Symmetry-Enhanced Fuzzy Logic Analysis in Parallel and Cross-Road Scenarios: Optimizing Direction and Distance Weights for Map Matching

Abstract

This study addresses the challenges of setting segmentation points in the membership function and determining appropriate weights for different types of information within a fuzzy logic algorithm for map matching. We use linear fitting to derive an empirical formula for setting segmentation points for the information membership function. Furthermore, we evaluate the effects of various weights for direction and distance information in parallel and cross-road scenarios. The research identified the optimal distance that achieves the highest matching accuracy and provided insights into how the weights of connection, direction, and distance information affect this accuracy. The simulations confirmed the critical importance of precise segmentation point settings and weight determinations in enhancing the accuracy of fuzzy logic algorithms for map matching. The results underscore the potency of our tailored parameter-setting strategy and contribute to knowledge of symmetry, offering practical insights for implementing fuzzy logic in map matching with a particular emphasis on the principle of symmetry in algorithm design and information processing.

1. Introduction

Map matching is a critical in-vehicle navigation technique designed to align the location points collected by an onboard device with the corresponding roads on a digital map [1]. This alignment is essential for accurate vehicle navigation. However, real-world applications frequently encounter inaccuracies in location data due to limitations in device precision, sampling errors, or obstructions like buildings [2,3], necessitating specialized algorithms to enhance the accuracy of matching these points to the correct roads [4,5,6].

Among the prevalent map-matching algorithms are the direct projection algorithm, the probabilistic statistical algorithm, the correlation analysis algorithm, and the D-S evidence reasoning algorithm [7]. The direct projection algorithm, which identifies the nearest road segment and aligns the location point with it, is straightforward. However, it often suffers from low matching efficiency and stability issues [8,9]. In contrast, the probabilistic statistical algorithm employs statistical techniques to delineate a search area for possible roads and retrieve matching road positions, offering higher accuracy at the cost of increased computational demand [10,11]. The correlation analysis algorithm excels when the vehicle’s travel direction changes markedly but may perform less effectively in other scenarios [12]. The D-S evidence reasoning algorithm, which builds a trust framework based on incomplete and imprecise evidence to determine the best match through evidence fusion, provides high accuracy and stability. Yet, it also requires significant computational resources [13,14].

The fuzzy logic algorithm, which integrates the principles of fuzzy mathematics with a weighted approach, uses fuzzy logic criteria to determine the travelled road of the vehicle [15]. This method stands out for its low computational demand, high efficiency, and adaptability to various road conditions [15,16,17,18]. Nonetheless, a significant limitation of the fuzzy logic algorithm is the lack of a theoretical foundation for establishing membership function segmentation points and weight coefficients [19,20]. Missteps in setting these parameters can severely undermine the algorithm’s performance. Nevertheless, the algorithm’s matching accuracy can be optimized by accurately adjusting the segmentation points and weights, thereby expanding its potential applicability in map matching [21,22,23].

For these issues, our contributions are as follows:

• (1). Parallel road segments: we analyze the impact of distance and connectivity information weights on the matching accuracy and derive an empirical formula for setting segmentation points for distance information membership functions to optimize the matching accuracy.

• (2). Intersection road segments: we summarize the impact of distance, direction, and connectivity information weights on the matching accuracy and identify a method for setting the direction information membership function.

The remainder of this paper is structured as follows: In Section 2, we provide an introduction to the foundational concepts and algorithms pertinent to our study, including an examination of existing map-matching techniques outlined in Section 3. Following this, in Section 3, we present our novel solution. We delve into the intricacies of our approach and provide a comprehensive overview of the methodology employed. Additionally, we critically analyze the outcomes achieved through the implementation of our proposed method. Subsequently, we dedicate Section 4 to an extensive review of related works in the field of map-matching algorithms, as well as an exploration of the geographical areas under study. Within this section, we discuss algorithms alongside their respective strengths and weaknesses, incorporating an in-depth analysis of ablation studies. Finally, we conclude our findings and insights in the concluding section, summarizing the key points of our research and highlighting avenues for future exploration and refinement.

2. Preliminaries

2.1. Summary of the Input Data

• Trajectory: the trajectory of a moving item is a series of GPS points that document its movement over a given time interval [X, Y].

• Digital road network: Topological and geometric data are present in all road networks. The primary classifications of a road network include intersections, squares, urban, rural, and highway routes. A road network created in a computer environment that resembles a real network map is called a digital road network.

Pattern recognition theory forms the basis of the map-matching algorithm. The matching procedure can usually make use of three key pieces of information: direction, connectedness, and distance. The aforementioned data are combined with fuzzy mathematical theory in the fuzzy logic-based map-matching technique to compute the comprehensive membership degree of candidate roads and identify the best matching road. Finding candidate roads, choosing the matching route, and pinpointing the precise location of the car are the three steps in the matching process. The precise procedure is displayed in Figure 1 down below.

2.2. Map-Matching Process

A GPS trajectory and a digitized road network are required inputs for this method. An arc-and-link-based simulation of the road system is called the digital road network. This simulation is made up of numerous roads, crossroads, and dead ends that imitate actual road networks [22,23]. Map matching is the process of mapping GPS coordinates to the digital road network’s linkages [24].

A car is traveling over a limited network of roads, 𝓝. Since the road system, 𝓝, is not well understood, we have a network representation, 𝓝, which is made up of a collection of curves in ℝ². It is assumed that the arcs in 𝓝 and the roads in 𝒩̅ correspond to each other exactly. Arcs are taken to represent single roadways and are thought to be piecewise linear. Consequently, a finite sequence of points (A₀, A₁,…, A_n) can define arc A, ρ𝓃. These locations, which are the line segment’s endpoints, really make up arc A. Generally speaking, the initial and last points are referred to as nodes. These are an arc’s endpoints, which enable transitioning between them. They therefore line up with junctions or dead ends in the road system. The position of the vehicle at time t is estimated. This estimate is represented by 𝒫t. The vehicle’s real location at time t is shown by 𝒫̅t. The map-matching method aims to achieve two objectives in relation to these: First, determine the street A̅ϵ𝒩̅ connection to the real position of the car 𝒫̅t, which is determined by comparing the estimated location, 𝒫t, with arc A, ρ𝓝. Secondly, identify the location on A that most closely matches 𝒫̅t [25,26].

In this paper, the ideas of matched points and fixed points have been applied, as shown in Figure 2. Fixed points are estimated positions of moving objects and show that no map-matching processing has been applied to them. On the other hand, the points that have undergone the matching process are the ones that are matched. Method of evaluation: The number of correctly matched and incorrectly matched roads in relation to parallel road scenes and cross-section scenes, as well as the processing time of the approach, are the two basic metrics for assessing the efficiency of the map-matching method.

2.3. Fuzzy Logic System

Fuzzy logic is a many-valued logic where each number’s variable value falls between 0 and 1, inclusive. There are three primary steps to it: 1. To create a fuzzy input set, fuzzification entails using membership functions to fuzz all “crisp” input values. 2. Interface engine: to compute fuzzy output functions, it operates all relevant rules in the “fuzzy rules base”. 3. Defuzzification: using “crisp” output values to produce fuzzy output. Figure 3 depicts this procedure.

3. Fuzzy Logic-Based Map-Matching Algorithm

The foundation of the map-matching algorithm is based on pattern recognition theory, which primarily leverages three critical types of information: direction, connectivity, and distance. The fuzzy logic-based map-matching technique integrates this information using fuzzy mathematical theory. This approach calculates the comprehensive membership degree of candidate roads to determine the most suitable matching road. The matching process encompasses three primary steps: identifying candidate roads, selecting the optimal matching route, and accurately determining the vehicle’s location. The detailed process is illustrated in Figure 4 below.

First, the candidate roads are determined; that is, the roads within the GPS error circle are included in the candidate set [16]. Then, feature extraction is performed on the candidate roads [27]. The extraction step is carried out according to three principles, namely the principle of the shortest distance, the principle of the minimum angle, and the principle of the strongest connectivity [21]. This yields the distance information, $u_1$; the direction information, $u_2$; and the connectivity information, $u_3$. At the same time, it is necessary to determine the membership functions and set the information weights, which are crucial steps that affect the algorithm’s performance [28,29].

3.1. Determination of Membership Function

Based on the evaluation set, two standard fuzzy patterns are established: A—good and B—poor. ${\mu }_A\left(u_i\right),{\mu }_B\left(u_i\right),i\in \left\{1,2,3\right\}$ represent the membership degrees of the $u_i$ factors corresponding to the A and B patterns.

Let ${\mu }_A\left(u_1\right)$ and ${\mu }_B\left(u_1\right)$, respectively, represent the membership degrees of the distance information belonging to the fuzzy subsets “good proximity between candidate roads and reference points” and “poor proximity between candidate roads and reference points”. The membership functions are as follows:

(1)${\mu }_A\left(u_1\right)=\left\{\begin{array}{cc}1-\frac{u_1}{d_0}& u_1\le d_0\\ 0& u_1>d_0\end{array}\right.,{\mu }_B\left(u_1\right)=\left\{\begin{array}{cc}\frac{u_1}{d_0}& u_1\le d_0\\ 1& u_1>d_0\end{array}\right.$

where $u_1$ represents the distance information and $d_0$ represents the segmentation point of the membership function for the distance information.

Let ${\mu }_A\left(u_2\right)$ and ${\mu }_B\left(u_2\right)$, respectively, represent the membership degrees of the direction information belonging to the fuzzy subsets “good minimum angle satisfaction between candidate roads and localization trajectory” and “poor minimum angle satisfaction between candidate roads and localization estimation”. The membership functions are as follows:

(2)${\mu }_A\left(u_2\right)=\left\{\begin{array}{cc}1-\frac{u_2}{{\theta }_0}& u_2\le {\theta }_0\\ 0& u_2>{\theta }_0\end{array}\right.,{\mu }_B\left(u_2\right)=\left\{\begin{array}{cc}\frac{u_2}{{\theta }_0}& u_2\le {\theta }_0\\ 1& u_2>{\theta }_0\end{array}\right.$

where $u_2$ represents the direction information and ${\theta }_0$ represents the segmentation point of the membership function for the direction information.

Let ${\mu }_A\left(u_3\right)$ and ${\mu }_B\left(u_3\right)$, respectively, represent the membership degrees of the connectivity information belonging to the fuzzy subsets “good connectivity between candidate roads and historical matching roads” and “poor connectivity between candidate roads and historical matching roads”. The membership functions are as follows:

(3)${\mu }_A\left(u_3\right)=\left\{\begin{array}{cc}\frac{u_3}{l_0}& u_3\le l_0\\ 1& u_3>l_0\end{array}\right.,{\mu }_B\left(u_3\right)=\left\{\begin{array}{cc}1-\frac{u_3}{l_0}& u_3\le l_0\\ 0& u_3>l_0\end{array}\right.$

where $u_3$ represents the connectivity information and $l_0$ represents the segmentation point of the membership function for the connectivity information. It is evident that the setting of $d_0,{\theta }_0,l_0$ will affect the results of fuzzy inference for each factor.

3.2. Setting of Information Weight

In the process of map matching, due to different road conditions, the importance of each information type varies, and different weights need to be set to achieve the best matching results [30,31]. Let the weight for the distance information be denoted as $W_1$, the weight for the direction information be denoted as $W_2$, and the weight for the connectivity information be denoted as $W_3$, $W_i>0\left(i=1,2,3\right)$. These weights should satisfy the normalization condition $W_1+W_2+W_3=1$.

Based on the membership degrees of each information type and the weights assigned to them, we can construct the comprehensive membership degree of candidate roads [32,33]:

(4)${\mu }_A\left(u_1,u_2,u_3\right)=W_1{\mu }_A\left(u_1\right)+W_2{\mu }_A\left(u_2\right)+W_3{\mu }_A\left(u_3\right)$

(5)${\mu }_B\left(u_1,u_2,u_3\right)=W_1{\mu }_B\left(u_1\right)+W_2{\mu }_B\left(u_2\right)+W_3{\mu }_B\left(u_3\right)$

The vehicle’s traveling route is determined using the direct method, which means

(6)$S_i=\max \left\{{\mu }_{Ai}\left(u_1,u_2,u_3\right)\right\},i=1,2,\cdots ,n$

In the equation, i represents the candidate road index and $S_i$ represents the maximum value for the similarity between the vehicle’s trajectory and the candidate road. Therefore, the i-th road is considered the matched road. If the matched road matches the vehicle’s traveling route, it is considered a correct match; otherwise, it is considered an incorrect match.

3.3. Algorithm

The enhanced fuzzy logic map-matching algorithm is given in Algorithm 1. This enhanced fuzzy logic map-matching algorithm takes a GPS trajectory and a digital road network as input and produces a map-matched trajectory as output. It first converts the trajectory into a spatial object and creates a digital road network from the input road network. Then, it initializes the map-matching process and iterates through each point in the trajectory to predict the matching value. If the predicted value is above a threshold (in this case, 60), it assigns the edge ID of the previous point to the current point. Otherwise, it updates the current link and assigns its edge ID to the current point. Finally, it converts the edited trajectory to a spatial point dataframe and returns the map-matched trajectory.

Algorithm 1: Enhanced fuzzy logic map-matching algorithm

Input: The algorithm takes as input a GPS trajectory represented by ‘trajectory = {p1, p2, …, pm}’ and a digital road network described by ‘roadnetwork = {(e1, (v1, v2), l1), (e2, (v2, v3), l2),…, (en, (vn, vp), lr)}’.Output: It generates a map-matched trajectory denoted as ‘matchedtrajectory = {(p1, e1), …, (pm, em)}’.1: Convert the GPS trajectory ‘trajectory’ into a Spatial Object.

2: Construct the digital road network ‘roads’ based on the information provided in ‘roadnetwork’.3: Initialize the map-matching process with the ‘trajectory’ and; ‘roads’, storing the results in ‘list’.4: Set ‘editedtrajectory’ to ‘list.trajectory’ and ’point-index’ to ‘list.index’.5: Set ‘current-link’ to ‘list.currentlink’.6: For each point index ‘j’ in ‘point-index’ do7:   Predict the matching value using Subsequent Map Matching-1 with parameters (‘editedtrajectory’, ‘roads’, ‘current-link’, ‘j’) and store the result in ‘predicted-value’.8:   If the ‘predicted-value’ is greater than or equal to 60 then9:       Assign the edge ID of the previous point to the current point: ‘editedtrajectory.EdgeID[j] = editedtrajectory.EdgeID[j − 1]’.10:   Else11:     Update ‘current-link’ using Subsequent Map Matching-2 with parameters (‘editedtrajectory’, ‘roads’, ‘current-link’, ‘j’).12:   Set the edge ID of the current link to the current point: ‘editedtrajectory.EdgeID = current-link.EdgeID’.13:   End if14: End for15: Convert the edited trajectory ‘editedtrajectory’ into a Spatial Point DataFrame, resulting in ‘matchedtrajectory’.16: Return the map-matched trajectory ‘matchedtrajectory’.

4. Analysis of the Influence of Parameter Setting on the Performance of Fuzzy Logic Algorithm

From Equations (4) and (6), it can be observed that the parameters $\left({\mu }_A\left(u_1\right),{\mu }_A\left(u_2\right),{\mu }_A\left(u_3\right)\right)$ and $\left(W_1,W_2,W_3\right)$ directly affect the matching result S. Additionally, considering Equations (1)–(3), when the parameter $\left(u_1,u_2,u_3\right)$ is the same for different candidate road segments, the value of the segmentation point $\left(d_0,{\theta }_0,l_0\right)$ of the membership function will affect the determination of the corresponding information membership degree $\left({\mu }_A\left(u_1\right),{\mu }_A\left(u_2\right),{\mu }_A\left(u_3\right)\right)$. Therefore, it can be considered that the fuzzy map-matching algorithm includes two categories of parameters: the segmentation points of the membership function $\left(d_0,{\theta }_0,l_0\right)$ and the information weights $\left(W_1,W_2,W_3\right)$. These parameters’ values significantly impact the final map-matching accuracy in practical applications. Therefore, studying the impact of parameter variations on the matching accuracy is of great significance for practical applications. This paper conducts simulation experiments based on two scenarios, parallel and intersection road segments, to determine the impact of parameter variations on the matching accuracy.

4.1. Parallel Road Scene

In parallel road conditions, the directional information of different candidate road segments is consistent, which means

(7)$u_{21}=u_{22}=\cdots =u_{2n},$

where $u_{2n}$ represents the directional information of the n-th road. Therefore, the segmentation points of the directional information membership function have no effect on the directional information membership degree. The directional information membership degrees of each road segment are the same:

(8)${\mu }_A\left(u_{21}\right)={\mu }_A\left(u_{22}\right)=\cdots ={\mu }_A\left(u_{2n}\right).$

At the same time, the weight, $W_2$, of the directional information has no effect on the overall membership degree. The expression of the overall membership degree is as follows:

(9)${\mu }_A\left(u_1,u_2,u_3\right)=W_1{\mu }_A\left(u_1\right)+W_3{\mu }_A\left(u_3\right)$

(10)${\mu }_B\left(u_1,u_2,u_3\right)=W_1{\mu }_B\left(u_1\right)+W_3{\mu }_B\left(u_3\right)$

Therefore, in parallel road segments, the segmentation points, ${\theta }_0$, of the directional information membership function and the weight, $W_2$, of the directional information have no impact on the final matching accuracy. The weight, $W_1$, of the distance information and the weight, $W_3$, of the directional information can be considered as a composite parameter, $W_1/W_3$, that affects the matching accuracy.

The simulated vehicle driving situation is shown in Figure 5. A simulation experiment is conducted to simulate the situation where a vehicle travels parallel to another candidate road. In order to ensure the validity of the simulation results, the variation range of parameter $d_0$ in the experiment is set to [0, 200], with a step size of 1. To reduce randomness, 100 experiments are performed for each value of parameter $d_0$, and the average of these 100 experiments is taken as the corresponding matching accuracy at that point. In order to explore the impact of membership segmentation points on the accuracy rate, irrelevant variables such as road spacing and GPS accuracy are selected as fixed values. Other simulation parameters are shown in Table 1. Figure 4 illustrates the impact of different values of the parameter $W_1/W_3$ on the segmentation points of the distance information membership function and the corresponding matching accuracy.

Figure 6 gives the influence on matching accuracy of distance information membership function segmentation point. Through a large number of simulation experiments, the following conclusions are drawn regarding parallel road segments:

Due to the excessive ratio, where the distance information has a significant weight, the connectivity information becomes meaningless. At this point, fuzzy logic map matching is equivalent to a simple projection algorithm, which has limited practical value and therefore is not studied. Here, we only focus on the scenario of $2<W_1/W_3<9$ and take $W_1/W_3=4$ and $W_1/W_3=8$ in Figure 4 as examples. From the figure, it can be observed that the accuracy increases initially as $d_0$ increases, reaches a peak, and then starts to decrease, eventually fluctuating at a relatively low level of accuracy. In the simulated range of $2<W_1/W_3<9$ studied, this pattern holds true. When $W_1/W_3$ takes different values, the maximum accuracy remains almost unchanged; only the segmentation points of the corresponding distance membership function vary, as shown in Table 2. When $W_1/W_3<2$ is considered, the peak value quickly drops as the ratio decreases, and the accuracy fluctuates around a low level, as shown in $W_1/W_3=1$ in Figure 4.

The segmentation points, $d_0$, corresponding to the maximum values of $W_1/W_3$ in Table 2 are linearly fitted, and the fitting result is shown in Figure 4. The corresponding mathematical relationship can be expressed as follows:

(11)$d_0=13.66\frac{W_1}{W_3}+4$

To obtain optimal results in the fuzzy logic matching algorithm for parallel road segments, it is advisable to assign a higher weight to the distance information in order to achieve higher road matching accuracy. A weight of approximately 4–5 times that of the connectivity information is found to be suitable. Moreover, the segmentation points, $d_0$, for the distance information should be set using the empirical formula, Formula (11), to maximize the effectiveness of the matching algorithm.

The data cleaning process effectively eliminated any erroneous values from both the X and Y datasets, as verified through a re-examination, as shown in Figure 7. Figure 7 is curve fitting results with the cleaned data and scattered data, respectively. Subsequently, a linear regression model was applied to the cleaned data, and a scatter plot featuring the fitted line was produced and saved as ‘scatter_plot_with_fitted_line_cleaned’. This visualization illustrates the correlation between the cleaned data points and the predictions of the linear model, offering enhanced insights into the model’s performance with the refined dataset.

4.2. Cross-Section Scene

We simulate a scenario in which vehicles travel at a constant speed through a diverging junction in a cross-road scenario, as shown in Figure 8. Unlike parallel road segments, the direction information for each candidate road in cross-road scenarios is different. Additional considerations need to be taken into account regarding the segmentation points for the direction information and the weights of the direction information based on the foundation of parallel road segments. During the simulation, the weight of the connectivity information, denoted as $W_3$, is fixed, and equal weights are assigned to the distance information and the direction information, which means

(12)$W_1=W_2=c{W}_3$

In order to facilitate research, the segmentation point, $d_0$, for the direction information membership function is fixed at 30. The variation range of the segmentation point for the direction information in the simulation experiment is represented as ${\theta }_0$ and ranges from 0 to 90, with a step size of 1. Similar to the parallel road segment scenario, the average of 100 experiments is taken as the matching accuracy for each ${\theta }_0$ value. The simulation parameters are shown in Table 3. The impact of the segmentation point, ${\theta }_0$, for the direction information on the matching accuracy is illustrated in Figure 9a.

From Figure 9a, it can be observed that as ${\theta }_0$ increases, the matching accuracy fluctuates around a certain value. Therefore, the average accuracy over the entire range of the independent variable is taken as an indicator to measure the impact of the c value on the algorithm’s performance. The average accuracy for different c values is shown in Table 4. When $c>1$ is set to $W_1=W_2>W_3$, the matching results have a higher average accuracy. From Table 4, it can be seen that at $c=4$, the average accuracy reaches its highest point and then starts to slowly decrease as the c value increases.

On the basis of the above, let us set $W_1=4W_3$ to study the change in accuracy when $W_1,W_2,W_3$ are different. At this time,

(13)$W_2=p{W}_3$

The impact of $W_2$ on the matching accuracy is shown in Figure 9b. From Figure 9b, it can be observed that in the application of the fuzzy logic-based map-matching algorithm at intersections, $W_2$ mainly affects the matching accuracy when ${\theta }_0$ takes larger values, while it has no significant impact on the accuracy when ${\theta }_0$ takes smaller values. When $p$ takes larger values and ${\theta }_0$ is also large, with an increase in ${\theta }_0$, the matching accuracy initially decreases and then increases, as shown in the case of $p=8$. When $p$ takes smaller values, the matching accuracy tends to slowly fluctuate and increase, as shown in the case of $p=2$. The simulation results indicate that to achieve stable and higher matching accuracy, the segmentation point, ${\theta }_0$, of the membership function for the directional information should be set to a smaller value, typically ranging from 10 to 30. If the best matching accuracy is desired, a smaller weight can be assigned to the directional information in practical applications, such as twice the weight of the connectivity information, while setting ${\theta }_0$ around 80.

4.3. Ablation Study

An ablation study was conducted to investigate the impact of various parameters on the performance of the fuzzy logic map-matching algorithm in both parallel road scene and cross-section scene scenarios, which is given in Table 5. In the parallel road scene analysis, the segmentation point (l₀) for the distance information membership function was determined through linear fitting to optimize the matching accuracy. The weight ratio (W₁/W₃) was varied to achieve peak accuracy, with the optimal ratio found to be around 4–5. However, the weight (W₂) of the direction information had no impact in this scenario. On the other hand, in the cross-section scene analysis, the segmentation point for the direction information was fixed at 30° to ensure consistent direction information. The weight ratio (W₁/W₃) was fixed at 1.0 to provide equal weightings of the distance and direction information.

The weight (W₂) for the direction information was varied to optimize the matching accuracy, with the highest average accuracy achieved when W₂ was set to 1.0. These findings demonstrate the importance of parameter optimization in enhancing the performance of the fuzzy logic map-matching algorithm, with different parameter settings yielding varying levels of accuracy in different scenarios.

5. Conclusions

We embark on simulation experiments to fine-tune the parameter settings within the fuzzy logic map-matching algorithm. Specifically, we scrutinize the effect of varying the segmentation point within the distance information membership function on the matching accuracy in parallel road scenarios. This investigation elucidates a direct correlation between the segmentation point and the distance information’s weight, establishing a formula to maximize the matching accuracy. In scenarios concerning intersecting roads, we unveil how the segmentation point of the directional information membership function influences the matching accuracy, leading to the proposition of a novel method for optimizing both the segmentation point and its associated weight. However, it is pertinent to note that this research is confined to analyzing only the most prevalent road configurations encountered in practical applications. Future endeavors will aim to navigate the complexities of more intricate scenarios, such as roads that spatially overlap, thus broadening the algorithm’s applicability and enhancing its precision.

Author Contributions

Conceptualization, W.Z. and H.G.; Methodology, W.Z. and H.G.; Software, W.Z. and H.G.; Validation, W.Z. and H.G.; Formal analysis, H.G.; Investigation, W.Z.; Resources, W.Z. and M.A.A.; Data curation, M.A.A.; Writing—original draft, H.G. and M.A.A.; Writing—review & editing, W.Z. and M.A.A.; Visualization, W.Z. and M.A.A.; Supervision, M.A.A.; Project administration, M.A.A.; Funding acquisition, M.A.A. All authors have read and agreed to the published version of the manuscript.

Data Availability Statement

The data that support the findings of this study are available from the corresponding author upon reasonable request.

Conflicts of Interest

The authors declare no conflicts of interest.

Footnotes

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Figures and Tables

Figure 1. Overall flow diagram for the determined candidate and selection road, a map-matching process.

Figure 2. The process of matching maps.

Figure 3. Fuzzy logic system block diagram.

Figure 4. Process flow diagram for matching fuzzy logic maps.

Figure 5. Parallel road section scene.

Figure 6. Influence on matching accuracy of distance information membership function segmentation point.

Figure 7. Curve fitting.

Figure 8. (A) Intersection diagram. (B) Intersection diagram.

Figure 8. (A) Intersection diagram. (B) Intersection diagram.

Figure 9. (a). Influence on matching accuracy of direction information membership function segmentation point; (b) influence on matching accuracy of W2.

Table 1

Parameters in parallel road simulation.

Road SpacingD (m)	Vehicle SpeedV (m/s)	GPS AccuracyS (m)	Sampling Intervalt (s)	Segmentation Point l0
20	10	20	5	5

Table 2

Results of parallel road simulation.

$\frac{{\mathit{W}}_1}{{\mathit{W}}_3}$	The Maximum Value Corresponds to the Direction Information Segmentation Point, d0	Maximum Correct Rate(%)
2	31.5	95.5956
3	43.2	96.3759
4	57.1	96.6736
5	76.4	96.9583
6	86.2	96.2712
7	99.2	96.2721
8	112.4	96.1414
9	126.5	96.1355

Table 3

Parameters in cross-road simulation.

Road Angleα (°)	Vehicle SpeedV (m/s)	GPS AccuracyS (m)	Sampling Intervalt (s)	Segmentation Point l0
45	2	20	5	5

Table 4

Results of cross-road simulation.

The value of c	0.2	0.5	1.0	1.5	2	3
Average accuracy (%)	85.11	88.16	90.15	91.78	92.63	93.21
The value of c	4	5	6	7	8	9
Average accuracy (%)	93.33	93.32	93.30	93.29	93.25	93.19

Table 5

Ablation study analysis.

Parameter	Parallel Road Scene Analysis	Cross-Section Scene Analysis
Segmentation Point (l0)	- Linearly fitted to optimize matching accuracy	- Set at 30° for consistent direction information
Weight (W1/W3)	- Varied to optimize matching accuracy	- Fixed at 1.0 for equal weightings of distance and direction information
Weight (W2)	- Not applicable, as direction information weight has no impact	- Varied to optimize matching accuracy
Matching Accuracy	- Reached peak accuracy when W1/W3 ratio was around 4–5	- Highest average accuracy achieved with W2 set to 1.0
	- Fluctuated around peak accuracy, then decreased with larger ratios	- Fluctuated around peak accuracy, then slightly decreased with larger W2
	- Segmentation point l0 varied linearly with W1/W3 ratio	- Matching accuracy fluctuated around a certain value with W2
	- Empirical formula (l0 = 18.526 × W1/W3) derived for optimal l0 setting	- Best results achieved with W2 set to 1.0 and l0 set to 30°

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