ) but the curve radius (R c ) is used because the recommended speed may depend on the shape of the curve, rather than on the particular driver on a particular data collection run.

number

[0162] In the formula, f max is the maximum lateral friction coefficient allowed by the recommended speed standard, and R c is the curve radius (ft), and V adv may be the recommended speed limit (MPH).

[0163] The 2009 MUTCD defines the recommended speed standards as a 16-degree ball bank for speeds of 20 MPH or less, a 14-degree ball bank for speeds of 25-30 MPH, and a 12-degree ball bank for speeds of 35 MPH or greater. This corresponds to maximum allowable side friction coefficients of 0.287 for speeds of 20 MPH or less, 0.249 for speeds of 25-30 MPH, and 0.212 for speeds of 35 MPH or greater. For data collected from a single run, the recommended speed can be calculated for each data point along the curve, and the result of the minimum recommended speed can be reported as the recommended speed for the curve.

[0164] Determining recommended speeds by collecting data from multiple runs

[0165] For data collected from multiple runs, the proposed computational framework can be used to process each individual data collection run. Because the recommended speed is determined based on the minimum recommended speed along the curve, noise or unreliable data can often reduce the recommended speed for the entire curve. Therefore, when processing data from multiple runs, the highest recommended speed from each run can be used as the recommended speed for the curve. Furthermore, the variability between individual runs can be used as an indicator to flag unreliable results, which recommends recollection of data. The final recommended speed result can be determined by comparing the recommended speeds obtained from the data from multiple runs. In addition to selecting the highest recommended speed calculated among the data from multiple runs as the final recommended design speed, a confidence level (L, M, or H) for the calculated recommended speed is recommended based on the variability between the recommended speeds calculated for a single run. This confidence level is a qualitative indicator. A low confidence level (L) indicates high data variability between different runs. In some cases, high data variability may lead to recollection of data in the field. A high confidence level indicates high consistency between measurements from different runs. A case study of multiple trip analysis using data collected on Georgia Highway 17 is presented below. In some embodiments, the multiple trip data used may be based on the results of recommended speeds. The rich data collected through multiple trip travel data collection has the potential to further be used for other analyses used to determine data quality and driver behavior.

[0166] Validating the proposed computational framework using mobile data collection devices

[0167] This section presents validation tests and results of an exemplary computational framework for curve safety assessment using mobile data collection devices. Two tests are described: a repeatability test to preliminarily evaluate the repeatability of mobile sensors across different devices, and a validation test to comprehensively evaluate the performance of the proposed computational framework when using mobile devices. The validation test was conducted on an external, closed test track at the National Center for Asphalt Technology (NCAT) to validate the proposed method using different driving speeds and different driver inputs. This section evaluates the calculation results for radius, BBI angle, superelevation, and recommended speed. To evaluate the feasibility of using the proposed method to estimate superelevation using a low-cost smartphone, the validation test focused on comparing the calculated superelevation results with manually measured superelevation on a road. There are at least two reasons for this design. First, superelevation can be an important component of the curve shape information required to determine an appropriate curve recommended speed. Because its accuracy may depend on other calculation factors, such as the path radius and BBI angle, accurate superelevation estimation may depend on accurate estimation of both the path radius and BBI angle. Second, superelevation, which is part of the curve geometry, can be physically measured and does not change during testing despite different driving speeds and driver inputs, facilitating evaluation of the exemplary methods disclosed herein by allowing data collected from different data collection runs to be compared to baseline superelevation values for the same terrain.

[0168] Mobile sensor repeatability test

[0169] The reliability and repeatability of mobile sensors are fundamental when using mobile devices to collect data for curb safety assessment. This test aimed to evaluate the repeatability of IMU data collected by multiple mobile devices in the same data collection environment. The test was designed to install multiple mobile devices in the same orientation inside a data collection vehicle and record IMU data as the vehicle moved. The test was performed using three different smartphones mounted on the dashboard: a Xiaomi Redmi Note 4 White (Xiaomi 1), a Google Pixel 3a (Pixel), and a Xiaomi Redmi Note 4 Black (Xiaomi 2).

[0170] All of these smartphones were installed in the same vehicle at the same time of data collection, so the data collection environment was identical for all devices. In other words, if data collected on different devices is perfectly reproducible, IMU data collected on different devices should have perfect correlation between devices.

[0171] The IMU data for each device provides linear acceleration, angular velocity, and magnetic field in all X, Y, and Z directions. However, in some embodiments, the calculation method uses only linear acceleration and angular velocity data from the IMU. For each sensor reading, the normalized cross-correlation was compared for each pair of devices. The normalized cross-correlation measures the similarity between two signals and is scaled between -1 and 1, with a correlation of 1 meaning the signals are perfectly similar. Table 1 shows the normalized cross-correlation of different sensor data between different device pairs. [Table 1]

[0172] The results show that most sensor data have high correlations (above 0.98), indicating that results calculated from data collected on one mobile device are reproducible on another. Among the different sensors, angular velocity in the Y direction exhibited the lowest normalized cross-correlation value, likely due to the way the devices were configured. The Y axis of the device is aligned with the driving direction, and in typical driving conditions, the vehicle does not rotate significantly around this axis. Therefore, there is no significant rotation signal collected by the sensor, and the correlation score is significantly affected by random sensor noise. Given that the quality of sensors within the same device is generally similar, the reproducibility of angular velocity Y should be similar to that of other axes when the device is positioned in different directions within the vehicle.

[0173] Validation test of example method

[0174] The purpose of the validation study was to evaluate the feasibility of an example method using a mobile device to collect and analyze curve safety assessment data. The study focused on verifying the accuracy of superelevation estimation. Superelevation is a key data item for determining appropriate curve speed recommendations, and superelevation is a part of curve geometry that can be physically measured to evaluate the accuracy of superelevation estimation. Evaluation of other calculated data items, such as BBI angle and speed limit, was extended from superelevation by back-calculating expected values using manually measured superelevation.

[0175] The National Center for Asphalt Technology (NCAT) as a validation testing site.

[0176] The National Center for Asphalt Technology (NCAT) in Auburn, Alabama, has an enclosed facility with a 1.7-mile oval test track for accelerated pavement testing. Because the NCAT test track is not a public road, it is an ideal location for conducting validation testing because superelevation measurements can be made manually without the need for traffic restrictions. Levels and cross sections are also available to provide curve geometry information. However, because the test track has been repaved multiple times since it was first constructed, superelevation values were measured manually across the curve to obtain the current superelevation of the test track.

[0177] Verification test design and test procedures

[0178] As mentioned above, the purpose of the test was to verify the data items calculated by the example method. However, the design of the verification focused on using superelevation as a physically measurable curve shape to verify the superelevation calculation. Alternatively, the verification used measured superelevation to back-calculate expected values to verify the BBI angle and recommended speed calculations. Additionally, the verification of curve radius estimation was performed by comparing the estimated curve radius with the radius shown on the track design drawings.

[0179] Manual Superelevation Measurement

[0180] To obtain detailed superelevation data on the NCAT test track, superelevation measurements were taken along the entire curve. The NCAT test track curve consists of a constant radius section with a 476-foot radius curve at the center and two increasing radius sections at the beginning and end of the curve, each following a tangent section of the track. Superelevation data was measured every 200 feet along the constant radius section and every 100 feet along the increasing radius section. Additional measurements were taken at the transitions between the tangent and increasing radius sections and between the increasing and circular radius sections. Figure 10 shows the locations where superelevation was manually measured on the NCAT test track.

[0181] Superelevation measurements were taken manually at each location shown in Figure 10 using an 8-foot straightedge and a digital level. Three measurements were taken at each location, spaced 1 foot apart. The average of the three measurements was used to represent the superelevation of the track. The digital level used is capable of providing slope readings down to a minimum slope of 0.1%.

[0182] According to the design drawings, the test track was designed to have a 15% gradient at full superelevation of the curve. Manual measurements showed that the current test track has a gradient of 14% to 16% at full superelevation of the curve.

[0183] Driving speed and behavior

[0184] Validation testing was conducted by collecting data from multiple runs at different driving speeds and different driving behaviors. Different driving speeds were achieved using the vehicle's cruise control system. Tests were conducted at five different speeds, from 30 MPH to 50 MPH, in 5 MPH increments. Five laps were run at each speed to evaluate the reproducibility of the calculations. Various driving behaviors were introduced. For example, the driver navigated curves as smoothly as possible to represent "good / optimal" driving behavior. On the final lap, the driver made abrupt steering adjustments that caused the vehicle to wobble in its lane to mimic "bad / undesirable" driving behavior.

[0185] Data Collection Devices and Preparation

[0186] The validation tests used three mobile devices: two Android smartphones and a GoPro camera with built-in GPS and IMU sensors. Two smartphones were installed to evaluate the effects of different mounting methods: smartphone 1 was attached to the dashboard with a clamp mount, and smartphone 2 was attached with a suction cup with an extension arm to secure the device. The GoPro camera was included to evaluate the effects of different sensors; the GPS and IMU sensors in the GoPro camera have a higher sampling frequency than smartphones, and the sensor quality may differ for the GoPro. Additionally, a Rieker inclinometer was included in the tests to represent a commercial solution for BBI angle measurement.

[0187] Test Procedure

[0188] The NCAT verification was carried out as follows:

[0189] Task 1: Investigate the superelevation of the NCAT test track. Use a measuring wheel to locate key control points (points between the increasing radius and tangent sections, and points between the circular and increasing radius sections). Starting at the midpoint of each curve, measure superelevation at the following distances from the midpoint: 0 ft, 200 ft, 400 ft, 543.7 ft, 600 ft, 700 ft, 800 ft, 900 ft, 951.7 ft, 1000 ft, and 1100 ft. At each location, take three superelevation measurements at 1-ft intervals. Report the average of the three measurements.

[0190] Task 2: Collect mobile data (on the move). Prepare the vehicle (Chevrolet Tahoe SUV) with data collection devices. Before the start of each data collection run, park the vehicle on a tangent section, preferably on the centerline to balance the lateral tilt. All test devices begin recording simultaneously. After recording begins, wait at least 10 seconds to allow BBI measurements to zero. Proceed with the data collection runs in Table 2 below. After each run, resume recording. [Table 2]

[0191] Verification test results - Curve radius calculation

[0192] The NCAT test track has two major curves (west curve and east curve) with the same curve radius. To verify the proposed method for calculating the curve radius, the estimated curve radius is compared with the curve radius on the design drawings.

[0193] An example method tested is the use of road centerlines to extract curve radii. For this test, Google Earth was used to extract the test track centerline. The "add path" tool was used to manually trace the test track centerline on the satellite map (using the pavement markings as reference).

[0194] After obtaining the centerline, the curve radius was calculated by estimating the radius using the Kasa fit method for the curved section on the road centerline by estimating the circle fitting using the least squares method. The curve radius estimated using the proposed method was 478.1 ft for the west curve and 481.4 ft for the east curve. The curve radius listed in the design drawings was 476 ft for the circular section of the curve. This shows that the curve radius can be estimated very reasonably using the road centerline using the example method.

[0195] Verification Test Results - Superelevation Calculation without Body Roll Calibration

[0196] As shown in Equation 7, an example method for calculating superelevation can use driving speed, route radius, and vehicle roll rate. However, vehicle roll rate may not be readily available. When roll rate information is unavailable, superelevation can be approximated by assuming small vehicle body roll such that the roll rate constant is equal to zero. While this assumption may be reasonable at low driving speeds, as a vehicle travels faster around a curve, the amount of body roll increases, making the assumption less accurate than it actually is. This section demonstrates the level of accuracy of superelevation calculations at different driving speeds when assuming no vehicle body roll.

[0197] Superelevation results at different driving speeds

[0198] Figures 11A-11C show the error of uncalibrated superelevation results calculated from three data collection devices. As shown, the error variance (vertical spread) is similar across all devices at all speeds, but the GoPro results show that the random error is smaller with the GoPro than with the smartphone. Additionally, the bias of the superelevation error tends to decrease as speed increases. This indicates that without calibration, the calculation tends to underestimate the superelevation of the road when the vehicle is traveling at high speeds. The amount of underestimation is positively related to driving speed. This behavior is expected and can be explained by Equation 7. Assuming no vehicle body roll, a large BBI angle (typically associated with high driving speeds) can result in a lower superelevation result.

[0199] Table 3 summarizes the root mean square error (RMSE) of the uncalibrated superelevation results, categorized by vehicle speed, mobile device, and driving behavior. The RMSE for superelevation is shown in Figure 12. The results show that the GoPro data is more accurate than the smartphone data. Smartphone 1 is slightly more accurate than Smartphone 2, suggesting that the mounting mechanism for Smartphone 1 (mounted with a dashboard clamp) may slightly improve accuracy. Finally, poor driving on curves (shown in Figure 13) reduces the accuracy of the superelevation calculation. However, the exemplary method tested increases the superelevation error level by less than 0.5% slope. [Table 3]

[0200] The importance of using path radius in superelevation calculations

[0201] As mentioned above in the validation test design, different driving behaviors were also introduced in the validation test to evaluate the robustness of the example method. Figure 13 shows the different driving behaviors applied during the validation test.

[0202] The radius of the vehicle's path was used to calculate superelevation. Generally, the radius of a curve's centerline is a good approximation of the path's radius. As shown in Figure 13, the curvature of a "well-driven" path generally resembles the curvature of the centerline. However, driving behaviors such as frequent lane sway or "jerking" the wheels when turning can cause the curvature of the driven path to differ significantly from the centerline. Therefore, at any point in time while turning a curve, the speed, BBI angle, and path radius corresponding to the vehicle at that time can be used to calculate the superelevation at that time.

[0203] The examples in Figures 14A-14B show that for "good driving," approximating the path radius using the curve radius can result in an acceptable cross-over estimation. However, when "bad driving" occurs, with jerky or shaky wheels, the curve radius can no longer represent the vehicle's path, potentially resulting in significant cross-over estimation errors (as shown in Figure 15).

[0204] Performance comparison of different path radius calculation methods

[0205] It would be logical to use GPS tracking the vehicle's trajectory to calculate the path radius. However, given the smartphone's GPS sampling rate (typically 1 Hz) and GPS accuracy (typically about 15 ft), subtle movements due to steering inputs may not be captured. Obtaining the path radius at a specific GPS point may require nearby points for least-squares fitting. Therefore, the path radius calculated from GPS may not represent the curvature of the path at a given moment, but may represent the curvature averaged over a short period of time.

[0206] With this in mind, an exemplary method can measure the path radius from angular velocity and vehicle speed. Figures 16A-16B are examples of "bad driving" cases that demonstrate the difference in superelevation measurement performance between using a path radius estimated from a GPS and a path radius estimated from a gyroscope.

[0207] These results show that there is still a significant error when using the GPS method. When calculating the route radius from the gyro sensor and vehicle speed, the curvature, or radius, at each point when turning a curve was accurately captured, and no significant difference in performance was observed compared to the "good driving" case.

[0208] Verification test results - Vehicle roll rate estimation

[0209] As seen in the uncalibrated superelevation results, vehicle speed can affect the accuracy of the results, as increased speed can cause more body roll, reducing the accuracy of the results. If the body roll rate is known, the induced error can be minimized. However, most vehicle owners may not know their vehicle roll rate. Therefore, the roll rate can be measured to calibrate the superelevation results.

[0210] An example method for estimating vehicle roll rate from collected movement data has been described above, so this section presents the results of the example method using data collected during the NCAT test. [Table 4]

[0211] Roll rate estimation when superelevation is known

[0212] As described in the previous section, this exemplary method uses the measured superelevation to calculate the side friction angle during data collection and estimates vehicle roll rate by comparing the relationship between the side friction angle (calculated using Equation 2) and the measured BBI angle (shown in Figure 17).

[0213] Roll rate estimation when superelevation is unknown

[0214] The advantage of roll rate estimation when superelevation is known is its ease of calculation, but detailed superelevation measurements may not be feasible in most situations. Therefore, as mentioned in the previous section, if superelevation measurements are not available, an alternative approach is to use a vehicle to collect travel data on the same curve at different speeds. Using data collected on two of five laps at five different speeds (30 MPH to 50 MPH) with NCAT, vehicle roll rate was estimated without measured superelevation. The estimation results are shown in Table 4, and it can be seen that the estimation results are similar across different devices. The standard deviation is slightly increased compared to the "known superelevation" method.

[0215] This method of estimating vehicle roll rate can utilize data collection from multiple runs at different speeds, but is considered more realistic to implement because it does not require knowledge of the shape of the curve and the repeatability is similar to the "known superelevation" method. [Table 5]

[0216] To explore the recommended speed differences between runs and between runs at each speed for this roll rate estimation method, Table 5 shows the estimated roll rates using different data collection strategies. While a larger number of runs generally improves the reproducibility of the method, it can be seen that the speed difference between the highest and lowest speeds of data collection can play a more important role in the reproducibility of the results. Therefore, if this method is formalized as a calibration method, a reasonable roll rate estimate can be obtained by simply conducting a calibration test at two different speeds and repeating each speed twice. Repeating each speed three (or more) times can provide a more reliable estimate.

[0217] Verification test results - Superelevation calculation with body roll calibration

[0218] The vehicle roll rate estimated by the exemplary method can be used to calibrate the superelevation results to correct for the effects of vehicle body roll. Figures 18A-18C show a comparison of superelevation errors before and after calibration using the estimated body roll rate. Table 6 summarizes the RMSE of the uncalibrated superelevation results, categorized based on vehicle speed, mobile device, and driving behavior. The superelevation RMSE is shown in Figure 19. The results show that after calibration, the accuracy of the superelevation measurement may be less affected by driving speed. The random noise level of the device (vertical spread at each speed) is not affected by the calibration.

[0219] The results showed that after calibration, the GoPro camera could measure superelevation with an accuracy of 0.598% incline, while the smartphone could achieve a measurement accuracy of 1.4%-1.5% incline. [Table 6]

[0220] Verification test results - BBI angle calculation

[0221] To assess the accuracy of the BBI angle measurements, manually measured superelevation values were used to back-calculate the predicted BBI angle based on the side friction angle and vehicle body roll. Table 7 shows the RMSE for the BBI angle measured by each device. The linear regressions between the measured and predicted BBI angles are also shown in Figures 20A-20D. [Table 7]

[0222] Because the predicted BBI angle is back-calculated from the side friction angle, the accuracy of the side friction angle, which depends on the measured superelevation, vehicle speed, and route radius estimation, can affect the predicted BBI angle. Therefore, the RMSE values shown in the table do not represent the BBI measurement error per se. However, since it is difficult to obtain the true BBI angle at each instant of data collection, the presented RMSE values are a good general indicator of the accuracy of the BBI measurement.

[0223] Verification test results - Recommended speed calculation

[0224] Table 8 shows the recommended speed results using the exemplary method of the present disclosure. From the manually measured superelevation, the correct recommended speed on the test track curve should be 49.7 MPH. Validation results show that without calibration, the determined recommended speed decreases as the data collection speed increases because the superelevation is underestimated. However, the recommended speed difference between the minimum and maximum data collection speeds is less than 2 MPH.

[0225] After calibration, superelevation was no longer underestimated at higher speeds. The recommended speed results were very consistent across different speeds. The recommended speed variance across all data collection speeds was less than 1 MPH. Compared to the recommended speed calculated from manually measured superelevation, the GoPro recommended speed results differed by less than 0.5 MPH (underestimation), and the smartphone recommended speed results differed by less than 1.3 MPH (underestimation). [Table 8]

[0226] Sensitivity of the recommended speed results and allowance for calculation error

[0227] Because the curves on the NCAT test track have only one curve shape, a mathematical sensitivity study was conducted to determine the margin of error for curves with different shapes. Because recommended speeds are typically rounded down to the nearest 5 MPH, the margin of error shown in Table 9 indicates the amount of error that can be tolerated in each element without changing the final calculated recommended speed. [Table 9]

[0228] The sensitivity of each element can depend on the shape of the curve and the characteristics of the data collection, as shown in Table 9. To obtain accurate results in all cases, it is desirable to have BBI accuracy within 1 degree, superelevation accuracy within 3%, and curve radius accuracy within 150 ft. From the validation results presented in this section, it can be concluded that the accuracy of the calculated BBI angle, superelevation, and curve radius is within the error tolerance.

[0229] Verification Summary

[0230] The validation tests presented herein demonstrate that using vehicle roll rate in superelevation calculations can reduce errors caused by different data collection speeds. The illustrated method also demonstrates that vehicle roll rate can be estimated to correct for superelevation calculations. Before calibration, the superelevation results showed an overall RMSE of approximately 1.0% for the GoPro camera and approximately 2.0% to 2.2% for the smartphone. Before calibration, the superelevation error increased with increasing driving speed, with the RMSE for superelevation at 50 MPH being approximately 1.8% for the GoPro camera and approximately 3.2% for the smartphone. After calibration, the superelevation error caused by driving speed almost completely disappeared, resulting in an overall RMSE of approximately 0.6% for the GoPro camera and approximately 1.4% to 1.5% for the smartphone. Validation of the BBI angle demonstrated that the GoPro camera (RMSE = 0.39°) could accurately estimate the BBI angle, comparable to a commercially available BBI device (RMSE = 0.52°). On the other hand, the RMSE for the smartphone was 0.9 degrees to 0.96 degrees, slightly worse than the commercial device but still accurate enough for determining the recommended speed.Finally, looking at the recommended speed results, the determined recommended speed was very close to the recommended speed calculated using the measured superelevation, with the difference being less than 3 MPH before calibration and approximately 1 MPH after calibration.

[0231] Case Study

[0232] This section presents a preliminary case study using smartphone data from five trips collected on Georgia Highway 17. This case study demonstrates the use of the exemplary method of the present disclosure using a smartphone to perform a curve safety assessment. The purpose of this case study is to demonstrate the feasibility of using the exemplary method to derive curve radius, BBI, superelevation, and recommended speed using a smartphone. Additionally, this case study also evaluates the reliability of the results. Furthermore, both a smartphone and a Rieker device were installed in the same vehicle, and data was collected simultaneously for comparison. This was done to compare the results obtained using the exemplary method of the present disclosure with those of a conventional assessment method currently commonly used, which utilizes a dedicated Rieker device.

[0233] Feasibility study of an example method using smartphone data collected on Georgia Highway 17

[0234] The purpose of this case study is to evaluate and demonstrate the feasibility of using the exemplary methods of the present disclosure to derive curve radius, BBI, superelevation, and recommended speed using a smartphone and smartphone data collected on Georgia State Highway (SR) 17.

[0235] Data collection

[0236] After discussing with Georgia Department of Transportation (GDOT) traffic engineers the best location to test the proposed method, SR17 was selected as the best location to conduct this feasibility study due to its curvilinear nature and the high incidence of crashes on this road. Figure 21 shows a map of the SR17 test site selected for data collection and a detailed view of the five curve sections used for detailed data processing and analysis in this feasibility study. The selected portion of SR17 is a two-lane, undivided rural secondary highway with an occasional painted / striped median. This portion of SR17 is mountainous and curvilinear.

[0237] Field data collection using smartphones was conducted with five trips in each direction. Data collection was conducted in four GDOT-owned Ford F150s and one Ford Fusion. Five trips in each direction were conducted under clear skies. One smartphone was installed in each vehicle for data collection. The smartphones were standard Android smartphones, and the same one was used for all field data collection. The smartphone data collected included 1) timestamp, 2) speed, 3) GPS data, and 4) IMU data.

[0238] Data Processing

[0239] The collected smartphone data, including timestamps, speed, GPS data, and IMU data, was processed for each of the five individual runs. Details of the data processing have been described previously and will not be repeated here. The next section describes the data analysis.

[0240] Data analysis

[0241] The data collected using the smartphone was processed to determine the curve radius, BBI, superelevation, and recommended speed at each location. Using data from five runs, the smartphone data allows for an assessment of the inherent variability in results. Table 10 shows the location and shape of the five curves tested. Table 11 shows the radius, BBI, superelevation, and calculated recommended speed range for each curve. The BBI and superelevation values refer to the point where the calculated recommended speed is at its minimum. [Table 10] [Table 11]

[0242] Using a sample of five curves on SR17, the average variation in measurements between data collection runs was found to be approximately 49 feet for radius, 8 degrees for BBI, 5% for superelevation, and 2 MPH for calculated recommended speed. Tables 11 and 12 list the range of values for estimated radius, measured BBI, estimated superelevation, and calculated recommended speed for the five selected curves in the northbound and southbound directions, respectively, using data from the five runs. The results indicate a high level of consistency in the calculation of recommended speeds between the five runs using smartphone data, which means the results are reliable.

[0243] When calculating recommended speeds, standard practice is to add 1 MPH and round the raw calculation down to the nearest multiple of 5 MPH to design recommended speed signs. If the rounded recommended speed calculation results are the same for all data collection runs, this indicates that the results are highly reliable. For the five sample curves surveyed in SR17, smartphone data collection was conducted 10 times, five times in each direction at each curve. The number of runs that resulted in the same recommended speed at each curve is shown in Table 12. [Table 12]

[0244] This demonstrates the high reproducibility of the results of the smartphone-based example method. It should be noted that due to the nature of rounding of recommended speeds, two very similar calculations may produce different recommended speeds (e.g., 29 rounds to 30 MPH, 28 rounds to 25 MPH). Therefore, some variability in the final calculated recommended speed is acceptable. If the recommended speeds calculated from different runs at a given curve vary by more than 5 MPH, the results will differ significantly enough to require recollection of data. Because the highest recommended speed calculated from multiple runs is likely to most closely represent actual road conditions, the highest calculated recommended speed can be selected when selecting an appropriate recommended speed for a curve. Erratic driver behavior (e.g., varying speeds, jerky steering, failure to follow road trajectory) can skew calculations artificially low. Conversely, because human error cannot artificially inflate the calculated recommended speed, the highest result most closely approximates the true value. Analysis of five curves on SR17 demonstrated that the exemplary method of the present disclosure, tested using a smartphone, is feasible for calculating curve radius, BBI, superelevation, and recommended speed.

[0245] Comparison of results from the example method using a smartphone with results from the method using a Rieker device

[0246] Because most transportation agencies currently use a dedicated Rieker device approach, we compared the results of the exemplary method of the present disclosure (using a smartphone) with the results of the currently commonly used method (using a dedicated Rieker device). To compare the performance of the exemplary method with that of the Rieker device approach, a single vehicle was equipped with both a smartphone and a Rieker device. Table 13 below compares the calculation results of the recommended speed output from each method. As shown, for these five sample curves, the proposed method and the Rieker method produce results within 6 MPH of each other. Therefore, the two methods are comparable. [Table 13]

[0247] The smartphone data and the Rieker data can also be compared in terms of reproducibility. The reproducibility of the calculated recommended speed is important because it can determine the overall reliability of the results. For the five sample curves mentioned above, the standard deviation of the calculated recommended speed between data collections of multiple runs was calculated. The results showed that the standard deviation of the calculated recommended speed from the smartphone data was 0.89 MPH, while the standard deviation of the calculated recommended speed from the Rieker data was 1.59 MPH. Therefore, the calculation of the recommended speed using the exemplary method of the present disclosure is more consistent.

[0248] It is to be understood that the embodiments and claims disclosed herein are not limited in their application to the details of construction and the arrangement of components described herein and illustrated in the drawings. Rather, the specification and drawings provide examples of contemplated embodiments. The embodiments and claims disclosed herein are capable of yet other embodiments and of being practiced and carried out in various ways. It is also to be understood that the phraseology and terminology employed herein are for the purpose of description and should not be regarded as limiting the scope of the claims.

[0249] As such, those skilled in the art will appreciate that the conception underlying the present application and claims may be readily utilized as a basis for the designing of other structures, methods and systems for carrying out the purposes of the embodiments and claims presented herein, and it is important, therefore, that the claims be regarded as including such equivalent constructions.

[0250] Furthermore, the purpose of the Abstract is to enable the U.S. Patent and Trademark Office and the general public, including those skilled in the art who are not particularly familiar with patent and legal terminology and language, to quickly grasp the content and gist of the technical disclosure of the application upon a single reading. The Abstract does not define the scope of the claims of the application or in any way limit the scope of the claims.

Claims

1. receiving data from a plurality of user devices disposed within each of the vehicles as the respective vehicles travel along one or more roads including one or more curves; determining, based at least in part on the data, desired curve markings to be displayed on the one or more curve segments; displaying a list of the desired curve markers to be displayed on the one or more curve portions; 10. A method for improving curve markings, comprising:

2. The method of claim 1 , wherein the data indicates a velocity of the user device.

3. The method of claim 1 , wherein the data indicates a GPS location of the user device.

4. The method of claim 1 , wherein the data includes IMU data for the user device.

5. The method of claim 4 , wherein the IMU data includes accelerometer data of the user device.

6. The method of claim 4 , wherein the IMU data includes gyroscope data of the user device.

7. The method of claim 4 , wherein the IMU data includes magnetometer data of the user device.

8. The method of claim 1 , wherein the data includes video data of the one or more roads.

9. The method of claim 1 , further comprising determining a position of the one or more curve portions based at least in part on the data.

10. The method of claim 9 , wherein determining the location of the one or more curve segments comprises determining a curve start point of the one or more curve segments.

11. The method of claim 9 , wherein determining the location of the one or more curve segments comprises determining curve endpoints of the one or more curve segments.

12. The method of claim 1 , wherein determining the desired curve markings to be displayed at the one or more curve portions comprises determining a curve radius for the one or more curve portions.

13. The method of claim 12 , wherein the curve radius is based at least in part on GPS data and / or road centerline data in the data obtained from the plurality of user devices.

14. The method of claim 1 , wherein determining the desired curve markings to be displayed on the one or more curve segments comprises determining a deviation angle for the one or more curve segments.

15. The method of claim 14 , wherein the deviation angle is based at least in part on GPS data and / or road centerline data in the data obtained from the plurality of user devices.

16. The method of claim 1 , wherein determining the desired curve markings to be displayed on the one or more curve portions comprises determining a superelevation of the one or more curve portions.

17. 17. The method of claim 16, wherein the superelevation is based at least in part on speed data in the data obtained from the plurality of user devices, and a path radius and BBI determined based at least in part on the data obtained from the plurality of user devices.

18. The method of claim 1 , wherein determining the desired curve markings to be displayed at the one or more curve sections comprises determining a recommended speed at the one or more curve sections.

19. 20. The method of claim 18, wherein determining the recommended speed for the one or more curved sections is based at least in part on a curve radius and superelevation of the one or more curved sections.

20. 20. The method of claim 19, wherein the curve radius and the superelevation of the one or more curve portions are determined based at least in part on the data obtained from the plurality of user devices.

21. The recommended speed is calculated using the formula: [Equation 1] (In the formula, f max is the maximum allowable lateral friction coefficient, and R c is the radius of the curve in feet for the one or more curved sections, and V adv 19. The method of claim 18, wherein the recommended speed is determined using:

22. The method of claim 1 , further comprising determining one or more motion characteristics of the vehicle traveling along one or more roads based at least in part on the data.

23. 23. The method of claim 22, wherein the one or more movement characteristics include a path radius taken by the vehicle while traveling along the one or more curved portions.

24. 24. The method of claim 23, wherein the path radius is based at least in part on speed data and IMU data in the data obtained from a plurality of user devices.

25. 23. The method of claim 22, wherein the one or more movement characteristics include a ball bank indicator (BBI) of the vehicle while traveling along the one or more curves.

26. 26. The method of claim 25, wherein the BBI is based at least in part on IMU data in the data obtained from a plurality of user devices.

27. The BBI has the formula: [Equation 2] (where α(t i ) is time t i is the BBI in V(t i ) is time t i is the velocity of each of the cars at the same speed, g is the gravitational force of the Earth, and R is the p (t i ) is time t i 27. The method of claim 26, wherein k is determined at least in part based on a path radius for each of said vehicles in k = 1 / k, and k is the roll rate for each of said vehicles in (rad / rad).

28. 2. The method of claim 1, wherein displaying the list of desired curve signs to be displayed on the one or more curve segments comprises displaying a list of coordinates each corresponding to a geographic location and a desired sign for each of the coordinates.

29. 2. The method of claim 1, wherein displaying the list of desired curve marks to be displayed at the one or more curve sections comprises displaying a map including the one or more curve sections and the desired curve marks to be displayed at the one or more curve sections.

30. The method of claim 1 , wherein the plurality of user devices are smartphones.

31. The method of claim 1 , wherein the plurality of user devices are tablets.

32. The method of claim 1 , further comprising determining existing markings currently displayed on the one or more curve portions based at least in part on the data.

33. The method of claim 32 , wherein the data includes video data.

34. 33. The method of claim 32, further comprising comparing the existing markings currently displayed on the one or more curve segments with the desired curve markings to be displayed on the one or more curve segments.

35. 35. The method of claim 34, further comprising matching the existing signs currently displayed on the one or more curve portions to the desired curve signs to be displayed on the one or more curve portions by generating a list of signs to be displayed on the one or more curve portions based at least in part on the comparison.

36. 36. The method of claim 35, further comprising displaying the list of signs to be displayed on the one or more curve portions.

37. 37. The method of claim 36, wherein displaying the list of signs to be displayed on the one or more curve portions comprises displaying a list of coordinates each corresponding to a geographic location and a desired sign for each of the coordinates.

38. 37. The method of claim 36, wherein displaying the list of signs to be displayed at the one or more curves comprises displaying a map including the one or more curves and the signs to be displayed at the one or more curves.

39. receiving data from a user device located within the vehicle as the vehicle travels along a road including a curve; determining a recommended driving speed for the curved portion of the road based at least in part on the data; generating an output indicative of the recommended driving speed for the curved portion of the road; 1. A method for calculating a recommended driving speed on a curved portion of a road, comprising:

40. 40. The method of claim 39, further comprising determining a curve radius and superelevation of the curve portion based at least in part on the data.

41. 41. The method of claim 40, wherein the recommended speed is determined based at least in part on the curve radius and the superelevation of the curve portion.

42. The recommended speed is calculated using the formula: [Equation 3] (In the formula, f max is the maximum allowable lateral friction coefficient, and R c is the radius of the curve in feet, and V adv 40. The method of claim 39, wherein the recommended speed is determined at least in part using:

43. 1. A system for improving curve markings, comprising one or more processors, The one or more processors may include: receiving data from a plurality of user devices disposed within each of the vehicles as the respective vehicles travel along one or more roads including one or more curves; determining, based at least in part on the data, desired curve markings to be displayed on the one or more curve segments; displaying a list of the desired curve markers to be displayed on the one or more curve portions; 1. A system, each system being individually and / or collectively configured to execute code that causes the system to:

44. 43. The system of claim 42, wherein the data indicates a velocity of the user device.

45. 43. The system of claim 42, wherein the data indicates a GPS location of the user device.

46. 43. The system of claim 42, wherein the data includes IMU data for the user device.

47. 47. The system of claim 46, wherein the IMU data includes accelerometer data of the user device.

48. 47. The system of claim 46, wherein the IMU data includes gyroscope data of the user device.

49. 47. The system of claim 46, wherein the IMU data includes magnetometer data of the user device.

50. 43. The system of claim 42, wherein the data includes video data of the one or more roads.

51. 43. The system of claim 42, wherein the one or more processors are individually and / or collectively configured to further execute code that causes the system to determine positions of the one or more curve portions based at least in part on the data.

52. 52. The system of claim 51, wherein the positions of the one or more curve segments are determined based at least in part on determining a curve start point for the one or more curve segments.

53. 52. The system of claim 51, wherein the location of the one or more curve segments is determined based at least in part on determining a curve end point of the one or more curve segments.

54. 43. The system of claim 42, wherein the desired curve markings to be displayed at the one or more curve portions are determined based at least in part on a determination of a curve radius for the one or more curve portions.

55. 55. The system of claim 54, wherein the curve radius is based at least in part on GPS data and / or road centerline data within the data obtained from the plurality of user devices.

56. 43. The system of claim 42, wherein the desired curve markings to be displayed at the one or more curve portions are determined based at least in part on determining a deviation angle of the one or more curve portions.

57. 57. The system of claim 56, wherein the deviation angle is based at least in part on GPS data and / or road centerline data within the data obtained from the plurality of user devices.

58. 43. The system of claim 42, wherein the desired curve markings to be displayed at the one or more curve portions are determined based at least in part on a determination of superelevation of the one or more curve portions.

59. 59. The system of claim 58, wherein the superelevation is based at least in part on speed data in the data obtained from the plurality of user devices, and a path radius and BBI determined based on the data obtained from the plurality of user devices.

60. 43. The system of claim 42, wherein the desired curve markings to be displayed at the one or more curve portions are determined based at least in part on a determination of a recommended speed at the one or more curve portions.

61. 61. The system of claim 60, wherein determining the recommended speed for the one or more curved sections is based at least in part on a curve radius and superelevation of the one or more curved sections.

62. 62. The system of claim 61, wherein the curve radius and the superelevation of the one or more curve portions are determined based at least in part on the data obtained from the plurality of user devices.

63. The recommended speed is calculated using the formula: [Equation 4] (In the formula, f max is the maximum allowable lateral friction coefficient, and R c is the radius of the curve in feet for the one or more curved sections, and V adv 61. The system of claim 60, wherein the recommended speed is determined at least in part based on:

64. 43. The system of claim 42, wherein the one or more processors are individually and / or collectively configured to further execute code that causes the system to determine, based at least in part on the data, one or more movement characteristics of the vehicle traveling along one or more roads.

65. 65. The system of claim 64, wherein the one or more movement characteristics include a path radius taken by the vehicle while traveling along the one or more curved portions.

66. 66. The system of claim 65, wherein the path radius is based at least in part on speed data and IMU data in the data obtained from a plurality of user devices.

67. 23. The system of claim 22, wherein the one or more movement characteristics include a ball bank indicator (BBI) of the vehicle while traveling along the one or more curves.

68. 68. The system of claim 67, wherein the BBI is based at least in part on IMU data in the data obtained from multiple user devices.

69. The BBI has the formula: [Equation 5] (where α(t i ) is time t i is the BBI in V(t i ) is time t i is the velocity of each of the cars at the same speed, g is the gravitational force of the Earth, and R is the p (t i ) is time t i 69. The system of claim 68, wherein k is determined at least in part based on a path radius for each of said vehicles in k = 1 / k, and k is the roll rate for each of said vehicles in (rad / rad).

70. 43. The system of claim 42, wherein the list of desirable curve signs includes a list of coordinates each corresponding to a geographic location and a desirable sign for each of the coordinates.

71. 43. The system of claim 42, wherein the list includes a map including the one or more curve segments and the desired curve markings to be displayed at the one or more curve segments.

72. 43. The system of claim 42, wherein the plurality of user devices are smartphones.

73. 43. The system of claim 42, wherein the plurality of user devices are tablets.

74. 43. The system of claim 42, wherein the one or more processors are individually and / or collectively configured to further execute code that causes the system to determine existing markings currently displayed on the one or more curve portions based at least in part on the data.

75. 75. The system of claim 74, wherein the data includes video data.

76. 75. The system of claim 74, wherein the one or more processors are individually and / or collectively configured to further execute code that causes the system to compare the existing markings currently displayed on the one or more curve portions with the desired curve markings to be displayed on the one or more curve portions.

77. 77. The system of claim 76, wherein the one or more processors are individually and / or collectively configured to further execute code that causes the system to match the existing markings currently displayed on the one or more curve portions to the desired curve markings to be displayed on the one or more curve portions by generating a list of markings to be displayed on the one or more curve portions based at least in part on the comparison.

78. 78. The system of claim 77, wherein the one or more processors are individually and / or collectively configured to further execute code that causes the system to display the list of signs to be displayed on the one or more curve portions.

79. 79. The system of claim 78, wherein the list of signs to be displayed on the one or more curve portions includes a list of coordinates each corresponding to a geographic location and a desired sign for each of the coordinates.

80. 79. The system of claim 78, wherein the list of signs to be displayed at the one or more curve portions includes a map including the one or more curve portions and the signs to be displayed at the one or more curve portions.

81. 1. A system for calculating a recommended driving speed on a curved section of a road, comprising one or more processors, The one or more processors may include: receiving data from a user device disposed within the vehicle, the data having been collected by the user device while the vehicle is traveling along the road including the curved portion; determining a recommended driving speed for the curved portion of the road based at least in part on the data; generating an output indicative of the recommended driving speed for the curved portion of the road; 1. A system, each system being individually and / or collectively configured to execute code that causes the system to:

82. 82. The system of claim 81, wherein the one or more processors are individually and / or collectively configured to further execute code that causes the system to determine a curve radius and superelevation of the curve portion based at least in part on the data.

83. 83. The system of claim 82, wherein the recommended speed is determined based at least in part on the curve radius and the superelevation of the curve portion.

84. The recommended speed is calculated using the formula: [Equation 6] (In the formula, f max is the maximum allowable lateral friction coefficient, and R c is the radius of the curve in feet, and V adv 82. The method of claim 81, wherein the recommended speed is determined at least in part using:

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