The rear-end collision warning system requires reliable warning decision mechanism to adapt the actual driving situation. To overcome the shortcomings of existing warning methods, an adaptive strategy is proposed to address the practical aspects of the collision warning problem. The proposed strategy is based on the parameter-adaptive and variable-threshold approaches. First, several key parameter estimation algorithms are developed to provide more accurate and reliable information for subsequent warning method. They include a two-stage algorithm which contains a Kalman filter and a Luenberger observer for relative acceleration estimation, a Bayesian theory-based algorithm of estimating the road friction coefficient, and an artificial neural network for estimating the driver’s reaction time. Further, the variable-threshold warning method is designed to achieve the global warning decision. In the method, the safety distance is employed to judge the dangerous state. The calculation method of the safety distance in this paper can be adaptively adjusted according to the different driving conditions of the leading vehicle. Due to the real-time estimation of the key parameters and the adaptive calculation of the warning threshold, the strategy can adapt to various road and driving conditions. Finally, the proposed strategy is evaluated through simulation and field tests. The experimental results validate the feasibility and effectiveness of the proposed strategy.
Vehicle and road safety has been a key issue for the communities and governments. With emerging new technologies and knowledge, the advanced driver assistance systems (ADAS) [
The FCW/FCA systems are designed to give a warning and/or perform autonomous braking when a collision is imminent [
Since the early 1990s, many FCW/FCA algorithms have been proposed [
In the existing FCW/FCA systems, the typical distance-based warning algorithms contain the fixed distance algorithm, the fixed time-headway algorithm [
Both the fixed distance algorithm and the fixed time-headway algorithm can adapt to the condition that the relative speed between SV and LV is low. However, the calculated safety distance is small and may lead to false negative (missed warning) in the condition of high relative speed. The numerical and driver algorithms model the nonlinear relationship between the warning threshold and the measured values, that is, speed, acceleration, and so forth, by fitting curves. Obviously these algorithms require a lot of experience or training data, so they are difficult to adapt to complex traffic environment and different drivers.
Among the existing distance-based algorithms, the kinematics-based algorithms are most widely used in the actual application. The kinematics-based algorithms calculate the warning threshold by analyzing the relative motion between SV and LV. The most well-known algorithms, such as Mazda algorithm, Honda algorithm, and Berkeley improved algorithm, belong to this category. However, each algorithm discussed above has its particular suitable condition and may cause large errors in other conditions. For example, Mazda algorithm is developed to suit the emergency stop condition of LV; thus the calculated safety distance in other conditions is too large and the warning time is too early, which may lead to false positive (false warning). Meanwhile, the calculated safety distances of the Honda algorithm and the Berkeley improved algorithm are too small and may lead to false negative.
It can be seen that there are some deficiencies in the existing algorithms discussed above. The main reason is that each algorithm is only suitable for a certain condition and unable to adapt to other conditions [
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As these key parameters are time-varying during vehicle operation and unable to be measured directly, the warning threshold of existing algorithms cannot be adaptively adjusted according to the actual driving conditions, which may result in serious false warning in complex traffic environment.
To realize reliable rear-end collision warning for the vehicle in complex traffic environments, this paper proposes an adaptive strategy based on the kinematics analysis of LV and SV. This strategy aims to address the practical aspects of the collision warning problem. In this strategy, both algorithms for key parameters estimation and the warning decision are developed to obtain higher performance. The novel aspects of this paper can be summarized as follows.
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It should be noted that this paper only focuses on the warning algorithm level of rear-end collision warning systems. However, the proposed strategy is not limited to the sensors described in this paper. Other advanced technologies, such as vehicle to vehicle communication (V2V), can also be applied to the proposed strategy.
The remainder of the paper is organized as follows. Section
The proposed strategy is shown in Figure
Proposed strategy for rear-end collision warning.
The multisensor module includes such sensors as millimeter-wave radar, wheel speed sensors, and low-cost GPS. The millimeter-wave radar provides the distance and relative speed between SV and LV with 20 Hz update rate. The low-cost GPS provides speed information of SV, and the vision sensor only provides the path offset information of SV. The accelerometer is only along the longitudinal axes in vehicle body frame.
Several estimation algorithms are developed to acquire the information of key parameters. First, a two-stage algorithm is designed to obtain accurate relative acceleration between SV and LV; thus the acceleration of LV can be calculated. The two-stage algorithm contains a Kalman filter and a Luenberger observer. Both the Kalman filter and Luenberger observer have been verified to be effective and robust for the system. Then, a Bayesian theory-based algorithm is presented to estimate the road friction coefficient which can represent the different types of road. The road friction coefficient directly affects the maximum braking deceleration and thus affects the calculation of the safety distance. In addition, a Back Propagation (BP) artificial neural network is designed to determine the driver’s reaction time. These parameters’ estimation algorithms can provide richer information for the subsequent warning method.
The variable-threshold method is proposed to realize the warning decision. Through the kinematics analysis of the relative motion between LV and SV, the warning threshold or safety distance is calculated in real-time. Due to the previous estimation of crucial parameters, the warning distance can be adaptively adjusted according to various road conditions and different driver’s states. Further, the variable-threshold method, respectively, calculates the safety distance according to the different driving states of SV, that is, acceleration, deceleration, and uniform motion, so it can remarkably reduce the missed warning and false warning compared with existing methods.
As discussed above, there are three key parameters that may affect the performance of the warning strategy, that is, the relative acceleration, the road friction coefficient, and the driver’s reaction time.
Accurate identification of LV’s driving state (i.e., accelerated motion state, constant speed state, and decelerated motion state) can improve the adaptability of the subsequent warning method. The calculation method of the safety distance should be different under the different states of LV. Meanwhile, the accurate estimation of the value of LV’s acceleration can improve the accuracy of the safety distance. The acceleration of LV can be calculated by the relative acceleration plus SV’s acceleration. However, the relative acceleration is hardly to be measured directly under the existing technologies. In the related literature, the relative acceleration is usually obtained by the following methods.
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A two-stage algorithm is developed to estimate the relative acceleration between SV and LV, as shown in Figure
The algorithm for relative acceleration estimation.
Describing the statistical distribution of the relative acceleration is a difficult problem. The commonly used CV and CA models are difficult to describe the dynamic change of the relative acceleration. Therefore, the “current” statistical model which is widely used in the navigation field [
The Kalman filtering process consists of the following two phases:
Time update:
Measurement update:
The relative acceleration, that is,
A Luenberger observer is designed to estimate the bias. Assume that
Based on (
The longitudinal road friction coefficient is an essential parameter for the vehicle braking performance. It directly affects the maximum braking deceleration and thus affects the safety distance. For example, if other conditions are the same, the safety distance in low friction coefficient road is obviously larger than that in high friction coefficient road. To illustrate the effect of the road friction coefficient on the calculation of the safety distance. One test under different road friction coefficients is shown in Figure
The calculation results of the safety distances under different road friction conditions.
It can be seen in Figure
Although Tang and Yip [
In the field of active safety control systems such as antilock braking system (ABS), the road friction coefficient estimation method based on the vehicle longitudinal dynamics is most feasible [
The most well-known research in this area is on the use of “slip-slope” for friction coefficient identification [
To solve these problems, an estimation algorithm based on the Bayesian theory is proposed in this paper. This algorithm utilizes the relationship between normalized longitudinal tire force and slip ratio to identify the longitudinal tire-road friction coefficient, which can quickly and accurately estimate the longitudinal road friction coefficient both at high and low slip ratio conditions, as shown in Figure
Flowchart of the road friction coefficient estimation.
Assuming that all wheels are under the same road surface condition, it means that the friction coefficient is assumed to be the same at each wheel of the SV, which is true for many driving situations.
If only longitudinal motion is considered and the lateral force is ignored, the normalized longitudinal tire force
The proposed estimation algorithm for road friction coefficient is described as follows:
(
(
Therefore, the normalized longitudinal tire forces of the front and rear wheel axles can be described as
Due to the assumption that the front and rear tires are on the same road condition, the total longitudinal force is
Assume that the road friction coefficients are
The longitudinal vehicle dynamics model [
Therefore, in the
(3) The defined deviations are
(
(5) The actual road friction coefficient can be identified as follows:
A large number of literature references and experimental results indicate that the driver’s reaction time is generally 0.3~1.5 s [
However, how to mathematically model the nonlinear relationship between the driver’s reaction time and these factors is a challenge. For this reason, a BP neural network-based algorithm is proposed to determine the driver’s reaction time according to its general ranges.
Neural network is powerful to model nonlinear function which can be trained offline utilizing the experiment data collected in specific environment. Compared with other modeling methods, neural network has higher generalization ability to adapt to more complex environments.
As shown in Figure
The structure of BP neural network.
There are 7 nodes in the hidden layer in the neural network. The model uses the standard BP algorithm, the transfer function from the input layer to the hidden layer is the bipolar function
The network weights and thresholds of the hidden layer and the output layer are obtained by using MATLAB offline training; then another set of inputs are simulated and analyzed; the results are shown in Table
Simulation results of BP neural network model.
Speed (m/s) | 10 | 15 | 20 | 25 | 30 | 35 |
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Learning data (s) | 0.33 | 0.52 | 0.76 | 0.99 | 1.13 | 1.27 |
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Simulation data (s) | 0.35 | 0.49 | 0.81 | 0.93 | 1.21 | 1.22 |
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Error rate (%) | 6 | 5 | 6 | 6 | 6 | 4 |
As shown in Figure
The rear-end collision scenario.
A variable-threshold calculation method of the safety distance is proposed in this section. This method adopts different calculation method under different states of LV. The speeds of SV and LV are
In (
The continuous braking time
(
In this case, the collision only occurs when the speed of SV is greater than the speed of LV. Therefore, only this condition is considered. If the SV slows down to the speed of LV, that is,
(
In this situation, the collision also only occurs when the speed of SV is greater than the speed of LV. Since LV is accelerating, the speed of LV reaches to
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This situation is very dangerous. In this situation, only the speed of SV can be reduced to 0 after braking, that is, in stationary state, and SV keeps a certain distance to LV at the moment SV stops; the safety can be guaranteed; namely,
This method can adaptively calculate the safety distance according to the different driving states of LV and thus can effectively avoid too large or too small safety distance. Assuming that the
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The proposed strategy was first evaluated through extensive simulations, which were performed under typical driving scenarios using CarSim in MATLAB/Simulink. Due to the experimental condition limitation and the safety concern, many algorithms are difficult to be verified in real experiments, that is, the road friction coefficient estimation algorithm and the variable-threshold method. Since the real experiments will be described in the next section, the simulations were only used to verify the road friction coefficient estimation algorithm and the variable-threshold method.
The proposed algorithm can be apt for both high and low slip ratios. However, the high ratio scenario is hard to achieve in experiment, and the low friction coefficient scenario is dangerous for the driver. Therefore, the effectiveness and feasibility of the proposed algorithm in extreme conditions are firstly verified by simulation.
The proposed algorithm is validated in high and low slip ratios conditions with the tire-road friction coefficient changed from 0.8 to 0.2, and the estimation results are compared with the conventional slip-slope algorithm. Simulation results show that the proposed algorithm can be applied to both high and low slip ratios and can quickly respond to the change of road condition with high accuracy.
Figures
Simulation results of low slip ratios. (a) Slip ratio. (b) Tire-road friction coefficient.
Simulation results of low slip ratios with friction coefficient changed. (a) Slip ratio. (b) Tire-road friction coefficient.
The conventional slip-slope algorithm is no longer suitable for the high slip ratios condition because the relationship between
Simulation results of high slip ratios. (a) Slip ratio. (b) Friction coefficient estimated by the proposed algorithm. (c) Friction coefficient estimated by the slip-slope method.
Simulation results of high slip ratios with friction coefficient changed. (a) Slip ratio. (b) Friction coefficient estimated by the proposed algorithm. (c) Friction coefficient estimated by the slip-slope method.
The real road test for warning method may be dangerous in some cases, especially in the extreme conditions such as the short distance between LV and SV or the emergency braking situation of LV. Therefore, the proposed warning method was firstly verified through simulation. Five cases are set up to emulate the typical rear-end collision warning conditions. To evaluate the effect of the proposed method, the widely used kinematics-based methods, that is, Mazda method, Honda method, and Berkeley improved method, are also investigated for comparison. It should be noted that the simulation only aims to verify the proposed variable-threshold method itself and does not consider the change of parameters.
Assume that the driver’s reaction time is 0.75 s and the road friction coefficient is 0.6. The five cases are set up as follows: LV and SV drive at constant speed, and the speeds of LV and SV are 100 km/h and 120 km/h, respectively. In the initial moment, the distance between LV and SV is 200 m. In the initial moment, the distance between LV and SV is 150 m, and the speeds of LV and SV are equal, that is, 90 km/h. Then LV drives at constant speed and SV starts to accelerate. The acceleration of SV is 2 m/s2. The initial speeds of LV and SV are equal, that is, 110 km/h; then SV drives at constant speed and LV starts to decelerate. The initial distance between LV and SV is 150 m. The deceleration of LV is −2 m/s2. LV and SV drive at constant speed in the initial moment, that is, 110 km/h, and then the emergency brake of LV is activated. The initial distance between LV and SV is 150 m. The deceleration of LV is −7 m/s2. LV and SV drive at constant speed in the initial moment, that is, 110 km/h, and then the LV suddenly stops due to the emergency situations (e.g., LV hits the obstacle). The initial distance between LV and SV is 150 m, and then the speed of LV suddenly becomes 0.
For the four methods, that is, proposed variable-threshold method, Mazda method, Honda method, and Berkeley improved method, Figure
The simulation results of variable-threshold method.
In Figure
The main advantage of the variable-threshold method is the appropriate value of the safety distance, that is, neither too large nor too small. If the safety distance is too large, the corresponding warning time is too early and may interfere with normal driving operation (i.e., false positive). If the safety distance is too small, the corresponding warning time is too late and the reaction time for driver is not sufficient to avoid collision (i.e., false negative).
Figures
Case
Case
Case
Through the above analysis, it is clear that each of the conventional methods has its specific case and can work well in this case. However, one method is unable to adapt to other cases and will lead to false negative or false positive in other cases. The proposed variable-threshold method can combine the advantages of these conventional methods; that is, it can adjust the calculation method of safety distance according to the driving state of LV to make the method adapt to various scenarios. In a particular scenario, the safety distance calculated by the proposed method is approximate to that of the corresponding method which can adapt to the certain scenario.
In addition, the proposed method has other advantages; for example, it can accommodate to different road conditions and driver’s states; that is, the road friction coefficient and driver’s reaction time can be estimated in real-time to further improve the adaptability under different driving scenarios. These characteristics are not verified by the simulation and will be validated through the real experiments in the next section.
To further verify the performance of the proposed warning strategy in practice, experiments were conducted on a Buick Sail SRV vehicle. It was equipped with many low-cost sensors as shown in Figure
In this experiment, the test duration is 50 s, and the experimental road contains the dry and wet asphalt roads. Parts of the signals collected by the sensors are shown in Figure
The information collected by the sensors in experiment
The estimation of the relative acceleration. (a) The preliminary and final estimation results by the proposed two-stage algorithm. (b) The estimation result by the Euler forward difference method. (c) The preliminary estimation bias. (d) The estimation results and the reference values. (e) The preliminary and final estimation errors.
It can be seen that the relative acceleration estimation result based on the Euler difference method (Figure
Obviously the corrected value has smaller error and better accuracy, and it is consistent with the change of the relative speed. Therefore, the proposed algorithm can provide more accurate relative acceleration information and then can improve the performance of subsequent warning method.
The estimation results of key parameters. (a) The road friction coefficient. (b) The driver’s reaction time.
To evaluate the performance of the proposed variable-threshold method, other commonly used methods, such as Mazda method, Honda method, and Berkeley improved method, are also investigated for comparison. Figure
The experimental results of safety distance calculation.
From Figure
In this experiment, the warning times of two methods, that is, Mazda method and the early warning of the Berkeley improved algorithm, are earlier than that of the propose strategy, and the warning is not activated in other methods.
Assuming that SV and LV keep their current state after 27 s, by analyzing the relative movement and calculating the time to collision (TTC), we can deduce the conclusion that the collision may occur within 5 s. Therefore, the warning is necessary in this situation, and the other methods which have no warning may lead to false negative. Taking the warning time of the Mazda method, that is, 15 s, as example, the TTC is about 25 s; namely, assuming that SV and LV keep their current state after 15 s, the collision may occur after 25 s. Obviously the warning time is too early and may lead to false positive.
The experiment contains different driving scenarios, that is, the acceleration and deceleration of LV and SV, and the road friction coefficient changes. Other methods are only suitable for a specific case and assume that the road friction coefficient is constant. The proposed method can combine the advantages of these conventional methods and can estimate the road friction coefficient in real-time, which can obviously improve the adaptability.
From the above analysis, we can get the similar conclusions as the simulation results in Section
Another experiment was carried out on the dry asphalt road. The test duration is 40 s, and the experiment also contains different driving scenarios, that is, the acceleration and deceleration of LV and SV. Parts of the signals collected by sensors are shown in Figure
The information collected by sensors in experiment
Figure
The key parameters estimation results of experiment
From Figures
Figure
The safety distance of experiment 2.
To realize reliable warning for rear-end collision of the vehicle, an adaptive distance-based warning strategy is proposed. The proposed strategy is based on the parameter-adaptive and variable-threshold approaches.
In the proposed strategy, both the parameter estimation algorithms and the warning decision method have been developed to obtain higher performance. First, the estimation algorithms for some key parameters are developed, which can provide accurate information for the subsequent warning method. Further, the variable-threshold method has been designed to realize reliable warning decision. The effectiveness of the proposed strategy has been verified comprehensively. The simulation and experimental results show that the proposed strategy has higher adaptability and reliability than existing methods.
The key parameter estimation algorithms in proposed strategy can equally be applied to other vehicle active safety systems such as antiskid brake system (ABS) and traction control system (TCS). Our future work will concern how to further improve the performance of the proposed parameter estimation algorithms and to solve other issues involved in the study of rear-end collision warning system, such as the further elimination of false alarm and anticollision problems in curve road and multilane scene.
The authors declare that there is no conflict of interests regarding the publication of this paper.
This work is supported by the National Natural Science Foundation of China (Grant no. 61273236), the Jiangsu Planned Projects for Postdoctoral Research Funds (Grant no. 1401012C), the Fundamental Research Funds for the Central Universities (Grant no. 2242015R20017), and the Project Funded by China Postdoctoral Science Foundation (Grant no. 2015M571631).