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25 C h a p t e r 5 As described in Chapter 2, the core use of the Site Observer is for addressing SHRP 2 Safety research questions via the use of crash surrogates (conflict measures that correlate with actual crashes) to provide a powerful tool to evaluate crash risk, factor dependencies, and the efficacy of any particular interventions. In this chapter the research team reviews the commonly used conflict metrics and uses a simulation study to evaluate the sensitivity of these metrics to track errors, thus providing benchmark requirements for track- ing accuracy. Intersection-related Conflict Metrics Defining and validating crash surrogates is by itself seen as an ongoing research issue, but in loose terms these are metrics that describe the normal vehicular interactions that are cor- related with conflict severity and crash risk, although possibly in some context-dependent manner. As such, standard con- flict metrics provide a suitable test case for the video tracking system; tracking errors should not be large enough to sub- stantially affect distributions of conflict metrics such as the time to collision. It is not the purpose here to seek to substantiate or validate the general method of traffic conflict theory. Rather, the cur- rent crop of metrics in use is summarized and it is noted that one important application of the SHRP 2 video tracking sys- tem will be a tool to enhance the future development and validity checking for the technique. Table 5.1 gives a summary of the major conflict metrics in common use for intersection crashes. These are directed toward path-crossing conflicts, although time to collision (TTC) is equally applicable to conflicts relevant to rear-end collisions, which is the primary conflict type for the chosen pilot intersection (see Chapter 7). A distinction should be made between two types of conflict metric: instantaneous and summary measures. The instanta- neous measures are defined for each vehicle and for each instant of time; gap time and TTC are examples of these. Typically there is an assumption that the vehicles continue to move on a given trajectory and at a constant speed. On the other hand, summary measures provide surrogates on a per event basis (e.g., PET or postencroachment time) or on a per time basis (e.g., time-integrated TTC and time-exposed TTC). The last four metrics in the tableâsignal encroachment time, signal transition deceleration time, signal transition acceleration time, and lateral encroachment timeâare asso- ciated with crashes involving red light violations. The inter- est in these metrics is to support a better understanding of the relationship between the time when the red light running occurs and particular conflict types. Intersection conflict types were identified by Najm, Smith, and Smith (2001) and illustrated in Figure 5.1. The authors organized conflicts at intersections based on precrash movement and proposed the following five categories: ⢠Left turn across path/opposite direction (LTAP/OD); ⢠Left turn across path/lateral direction (LTAP/LD); ⢠Left turn into pathâmerge conflict (LTIP); ⢠Right turn into pathâmerge conflict (RTIP); and ⢠Straight crossing path (SCP). Najm, Smith, and Smith also recommended considering the type of control device regulating the intersection and dis- tinguished between signal, stop sign, no controls and others. An example of how red light running and conflict type can be associated is found in Zimmerman and Bonneson (2005), who reviewed samples of crash data and distinguished between two conflicts involving red light running: LTAP/ OD and SCP. The main difference between the two conflicts is found in the timing of the collision relative to the red light onset. In the case of LTAP/OD, most collisions occurred within the first 5 s after the transition, whereas most of the SCP collisions occurred after the first 5 s after the transition. Conflict Metrics and Crash Surrogates
26 Table 5.1. Summary of Kinematic Conflict Metrics Surrogate Conflict Measure Description Gap time (Gettman and Head 2003) Time lapse between completion of the encroachment by turning vehicle and the arrival time of crossing vehicle if they continue with the same speed and path. Encroachment time (Gettman and Head 2003) Time duration during which the turning vehicle infringes upon the right-of-way of through vehicle. Deceleration rate (Gettman and Head 2003) Rate at which crossing vehicle must decelerate to avoid collision. Proportion of stopping distance (Gettman and Head 2003) Ratio of distance available to maneuver to the distance remaining to the projected location of collision. Postencroachment time (Gettman and Head 2003) Time lapse between end of encroachment of turning vehicle and the time that the through vehicle actually arrives at the potential point of collision. Initially attempted postencroachment time (Gettman and Head 2003) Time lapse between commencement of encroachment by turning vehicle plus the expected time for the through vehicle to reach the point of collision and the completion time of encroachment by turning vehicle. Time to collision (TTC) (Gettman and Head 2003) Expected time for two vehicles to collide if they remain at their current speed and on the same path. Time-exposed TTC (Archer 2001) The length of time that all vehicles involved in conflicts spent under a designated TTC minimum threshold during a specified time period. Time-integrated TTC (Archer 2001) Integral of TTC profile of drivers to express the level of safety over the specified time period. Time to accident (Archer 2001) Point at which the aversive action is taken. This measure, combined with the conflicting speed, allows determination of the level of severity of a conflict. Signal encroachment time Time lapse between the onset of red cycle and vehicle entering intersection. Signal transition deceleration time Time lapse between the transition of signal (green to amber or amber to red) and deceleration onset. Signal transition acceleration time Time lapse between the transition of signal and acceleration onset. Lateral encroachment time Time duration during which the violating vehicle infringes upon the right-of-way of through vehicle. Source: Najm, Smith, and Smith 2001. (a) (b) (c) (d) (e) Figure 5.1. Intersection conflict types.
27 The implication is that, for LTAP/OD cases, the driver is waiting to make a turn and is under pressure to clear the intersection and might misinterpret the oncoming driver decision to stop at the red light. From this perspective, the research team attempted to organize the potential crash surrogates relative to the conflict type and proposed causal factors in Table 5.2, where the causal factor could be observed via a set of surrogate mea- sures departing from baseline driving. It seems reasonable to conclude that any one of the metrics in Table 5.1 may be used for future analysis using the video tracking system results. Although other metrics might also be of interest (for example, time to lane crossing [TTLC]) when studying lane departures or road departures, the intersection conflicts provide a reasonable benchmark for the tracking system. The research team considers what level of time and space resolution and accuracy are needed to support their use in safety studies. Table 5.2. Conflict Type and Surrogate Measures for Signalized Intersections Conflict Type Scenario Causal Factors Surrogate Set LTAP/OD A vehicle turning left at an intersection collides with a vehicle from the oncoming traffic. Failure to yield right-of-way Underestimation of oncoming traffic speed ⢠Gap time ⢠Encroachment time ⢠Deceleration rate ⢠Proportion of stopping distance ⢠Postencroachment time ⢠Initially attempted post encroachment time Understanding of right-of-way ⢠Gap time ⢠Encroachment time ⢠Deceleration rate ⢠Proportion of stopping distance ⢠Postencroachment time ⢠Initially attempted postencroachment time Run signal Did not see light status ⢠Signal encroachment time ⢠Signal transition deceleration time ⢠Lateral encroachment time Vision obscured ⢠Distance to intersection ⢠Signal transition deceleration timea Distraction ⢠Distance to intersection ⢠Signal transition deceleration timeb Tried to beat amber light ⢠Signal transition acceleration time ⢠Signal encroachment time Deliberately ran red light ⢠Signal transition acceleration time ⢠Signal encroachment time LTAP/LD A vehicle turning left at an intersection collides with a vehicle from the lateral direction. Run signal Did not see light status ⢠Signal encroachment time ⢠Signal transition deceleration time ⢠Lateral encroachment time Vision obscured ⢠Distance to intersection ⢠Signal transition deceleration time Distraction ⢠Distance to intersection ⢠Signal transition deceleration time Tried to beat amber light ⢠Signal transition acceleration time ⢠Signal encroachment time Deliberately ran red light ⢠Signal transition acceleration time ⢠Signal encroachment time (continued on next page)
28 LTIP A vehicle turning left at an intersection collides with a vehicle in the flow in which it is inserting. Run signal Did not see light status ⢠Signal encroachment time ⢠Signal transition deceleration time ⢠Lateral encroachment time Vision obscured ⢠Distance to intersection ⢠Signal transition deceleration time Distraction ⢠Distance to intersection ⢠Signal transition deceleration time Tried to beat amber light ⢠Signal transition acceleration time ⢠Signal encroachment time Deliberately ran red light ⢠Signal transition acceleration time ⢠Signal encroachment time RTIP A vehicle turning right at an intersection collides with a vehicle in the flow in which it is inserting. Failure to yield right-of-way Underestimation of on- coming traffic speed ⢠Gap time ⢠Encroachment time ⢠Deceleration rate ⢠Proportion of stopping distance ⢠Postencroachment time ⢠Initially attempted postencroachment time Understanding of right-of-way ⢠Gap time ⢠Encroachment time ⢠Deceleration rate ⢠Proportion of stopping distance ⢠Postencroachment time ⢠Initially attempted postencroachment time Run signal Did not see light status ⢠Signal encroachment time ⢠Signal transition deceleration time ⢠Lateral encroachment time Vision obscured ⢠Distance to intersection ⢠Signal transition deceleration time Distraction ⢠Distance to intersection ⢠Signal transition deceleration time Tried to beat amber light ⢠Signal transition acceleration time ⢠Signal encroachment time Deliberately ran red light ⢠Signal transition acceleration time ⢠Signal encroachment time SCP A vehicle going straight at an intersection collides with a vehicle from the lateral direction. Run signal Did not see light status ⢠Signal encroachment time ⢠Signal transition deceleration time ⢠Lateral encroachment time Vision obscured ⢠Distance to intersection ⢠Signal transition deceleration time Distraction ⢠Distance to intersection ⢠Signal transition deceleration time Tried to beat amber light ⢠Signal transition acceleration time ⢠Signal encroachment time Deliberately ran red light ⢠Signal transition acceleration time ⢠Signal encroachment time a When the driversâ view of the signal is obscured by some static element (e.g., foliage, building), the data can be expected to show that drivers within specific distance from the intersection do not respond to signal transition. b However, if there is no visual obstruction, the point of no response to signal change could be anywhere in the intersection. Table 5.2. Conflict Type and Surrogate Measures for Signalized Intersections (continued) Conflict Type Scenario Causal Factors Surrogate Set
29 accuracy requirements from Conflict Metric analysis Because the estimation of distributions of conflict metrics is a critical application for the system, these provide a signifi- cant test case for accuracy requirements: when errors occur in positions and velocities recorded in the trajectory record, these will induce errors in the relevant conflict metrics. To investigate this, one must have an unperturbed exact set of trajectories, which are here provided by simulation, together with an error model. From Monte Carlo simulation, a result- ing distribution of conflict metrics can be obtained. Based on the review of conflict metrics in Chapter 4, two particular intersection conflict types, and in each case, two conflict metrics are considered here. These are: 1. LTAP/OD (Figure 5.1a), with metrics of gap time and postencroachment time; and 2. LTIP (Figure 5.1c), with metrics of time to collision and deceleration rate. For simplicity, no traffic signal timing is considered, and the arrival times of the vehicles have been set so that although no collision occurs, the postencroachment time (Case 1) and time to collision (Case 2) are short but realistic. Each scenario is considered here. Left Turn Across Path Figure 5.2 shows the simple intersection used for simulation. The subject vehicle (SV) has approached from the right, stopped briefly, and is now just starting to make a turn across the path of the principal other vehicle (POV) moving from the left. In this example, the POV initially is moving with constant speed and stays in its current lane but brakes for a short period to avoid hitting the turning vehicle. Figure 5.3 shows the speed and acceleration of the two vehicles during the maneuver. Figure 5.3 shows the results of predicted arrival times at the intersection by the POV (where the front of the POV intersects the right boundary of the SV path) and the pre- dicted exit time for the SV (when the rear of the SV clears the right boundary of the POV path). These predictions are made at each time instant and assume no change in path or speed, as is normally the case for the metrics chosen. The difference between these times is the gap time, and it can be seen that only as the conflict point is reached does the gap time rise above zero so the collision is avoided (Figure 5.4). Although the (predicted) gap time has a time history over the entire interaction, the PET is a single value, namely, the actual time gap between the subject vehicle leaving the point of encroachment and the POV reaching it, and in the particu- lar simulation, PET = 0.363 s. This is a suitable statistic to con- sider for sensitivity to path estimation error but clearly ignores the role of the POV driver in intervening to prevent the crash; thus, another pair of statistics is considered as well. These are the minimum and maximum gap time during the 2 s before the POV arrives at the zone of encroachment, which does include the effect of POV intervention; these values are GTmin = -0.0060 s, GTmax = 0.363 s. Not surprisingly, in this case GTmax equals PET, but this need not always be the case. Meters M et er s Figure 5.2. LTAP/OD scenario.
30 0 2 4 6 8 10 12 14 16 18 20 0 10 20 30 time (s) sp ee d (m sâ1 ) SVPOV 0 2 4 6 8 10 12 14 16 18 20 -4 -2 0 2 4 time (s) a cc e le ra tio n (m sâ2 ) SV POV Figure 5.3. Simulated speeds and accelerations of the two vehicles. 0 2 4 6 8 10 12 14 16 18 20 -10 -8 -6 -4 -2 0 2 4 6 8 10 time (s) tim e (s ) pred time to POV entry pred time to SV exit pred gap time Figure 5.4. Predicted times of encroachment and gap time for LTAP/OD scenario. Left Turn into Path In this scenario, the same simple intersection geometry is used, but this time the SV approaches from the upper road, slows and does not stop, then turns into the same path as the approaching POV. In this simulation, the POV has a higher initial speed and again decelerates to avoid a collision. The conflict measures chosen in this case are more appropriate for the case in which paths are coincident (after a certain instant in time). Figure 5.5 shows the trajectories and Figure 5.6 pre- sents speed and longitudinal acceleration data for the conflict. Figure 5.7 shows the time variation of the selected metrics for the conflict. On the left is the time to collision, the time at which a collision would occur if the speeds and paths remained
31 POV subject vehicle Figure 5.5. Vehicleâs paths. unchanged. The second was chosen as the acceleration rate of the turning (SV) required to avoid collision (assuming the POV maintains a constant speed at each instant). This is simi- lar to the deceleration rate mentioned earlier, although in this case the SV clearly needs a positive acceleration to avoid a collision. The (predicted) time to collision falls to approxi- mately 1 s, while at about the same time the acceleration required (AR) for the subject vehicle increases to almost 4 ms-2. Here both metrics are continuous variables, so for the error analysis, TTCmin and ARmax are used as summary metrics of interest. Sensitivity Analysis The effect of tracking errors on the summary conflict mea- sures is considered here. The basic idea is to corrupt the tra- jectories by adding some form of error to include in the âmeasuredâ locations or times of the trajectories. There are many ways in which this can be done, and here the aim is to keep the analysis relatively simple and not to deliberately amplify or overexaggerate the possible effects of the errors. The simplest and perhaps most common form of error signal is a Gaussian variable, which is uncorrelated between samples; 0 2 4 6 8 10 12 14 16 18 20 0 10 20 30 time (s) sp ee d (m sâ 1 ) SV POV 0 2 4 6 8 10 12 14 16 18 20 -4 -2 0 2 4 time (s) ac ce le ra tio n (m sâ 2 ) SV POV Figure 5.6. Vehicleâs speeds and longitudinal accelerations.
32 0 5 10 15 0 1 2 3 4 5 6 7 8 9 10 ti me (s ) TT C (s ) 0 5 10 15 0 1 2 3 4 5 6 7 8 9 10 ti me (s ) AR (m sâ 2 ) Figure 5.7. Conflict metrics for LTIP scenario. that is, it is a discrete-time Gaussian white noise (GWN) error. In addition, when such errors arise in the data collection sys- tem, some form of filtering (e.g., Kalman filtering) undoubt- edly will be applied (see Chapter 10), reducing the bandwidth and the RMS error induced. Put another way, GWN can show large errors that may be reduced because it is only the lower frequency components that can be confused with vehicle dynamic motions. Therefore, we will use a filtered form of the GWN, using a simple first order filter with a bandwidth of 1 Hz, which means that the errors become largely indistin- guishable from the dynamics of a maneuvering vehicle. Two independent equal variance error signals are generated, applied to the x and y coordinates of the subject vehicle, while for sim- plicity the POV trajectory is left unchanged (a more realistic method might be to assign errors that are correlated as a func- tion of vehicle speed and spatial location, but the detailed modeling of errors in the camera and video processing sys- tem rapidly become very complex indeed). The RMS errors of these signals are then scaled according to three assumptions about the measurement system: (1) low level, RMS = 0.2 m; (2) medium level, RMS = 0.5 m; and (3) high level, RMS = 1 m. Figure 5.8 shows the effect on the estimated spatial trajec- tory when the medium level of error is used. Figures 5.9 and 5.10 show the effects on the three summary statistics when low- and medium-level errors are used. It may be noticed that the trajectory errors, although smoothed to some extent through the limited bandwidth of the filter, are still relatively coarse; it is certainly possible that an optimal filter can reduce the errors further. On the other hand, the errors shown are by no means worst case (recall that the POV trajectory is uncorrupted). If we were not looking at criti- cal events, the spread in these distributions would not be unreasonable, but when the signal (gap-related timing) is close to zero, as in this case, and deviations from zero are highly significant (crash or no crash, for example), it is clear that even for medium error levels the noise-to-signal ratio is too high to be very useful. The conclusion is that when RMS errors in the vehicle location are on the order of 0.5 m or higher, the effects of errors on computed metrics are too high to be much use to the analysis of near-crash events. This con- clusion depends on the simple assumptions made about the error process and would not apply, for example, to a camera calibration error that could be corrected in postprocessing. But for band-limited random errors in the vehicle path track- ing, errors should not be any worse than around 20 cm in RMS. Presenting results for high-level errors has turned out to be unnecessary, but in this case the noise totally dominates the signal, and the resulting trajectories would be practically useless for the analysis of near-critical events. The same analysis was applied to the second scenario (LTIP) with similar results. Figures 5.11 and 5.12 show corresponding histograms for the minimum TTC and maximum AR. The low level of simulated errors provides convincing results, whereas especially for the minimum TTC, the medium-level error case gives a noise level in the computed metrics that is comparable to the signal amplitude. The same conclusion applies: displacement errors should be no more than approx- imately 20 cm in RMS terms for conflict metrics to be com- puted with reasonable confidence, at least after postprocessing filters have been applied.
33 0 5 10 15 20 Meters M et er s 25 30 35 40 -20 -15 -10 -5 0 5 10 Figure 5.8. Effect of medium level spatial errors on the trajectory (blue: reference; black: perturbed). -0.5 0 0.5 0 2 4 6 8 10 12 14 16 18 20 minimum gap 0 0.5 0 5 10 15 20 25 30 maximum gap 0 0.5 0 5 10 15 20 25 30 PET Figure 5.9. Frequency distribution of summary metrics (LTAP/OD: 100 simulations, low-level error).
34 -4 -2 0 0 5 10 15 20 25 minimum gap -2 0 2 0 2 4 6 8 10 12 14 16 18 maximum gap -1 0 1 0 5 10 15 20 25 PET Figure 5.10. Frequency distribution of summary metrics (LTAP/OD: 100 simulations, medium-level error). 1.05 1.1 1.15 1.2 1.25 0 5 10 15 20 25 minimum TTC 3.9 4 4.1 4.2 0 5 10 15 20 25 maximum AR Figure 5.11. Frequency distribution of summary metrics (LTIP: 100 simulations, low-level error).
35 0 0.5 1 1.5 0 5 10 15 20 25 minimum TTC 4 4.5 5 5.5 0 2 4 6 8 10 12 14 16 maximum AR Figure 5.12. Frequency distribution of summary metrics (LTIP: 100 simulations, medium-level error).
