Abstract
Most of the collision warning systems that are available in the automotive market are mainly designed to detect imminent rear-end and/or lane-departure collisions. So far, no collision warning system is commercially available to detect imminent angle and turning collisions at semi-controlled intersections where the driver of a vehicle attempts to depart a minor road (controlled by a stop sign) to turn right, to turn left, or to cross an uncontrolled major road. One of the major causes for collisions at non-signalized intersections is the human error and misjudgment of the driver of the minor-road vehicle. Therefore, using a properly-designed collision warning system will have the potential to reduce, or even eliminate, this type of collision by reducing human error. This paper introduces a technology-independent algorithm for a collision warning system that can detect imminent collisions at semi-controlled intersections. The system utilizes commercially-available detectors to detect the approaching vehicles on the major road and calculate their speeds, accelerations, and rates of change of acceleration to estimate the time required to reach the intersection. The time required by the minor-road vehicle to clear the intersection is modeled as a function of driver and vehicle characteristics. By comparing the two times, the system displays a message for the driver of the minor-road vehicle when the departure maneuver is safe. An application example is provided to illustrate the proposed algorithm.1.0 Introduction
1 Angle and turning collisions at intersections are one of the most common types of collisions that have higher rates of fatalities and injuries than other types of collisions. In Ontario, Canada, there were 56,257 such collisions in 2006 that caused 133 fatalities and 14,456 injuries (Ministry of Transportation of Ontario, 2006). This is compared to 59,221 rear-end collisions that caused 39 fatalities and 13,238 injuries. Despite the fact that intersection collisions are more frequent and more severe than rear-end collisions, most of the collision warning systems available in the automotive market are designed to detect potential rear-end and/or lane-departure collisions (NHTSA, 2000; Brown et al., 2000; Dravidam and Tosunoglu, 2000; Taylor, 2005; VORAD, 2009).
2 One of the main factors that may lead to collisions at non-signalized intersections is the driver’s misjudgment of the speed and acceleration of the vehicles in the cross traffic stream on the major road, which resulted in approximately 36.1% of collisions at non-signalized intersections (Pierowicz et al., 2000). This inadequacy in judging the speed and acceleration of other vehicles is common among drivers with some variations due to age, health conditions and other factors. Although the human visual system is extremely sophisticated, psychophysical evidence found that it was insensitive to the acceleration of objects with no direct perceptual mechanisms to support the perception of acceleration (Watamaniuk and Duchon, 1992). A properly-designed collision warning system might mitigate this problem by detecting and analyzing all the information, including reaction time and acceleration rate of the driver of the minor-road (equipped) vehicle, and giving a visual, auditory, or haptic signal to the driver of the equipped vehicle to start the departure movement when conditions are safe.
3 Limited research efforts have been directed to designing vehicle-mounted warning systems for intersection collisions, including the Intersection Collision Avoidance (ICA) system developed by the Calspan SRL Corporation (Pierowicz et al., 2000);, the Intersection Crash Avoidance Violation warning system (ICAV) proposed by Virginia Tech Transportation Institute (NHTSA, 2004); and the INTERSAFE system developed by the European Commission (Fuerstenberg and Chen, 2007). The main features of these systems are presented in Table 1. Each of those systems used a pair of detectors (either radar sensors for the ICA and ICAV systems or laser scanners for the INTERSAFE system) installed at the left and right front corners of the equipped vehicle to detect the approaching vehicles, determine their speeds and time-to-collision, and trigger a warning if they are found to be conflicting with the path of the equipped vehicle. However, none of those research projects have considered measuring the acceleration of the detected vehicles or the time required for the driver of the equipped vehicle to perceive the message given by the system and react to it. The desired acceleration rate of the driver of the equipped vehicle is another human factor that has not been considered by these previous research projects.
4 This paper proposes a conceptual framework for a technology-independent collision warning system that can detect imminent angle and turning collisions at semi-controlled intersections by utilizing a pair of detectors (either radar sensors or laser scanners). Unlike other proposed systems, this system models the variations among drivers in their perception-reaction times (PRT) and departure acceleration characteristics. The following section presents the proposed warning system, including technical specifications, system algorithm, and other aspects. Application of the system is then illustrated using an example. The limitations of the system are then discussed, followed by concluding remarks.
Table 1. Comparison of different vehicle-based intersection collision warning systems
2.0 Proposed Warning System
5 Similar to the existing warning systems, the proposed system utilizes a pair of detectors installed at the left and right front corners of the equipped (target) vehicle to detect approaching (bullet) vehicles on the major road, as shown in Figure 1. Using the detectors, along with a processing unit and a driver-vehicle interface unit, the system determines whether a ‘Not Safe’ or ‘Proceed with Caution’ message should be displayed to the driver of the target vehicle.
2.1 Minimum Technical Specifications of Detectors
6 Each detector (either radar sensor similar to the ICA and ICAV systems, or laser scanner similar to the INTERSAFE system) sends a beam every time interval, t, to scan the cross-traffic lanes on the major road. The time interval ranges from 0.04 sec to 1.5 sec, depending on the type of the detector used. Based on previous research (NHTSA 2004) an update rate of 10 Hz, with 0.1 second time interval, is recommended to provide acceptable range and range-rate resolution. The opening angles of the left and right detector are denoted by P L2 and P R2 , respectively. The width of the beam is designed so that the angle between the outer left edge of the beam and the face plane of the vehicle P L1 can detect the approaching vehicles from the left within a safe intersection sight distance for a typical semi-controlled two-way stop-controlled (TWSC) intersection (and similarly for P R1 for the right direction). From geometric design guides, the intersection sight distance for a design speed of 70 km/h is 150 m (American Association of State Highway and Transportation Officials, 2004). This design speed was selected as it is the maximum design speed for a major urban road. It should be noted that the sight distance is used here for the purpose of selecting the appropriate opening angle for the detectors. The actual distance between the approaching bullet vehicle and the intersection is calculated based on the actual detected location, speed, and acceleration rate of the bullet vehicle.
Figure 1. Typical system configuration at a non-signalized intersection
Display large image of Figure 1
7 For vehicles approaching from the left side (Figure 1), the angle with the plane face of the vehicle, is 0° (conservatively assuming no setback). To detect vehicles in the near lane, the opening (azimuth) angle equals tan (150/3.5) which yields an opening angle of approximately 88°. For vehicles approaching from the right side, another detector is used with an angle with the plane of the vehicle approximately equal to tan (3.5/150) or 1.3°. The opening angle equals tan (150/7) or approximately 87° to detect vehicles in the near lane (this angle is calculated assuming one lane in each direction of the major road with no setback, which would be conservative for roads with more lanes).
8 Based on the preceding considerations and previous research (United States Department of Transportation, 2003; NHTSA, 2004), the required specifications for the proposed detectors are as follows:
9 These minimum specifications are technology-independent and further research will be required to select the product that meets them. Possible candidates include the following:
2.2 System Algorithm
10 The algorithm procedures are as follows (Figure 2):
11 The proposed algorithm tracks different approaching vehicles on all lanes and the above procedures are followed for each vehicle with the ‘Not Safe’ message displayed until all lanes are clear of approaching vehicles that may collide with the turning vehicle. Similar to the preceding ICA, ICAV and INTERSAFE systems, vehicle tracking is achieved by using a Kalman filter (Kalman 1960). The Kalman filter performs tracking by estimating the state of dynamic objects (i.e., the approaching vehicles) at different times from a series of incomplete and noisy measurements (taken by detectors) and provides accurate continuously-updated information about the position and speed of the approaching vehicles. A bounding box is placed around the predicted positions of approaching vehicles and logic is used to determine if the detection is within that bounding box and hence is associated with a specific track. More information about vehicle tracking using the Kalman filter can be found in the literature (Maybeck, 1979; Grewal and Andrews, 1993; and Pierowicz et al., 2000).
12 The time anticipated for the bullet vehicle to reach the intersection, tbullet, and the time required for the target vehicle to depart the intersection, ttarget, are affected by the intended movement of the target vehicle and the travel direction of the bullet vehicle, as illustrated in Figure 3. There are three possible cases, as follows:
13 Note that the flashing turning signal of the equipped vehicle, activated by its driver, provides the required information for the algorithm to determine the intended departure path of the target vehicle, while the signal received from the detectors provides the required information about the path of the approaching vehicles. It is assumed that the drivers will always use the signal indicator when turning. In all cases, the system does not commence until the brakes are activated in a full stop. The modeling of the bullet vehicle location and the bullet and target vehicle times the two conflict cases described above is presented in the next section.
Figure 2. Flow chart for the proposed algorithm Figure 3. Conflict cases for a typical TWSC intersection: (a) paths of target and bullet vehicles are parallel with no conflict, (b) paths of target and bullet vehicles are perpendicular, and (c) target and bullet vehicles are in the same direction and the same lane.2.3 Bullet Vehicle Location
14 To calculate the time required for a detected bullet vehicle to reach the intersection, tbullet, a detection beam is generated, from one of the two detectors, at time T to scan the cross-traffic lanes. If no object is detected from both detectors, or if a vehicle is detected approaching from the right while the equipped vehicle’s intended path is to turn right, a ‘Proceed with Caution’ message is displayed to the driver. Otherwise, the nearest vehicle detected, vehicle A, is recorded at range d1 and azimuth angle θ1 where polar coordinates are used with the origin point coinciding with the location of the radar sensor that detected the vehicle (Figure 4a).
15 Another detection beam is generated, from the same detector, at T+t, where t is the time interval of the detector, and the new location of vehicle A is recorded at range d2 and azimuth angle θ2 (Figure 4b). If d1 and d2 were found to be equal to each other, the algorithm concludes that the object is not moving (e.g., a tree or a building), and a ‘Proceed with Caution’ message is displayed (unless another object is detected by any of the two detectors). If d2 was found to be greater than d1, the algorithm concludes that the object is moving away from the turning (target) vehicle, and a ‘Proceed with Caution’ message is also displayed to the driver (unless another object is detected by any of the two radar sensors). Finally, if d2 was found to be less than d1, the distance traversed by the approaching vehicle during the first time interval, dv1, is calculated as (Figure 5)
16 Similarly, a third and a fourth radar beams are generated at T+2t and T+3t, respectively. The information for the bullet vehicle at each time is recorded, (d3, θ3) and (d4, θ4), respectively. The distances traversed by the vehicle during the second and third time intervals, dv2 and dv3, respectively are calculated similar to calculating dv1. Assuming a linear time-dependant acceleration model, the rate of change in acceleration, r, can be calculated by the following equation:
The acceleration, speed, and distance at any time, t, can be directly computed by integrating the above equation three consecutive times. At T+t, for example, these parameters are given by
Similarly, the same parameters associated with the second and third time intervals can be computed as follows:
By solving the above equations together, the rate of change in acceleration is then given by
where dv1, dv2, and dv3 are the distances at T+1t, T+2t, and T+3t, respectively.
17 The side offset between the bullet vehicle and the target vehicle, wf, is computed as the mean value to reduce the likelihood of reading errors:
18 Note that the side offset wf, can be used to help reduce unnecessary warning signals when the target vehicle is turning right while the bullet vehicle is approaching from the left. If the side offset, wf, exceeds the sum of the lane width and the setback, this indicates that the bullet vehicle is not traveling on the nearest lane, which is occupied by the turning target vehicle, and in this case a ‘Proceed with Caution’ message can be displayed by the system (unless other vehicles are detected). In applying this criterion, the conservative approach is to implement the maximum values for the lane width and setback presented by the design guides ransportation Association of Canada, 2007; American Association of State Highway and Transportation Officials, 2004).
19 The distance from the bullet vehicle (at T+3t) to the intersection, df, is given by (Figure 6)
20 Based on the conflict type between the bullet and target vehicles (perpendicular paths or traveling on the same lane), the bullet time, tbullet, and target time, ttrget, can be computed as described in the next two sections.
2.4 Conflicting Vehicles have Perpendicular Paths
2.4.1 Bullet Vehicle Time
21 When the bullet and target vehicles have perpendicular paths (Figure 3b), the bullet time, tbullet, is the smallest positive real root of the following polynomial (Dabbour and Easa, 2009).
where df, vT+3t, aT+3t, and r are given by Equations 14, 10, 9, and 12, respectively. If Equation 15 returns no positive roots, the system triggers a ‘Proceed with Caution’ message as this indicates that the approaching vehicle is decelerating for a full stop before reaching the intersection. If more than one positive root were returned, the smaller one is used by the system for further calculations.
Figure 4. Measuring range and azimuth angle at T and (T+t)
Display large image of Figure 4
22 To keep the system consistent with driver’s habits without causing nuisance, the bullet time calculated by the system should not be less than 7.5 seconds plus 0.5 seconds for each additional lane that should be crossed, where the number of lanes to be crossed is determined from the side offset calculated by Equation 13. This is based on previous studies that reported that a passenger car driver who is departing a minor road onto a two-lane major road in a TWSC intersection mentally needs the above minimum value for the total gap available for departure (American Association of State Highway and Transportation Officials, 2004; Harwood et al., 1996). If the bullet time calculated by the system was found to be less than the minimum gap required, the system would not trigger a ‘Proceed with Caution’ message even if the target time was found to be less than the bullet time calculated by the system. However, this additional condition may be eliminated eventually in a later stage after the driver gets used to the system and gains more confidence in it.
Figure 5. Calculating traversed distance during the first time interval Figure 6. Schematic illustration of bullet vehicle locations at (T+2t) and (T+3t)2.4.2 Target Vehicle Time
23 The total time required for the driver of the target vehicle to clear the intersection is given by
where t1 is driver’s PRT and t2 is the travel time required for the target vehicle to accelerate and clear the path of the approaching bullet vehicle.
2.4.3 Perception-reaction Time
24 The driver’s perception-reaction time, t 1 , is different for the cases of a vehicle with and without a collision warning system. For a vehicle with a collision warning system, the PRT is the time required to perceive the message given by the collision warning system and react accordingly by activating the throttle. On the other hand, for a vehicle without a collision warning system, the driver has to perceive the whole situation, analyze it, make a decision, and take the appropriate action by activating the throttle. Theoretically, the PRT for a vehicle with a collision warning system is expected to be less than that for a vehicle without one due to the fewer mental tasks performed by the driver (no analysis or decision-making required). However, this expectation is influenced by several factors, including the reliability of the warning system and driver’s familiarity and trust with it.
25 To address the preceding issues, a regression model was developed to model the driver’s PRT in terms of the driver’s gender and age. The model was developed using data collected from 60 drivers representing both genders and different age groups as shown in Table 2. The sample was selected to proportionally represent the population of licensed drivers in Canada (Transport Canada, 2003). Every driver was asked to drive simulation scenarios on the STISIM driving simulator (STISIM, 2009) located at Ryerson University (Canada). The scenarios were designed to simulate a series of non-signalized intersections where drivers were asked to perform all available departure maneuvers (turning left, turning right and crossing). The algorithm was encoded into the scenarios so that at each intersection the driver would hear a buzz signal indicating that it was not safe to depart the intersection. The driver was instructed to depart the intersection as soon as the buzz signal stops for that intersection. The data collected included the PRT for the driver measured from the time the buzz signal stops to the time when he/she starts to engage the throttle to start departure. A total of 2160 observations were used to calibrate the regression model which is given by
where t1 is the PRT for the driver, AGE is the age of the driver (in years), and GENDER is a dummy variable that represents driver’s gender (0 for male and 1 for female). The coefficients of all independent variables were significantly different from zero at the 95% confidence level.
Table 2 Sample selection compared to licensed drivers in Canada (2003 data)
2.4.4 Driver’s Acceleration Rate
26 The acceleration rate selected by the driver is the maximum acceleration rate provided by the mechanical characteristics of the vehicle (as given by the vehicle’s performance data) multiplied by a correction factor, cd, that depends on driver’s characteristics as well as on the distance and speed of the nearest approaching vehicle. A regression model was calibrated using observations taken from the same driver sample used for calibrating the PRT model. The model is given by
where cd is the driver’s correction factor for the acceleration rate, df is the distance (in meters) to the nearest detected approaching vehicle (as was calculated from Equation 14), vT+3t is the detected speed (m/sec) of the nearest approaching vehicle during the last time interval used by the algorithm (as was calculated from Equation 10), and GENDER and AGE are as previously defined. The coefficients of all independent variables are significantly different from zero at the 95% confidence level. The signs of all the variables are logical.
2.4.5 Travel Time
27 The vehicle travel time, t2, when the bullet and target vehicles have perpendicular paths (Figure 3b), is computed as follows. First, the total distance to be crossed by the target vehicle, S, is calculated by
where wf is the offset, L is the length of the target vehicle, and CW is a correction factor. This factor corrects for the distance between the ‘reflective’ point (or the centre of a cluster of reflective points) in the approaching vehicle detected by the sensor and the far edge of the approaching vehicle to ensure safe departure. The reflective point detected by the sensor should be determined based on the technical specifications of the sensor used. If the reflective point is located at the near edge of the approaching vehicle, CW equals the full width of the approaching vehicle, which is typically 2.13 m (American Association of State Highway and Transportation Officials, 2004). If the reflective point is located at the centre of the approaching vehicle, CW equals a half vehicle width, and if the reflective point is located at the far edge of the approaching vehicle, CW equals zero. Using the linear decay acceleration model (Drew, 1968; Long, 2000), the acceleration of the target vehicle at any time can be computed by the following equation:
where at is the acceleration rate at time t; av is the maximum acceleration rate provided by the mechanical characteristics of the vehicle at the start of its movement; vt is the speed of the vehicle at time t; and ve is the equilibrium speed (the crawl speed) where the acceleration decreases to zero, which also depends on the mechanical characteristics of the vehicle. By integrating Equation 20, the following two equations compute speed, vt, and distance, dt, at any time t:
28 The driver’s desired acceleration, ad, is based on driver’s characteristics as well as on vehicle performance. This can be represented by the following equation:
where Cd is the driver’s correction factor for the acceleration rate as computed by Equation 18. The acceleration, at, speed, vt, and distance, dt, at any time t can be computed from the following equations:
29 The time required for crossing, t2, is then computed by solving the following equation
where the only unknown variable is the crossing time, t2.
2.5 Conflicting Vehicles Travelling on the Same Lane
30 Where both the target and bullet vehicles travel on the same lane (Figure 3c), the conflict point is located somewhere between the intersection and point B, which is the location where the target vehicle accelerates to 70% of the speed of the bullet vehicle (as shown in Figure 7). The conflict scenario is summarized as follows:
Figure 7. Geometry for conflicting vehicles travelling on the same lane
Display large image of Figure 7
3.0 Application Example
31 Assume a target vehicle with a length of 4.2 m, a maximum rate of acceleration of 5.25 m/sec2 and an equilibrium speed of 40 m/sec [144 km/hr]. The driver of that target vehicle is turning left from a minor road, controlled by a stop sign, into an uncontrolled major road. The driver is a 32 year old male. Using a detector with interval time of 0.5 sec (update rate 2 Hz), a cross-traffic vehicle was detected approaching from the left with four consecutive readings for the range found to be 125.17 m, 115.09 m, 104.82 m and 94.35, respectively. The corresponding azimuth angle readings were 2.98°, 3.24°, 3.56° and 3.95°, respectively.
32 From Equation 1, the distance traversed by the approaching bullet vehicle during the three detection intervals are 10.095 m, 10.288 m and 10.492 m. From Equation 12, the rate of change of acceleration, r, is calculated as 0.088 m/sec3. From Equation 13, the side offset between the bullet and target vehicles is calculated as 6.50 m. The distance from the bullet vehicle (at T+3t), to the intersection, df, is calculated from Equation 14 and found to be 94.13 m. Based on that, the bullet time, tbullet, is calculated from Equation 15 and found to be 4.09 seconds.
33 As per Equation 16, the target time, ttarget, is the sum of the perception-reaction time, t1, and the target vehicle’s acceleration time, t2. From Equation 17, the perception-reaction time, t1, is found to be 1.26 seconds. From Equation 18, the correction factor for the departure acceleration rate, cd, is found to be 0.92; and therefore, from Equation 20, the driver’s departure acceleration rate is 4.83 m/sec2. From Equation 19, the total distance to be crossed by the target vehicle, S, is calculated as 12.83 m (assuming that the reflective point is located at the near edge of the approaching vehicle); and therefore, the target vehicle’s acceleration time, t2, is calculated as 2.31 seconds from Equation 27. Based on that, the total target time, ttarget, should be 3.57 seconds. Since ttarget is found to be less than tbullet, the system should display a ‘Proceed with Caution’ message to the driver. If the driver of the equipped vehicle is older, his perception-reaction time will be longer and his selected acceleration will be slower; and therefore, a ‘Proceed with Caution’ message may not be warranted. The maximum acceleration rate provided by the mechanical characteristics of the target vehicle is another important factor that influences the decision made by the warning system. For example, if the maximum rate of acceleration is 4.50 m/sec2 or less, the target vehicle’s acceleration time, t2, will increase and a ‘Proceed with Caution’ message may not be warranted.
4.0 Limitations of Proposed System
34 The proposed methodology for the in-vehicle collision warning system represents a first step toward a complete system, but it still has a number of issues and limitations that need to be resolved. These limitations include the following:
4.0 Concluding Remarks
35 This paper has presented a technology-independent algorithm for a collision warning system for semi-controlled intersections. The system uses a pair of detectors (either radar sensors or laser scanners) to detect different vehicles traveling on the cross-traffic stream and determines their speeds and acceleration characteristics. Therefore, the algorithm can estimate the expected time required for the approaching vehicles to reach the intersection. The system also estimates the time required for the equipped vehicle to clear the intersection and by comparing the two times, the system displays a message for the driver of the equipped vehicle when it is safe to start departure. This will help reduce the human errors related to the driver of the equipped vehicle by avoiding the misjudgment related to perceiving the speeds and acceleration rates of the approaching vehicles. The time required for the equipped vehicle to depart the intersection depends on its intended path of departure and the time required for the driver to perceive the message received from the system and react to it. The departure time also depends on the driver’s desired rate of acceleration when departing the intersection. Based on this study the following comments are offered:
Acknowledgement
This research is financially supported by a Discovery Grant from the Natural Sciences and Engineering Research Council of Canada (NSERC) and an NSERC Postgraduate Scholarship. The authors are grateful to two anonymous reviewers for their thorough and most helpful comments.References
Alexander, J., P. Barham, and I. Black, (2002). Factors influencing the probability of an incident at a junction: results from an interactive driving simulator. Accident Analysis and Prevention, 34 (6): 779–792.
American Association of State Highway and Transportation Officials (2004). A policy on geometric design of highways and streets. Washington, D.C.
American Automobile Association (1958). Reaction time as related to age. Research Report No.69. Washington, D.C.
Brown, T.L., J.D. Lee, and D. V, McGehee, (2000). Attention-based model of driver performance in rear-end collisions. Transportation Research Record 1724:14 – 20.
Dabbour, E. and S.M. Easa, (2009). Perceptual framework for a modern left-turn collision warning system. International Journal of Applied Science, Engineering and Technology.
Dravidam, U. and S. Tosunoglu, (2000). Driver behavioral factors in rear-end collision avoidance system. Florida Conference on Recent Advances in Robotics, Florida Atlantic University, Boca Raton, Florida, May 4–5.
Drew, D.R. (1968). Traffic flow theory and control., New York: McGraw-Hill USA. 5(1): 8-14.
Easa, S.M. and Z.A. Ali, (2005). Modified guidelines for left-turn lane geometry at intersections. Journal of. Transportation Engineering, ASCE, 131(9), 677-688.
Easa, S.M., E. Dabbour, and Z.A. Ali, (2004). Three-dimensional model for stop-control intersection sight distance. Journal of. Transportation Engineering, ASCE, 130(2), 261-270.
Fuerstenberg, K. Ch. and J. Chen, (2007). New European approach for intersection safety – results of the EC-Project INTERSAFE. Advanced Microsystems for Automotive Applications 2007.. Berlin: Springer-Verlag 61-74.
Grewal, M.S., and A.P. Andrews, (1993). Kalman Filtering Theory and Practice. New Jersey: Prentice Hall.
Harwood, D. W., J.M. Mason, R.E. Brydia, M.T. Pietrucha, and G.L. Gittings, G.L., (1996). Intersection sight distance. National Cooperative Highway Research Program Report 383.,Washington, D.C.: Transportation Research Board.
IBEO Automobile Sensor (2009). IBEO laser scanner LUX. www.ibeo-as.com. Accessed 24 January, 2010.
Kalman, R.E. (1960). A New Approach to linear filtering and prediction problems. Journal of Basic Engineering, 82 (1): 35 – 45.
Lerner, N. D., R.W. Huey, H.W. McGee, and A. Sullivan, A., (1995). Older driver perception-reaction time for intersection sight distance and object detection. Federal Highway Administration Report No. FHWA-RD-93-168.Washington, D.C.
Long, G. (2000). Acceleration characteristics of starting vehicles. Transportation Research Record 1737: 58-70.
Maybeck, P. (1979). Stochastic Models Estimation and Control.. New York: Academic Press.
Ministry of Transportation Ontario (2006). Ontario Road Safety Annual Report. Ministry of Transportation (MTO), Ontario, Canada.
NHTSA (2000). Automotive Collision Avoidance Systems (ACAS) Program. Final Report DOT HS 809 080. NHTSA, U.S. DOT, Washington, D.C., USA.
NHTSA (2004). Vehicle-based countermeasures for signal and stop sign violation. Progress Report DOT HS 809 716. NHTSA, U.S. DOT, Washington, D.C., USA.
Pierowicz, J., E. Jocoy, M. Lloyd, A. Bittner, and B. Pirson, B. (2000). Intersection collision avoidance using ITS countermeasures. Task 9: Final Report. National Highway Traffic Safety Administration Report No. DOT HS 809 171. Washington, D.C.
Smart Microwave Sensors SMS (2009). Smart Microwave Sensors. www.smartmicro.de. Accessed 25 January, 2010.
STISIM (2009). STISIM User’s Guide. Systems Technology Inc., Hawthorne, CA. www.systemstech.com. Accessed 25 January, 2010.
Taylor, S.J. (2005). Development of a Bayesian Decision Theory Framework to Enhance The Design of Rear-end Collision Warning Systems. Unpublished doctoral dissertation, Carleton University, Ontario, Canada.
Transportation Association of Canada (2007). Geometric design guide for Canadian roads. Transportation Association of Canada, Ottawa, ON, Canada.
Transport Canada (2003). Road Safety in Canada – 2003. TP 13951 E, Ottawa, Canada.
U.S. Department of Transportation (2003). Intersection Collision Avoidance Study. Final report published by Department of Transportation (DOT) and Federal Highway Administration (FHWA) Safety Office. Washington, D.C., USA. www.itsdocs.fhwa.dot.gov//JPODOCS/REPTSTE//14105.htm Accessed 25 January, 2010.
VORAD (2009). VORAD Collision Warning System. Eaton Corporation, Cleveland, Ohio, USA. www.vorad.com. Accessed 25 January, 2010.
Watamaniuk, S.N.J. and A. Duchon,(1992). The human visual system averages speed information. Vision Research, 32(5):. 931 – 941.
Yan, X., E. Radwan, and D. Guo, (2007). Effects of major-road vehicle speed and driver age and gender on left-turn gap acceptance. Accident Analysis and Prevention, 39(5): 843-852.