Rearend collisions are one of the most common types of accidents on roads. Global Satellite Navigation Systems (GNSS) have recently become sufficiently flexible and costeffective in order to have great potential for use in rearend collision avoidance systems (CAS). Nevertheless, there are two main issues associated with current vehicle rearend CAS:
Rearend collisions are a common type of traffic accident in which a vehicle crashes into the vehicle in front of it. According to statistics from the National Highway Traffic Safety Administration (NHTSA), this type of accident accounts for about onethird of all traffic accidents [
Various methods and algorithms related to rearend collision avoidance have been described in the literature in recent years. Araki et al. [
Although the aforementioned rearend collision avoidance detection approaches have shown some potential in certain conditions, several technical barriers remain to be surmounted. First, most of the research uses vision sensors, which are weather sensitive and thus not adaptive for wide applications. In addition, some research has adopted technologies such as scanning radar to provide relative positioning for the collision avoidance system, but in these cases the system performance is highly related to the cost of the sensors. Compared with the other technologies, GNSS and its fusion with other data sources are an optimal method for collision avoidance systems due to low cost and insensitivity to the weather. The relative position and realtime dynamic information between two GNSS users can be obtained from wireless communication in order to assess the safety situation for the avoidance of rearend collisions. In current GNSS based rearend collision avoidance systems, however, the accuracy of the realtime estimation of positioning and dynamic states can be affected by abrupt manoeuvers by the drivers [
In this paper, a GNSS/compass fusion/lane information fusion, with an Adaptive Neurofuzzy Inference System (ANFIS) based VehicletoVehicle (V2V) rearend collision avoidance system is developed. The estimation of realtime vehicle states is achieved using a Cubature Kalman Filter (CKF) based algorithm. The different features extracted from the fusion results, that is, the Relative Distance, velocity, and heading between the leading vehicle and following vehicle, are used as input to the ANFIS for its automatic FIS membership functions and rules generation based on its learning algorithm. The carfollowing status is therefore predicted based on the ANFIS output. The contributions of the paper are summarized as follows:
A newly designed CKF model for realtime vehicle status estimation
A novel ANFISbased carfollowing status decision algorithm with the advantage of early prediction warning and high detection accuracy
Field experiments presented to demonstrate the successful application of the designed rearend collision avoidance algorithm.
The rest of the paper is organized as follows. The design of the GNSS fusionbased rearend collision avoidance system is presented in Section
A flowchart of the CKFbased GNSS/compass fusion for VehicletoVehicle (V2V) rearend collision avoidance system is illustrated in Figure
System overview.
The ability to locate and track the vehicles in space, velocity, and time is fundamental to predict collisions. It is therefore critical to choose an appropriate technology to determine the relative positioning and velocities of vehicles with sufficient accuracy and reliability to ensure high performance collision prediction. In order to improve the accuracy of GNSS for the collision avoidance application, GNSS/compass/lane information fusion is employed. Nonlinear filters, such as the Extended Kalman Filter (EKF), which linearizes the nonlinear system based on the 1storder Taylor series expansion, have been applied for GNSS fusion for many years. Although EKF returns acceptable results in many ITS applications, it cannot however estimate vehicle manoeuvres accurately when sudden stops or turns occur, due to the shortcomings of Taylor linearization. In recent years, therefore, some improved algorithms have been developed based on EKF to improve the calculation accuracy and stability, such as UKF and CKF [
The steps for the CKFbased GNSS/compass/lane information fusion are presented below.
Lane segment model.
Time update
Assume at time
where the Cholesky decomposition is applied to factorize the covariance
Evaluate the cubature points
Propagate cubature points (
Calculation of predicted error covariance:
Measurement update
Factorize
Evaluate the cubature points (
Update the output vectors: calculate predicted measurement and the innovation covariance matrix according to (
Calculate the cross covariance matrix and the cubature Kalman gain. The cross covariance matrix and the cubature Kalman gain vector are calculated according to (
Update the state and the corresponding error covariance. Calculation of the estimated state and the covariance based on the generic Kalman Filter:
The variables used in the CKF algorithm are illustrated as follows:
Fuzzy Inference Systems (FIS) can be used to link nonlinear phenomena to relative variables based on fuzzy logic rules, since this is difficult to model using conventional mathematical models. In contrast to traditional binary logic theory, fuzzy logic variables define the true value of the system as partially true or false with a value ranging from 0 to 1. With this advantage over traditional logic, FIS has been widely used for vehicle collision warning systems in recent years [
Structure of the ANFISbased collision avoidance system.
For a firstorder Sugeno fuzzy model, a common rule is given below.
Once the FIS rules are obtained after the training, they can be used for any input variables in order to get the corresponding output values. For example, if we apply the extracted FIS rules on the set of input Relative Distance (RD), Relative Velocity (RV), and Relative Heading (RH) for the following and leading vehicles, the corresponding output value can be predicted. In this paper, we define the warning status (labelled as “1”) and normal status (labelled as “0”) for the output value classification. The predicted values from the ANFIS will be rounded to the integer “0” or “1” for the classification. The details will be discussed in the next section.
The performance of the designed CKFbased GNSS/compass/lane information fusion for the avoidance of vehicle rearend collisions will be discussed in this section. The experiment setup and data collection will be introduced in Section
The carfollowing data was collected near Lincheng Industrial Park, Zhoushan City, China. The data used in the experiment includes the training data and testing data. The training data was collected in advance with their danger status recorded and labelled. In order to ensure the safety of the experiment, a simulated very close carfollowing situation was used throughout the whole experiment instead of real collisions. These data were collected and recorded based on the high grade GNSS/Inertial Navigation System (INS) integrated sensors. Different manoeuvres were performed manually and recorded. For the dangerous driving behaviours, the driver of the following vehicle conducted aggressive manoeuvres, including abrupt acceleration and deceleration with different velocities and headings so that the following vehicle closed rapidly with the leading vehicle. For the normal data, we just drove smoothly and maintained a distance of more than 5 m between the two cars (here the distance used is the distance between two antennas on both cars). We tried our best to simulate driving situations that would represent different types of dangerous status in real driving. The testing rearend collision data were captured from 07:15:00 to 07:26:00 in Universal Coordinated Time (UTC) with total five times of the simulated collision sessions. During the test, the Buick was assigned as the following vehicle and the Nissan was assigned as the leading vehicle. The test vehicles and onboard sensors are shown in Figure
Demonstration of a rearend collision in the test (a) and the onboard equipment (b).
For both vehicles, two types of data were collected and used in the field test:
In order to obtain the realtime lateral displacement and curvature angle of the vehicle in the related lane segment, the coordinates of the lane’s central line for the experiment area were collected in advance by a vehicle with a high grade integrated sensor. This data was then postprocessed to be recognized as the position of the lane’s central line. The lateral displacement of the vehicle was calculated by finding the two measurement points on the central line that were closest to the vehicle and then calculating the perpendicular distance from the vehicle to the line segment containing these two points.
This section discusses the CKFbased GNSS/compass/lane information fusion algorithm for the estimation of the positioning and dynamic parameters for both the leading and following vehicles. Table
The comparison of the navigation performance of the leading and following vehicles.
Positioning method  Following vehicle performance (Buick)  

Positon RMSE (m)  Velocity RMSE (m/s)  Availability  
RTK GNSS only  0.4473  2.8692  97.58% 
CKFbased fusion results  0.3025  2.1524  100% 


Positioning method  Leading vehicle performance (Nissan)  
Positon RMSE (m)  Velocity RMSE (m/s)  Availability  


RTK GNSS only  0.3609  2.682  98.94% 
CKFbased fusion results  0.2056  2.1027  100% 
The trajectory of the leading vehicle and the comparison between the fusion results and the measurements with respect to the reference.
The training data used for ANFIS rules extraction contained a total of 18151 samples, including 865 samples considered as having a collision warning status (labelled as “1”) and 17286 samples with normal status (labelled as “0”). The testing data includes 1809 samples with 76 with collision warning and 1733 normal ones. Based on the adaptive training of data for 100 steps, the rules for the input RV, RD, RH, and the output status can be established; see Figure
Surface view of the trained rules for RV and RD and the corresponding output level.
Membership function before and after training with ANFIS.
The comparison between the fusion results with the ANFIS predicted output level, and the reference output level, are displayed in Figure
Confusion matrix of the identification results.
GNSS fusion with ANFIS predicted results  Reference with ANFIS predicted results  

Labelled result  0  1  0  1  
0  1730  4  0  1731  3  
1  3  72  1  1  74 
Comparison between the fusion results with ANFIS predicted output level and the reference output level.
In this section we compare the proposed algorithm with the most commonly used stateoftheart algorithm from relevant literature. According to our literature review, although research to date has explored a number of aspects of rearend collision detection, the assumptions and test data used for such collision detection are different. Nonetheless, some of their methodologies can still be adopted to design rearend collision avoidance detection by using the field test data in this paper. These typical methods include the traditional fuzzy logic based algorithm with the input of Time to Collision (TTC) and Time Gap (TG) based collision avoidance system in [
The confusion matrix of the identification results.
Performance  Proposed algorithm  Fuzzy logic based algorithm in [ 
Distancebased algorithm in [ 

Accuracy  99.61%  98.34%  97.18% 
False alarm rate  5.26%  26.32%  39.29% 
It can be seen that the proposed algorithm outperforms its competitors. Although the accuracy for the proposed algorithm (i.e., 99.61%) is only slightly higher than the algorithm in [
This paper presents a novel rearend collision detection algorithm by combining CKFbased GNSS/compass/lane segment fusion with an ANFIS decision system. The field test has demonstrated the practicality of this approach using costeffective sensors and relative map information. It is shown that the proposed algorithm has not only improved the positioning accuracy and availability of the vehicle navigation performance, but also provides solid collision avoidance detection with high detection accuracy (i.e., 99.61%) and a low false alarm rate (i.e., 5.26%) at a 10 Hz output rate. In the future, more indicators will be developed to evaluate the designed algorithm and comparisons will be carried out between the designed algorithm and the other advanced algorithms using more scenarios.
The authors declare that they have no conflicts of interest.
This work is partially supported by the National Natural Science Foundation of China (no. 41704022, no. 61601228), National Natural Science Foundation of Jiangsu Province (nos. BK20170780, BK20161021), Fundamental Research Funds for the Central Universities (no. NJ20160015, no. NS2017043), and the Natural Science Foundation of Jiangsu Higher Education Institution (15KJB510016). The authors express thanks to the staff in Zhejiang Zhongyu Communication Co., Ltd, for their support in the field test.