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B-1 A P P E N D I X B Experimental Evaluation of Inertial Profilers for Use on Urban and Low-Speed Roadways This appendix describes an experiment conducted to examine the effects of potentially adverse operational conditions on the measurement of longitudinal road profile by high-speed inertial profilers. The experiment included staged reproductions of common operational conditions encountered while conducting network-level profile measurements on urban and low-speed roadways, such as â¢ operation at low speed, â¢ acceleration or deceleration, â¢ stop-and-go operation, â¢ profiling from a dead stop, â¢ initiation of profile collection before real-time filters have stabilized, â¢ operation on a curve, and â¢ operation on a transition into and out of a curve. Overall, the experimental plan included 30 test conditions composed of repeated runs under ideal conditions and multiple iterations of those listed above. All of these runs were performed on the low-volume loop at the MnROAD test track near Albertville, Minnesota. Each profiler also obtained measurements on a segment of a nearby urban street. Six commercially available high-speed inertial profilers participated in the experiment. Together, the six manufacturers build most of the equipment in use for measurement of longitudinal profile for network-level pavement management in the United States. The experiment demonstrated the effect on profile of errors in the measurement of the inertial reference caused by (1) accelerometer tilting and changes in accelerometer tilt during horizontal acceleration of the host vehicle, (2) limitations in accelerometer resolution, and (3) limitations in real-time and post-processing filtering procedures. This appendix describes the test sections, participating profilers, and experimental procedures in detail. This appendix also lists cross correlation values that compare repeated measurements by each of the participating inertial profilers over the same test section at various speeds. Chapter 3 of the main report provides technical background, a brief description of the experiment, and the results. B.1 Test Sections The testing took place on a tangent section and a curved section on the MnROAD low volume loop and at a pavement segment on a nearby urban road. The low volume loop is part of the MnROAD research facility near Albertville, Minnesota. It is a 2.5-mi (4-km) loop dedicated to pavement-related research by the Minnesota Department of Transportation (DOT). The loop is a two-lane undivided roadway that is closed to public traffic. It consists of two parallel 0.9 mi (1.45-km) long straightaways with 270-ft (80-m) radius âloopsâ at each end for reversing direction. The straightaways run approximately northwest and southeast.
B-2 B.1.1 Tangent Section Most of the testing took place on a tangent section running southeast along the northern straightaway on the MnROAD low volume loop. Figure B-1 shows the layout. The test section start was located 338 ft (103 m) downstream of the cell 33 start. This provided sufficient distance for drivers entering the test section from the west loop to achieve the requested speed in each run. For the lower speed runs, drivers often began accelerating from the west crossover. Figure B-1. Tangent section layout. The test section was 1502 ft (458 m) long. A long section was needed to observe the effects on measurement of long-wavelength content during operation at very low speed and long transient effects that occurred during acceleration and deceleration, as well as the residual effects of high-pass filter settling behavior. Although most of the test section was surfaced with asphalt concrete (AC), it included a transition to Portland cement concrete (PCC) about 110 ft (33.5 m) upstream from the section end. The overall International Roughness Index (IRI) of the section, determined from reference measurements, was 112 in/mi (1.76 m/km) in the left wheel path and 111 in/mi (1.75 m/km) in the right wheel path. An area of localized roughness occurred at a deep transverse crack followed by a shallow dip in the transition area between cell 34 and 35. The short-interval roughness profiles included a peak value above 200 in/mi
B-3 (3.16 m/km) on both sides at this location. [In this Appendix, a short-interval roughness profile signifies averaging with a base length of 25 ft (7.62 m).] Severe localized roughness also appeared near the end of the section in the transition area between cell 35 and 36. This area included an AC patch followed by a transition to PCC, which was in turn followed by two closely spaced, severe transverse cracks in the PCC. The short-interval roughness profiles for both wheel paths included peak values above 200 in/mi (3.16 m/km) at three locations: (1) the leading edge of the AC patch, (2) the trailing edge of the AC patch, and (3) the transverse cracks. A 1,000-ft (304.8-m) long sub-section was laid out within the test section for calibrating the distance measurement instrument (DMI) of the profilers before they started testing. A steel tape measurement of the section, where measurements were made at 100-ft (30.48-m) intervals, showed that its length was 1,000.075 ft (304.823 m) after correction of the measurement for temperature. The start and end of the test section were marked with 6-in (150-mm) wide temporary reflective tape that was 3/32 in (2.4 mm) thick, which was laid transversely across the travel lane. Diamond shaped marks were painted 18 in (45.7 cm) to the right of the left wheel path to help drivers maintain the lateral position of their profilerâs footprint accurately and consistently. The lateral offset of 18 in (45.7 cm) was intended to serve as a lateral reference at or near the center of the driverâs chest. For the six vehicles that participated in the experiment, an offset of 12 in (30.5 cm) would have been a more representative dimension. The marks were 8 in (20 cm) long, 6 in (15 cm) wide, and were placed about 20 ft (6 m) apart within this section and up to a distance of 300 ft (91.44 m) before the start of the section. Figure B-2 shows the tape placed at the start of the section and some of the diamond markings. Figure B-2. Tangent section starting point. The layout of the test section included 11 landmarks needed for staging specialized speed profiles. A âprimaryâ landmark placed 728.5 ft (222.0 m) from the start of the section was used in many of the staged events. Depending on the event, this was the location where profilers would either stop, begin profiling from a dead stop, suddenly initiate data collection, transition from constant-speed operation to coasting, or transition from acceleration or deceleration to constant speed operation. The 10 âsecondaryâ landmarks were placed at various distances upstream of the primary landmark. These were placed at locations where acceleration or deceleration would have to begin to achieve the requested speed change at the primary landmark that followed. During each staged event, two cones were placed near the right lane edge at the primary landmark and a single cone was placed at the secondary landmark if needed. B.1.2 Curve Runs were conducted at various speeds on the west loop at MnROAD in the counter-clockwise direction. Figure B-3 shows the layout of the section. The section used for these runs was 2,100 ft (640 m) long and
B-4 began on a tangent at the transition between cell 33 and cell 43 and terminated on a tangent heading southeast. The section included a 75-degree change in direction to the right on a 200-ft (61-m) radius curve, followed by a short (< 35 ft (11 m)) transition to a 270-ft (80-m) radius loop running counter-clockwise. This provided four âeventsâ for each run over the section: (1) transition to rightward lateral acceleration from operation on a tangent, (2) transition from rightward lateral acceleration to leftward acceleration over a short time interval, (3) operation at a constant leftward lateral acceleration over several seconds, and (4) transition from leftward lateral acceleration to operation on a tangent. Figure B-3. Curved section layout. The loop was a jointed PCC pavement with transverse tining, skewed joints (1/6), and a joint spacing of 20 ft (6.1 m). The slabs were curled downward throughout the testing period. The start and end of the section included a short length of AC pavement along the tangents. Diamond-shaped marks were painted on this section using the same procedure that was used for the tangent section. Reference measurements were obtained on this section with a SurPRO 3500. The measurements indicated that the IRI of the left wheel path was 163 in/mi (2.57 m/km) and the IRI of the right wheel path was 158 in/mi (2.50 m/km). Cross slope measurements were collected using the SurPRO at locations about 200 ft (61 m) apart, as shown in Figure B-3. On the PCC pavement, the cross slope was measured at center-
B-5 slab locations. Table B-1 lists the measured cross slope values. A negative value indicates that the pavement was lower on the left side of the lane for counter-clockwise travel around the curve. Table B-1. Cross slope along the curved section. Landmark Approx. Distance from Section Start (ft) Cross Slope (deg) 1 0 1.0 2 200 1.5 3 400 3.0 4 600 0.0 5 800 â3.6 6 1,000 â3.7 7 1,200 â3.8 8 1,400 â3.6 9 1,600 â3.4 10 1,800 â3.3 11 2,000 0.5 B.1.3 Urban Street Each profiler collected data on Pine Street in Monticello heading north from 6th Street to 4th Street in the outer lane. This segment begins and ends at traffic signals. This lane is narrow; therefore the curb that is present on the roadway is very close to the right wheel path. This roadway also has several drainage inlets along the curb, abutting driveways, and a railroad crossing. The posted speed limit is 30 mi/hr (48 km/hr). B.2 Profilers Table B-2 lists the profilers that participated in the experiment, the owner of each device, the operator, and the driver (if different). Photos of the profilers are shown in Figures B-4 through B-9. Throughout the rest of this report, each profiler is identified using a number with no reference to its make or owner. Table B-2. Participating profilers. Make, Model Owner Operator(s) SSI CS9100 Mid Mount SSI Nick Schaefer Pathway Services Pathrunner XP Minnesota DOT Gary Wallner ICC Iowa DOT Jason Omundson, Ricardo Corona Dynatest RSP Mark III Dynatest Bob Briggs, Don Noah Fugro Roadware ARAN 9000 South Dakota DOT Chris Koos, Justin Cook Ames Engineering 8300 Ames Engineering Dustin Reid SSIâSurface Systems and Instruments, Inc. ICCâInternational Cybernetics Corp. ARANâAutomatic Road ANalyzer
B-6 Figure B-4. SSI CS9100 Mid Mount high-speed inertial profiler. Figure B-5. Pathway Services Pathrunner XP high-speed inertial profiler. Figure B-6. ICC high-speed inertial profiler.
B-7 Figure B-7. Dynatest RSP 5051 Mark III highâspeed profiler. Figure B-8. Fugro Roadware ARAN 9000 high-speed profiler. Figure B-9. Ames Engineering 8300 high-speed profiler.
B-8 B.3 Reference Measurements Reference profile data were collected using a SurPRO 3500 on the curved section and the tangent section. This device recorded profile data at 1-in (25.4-mm) intervals. The SurPRO 3500 is an inclinometer-based device that is supported by two wheels 9.84 in (250 mm) apart. It is pushed along a test section at walking speed and constructs a profile by accumulating changes in height using a series of slope values recorded at a constant longitudinal distance interval. At the tangent section, three repeat passes were made in each wheel path. The distance between the wheel paths was 69 in (175.3 cm). At the curved section, two repeat passes were made along the left wheel path and three repeat passes were made along the right wheel path. B.4 Speed/Location Measurement A custom-built Global Positioning System (GPS) data logging system was mounted on each profiler prior to data collection to provide independent measurements of the profilerâs speed and position during all of the runs performed at MnROAD. The system included corrections provided by the Minnesota DOTâs network of continuously operating reference stations (CORS) captured via cellular modem at 1 Hz. The GPS receiver output a velocity vector record and a position record at 20 Hz. In this system, the expected position accuracy for the roving GPS receiver with the correction signal is 0.04 in (1 cm) + 1 ppm. The specification â1 ppmâ refers to parts per million using the distance between the roving receiver and the reference station as a baseline. The baseline during the testing at MnROAD was a maximum of 1 mi (1.6 km). The expected root mean square velocity error is 0.07 mi/hr (0.03 m/s). The recorded data also include a GPS timestamp and continuously updated measures of system accuracy. Table B-3 lists the components of the GPS data logging system. All of the components are contained in a weatherproof case for transport. When conducting measurements, the GPS antenna and cell antenna are fixed to a high point on the vehicle (e.g., the roof) with magnetic mounts. The antennas communicate with the modem and receiver using wired connections to ports on the outside of the case, which in turn communicates using wired connection to a laptop computer through another port. The laptop records data from the GPS system and displays live updates of speed, horizontal acceleration, and GPS status. Table B-3. GPS system components. Component Make/Model Receiver Novatel Flexpak6 Model G2L-RPG-TTN GPS Antenna Novatel 702-GG Cell Modem Sierra Wireless RavenX HSUPA Cell Antenna Taoglas MB.TG30.A.305111 Battery PowerSonic PS-12140 Charger PowerSonic PSC-122000AC Case Pelican 1550 The technician who observed the testing recorded the position of the GPS antenna on each host vehicle relative to the profilerâs laser footprint. This, in conjunction with the lateral sensor spacing, provided a way to transform the raw measurements of antenna position to positions of the tracks followed by the left- and right-side profiler sensors. Table B-4 provides the antenna location for each profiler using the SAE J670:2008 Z-Up axis system (X forward, Y to the left, and Z upward). Longitudinal (X) coordinates are given relative to the profiler, lateral (Y) coordinates are given relative to the vehicle centerline, and vertical (Z) coordinates are given relative to the ground. Two sets of coordinates are given for the ARAN because the test series was completed in two sessions.
B-9 Table B-4. GPS antenna locations relative to profiler footprint. GPS Antenna Location Device X (in) Y (in) Z (in) Pathway Services Pathrunner XP â37 â29 52 SSI CS9100 Mid Mount â85 23 78 Dynatest RSP Mark III â143 â16 83 Ames Engineering 8300 â100 0 84 Fugro Roadware ARAN 9000a 91 0 84 Fugro Roadware ARAN 9000b 73.5 0 84 ICC MDR â116 0 85 a First session b Second session B.5 Driver Instructions This section describes the 30 staged test conditions included in the experiment. Each driver was asked to collect longitudinal profile for three repeated passes over the section that approximated the requested speed profile and measurement procedures specified for each condition. In many cases, such as speed profiles with a specified acceleration or deceleration level, more than three passes were needed to get an acceptable set of three runs for a given speed profile. The GPS data logger described above was monitored by a technician riding in the profiler to provide feedback to the driver in real time or just after a given pass to help make adjustments for the next pass. Specific instructions were provided to the driver and operator for each run. With the exception of the âdead stopâ runs, the following instructions were provided: â¢ Set cruise control at the target speed well in advance of the section start. For low speed, where the use of cruise control is not possible, maintain the target speed as consistently as possible using the accelerator pedal. â¢ Initiate profile data collection before reaching the landmark placed 450 ft (137 m) upstream of the start of the section. â¢ Automatically trigger data collection at the start of the section and automatically terminate data collection at the end of the section. If auto-triggering is not available, manually trigger data collection before reaching the start of the section and manually terminate data collection after reaching the end of the section. Additional instructions that were provided specific to each type of staged condition are described below. With the exception of âoperation on curves,â all of these tests were performed on the tangent section. B.5.1 Constant Speed The following instruction was provided: â¢ Measure the tangent section at constant speeds of 60, 50, 45, 40, 30, 25, 20, 15, and 10 mi/hr (97, 80, 72, 64, 48, 40, 32, 24, and 16 km/hr). Profiler 1 collected data at 35 mi/hr (56 km/hr) instead of 45 mi/hr (72 km/hr). In most cases, the driver set cruise control at the target speed while approaching the test section for runs at speeds of 25 mi/hr (40 km/hr) and above. B.5.2 Coasting The following instructions were provided: â¢ Enter the tangent section at 45 mi/hr (72 km/hr).
B-10 â¢ Disengage the throttle and/or the cruise control at the primary landmark and coast to the end of the section. B.5.3 Acceleration/Deceleration These tests included longitudinal acceleration or deceleration within the test section, typically from operation at one preset constant speed to another. The following instructions were provided: â¢ Enter the tangent section at the requested initial speed. â¢ At the location of the first landmark, accelerate or decelerate at the requested level until reaching the requested final speed. â¢ If the average acceleration or deceleration was as intended, the requested final speed should be reached at the second (i.e., primary) landmark. â¢ Once acceleration or deceleration begins, maintain a constant level until the requested final speed is reached. Do not adjust braking or throttle after the onset of deceleration or acceleration to reach the second (i.e., primary) landmark at the requested speed. â¢ Once the requested final speed is reached, continue at that speed until the end of the section. In many cases, the driver required a few passes before gaining enough experience to provide the requested deceleration level reliably. Often, the driver practiced runs with braking on the return trip to the section start between runs using the cones as a guide in the reverse order. In a few cases, the driver practiced the speed profile that was next on the list on the return trip. Very often, the intended average deceleration level was achieved, but the deceleration reached a peak level that was higher than the requested level at the onset of braking, and settled to a value below the requested level. The monitoring technician typically reported a peak and settling level as feedback to the driver after each pass. Table B-5 lists the requested initial speed, target acceleration (negative for braking), and target final speed for the seven test conditions. Table B-5 also lists the approximate distance between the first and second set of landmark cones. This is the distance needed to transition from the initial speed to the final speed at the targeted acceleration or deceleration level. The second (i.e., primary) landmark remained at the same location, which was 728.5 ft (222 m) from the start of the section, for all test conditions. The first landmark was adjusted to the proper location upstream for each condition. For the âthrottleâ runs, the original target acceleration level of 0.15 g was sometimes difficult to achieve, depending on the vehicleâs power, weight, and transmission shifting schedule. The target acceleration level was changed to ânatural,â which is the typical level of acceleration that is applied to a vehicle when accelerating. Table B-5. Specifications for acceleration and deceleration events. Disturbance Landmark Spacing (ft) Initial Speed (mi/hr) Target Accel. (g) Final Speed (mi/hr) Braking 543 45 â0.1 20 Braking 272 45 â0.2 20 Braking 181 45 â0.3 20 Braking 226 30 â0.1 15 Braking 113 30 â0.2 15 Braking 75 30 â0.3 15 Throttle 362 20 natural 45
B-11 B.5.4 Stop-and-Go Operation These tests included a stop within the tangent section from operation at one preset constant speed, followed by acceleration back to the preset speed. The following instructions were provided: â¢ Enter the tangent section at the requested initial speed. â¢ At the location of the first landmark, which is denoted by a single cone at the right lane edge, decelerate at the requested level in order to come to a stop at the second (i.e., primary) landmark, which is denoted by two cones at the right lane edge. â¢ Once deceleration begins, maintain a constant level until the vehicle stops. Do not adjust braking after the onset of deceleration to stop directly at the second (i.e., primary) landmark. â¢ Once the vehicle stops, wait for the requested length of time. â¢ Accelerate at a natural level (i.e., the level of acceleration typically used by the driver) back to the initial speed, and then continue at this speed until the end of the section. As was the case with the deceleration runs, drivers often required practice, and often practiced while driving upstream between passes. However, they had typically just completed the deceleration runs, which provided some useful preparation. Often, drivers interpreted a small (~10-20 ft) error in the location where the stop was achieved as a sign of a failed run, even though they had achieved the requested deceleration level within an acceptable tolerance. It was difficult for drivers to avoid adjustments in deceleration near the second (i.e., primary) landmark as a result. Table B-6 lists the requested initial speed, target deceleration, and the dwell time (i.e., the length of time to remain stopped) for the four test conditions defined for the experiment. Table B-6 also lists the approximate distance between the first and second set of landmark cones. The second landmark remained at the same location, which was 728.5 ft (222 m) from the start of the section, for all test conditions. The first landmark was adjusted to the proper location upstream for each condition. Table B-6. Specifications for stop-and-go events. Initial Speed (mi/hr) Target Acceleration (g) Dwell Time (sec) Landmark Spacing (ft) 30 â0.1 5 301 30 â0.2 5 150 45 â0.2 5 338 45 â0.2 1 338 B.5.5 Dead Stop In these tests, profile data were collected on the tangent section from a dead stop. The following instructions were provided: â¢ Launch the profiler data collection software, but do not begin collecting profile. â¢ Come to stop at the primary landmark. â¢ Initiate profile data collection while the vehicle is stationary. â¢ Accelerate to 45 mi/hr (72 km/hr), and then maintain a constant speed until reaching the end of the section. One set of repeat runs was requested with ânaturalâ acceleration (i.e., the level of acceleration typically used by the driver) to 45 mi/hr (72 km/hr), and another set was requested with heavy (e.g., maximum) acceleration.
B-12 B.5.6 Sudden Initiation of Profile Collection In these tests, operators were asked to initiate collection of profile while the vehicle was in motion without lead in for filter initialization. The following instructions were provided: â¢ Enter the tangent section at the requested initial speed. â¢ Initiate profile data collection at the location of the primary landmark. â¢ Continue at the initial speed to the end of the section. Four sets of runs were requested, comprising a matrix of two travel speeds (25 mi/hr and 45 mi/hr; 40 km/hr and 72 km/hr) and two high-pass filter cut-off values (200 ft and 300 ft; 61 m and 91 m). These runs were intended to examine the effects on profile of high-pass filter initialization. Most of the profilers would not permit data to be recorded until travel over a sufficient distance with the data collection software running for filter initialization. Other profilers would not allow data to be recorded until initialization was complete. As such, this portion of the experiment was abandoned. B.5.7 Operation on Curves These runs were performed on the curved section. The following instructions were provided: â¢ Measure the curved test section at a constant speed. â¢ Maintain a constant lane position during the run, and avoid sudden steering corrections. Tests were performed at 20, 30, and 40 mi/hr (32, 48, and 64 km/hr), which correspond to lateral accelerations of about 0.1, 0.22, and 0.4 g, respectively, on the clockwise portion of the curve. B.6 GPS Data Processing The GPS data logging system recorded the time (GPS week and time), position (latitude, longitude, height above sea level), velocity (horizontal speed, heading, vertical speed), and diagnostics (latency, number of satellites, solution type) with real-time corrections at a rate of 20 Hz. This section describes the processing applied to the recorded data to characterize the speed profile of each run. For each type of staged run, additional processing was applied to define landmarks, such as the location of the onset of disturbances or stops. Additional processing was also applied to quantify the relative strength of acceleration and deceleration pulses, and the duration of stops. B.6.1 Section Endpoints Static GPS readings were collected over a 50-second time interval with the receiver on the pavement surface at the start and end of both test sections. These signals characterize the static noise in velocity and position measurements and provide the basis for transformation of latitude and longitude into a local horizontal coordinate system. Table B-7 lists the mean latitude, longitude, and height above sea level observed over 50 seconds for the left and right side of the lane at the start and end of each test section. On the tangent section, the receiver was placed at the intersection of each wheel path of interest with the longitudinal center of the start and end stripe. On the curved section, the receiver was placed at the intersection of the lane edges with the start and end stripe. Table B-8 lists the standard deviation of position and speed measurements observed over the 50-second measurement interval. Many of the distributions were not Gaussian. In particular, distributions of position quantities measured on the left side at both the start and end of the tangent section and the right side at the end of the curved section had positive excess kurtosis (i.e., thin at the center with long tails). Typically, this system applied a new position correction every 0.8â1.2 seconds. The largest step changes in position quantities and larger speed values often corresponded to a recorded sample with a fresh position correction. Noise observed in the position quantities from this source was often correlated among the signals (latitude, longitude, and height).
B-13 At this location, an increase in latitude of 10-8 deg corresponds to a shift northward of 0.044 in (1.1 mm), and a change in longitude of 10-8 deg corresponds to a shift eastward of 0.031 in (0.78 mm). Table B-7. Test section endpoint positions. Landmark Latitude (deg) Longitude (deg) Height (ft) Tangent, Left Start 45.265437474 â93.715535338 963.235 Tangent, Right Start 45.265424849 â93.715548998 962.820 Tangent, Left End 45.262924594 â93.710912428 970.906 Tangent, Right End 45.262912107 â93.710925729 970.839 Curve, Left Start 45.266010637 â93.716569164 962.146 Curve, Right Start 45.266034689 â93.716543186 962.120 Curve, Left End 45.266769037 â93.718453994 961.716 Curve, Right End 45.266744869 â93.718480066 961.589 Table B-8. Static measurement noise. Landmark Latitude (deg) Longitude (deg) Vertical Speed (mi/hr) Horizontal Speed (mi/hr) Height (in) Tangent, Left Start 2.50x10-8 5.57x10-8 0.371 0.067 0.75 Tangent, Right Start 1.32x10-8 1.93x10-8 0.120 0.024 0.16 Tangent, Left End 4.64x10-8 5.34x10-8 0.147 0.052 0.26 Tangent, Right End 1.33x10-8 1.75x10-8 0.107 0.025 0.17 Curve, Left Start 2.96x10-8 3.80x10-8 0.127 0.022 0.38 Curve, Right Start 5.76x10-8 6.16x10-8 0.189 0.023 0.87 Curve, Left End 1.47x10-8 1.72x10-8 0.132 0.032 0.18 Curve, Right End 2.88x10-8 3.21x10-8 0.187 0.069 0.47 B.6.2 Local Coordinates For the tangent and curved sections, measurements of latitude and longitude were transformed to local Cartesian coordinate systems with axes aligned eastward, northward, and upward. On each section, the origin was placed at the intersection of the left wheel path with the starting stripe. Locations north (dN) and east (dE) of the section origin were calculated from instantaneous readings of latitude (Ï), longitude (Î»), and height (H) as follows: (B-1) (B-2) where the symbols Ï0, Î»0, and H0 denote the latitude, longitude, and height above sea level, respectively, at the test section origin (see Table B-7). R is an estimate of the Earthâs radius at the origin. For both test
B-14 sections, this was approximately 3,956.944 mi (6,368.084 km). The influence of changes in height at points away from the origin was neglected in these calculations. For the tangent section, data were further transformed in the horizontal plane to distance forward dF and distance leftward dL along the section. This re-oriented the horizontal axes to include an axis (with the original origin) that passed through the left wheel path endpoint. In particular: (B-3) and: (B-4) where dNEnd and dEEnd are the distance northward and eastward to the end of the section, respectively. (The atan function must return a value ranging from â180 to 180 deg, depending on the sign of the numerator and denominator.) Subsequently, the coordinates were offset to provide the location of the left-side profiler sensors on each vehicle instead of the position of the GPS antenna (see Table B-4). For the curved section, distance travelled between readings was estimated by comparing successive position values in the âEast-Northâ system for each time step. Accumulated travel distance was estimated by summing these values beginning from the instant when the profiler crossed the curved section starting point. B.6.3 Speed and Acceleration, Tangent Section For data recorded during travel over the tangent section, readings of horizontal speed and heading were resolved to âforwardâ and âleftwardâ components using the coordinate system aligned with the test section. The forward and leftward speed signals were differentiated in time to obtain estimates of horizontal acceleration. However, the resulting signals were very noisy, in part due to system noise and in part due to vibration of the host vehicle in response to disturbances from the road and driver inputs. In addition, the GPS system did not update its measurement of horizontal speed or heading in the first sample recorded after a new position correction. (It is believed that the 0.05-second cycle time did not provide an adequate opportunity to resolve the Doppler velocity estimate with a new kinematic correction.) As such, instantaneous readings of peak acceleration were considered inaccurate, and acceleration records were inspected, analyzed, and plotted after application of a 1-second moving average. B.6.4 Speed and Acceleration, Curved Section For data recorded during travel over the curved section, horizontal speed was used directly as a surrogate for forward speed. At each time step, longitudinal and lateral (i.e., forward and leftward) acceleration were estimated for a coordinate system fixed in the vehicle. This was done using simple differentiation: (B-5)
B-15 where ÎÏ is the change in heading angle with the sign reversed for a X-forward, Y-leftward, and Z-upward coordinate system. (GPS provides compass heading, which sweeps from north to east.) V is horizontal speed; and Ît is the time elapsed between sample i and i+1. As shown, longitudinal acceleration (Ax), and lateral acceleration (Ay) are calculated by resolving the horizontal speed vector of the next reading into the vehicle body axis system for the current reading and differentiating between the two. Acceleration signals calculated this way were noisy. As such, acceleration records were inspected, analyzed, and plotted after application of a 1-second moving average. B.6.5 Diagnostics The system recorded several diagnostic items, including the position type, the number of satellite ranges above the designated mask angle of 5 degrees for each waveband (L1 and L2), and standard deviation values associated with each value of latitude, longitude, and height. Very few runs were conducted with position and velocity based on fewer than six satellites, with seven to nine available for a majority of the runs. With one exception, all of the readings were recorded with the system in âinteger narrow-lane ambiguityâ mode, which implies that the system was confident it had eliminated carrier phase ambiguity prior to passing over the test section. B.7 Cross Correlation of Constant-Speed Runs This section presents the results of cross correlation analysis on profiles collected at constant speed on the tangent section (see Section B.5.1). Each profiler measured the tangent section up to three times at 10 speeds from 10 mi/hr (16 km/hr) to 60 mi/hr (97 km/hr). Cross correlation was applied to the profiles in two wavebands: 1. IRI Waveband: Profiles were processed with the IRI algorithm, including conversion to slope, smoothing with a 9.84-in (250-mm) moving average, and application of the Golden-Car simulation. 2. Long Waveband: Profiles were converted to slope using a finite difference, high-pass filtered with a cut-off wavelength of 220 ft (67 m), and low-pass filtered with a cut-off wavelength of 26.2 ft (8 m). The high-pass and low-pass filter include application of four Butterworth filters in the following sequence: (1) first order, forward direction, (2) second order, reverse direction, (3) second order, forward direction, and (4) first order, reverse direction. The calculation procedures for both wavebands are described elsewhere (Karamihas 2009). The analysis was applied to profiles from the left wheel path over the range from 262.5â1,378.0 ft (80â 420 m). In this range, the left wheel path included less transverse variation than the rest of the tangent section. For Profiler 6, the analysis was applied to profiles from the right wheel path over the range from 65.6â1,378.0 ft (20â420 m) because it did not measure the left wheel path. The cross correlation analysis included an iterative search for the longitudinal distance measurement offset that yielded the highest agreement score for each pair of profiles. Tables B-9 through B-14 present the results for the IRI waveband. The diagonal entries in each table represent the repeatability of profile measurement in the designated waveband at each speed. The non-diagonal entries represent reproducibility at different speeds. Unless otherwise indicated, three passes were included for each measurement speed. As such, the diagonal values are usually the average of three agreement scores, and the non-diagonal values are the average of nine agreement scores. In many cases, the agreement scores include a penalty associated with inconsistency in longitudinal distance measurement. To help differentiate inconsistency in profile elevation change from inconsistency in longitudinal distance measurement, the cross correlation analysis was repeated with an iterative search for the optimal DMI adjustment factor. That is, an agreement score âwith DMI adjustmentâ is the highest cross correlation value observed with the recording interval and starting point of one profile adjusted for
B-16 compatibility with the other. Tables B-15 through B-20 present the results for the IRI waveband, and Tables B-21 through B-26 present the results for the long waveband. Table B-9. Agreement scores, IRI waveband, no DMI correction, profiler 1, left. 10 mph 15 mph 20 mph 25 mph 30 mph 35 mph 40 mpha 50 mph 60 mphb 0.890 0.868 0.860 0.908 0.930 0.934 0.925 0.934 50 mph 0.904 0.876 0.868 0.906 0.935 0.940 0.906 0.958 40 mpha 0.896 0.902 0.913 0.939 0.927 0.933 0.964 35 mph 0.906 0.905 0.901 0.941 0.956 0.947 30 mph 0.911 0.917 0.919 0.951 0.973 25 mph 0.911 0.935 0.944 0.972 20 mph 0.890 0.928 0.944 15 mph 0.896 0.917 10 mph 0.883 a Two passes collected at 40 mph. b One pass collected at 60 mph. Table B-10. Agreement scores, IRI waveband, no DMI correction, profiler 2, left. 10 mph 15 mph 20 mph 25 mph 30 mph 40 mph 45 mph 50 mph 60 mph 60 mph 0.414 0.354 0.692 0.828 0.831 0.849 0.876 0.881 0.883 50 mph 0.497 0.388 0.775 0.963 0.965 0.970 0.973 0.968 45 mph 0.505 0.389 0.776 0.960 0.960 0.972 0.973 40 mph 0.526 0.391 0.798 0.981 0.978 0.978 30 mph 0.521 0.384 0.800 0.984 0.980 25 mph 0.529 0.386 0.806 0.983 20 mph 0.632 0.482 0.616 15 mph 0.627 0.447 10 mph 0.696 Table B-11. Agreement scores, IRI waveband, no DMI correction, profiler 3, left. 10 mph 15 mph 20 mph 25 mph 30 mph 40 mph 45 mph 50 mph 60 mph 60 mph 0.820 0.925 0.929 0.939 0.935 0.943 0.950 0.958 0.948 50 mph 0.839 0.947 0.950 0.966 0.958 0.970 0.969 0.980 45 mph 0.852 0.957 0.963 0.969 0.965 0.966 0.965 40 mph 0.848 0.956 0.956 0.970 0.966 0.964 30 mph 0.857 0.961 0.963 0.969 0.958 25 mph 0.858 0.968 0.968 0.972 20 mph 0.863 0.964 0.967 15 mph 0.869 0.961 10 mph 0.958
B-17 Table B-12. Agreement scores, IRI waveband, no DMI correction, profiler 4, left. 10 mph 15 mph 20 mph 25 mph 30 mph 40 mph 45 mph 50 mph 60 mph 60 mph 0.896 0.891 0.909 0.905 0.928 0.939 0.944 0.940 0.960 50 mph 0.921 0.918 0.932 0.922 0.947 0.960 0.962 0.949 45 mph 0.925 0.922 0.933 0.922 0.949 0.966 0.960 40 mph 0.959 0.957 0.960 0.955 0.974 0.976 30 mph 0.974 0.973 0.972 0.970 0.977 25 mph 0.973 0.974 0.970 0.973 20 mph 0.972 0.971 0.960 15 mph 0.981 0.980 10 mph 0.978 Table B-13. Agreement scores, IRI waveband, no DMI correction, profiler 5, left. 10 mph 15 mph 20 mph 25 mph 30 mph 40 mph 45 mph 50 mph 60 mph 60 mph 0.649 0.711 0.741 0.800 0.800 0.811 0.756 0.794 0.947 50 mph 0.760 0.818 0.863 0.915 0.919 0.913 0.895 0.919 45 mph 0.723 0.798 0.827 0.896 0.887 0.884 0.944 40 mph 0.775 0.828 0.876 0.936 0.938 0.961 30 mph 0.793 0.845 0.900 0.942 0.948 25 mph 0.771 0.834 0.887 0.940 20 mph 0.827 0.886 0.912 15 mph 0.830 0.868 10 mph 0.900 Table B-14. Agreement scores, IRI waveband, no DMI correction, profiler 6, right. 10 mph 15 mph 20 mph 25 mph 30 mph 40 mph 45 mph 50 mph 60 mph 60 mph 0.912 0.929 0.919 0.948 0.930 0.951 0.946 0.969 0.986 50 mph 0.935 0.950 0.948 0.957 0.950 0.971 0.959 0.973 45 mph 0.930 0.944 0.947 0.951 0.951 0.961 0.937 40 mph 0.954 0.964 0.965 0.962 0.959 0.968 30 mph 0.935 0.948 0.956 0.947 0.940 25 mph 0.957 0.966 0.955 0.961 20 mph 0.960 0.964 0.958 15 mph 0.968 0.963 10 mph 0.967
B-18 Table B-15. Agreement scores, IRI waveband, DMI correction, profiler 1, left. 10 mph 15 mph 20 mph 25 mph 30 mph 35 mph 40 mpha 50 mph 60 mphb 0.918 0.908 0.899 0.926 0.946 0.944 0.928 0.944 50 mph 0.913 0.889 0.879 0.908 0.936 0.942 0.911 0.959 40 mpha 0.918 0.934 0.941 0.952 0.936 0.940 0.970 35 mph 0.916 0.920 0.913 0.944 0.959 0.951 30 mph 0.917 0.926 0.925 0.951 0.973 25 mph 0.916 0.940 0.948 0.972 20 mph 0.897 0.928 0.945 15 mph 0.904 0.918 10 mph 0.897 a Two passes collected at 40 mph. b One pass collected at 60 mph. Table B-16. Agreement scores, IRI waveband, DMI correction, profiler 2, left. 10 mph 15 mph 20 mph 25 mph 30 mph 40 mph 45 mph 50 mph 60 mph 60 mph 0.957 0.961 0.981 0.979 0.978 0.976 0.964 0.974 0.980 50 mph 0.962 0.966 0.978 0.977 0.977 0.976 0.973 0.969 45 mph 0.962 0.958 0.972 0.974 0.973 0.978 0.973 40 mph 0.971 0.967 0.982 0.983 0.98 0.979 30 mph 0.966 0.970 0.985 0.984 0.981 25 mph 0.973 0.971 0.986 0.984 20 mph 0.969 0.973 0.989 15 mph 0.956 0.955 10 mph 0.970 Table B-17. Agreement scores, IRI waveband, DMI correction, profiler 3, left. 10 mph 15 mph 20 mph 25 mph 30 mph 40 mph 45 mph 50 mph 60 mph 60 mph 0.847 0.952 0.955 0.964 0.958 0.962 0.964 0.966 0.953 50 mph 0.848 0.955 0.958 0.973 0.965 0.974 0.971 0.981 45 mph 0.855 0.959 0.966 0.970 0.967 0.967 0.966 40 mph 0.850 0.957 0.957 0.970 0.966 0.964 30 mph 0.857 0.962 0.963 0.969 0.958 25 mph 0.859 0.968 0.968 0.972 20 mph 0.864 0.964 0.967 15 mph 0.870 0.961 10 mph 0.958
B-19 Table B-18. Agreement scores, IRI waveband, DMI correction, profiler 4, left. 10 mph 15 mph 20 mph 25 mph 30 mph 40 mph 45 mph 50 mph 60 mph 60 mph 0.972 0.970 0.970 0.973 0.972 0.964 0.953 0.951 0.972 50 mph 0.961 0.959 0.960 0.954 0.964 0.966 0.963 0.950 45 mph 0.966 0.964 0.961 0.955 0.966 0.972 0.960 40 mph 0.976 0.976 0.971 0.967 0.978 0.976 30 mph 0.981 0.981 0.977 0.974 0.980 25 mph 0.974 0.975 0.972 0.974 20 mph 0.975 0.975 0.966 15 mph 0.981 0.981 10 mph 0.979 Table B-19. Agreement scores, IRI waveband, DMI correction, profiler 5, left. 10 mph 15 mph 20 mph 25 mph 30 mph 40 mph 45 mph 50 mph 60 mph 60 mph 0.660 0.752 0.762 0.831 0.821 0.825 0.842 0.822 0.953 50 mph 0.778 0.842 0.875 0.929 0.932 0.923 0.930 0.950 45 mph 0.773 0.837 0.861 0.931 0.926 0.928 0.979 40 mph 0.783 0.847 0.878 0.941 0.940 0.961 30 mph 0.804 0.864 0.904 0.949 0.955 25 mph 0.787 0.856 0.892 0.953 20 mph 0.839 0.906 0.915 15 mph 0.861 0.919 10 mph 0.919 Table B-20. Agreement scores, IRI waveband, DMI correction, profiler 6, right. 10 mph 15 mph 20 mph 25 mph 30 mph 40 mph 45 mph 50 mph 60 mph 60 mph 0.971 0.972 0.957 0.976 0.949 0.967 0.955 0.973 0.986 50 mph 0.971 0.973 0.967 0.969 0.957 0.976 0.960 0.973 45 mph 0.954 0.958 0.958 0.956 0.954 0.962 0.937 40 mph 0.969 0.972 0.970 0.965 0.961 0.969 30 mph 0.950 0.955 0.961 0.949 0.944 25 mph 0.964 0.968 0.956 0.962 20 mph 0.963 0.965 0.958 15 mph 0.970 0.963 10 mph 0.968
B-20 Table B-21. Agreement scores, long waveband, DMI correction, profiler 1, left. 10 mph 15 mph 20 mph 25 mph 30 mph 35 mph 40 mpha 50 mph 60 mphb 0.908 0.897 0.931 0.951 0.914 0.953 0.946 0.955 50 mph 0.898 0.865 0.910 0.914 0.884 0.943 0.936 0.937 40 mpha 0.911 0.888 0.927 0.892 0.881 0.920 0.961 35 mph 0.888 0.868 0.910 0.923 0.903 0.948 30 mph 0.827 0.840 0.884 0.915 0.893 25 mph 0.868 0.881 0.912 0.950 20 mph 0.892 0.890 0.899 15 mph 0.861 0.839 10 mph 0.876 a Two passes collected at 40 mph. b One pass collected at 60 mph. Table B-22. Agreement scores, long waveband, DMI correction, profiler 2, left. 10 mph 15 mph 20 mph 25 mph 30 mph 40 mph 45 mph 50 mph 60 mph 60 mph 0.932 0.904 0.992 0.996 0.996 0.996 0.995 0.996 0.997 50 mph 0.932 0.904 0.992 0.995 0.995 0.996 0.996 0.998 45 mph 0.931 0.905 0.992 0.994 0.994 0.995 0.994 40 mph 0.932 0.905 0.992 0.996 0.996 0.995 30 mph 0.933 0.904 0.992 0.997 0.997 25 mph 0.935 0.905 0.992 0.995 20 mph 0.930 0.902 0.986 15 mph 0.861 0.822 10 mph 0.897 Table B-23. Agreement scores, long waveband, DMI correction, profiler 3, left. 10 mph 15 mph 20 mph 25 mph 30 mph 40 mph 45 mph 50 mph 60 mph 60 mph 0.824 0.973 0.986 0.987 0.989 0.988 0.990 0.990 0.982 50 mph 0.825 0.976 0.992 0.992 0.994 0.993 0.996 0.994 45 mph 0.823 0.975 0.993 0.993 0.993 0.992 0.998 40 mph 0.820 0.978 0.988 0.989 0.992 0.991 30 mph 0.824 0.976 0.990 0.991 0.990 25 mph 0.828 0.974 0.992 0.989 20 mph 0.828 0.974 0.993 15 mph 0.807 0.967 10 mph 0.970
B-21 Table B-24. Agreement scores, long waveband, DMI correction, profiler 4, left. 10 mph 15 mph 20 mph 25 mph 30 mph 40 mph 45 mph 50 mph 60 mph 60 mph 0.963 0.971 0.983 0.983 0.976 0.972 0.974 0.974 0.990 50 mph 0.942 0.954 0.976 0.984 0.986 0.987 0.992 0.992 45 mph 0.942 0.955 0.978 0.986 0.989 0.990 0.992 40 mph 0.941 0.955 0.980 0.985 0.992 0.991 30 mph 0.946 0.961 0.984 0.991 0.996 25 mph 0.953 0.966 0.988 0.991 20 mph 0.954 0.969 0.986 15 mph 0.958 0.964 10 mph 0.948 Table B-25. Agreement scores, long waveband, DMI correction, profiler 5, left. 10 mph 15 mph 20 mph 25 mph 30 mph 40 mph 45 mph 50 mph 60 mph 60 mph 0.760 0.871 0.937 0.944 0.959 0.986 0.991 0.973 0.993 50 mph 0.754 0.863 0.927 0.925 0.940 0.967 0.979 0.991 45 mph 0.761 0.873 0.939 0.944 0.959 0.987 0.992 40 mph 0.763 0.877 0.942 0.954 0.970 0.989 30 mph 0.770 0.873 0.938 0.980 0.985 25 mph 0.774 0.870 0.935 0.982 20 mph 0.757 0.852 0.895 15 mph 0.703 0.789 10 mph 0.634 Table B-26. Agreement scores, long waveband, DMI correction, profiler 6, right. 10 mph 15 mph 20 mph 25 mph 30 mph 40 mph 45 mph 50 mph 60 mph 60 mph 0.954 0.969 0.972 0.970 0.983 0.993 0.991 0.994 0.995 50 mph 0.953 0.968 0.969 0.967 0.980 0.994 0.992 0.995 45 mph 0.952 0.968 0.971 0.969 0.980 0.992 0.988 40 mph 0.952 0.968 0.969 0.967 0.979 0.992 30 mph 0.945 0.968 0.983 0.984 0.986 25 mph 0.934 0.961 0.980 0.986 20 mph 0.940 0.961 0.977 15 mph 0.941 0.953 10 mph 0.919 B.8 References Karamihas, S. M. 2009. Benchmark Testing Plan. FHWA Contract DTFH61-07-C-00024 Task B Report, University of Michigan Transportation Research Institute.