Improving the Accuracy of Under-Fog Driving Assistance System

Driving in fog condition is dangerous. Fog causes poor visibility on roads leading to road traffic accident (RTA). RTA in Albaha is common because of its rough terrain, in addition to the climate that is mainly rainy and foggy. The rain season in Albaha region begins in October to February characterized by rainfall and fog. Many studies have reported the adverse effects of the rain on RTA which results in an increased rate of crashes. On the other hand, Albaha region is not supported by a proper intelligent transportation system and infrastructure. Thus, a Driver Assistance System (DAS) that requires minimum infrastructure is needed. A DAS under fog called No_Collision has been developed by a researcher in Albaha University. This paper discusses an implementation of adaptive Kalman Filter by utilizing Fuzzy logic system with the aim to improve the accuracy of position and velocity prediction of the No_Collision system. The experiment results show a promising adaptive system that reduces the error percentage of the prediction up to 56.58%.


Introduction
Driving under the present of thick fog is one of the most hazardous situations.
The driver's visibility distance decreases exponentially as fog density increases; however drivers tend to overestimate their visibility and drive with excessive speeds. A lack of adherence of some drivers to traffic instructions during fog also contributes to the high statistics. Statistics on traffic accident during fog in Saudi Arabia is quite high. A lack of adherence of some drivers to traffic instructions during fog contributes to the high statistics. Albaha is among the region in Saudi How to cite this paper: Kerim, B. (2020) Improving the Accuracy of Under-Fog Arabia that is affected and often enveloped in thick fog during the winter. Researchers in Albaha have developed driver assistance system (DAS) under fog condition, named No_Collision [1]. Due to the minimum infrastructure of the traffic in Albaha, the system relies on GPS system of mobile phone and connects to a server using Internet and predicts the distance/position and velocity of other surrounding vehicles using Kalman Filter. Nevertheless, the system still faces accuracy problem in the prediction. This paper attempts to improve the accuracy for the position and velocity prediction by combining Kalman Filter method and Fuzzy logic technique. Many research works on DAS under fog have been carried out, including the use of traditional and intelligent techniques such as works in [2] [3] [4] [5]. Nevertheless, the works are based sensors, camera as well as other modern/intelligent traffic infrastructures. Acosta and Toloza [6] use a low cost GPS tool with differential relative positioning way with the aim to increase the accuracy of the positioning.  [16]. This paper extends the work in [1] and adopts the idea of the work in [6] to develop an intelligent engine that improves the accuracy of the position and velocity prediction and incorporate the engine into the existing under fog driving assistance system (No_Collision Apps.)

Position and Speed Estimation
This work follows the method used in [2] and employs a two-stage Bayesian filter to track the vehicle's position and use smartphone inertial sensors combined with standard Kalman filter to estimate movement heading. Algorithm 1 represents the procedure.

Algorithm 1
Step 1: Calculating safe distance and speed from received GPS data (based on  Step 2: for Case straight road (see Figure 1) Get the geo fence of the anchor vehicle; Compute the intersection location; Compute the velocity; Display the vehicle in the Quadrant.
This paper chooses the Kalman Filter for tracking and prediction because it has been recognized as the optimal solution for tracking and data prediction problems [17] [18]. Equation (1) to Equation (5) represent the Kalman Filter recursive algorithm for prediction.
Kalman Gain: Update Covariance: Project into k + 1: Q = covariance between the two noise models. Φ = the state transition matrix of the process from the state at k to the state at k + 1.
= state projection at time k + 1. The author also set the minimum distance among vehicles is 5 meters. The proposed system uses client-server configuration as depicted in Figure 3 [1].

Fuzzy Logic for Improving the Accuracy
This work uses fuzzy logic to prevent the Kalman filter divergence. Hence, the system adjusts the covariance matrix of the model measurement noise in real time fashion to shape it close to the real value, and ultimately escape the divergence of the Kalman filter. Thus, this work modifies the noise covariance matrix of the model to where α is the adjustment factor obtained from the fuzzy logic. Rewrite the iterative filtering algorithm in (1) as ( ) In Equation (7), the Kalman filter develops an adaptive capability and improves the accuracy of the last estimation.
The main output parameter of the GPS receiver is Position dilution of precision (PDOP). The PDOP represents directly the accuracy of the positioning.
Therefore, PDOP reflects the change of the covariance matrix of the measurement noise R. Thus, this work defines the formula for PDOP to adjust the value of α as shown in Equation (8) [19].
where σ is the pseudo-range error factor, σ x , σ y and σ z are the positioning errors in the earth coordinate system on the three axes (x-y-z), correspondingly. Journal of Signal and Information Processing This work uses Sugeno fuzzy logic system with the rational that the system has already been applied in many fields, it is easy to be implemented and it is more efficient compared to other fuzzy systems. In addition it can generate complex non-linear function with only a few language rules [20]. Authors in [21] [22] give the overall expression of Sugeno fuzzy system as follows.
here n A′ is a fuzzy set, M is the rule section number, is the real number of the i th rule. The output PDOP value from the GPS receiver acts as the input of the fuzzy system. If the PDOP value is small (the GPS positioning error is relatively small), then a larger α is used to increase the confidence level.
Whereas if the PDOP value is large (the positioning error of GPS is large), then set a small α to reduce the confidence level for the measurement values. Figure 5 illustrates the membership function of the fuzzy system used in this work. The membership function represents the membership of the input PDOP value in the domain of the fuzzy sets and represented as ( ) the Fuzzy Inference System (FIS) to adjust α are as follows, If PDOP is a, then α = f a (PDOP); where "PDOP" represents the output position error of the GPS receiver, a represent "less", "equal" or "more", f a (PDOP) is a linear function of PDOP, α is a factor to adjust the measurement noise.

Experimental Set Up
For server side this work uses Go language programming (Golang). Golang is a programming language initially developed at Google in year 2007 by Griesemer et al. [23]. Go programming language is a statically-typed language with syntax Then the fuzzy inference system is deployed to improve the accuracy of the position and velocity.

Results and Analysis
The experiment took place in the area close to Albaha University campus. Four cars are driven with different route and the No_Collision App is run. At the same time, another mobile phone that running simple App developed using MathWorks is used to capture the true value of the position of the car every 5 minutes. Table 1 shows sample of data taken from the first car during the experiment. Then, manually, the errors are calculated. Table 2 shows the computation results of error percentage of the Kalman Filter (KF) and the adaptive Kalman Filter using FIS (KF-FIS). From Table 2, it is observed that the accuracy of the proposed adaptive Kalman filter provides accuracy improvement of 55.47%, 51.81%, 50.972%, and 56.58% compared to standard Kalman filter. As expected, the error percentage the adaptive KF provides more accurate prediction for the position. This improvement due to the fact that fuzzy system helps the filter converges.

Conclusions
The use of Fuzzy system as expected helps the Kalman Filter to be an adaptive system and converges to more accurate predictions of the GPS-based position.
This improvement increases the usefulness of the No_Collision application in assisting driver during fog in the region that is not fully supported by modern/intelligent transportation system.   The author considers implementing other scenarios: U-turn situation, roundabout situation, and junction situation.

Conflicts of Interest
The author declares no conflicts of interest regarding the publication of this paper.