RSU-assisted autonomous vehicle high-precision positioning method under GNSS-free condition

Abstract

The invention discloses a method for assisting high-precision positioning of an automatic driving vehicle by a Roadside Unit (RSU) under the condition of no global navigation satellite system (GNSS), the method improves the positioning precision of the automatic driving vehicle by optimizing the RSU layout, and relates to the field of vehicle positioning, and the method comprises the following steps: firstly, according to the influence of the RSU layout on the positioning precision of a stationary target, determining the positioning precision of the stationary target according to the influence of the RSU layout on the positioning precision of the stationary target; constructing a target function of RSU layout optimization by combining the dynamic characteristics of the automatic driving vehicle, utilizing the geometric accuracy factor and taking the minimum accumulated geometric accuracy factor as an optimization target; then, designing constraint conditions suitable for a specific actual scene according to limiting conditions such as the position, the number and the communication range of the RSU; then, in combination with the optimization objective function, constructing a nonlinear optimization mathematical model; and finally, taking the RSU initial layout position coordinates as input parameters, and solving the established optimization mathematical model by using optimization algorithms such as sequential quadratic programming and the like to obtain an RSU optimization layout scheme. The RSU optimized layout scheme provided by the invention not only can meet the high-precision positioning requirement of the automatic driving vehicle under the GNSS-free condition, but also can save the layout cost of the RSU, and is expected to have a wide application prospect.

Description

Technical Field

[0001] The present invention relates to the field of positioning systems and autonomous driving technology, and in particular to a method for optimizing RSU by a constrained nonlinear algorithm under the condition of no GNSS (Global Navigation Satellite System) to improve the positioning accuracy of an autonomous driving vehicle. Background Art

[0002] In the development of autonomous vehicles, high-precision positioning information is crucial to ensure driving safety and improve driving efficiency. Traditional positioning methods mainly rely on GNSS, but GNSS may be interfered with or restricted in certain environments, such as tunnels, under bridges, and in densely populated areas with high-rise buildings in cities, resulting in reduced positioning accuracy or even failure. In order to overcome these limitations, researchers began to explore positioning methods without GNSS.

[0003] In the absence of GNSS, RSU acts as an anchor point with a known and precise location, providing a reliable positioning reference for autonomous vehicles. Autonomous vehicles exchange information with RSUs within their communication range, use the precise location information of RSUs and the vehicle's own sensor data, and use corresponding positioning algorithms to estimate their location. Therefore, the layout of RSUs has a decisive influence on the positioning accuracy of autonomous vehicles.

[0004] However, the existing RSU layout is often based on fixed rules or experience, and lacks optimization for the positioning needs of autonomous vehicles. This layout may not fully utilize the communication range and positioning accuracy of the RSU, resulting in limited positioning accuracy of autonomous vehicles. In order to improve the positioning accuracy of autonomous vehicles, the layout of the RSU needs to be optimized to make it more suitable for the needs of autonomous vehicles.

[0005] To this end, the present invention proposes a high-precision positioning method for RSU-assisted autonomous driving vehicles without GNSS conditions. The method constructs the optimization index cumulative geometric precision factor of the RSU layout, and optimizes the RSU layout position coordinates using a constrained nonlinear optimization algorithm to reduce the cumulative geometric precision factor, thereby improving the positioning accuracy of the autonomous driving vehicle. By optimizing the layout of the RSU, the present invention can effectively improve the positioning accuracy of the vehicle without GNSS conditions, providing a strong guarantee for the safe application of autonomous driving technology. Summary of the invention

[0006] The purpose of the present invention is to provide an RSU layout optimization method for assisting vehicles in high-precision positioning under GNSS conditions. This method can significantly improve the positioning accuracy of autonomous driving vehicles by optimizing the layout of RSUs under GNSS conditions, thereby ensuring the safe and efficient operation of autonomous driving vehicles in complex environments.

[0007] The present invention adopts the following technical solutions to solve the above technical problems:

[0008] Preliminary knowledge: Establish the formula for static geometric dilution of precision (GDOP), specifically:

[0009] For a vehicle with static coordinates (x, y), within the communication range, there are N RSUs assisting in its positioning, then the current geometric precision factor is expressed as follows:

[0010]

[0011] Among them, u i It means that the vehicle position (x, y) is the starting point coordinate, the i-th RSU position (x i ,y i ) is the vector of the end point coordinates. Similarly, u i It means that the vehicle position (x, y) is the starting point coordinate, the jth RSU position (x j ,y j ) is the vector of the end point coordinates. i and u j It is expressed as follows:

[0012] u i =(x i -x,y i -y)

[0013] u j =(x j -x,y j -y)

[0014] In the expression of geometric precision factor, there are N vectors composed of vehicles and RSUs. From the N vectors, any two vectors are selected to combine, and there are combinations. The range of the angle of each set of vectors is [0°, 180°]. The square of its sine value is calculated, and the square of all sets of sine values ​​are summed as the denominator of the geometric precision factor expression. Ideally, the closer the angle of each set of vectors is to 90°, the more uniform the RSU distribution is. Correspondingly, the more uniform the RSU distribution is, the smaller the geometric precision factor of the layout is, and the higher the positioning accuracy is. Therefore, for static vehicles, the geometric precision factor value is an inverse indicator of positioning accuracy. The smaller the geometric precision factor, the more accurate the positioning is.

[0015] S1. Construct the objective function of RSU layout optimization, specifically:

[0016] (1) Design optimization goals

[0017] For a stationary positioning target, the network environment formed by the RSUs within the wireless communication coverage of the surrounding area is relatively fixed, and the vehicle itself does not migrate. Therefore, the evaluation result of the geometric precision factor based on the current configuration is constant and will not change over time. In this scenario, the geometric precision factor essentially reflects the positioning accuracy potential under static conditions. Its value is directly related to the geometric layout of the surrounding RSUs and does not involve dynamic changes in the time series.

[0018] However, when the autonomous vehicle enters the dynamic driving mode, the situation is significantly different. As the vehicle continues to move on the road, the continuous update of its instantaneous position leads to two important changes: on the one hand, the relative position relationship between the vehicle and each RSU is dynamically adjusted, which directly changes the calculation basis of the geometric precision factor; on the other hand, the number N and combination (u) of RSUs that enter and exit the communication range during the vehicle's driving process i ,u j ) also changes frequently, further exacerbating the time-varying characteristics of the geometric precision factor. This dynamic change requires us to consider not only the geometric precision factor value at a single moment, but also the overall trend of the geometric precision factor evolving with the vehicle trajectory.

[0019] Therefore, in order to comprehensively evaluate and optimize the performance of the positioning system for mobile vehicles, it is necessary to introduce a global optimization indicator that can integrate the local geometric precision factor values ​​experienced by the vehicle on the moving path, that is, the cumulative geometric precision factor. This process is essentially the accumulation and integration of local geometric precision factor values ​​at different geographical locations during vehicle driving, aiming to capture the overall performance and potential fluctuations of positioning accuracy from a macro perspective. In this way, the stability and reliability of the vehicle's positioning system in complex driving routes and dynamic communication environments can be more accurately reflected. The expression of the cumulative geometric precision factor is as follows:

[0020]

[0021] For the convenience of research, it is assumed that the longitudinal coordinate of the vehicle remains unchanged and only moves in a straight line in the lateral direction. l is the total lateral displacement. The lateral displacement of the vehicle is used as the integral variable, and the static geometric precision factor is used as the integrand. where represents the number of RSUs within the vehicle's communication range, as follows:

[0022]

[0023] Assume the position of the vehicle is (x, y), and the position of each RSU is (x i ,y i), where i is the index of the RSU. Assuming that the communication radius of the vehicle is R, the number of RSUs that the vehicle can communicate with can be given by the above function expression. Where represents the total number of RSUs in the scene. I(·) is the indicator function, also known as the characteristic function, defined as:

[0024] I(True)=1

[0025] I(False)=0

[0026] (2) Constructing the objective function formula

[0027] The cumulative geometric precision factor is an indicator that measures the comprehensive effect of positioning accuracy caused by the changes in the geometric layout of the positioning system over time and space during dynamic or continuous positioning. It is calculated by integrating the local geometric precision factors at different time points or spatial positions, and reflects the average or overall positioning accuracy of the entire measurement sequence or driving path. The local geometric precision factor itself is an assessment of the expected positioning accuracy at a single location point at a certain moment due to the amplification effect of the observed geometric distribution on the positioning error. The cumulative geometric precision factor extends this accuracy assessment to the entire time period or spatial path, taking into account the comprehensive impact of the positioning environment changing over time or space on the positioning performance. The goal is to minimize the cumulative geometric precision factor, that is, the integral of the local geometric precision factor at any position of the vehicle in the tunnel. The theoretical formula of the objective function is as follows

[0028]

[0029] The optimization variable is the coordinates of the N RSUs, and the integral variable is the vehicle horizontal coordinate x. The lower limit of the integral is 0, and the upper limit of the integral is the maximum value L of the vehicle horizontal coordinate displacement. In the optimization function, the expression of the geometric precision factor is expanded as follows:

[0030]

[0031] Within the vehicle communication and positioning optimization framework of this study, we make a basic assumption that the coordinate position y of the vehicle perpendicular to the tunnel axis remains unchanged on the driving path, so the coordinate value is regarded as a known constant and does not participate in the dynamic adjustment of the optimization algorithm.

[0032] In the geometric dilution of precision, u i It means that the vehicle position (x, y) is the starting point coordinate, the i-th RSU position (x i ,y i ) is the vector of the end point coordinates. Similarly, u j It means that the vehicle position (x, y) is the starting point coordinate, the jth RSU position (x j ,y j ) is the vector of the end point coordinates.i (x) and u j (x) is represented as follows:

[0033] u i (x)=(x i -x,y i -y)

[0034] u j (x)=(x j -x,y j -y)

[0035] In our analysis framework, a function N(x) is defined to describe the number of RSUs that can establish a communication connection with a given vehicle at its lateral coordinate x. Since the longitudinal coordinate yy of the vehicle and the fixed communication radius R of the communication system are both considered constant parameters, the value of N(x) depends only on the lateral position x of the vehicle, which can be expressed mathematically as:

[0036] N(x)=f(x;y,R)

[0037] The calculation function of N(x) is as follows:

[0038]

[0039] Where I(·) is the indicator function, also called the characteristic function, defined as:

[0040] I(True)=1

[0041] I(False)=0

[0042] (3) Discretize the objective function formula and solve it

[0043] In the optimization problem, the objective function is a complex integral that is difficult to calculate directly. In order to simplify the solution process, the present invention adopts a strategy of approximating the original integral expression through a numerical integration method. The core of this conversion is to use technical means in the field of numerical analysis to convert the continuous integral operation problem into a series of discrete and computable numerical estimates, thereby bypassing the obstacles of direct analytical integration.

[0044] When the number N(X) of RSUs used to assist the current vehicle positioning is less than 2, the cumulative geometric precision factor, which is a key indicator for evaluating the performance of the positioning system, has a mathematically singular phenomenon in the integral domain. In view of the challenges faced by direct analytical calculation under this special condition, the present invention adopts an efficient numerical integration technology, namely an adaptive integration algorithm, to deal with the evaluation problem of the cumulative geometric precision factor integral. The algorithm intelligently adjusts the integration interval subdivision strategy, especially implements a denser sub-interval division in the local area close to the singular point of the geometric precision factor function, and reasonably reduces the calculation density in the non-singular area, so as to ensure that when dealing with integral problems containing singularities, it can not only maintain a high degree of calculation accuracy, but also effectively improve the execution efficiency and robustness of the algorithm, and finally achieve accurate estimation of the cumulative geometric precision factor value under low RSU conditions. Specifically, the adaptive Simpson's rule is adopted. This method combines the Simpson's rule (a method for integration based on the area under the quadratic polynomial approximation curve) with the adaptive strategy, and can automatically adjust the division of the integral interval according to the function characteristics in the integral area to achieve the established accuracy requirements. The details are as follows:

[0045] Step 1: Initial setting: Select an integration interval [a, b], initial values ​​a=0, b=L, and set an allowable error limit T and a maximum iteration depth M.

[0046] Step 2: Three-point estimation: First, use the basic form of Simpson's rule (i.e., use the function values ​​at the two end points and the midpoint of the interval) to estimate the integral value S of the entire interval [a, b].

[0047]

[0048] Step 3: Error evaluation: Set the end point of the interval [a, b] to c.

[0049] |S(a,c)+S(c,b)-S(a,b)|<15T

[0050] Or when the iteration depth reaches M, the numerical integration result of the interval [a, b] is returned. Otherwise, the current interval [a, b] is divided into two equal parts, and steps 2 and 3 are repeated for each subinterval. This process is performed recursively until the tolerance T is met or the maximum iteration depth M is reached. When performing recursive calculations, special attention should be paid to the adjustment of the tolerance T. Specifically, every time the depth of the recursion increases by one layer, that is, when entering the next level of recursion, the tolerance T should be updated to half of its current value, that is, T / 2. This tolerance reduction strategy is to adapt to the different requirements for calculation accuracy or error range at different recursive levels, and to ensure the stability and accuracy of the recursive process.

[0051] Step 4: Merge results: When the integration of all subintervals is completed and satisfies T or reaches the maximum recursive depth M, merge the integration results of all subintervals to obtain the final integral value.

[0052] S2. According to the location, quantity, communication range and other constraints of RSU, parameterize the scenario model and design constraints suitable for specific actual scenarios, specifically:

[0053] (1) Parameterized scene model

[0054] In this paper, our goal is to design an optimization strategy for deploying a certain number of RSUs in a specific tunnel environment to ensure continuous and high-quality vehicle communication and positioning services. The specific scenarios are as follows:

[0055] Environment setting: Consider a tunnel with a total length of L meters, in which a vehicle travels uniformly along a straight path at a constant speed, and its ordinate increases uniformly from 0 meters at the entrance of the tunnel to L meters at the exit. There are fixed-height installation platforms on both sides of the tunnel, located at ordinates Y1 and Y2 respectively.

[0056] Technical equipment: It is planned to deploy N RSUs, each with a signal coverage radius of R meters, responsible for providing necessary communication services and assisting vehicle positioning.

[0057] Core goal: Ensure that the vehicle is effectively covered by at least m RSUs at any location in the tunnel, so as to maintain communication continuity and improve positioning accuracy. "Effective coverage" here means that the RSU signal can reach the current location of the vehicle and the coverage range meets the set radius requirements.

[0058] Performance index: Propose to solve the optimal cumulative geometric precision factor, which is a comprehensive index obtained by integrating all local geometric precision factors (local and immediate geometric precision factors, which are directly affected by the vehicle position and the surrounding RSU layout) along the vehicle's driving path. The smaller the cumulative geometric precision factor value, the more stable and reliable the positioning accuracy is during the entire driving process.

[0059] (2) Design constraints

[0060] Coverage constraint: Ensure that at any position of the vehicle in the tunnel, there are at least m RSUs that can cover that position. This means that for any x, located in [0, L], and a fixed ordinate y, there are at least m RSUs whose Euclidean distances between their horizontal and vertical coordinates and the vehicle position (x, y) do not exceed a given coverage radius R. Mathematically, this can be expressed as:

[0061]

[0062] RSU location constraint: Each RSU must be placed within the lateral coordinate range of the tunnel, i.e.

[0063] x i ∈[0,L]

[0064] At the same time, their longitudinal coordinates can only choose one of two fixed values, which are the longitudinal coordinates on both sides of the road.

[0065] y i ∈[Y1,Y2]

[0066] Uniqueness constraint: ensure that the layout positions of all RSUs do not overlap, that is, for any two different RSUs (set as i and j), their horizontal coordinates satisfy .

[0067] x i ≠x j (i≠j)

[0068] RSU quantity restriction: The total number of deployed RSUs must be strictly equal to a predetermined value N. In other words, there must be exactly N RSUs, neither less nor more than the predetermined N units.

[0069] N RSU =N

[0070] These constraints together form the basis of an optimization problem aimed at designing the optimal layout of RSUs to ensure continuous coverage and positioning accuracy of vehicles over the entire tunnel length, while taking into account the feasibility and uniqueness requirements of the deployment.

[0071] S3. Convert the RSU layout optimization problem into a nonlinear optimization problem with constraints, and construct a nonlinear optimization mathematical model by combining the objective function and the constraints, specifically:

[0072] Objective function:

[0073]

[0074] Constraints:

[0075]

[0076] x i ∈[0,L]

[0077] y i ∈[Y1,Y2]

[0078] x i ≠x j (i≠j)

[0079] N RSU=N

[0080] S4. Initialize the initial layout position of RSU and use the optimization algorithm to solve the nonlinear optimization mathematical model, specifically:

[0081] (1) Optimization algorithm

[0082] In order to solve the above optimization model, a nonlinear constrained optimization algorithm is required. The present invention takes the Sequential Quadratic Programming (SQP) algorithm as an example. The SQP algorithm is an effective nonlinear constrained optimization algorithm. It solves the original problem by converting it into a series of quadratic programming sub-problems, gradually approximating it, and has good global convergence. In the present invention, the SQP algorithm is used to determine the optimal layout of the RSU, that is, to determine the position of the RSU to minimize the cumulative geometric precision factor, so as to achieve the purpose of improving the positioning accuracy of the autonomous driving vehicle.

[0083] The core idea of ​​the SQP algorithm is to transform the original problem, that is, the optimization problem with nonlinear objective function and constraints, into a series of solvable quadratic programming subproblems. In each iteration, the SQP algorithm performs the following main steps:

[0084] Problem definition: Assume that the objective function is f(x), x∈R n , is an n-dimensional vector. The constraints include the inequality constraint g(x)≤0 and the equality constraint h(x)=0, where g(x) is an m1-dimensional vector function and h(x) is an m2-dimensional vector function.

[0085] Step 1. Select an initial solution: Select an initial solution x0 and try to find an initial Lagrange multiplier vector λ0 and μ0 (for inequality and equality constraints).

[0086] Step 2: Construct a quadratic approximation model: k By Taylor expansion, the original problem is approximated as a quadratic programming problem. The quadratic approximation model is:

[0087]

[0088] Among them, f(x k ) is the value of f(x) at x k The gradient vector at is f(x) at x k The Hessian matrix at k and μ k are the Lagrange multipliers and slack variables respectively.

[0089] Step 3: Solve the following quadratic programming subproblem:

[0090] min Δx Q(x k , Δx)

[0091]

[0092]

[0093] in, and The constraints g(x) and h(x) are k The gradient vector at .

[0094] Step 4: Update the iteration point: According to the solved Δx * , update the iteration point:

[0095] x k+1 =x k +αΔx *

[0096] Here, ɑ is the step size factor, which can be determined by methods such as line search.

[0097] Step 5: Check convergence: Check x k+1 Whether the constraints g(x)≤0 and h(x)=0 are satisfied. If so, the algorithm converges. k+1 It is the optimal solution; otherwise, return to step 2 and continue iterating.

[0098] (2) Iterative solution of RSU optimization layout

[0099] The nonlinear optimization algorithm is used for iterative calculation to obtain the optimal RSU layout solution, as follows:

[0100] In the scenario of RSU position prior constraints, this process aims to improve the layout of RSU through iterative nonlinear optimization strategy. The specific implementation steps are described below, aiming to achieve a more optimized RSU layout scheme, focusing on reducing the cumulative geometric precision factor value, thereby improving positioning accuracy.

[0101] Initialization phase: First, a set of RSU layout location coordinates is randomly generated, which is used as the starting point of the optimization algorithm. Each coordinate represents a preset geographical location of an RSU. This step aims to explore the possible layout space.

[0102] Nonlinear optimization intervention: This initial layout is fed into a carefully chosen nonlinear optimization algorithm that uses the relative positions of the RSUs and their potential impact on the overall positioning system accuracy (measured as the cumulative geometric dilution of precision) as evaluation criteria.

[0103] Evaluation and feedback: After the algorithm runs, it will output a new set of RSU layout positions. At this point, the key is to compare the cumulative geometric precision value of this optimized layout with the cumulative geometric precision value of the initial layout.

[0104] Decision judgment: If the optimized layout shows a lower cumulative geometric precision factor value, it means that the positioning accuracy has been improved. At this time, the optimization is considered to have achieved the expected goal, the process is terminated, and the current RSU layout position coordinates are used as the final output result. On the contrary, if the optimization does not bring about a significant reduction in the cumulative geometric precision factor value, it means that the current iteration is not optimal. At this time, the layout position obtained by this round of optimization is used as a new input, and the nonlinear optimization algorithm is started again for the next round of iteration.

[0105] Iterative loop: The above-mentioned "evaluation and feedback" and "decision-making and judgment" steps form a closed loop, which continues until the optimized cumulative geometric precision factor value is significantly lower than that of the previous round and reaches the preset stopping condition, thereby ensuring that the optimal solution is gradually approached.

[0106] The present invention achieves the following significant effects, greatly promoting the application of autonomous driving technology in complex environments:

[0107] Significantly improve positioning accuracy: Through sophisticated RSU layout optimization, autonomous vehicles can achieve high-precision positioning even in the absence of GNSS signals. This reduces the risk of relying on a single navigation system and improves the safety and reliability of vehicle driving, especially in environments such as tunnels and urban areas with tall buildings where traditional positioning is more challenging.

[0108] Cost-effectiveness: The above accuracy improvement is achieved without adding additional hardware equipment (i.e. the total number of RSUs remains unchanged), which means that the present invention can achieve the greatest performance improvement with the lowest cost investment. This is an extremely important economic benefit consideration for commercially operated autonomous driving fleets and smart city construction. BRIEF DESCRIPTION OF THE DRAWINGS

[0109] Figure 1 Scene model diagram

[0110] Figure 2 Optimized layout diagram for RSU

[0111] Figure 3 The root mean square error curve of vehicle lateral positioning under different RSU layouts

[0112] Figure 4 The root mean square error curve of vehicle longitudinal positioning under different RSU layouts

[0113] Figure 5Cumulative distribution function diagram of vehicle lateral positioning error under different RSU layouts

[0114] Figure 6 Cumulative distribution function diagram of vehicle longitudinal positioning error under different RSU layouts

[0115] Figure 7 Flow chart of the present invention DETAILED DESCRIPTION

[0116] The preferred embodiments of the present invention are described in detail below in conjunction with the accompanying drawings so that the advantages and features of the present invention can be more easily understood by those skilled in the art, thereby making a clearer and more definite definition of the protection scope of the present invention.

[0117] Before describing the embodiments of the present invention in detail, a specific scenario example is used to reveal the scenario in which the technical solution of the present invention can be used. Figure 1 As shown in FIG. 1 , a scene model diagram of a vehicle using RSU to assist positioning without GNSS is shown in an example of the present invention. Some relevant settings of the scene model are as follows:

[0118] S1. Scene Modeling

[0119] In this paper, we aim to design an optimization strategy for deploying a certain number of roadside units (RSUs) in a specific tunnel environment to ensure continuous and high-quality vehicle communication and positioning services. The parameters of the specific scenario are as follows:

[0120] Environment setting: Consider a tunnel with a total length of L meters, in which a vehicle travels uniformly along a straight path at a constant speed, and its ordinate increases uniformly from 0 meters at the entrance of the tunnel to L (L = 3000) meters at the exit. There are fixed-height installation platforms on both sides of the tunnel, located at the ordinates Y1 (Y1 = 0) and Y2 (Y2 = 16), respectively.

[0121] Technical equipment: It is planned to deploy N (N=30) RSUs. The signal coverage radius of each RSU is R (R=200) meters. It is responsible for providing necessary communication services and assisting vehicle positioning.

[0122] Core goal: Ensure that any position of the vehicle in the tunnel is effectively covered by at least m (m = 3) RSUs, so as to maintain communication continuity and improve positioning accuracy. Here, "effective coverage" means that the RSU signal can reach the current position of the vehicle and the coverage range meets the set radius requirements.

[0123] Performance index: Propose to solve the optimal cumulative geometric precision factor, which is a comprehensive index obtained by integrating all local geometric precision factors (local and immediate geometric precision factors, which are directly affected by the vehicle position and the surrounding RSU layout) along the vehicle's driving path. The smaller the cumulative geometric precision factor value, the more stable and reliable the positioning accuracy is during the entire driving process.

[0124] S2. Design optimization goals

[0125] The expression for accumulating geometric precision dilution is as follows:

[0126]

[0127] For the convenience of research, it is assumed that the longitudinal coordinate of the vehicle remains unchanged and only moves in a straight line in the lateral direction. l is the total lateral displacement. The lateral displacement of the vehicle is used as the integral variable, and the static geometric precision factor is used as the integrand. where represents the number of RSUs within the vehicle's communication range, as follows:

[0128]

[0129] Assume the position of the vehicle is (x, y), and the position of each RSU is (x i ,y i ), where i is the index of the RSU. Assuming that the communication radius of the vehicle is R, the number of RSUs that the vehicle can communicate with can be given by the above function expression. Where represents the total number of RSUs in the scene. I(·) is the indicator function, also known as the characteristic function, defined as:

[0130] I(True)=1

[0131] I(False)=0

[0132] S3. Construct the optimization objective function of RSU layout. The theoretical formula of the objective function is as follows:

[0133]

[0134] S4. Design constraints suitable for specific scenarios based on the location, quantity, communication range and other constraints of the RSU

[0135] Coverage constraint: Ensure that at any position of the vehicle in the tunnel, there are at least m RSUs that can cover that position. This means that for any x, located in [0, L], and a fixed ordinate y, there are at least m RSUs whose Euclidean distances between their horizontal and vertical coordinates and the vehicle position (x, y) do not exceed a given coverage radius R. Mathematically, this can be expressed as:

[0136]

[0137] RSU location constraint: Each RSU must be placed within the lateral coordinate range of the tunnel, i.e.

[0138] x i ∈[0,L]

[0139] At the same time, their longitudinal coordinates can only choose one of two fixed values, which are the longitudinal coordinates on both sides of the road.

[0140] y i ∈[Y1,Y2]

[0141] Uniqueness constraint: ensure that the layout positions of all RSUs do not overlap, that is, for any two different RSUs (set as i and j), their horizontal coordinates satisfy .

[0142] x i ≠x j (i≠j)

[0143] RSU quantity restriction: The total number of deployed RSUs must be strictly equal to a predetermined value N. In other words, there must be exactly N RSUs, neither less nor more than the predetermined N units.

[0144] N RSU =N

[0145] These constraints together form the basis of an optimization problem aimed at designing the optimal layout of RSUs to ensure continuous coverage and positioning accuracy of vehicles over the entire tunnel length, while taking into account the feasibility and uniqueness requirements of the deployment.

[0146] S5. Convert the RSU layout optimization problem into a nonlinear optimization problem with constraints, and construct a nonlinear optimization mathematical model by combining the objective function and the constraints, as follows:

[0147] Objective function:

[0148]

[0149] Constraints:

[0150]

[0151] x i ∈[0,L]

[0152] y i ∈[Y1,Y2]

[0153] x i ≠x j (i≠j)

[0154] N RSU =N

[0155] S6. Apply the mathematical model to the nonlinear constrained optimization algorithm to obtain the optimized layout, as follows:

[0156] Initialization phase: First, a set of RSU layout location coordinates is randomly generated, which is used as the starting point of the optimization algorithm. Each coordinate represents a preset geographical location of an RSU. This step aims to explore the possible layout space.

[0157] Nonlinear optimization intervention: This initial layout is input into a carefully selected nonlinear optimization algorithm (the present invention takes the SQP algorithm as an example). The algorithm uses the relative positions between RSUs and their potential impact on the overall positioning system accuracy (measured by the cumulative geometric precision factor) as evaluation criteria.

[0158] Evaluation and feedback: After the algorithm runs, it will output a new set of RSU layout positions. At this point, the key is to compare the cumulative geometric precision value of this optimized layout with the cumulative geometric precision value of the initial layout.

[0159] Decision judgment: If the optimized layout shows a lower cumulative geometric precision factor value, it means that the positioning accuracy has been improved. At this time, the optimization is considered to have achieved the expected goal, the process is terminated, and the current RSU layout position coordinates are used as the final output result. On the contrary, if the optimization does not bring about a significant reduction in the cumulative geometric precision factor value, it means that the current iteration is not optimal. At this time, the layout position obtained by this round of optimization is used as a new input, and the nonlinear optimization algorithm is started again for the next round of iteration.

[0160] Iterative loop: The above-mentioned "evaluation and feedback" and "decision-making and judgment" steps form a closed loop, which continues until the optimized cumulative geometric precision factor value is significantly lower than that of the previous round and reaches the preset stopping condition, thereby ensuring that the optimal solution is gradually approached.

[0161] S7. Use the RSU-assisted positioning algorithm to verify the positioning accuracy of the RSU optimized layout

[0162] After obtaining the optimized RSU layout, an RSU auxiliary positioning algorithm is selected. The present invention selects the Cooperative Localization Using Posterior Linearization Belief Propagation (PLBP) algorithm to verify the result.

[0163] At this point, all implementation processes of this example have been completed.

[0164] Finally, the effectiveness of the method of the present invention is verified by computer simulation. The experimental parameters are as follows:

[0165] Table 1 Experimental parameters

[0166]

[0167]

[0168] The present invention uses the root mean square error and cumulative distribution function to measure the positioning accuracy of the vehicle. The experiment compares the effects of three RSU layout methods, namely random layout, uniform layout and optimized layout, on the positioning accuracy of the vehicle. The optimized layout is the RSU layout obtained by the present invention, such as Figure 2 Note that the transverse direction is the direction in which the vehicle is traveling, and the longitudinal direction is the direction perpendicular to the direction in which the vehicle is traveling.

[0169] (1) The impact of different layout methods on vehicle lateral positioning error:

[0170] like Figure 3 It is intuitively shown that, over time, the positioning error of the vehicle in the absence of continuous GNSS signal assistance shows an obvious cumulative trend. Randomly arranged RSU layout scenario and uniformly distributed RSU layout scenario. Under these two layout strategies, the vehicle's lateral positioning accuracy (with the root mean square error as a quantitative indicator) exceeds the threshold of 1 meter. It shows that it is difficult to meet the needs of high-precision positioning in long-term operation, especially in autonomous driving application scenarios with strict requirements on positioning accuracy. However, the situation is greatly improved by adopting the RSU optimization layout method proposed in the present invention. Even under the same unfavorable conditions of no GNSS signal, the vehicle's lateral positioning root mean square error is not only effectively controlled, but also maintained below 1 meter throughout the entire observation period. Figure 5 It can also be seen from the cumulative distribution function diagram that at the statistical data level of lateral errors, the RSU optimized layout scheme is also better than the other two schemes.

[0171] (2) The impact of different layout methods on vehicle longitudinal positioning error:

[0172] like Figure 4 ,Since the longitudinal error does not accumulate the positioning error, the RMS errors of the three RSU layout schemes all show a decreasing trend.,Nevertheless, there are still significant differences in the performance of the three layout,schemes.

[0173] It is particularly noteworthy that the RSU optimization layout strategy designed according to the present invention shows particularly outstanding advantages in longitudinal positioning accuracy. Compared with the random layout and uniform layout scenarios, the longitudinal root mean square error under the optimized layout not only has a lower initial value, but also decreases more rapidly, which clearly reflects the effectiveness of this layout scheme in maximizing the performance of the positioning algorithm. This finding further verifies that by fine-tuning the position distribution of the RSU, not only can the positioning error be effectively reduced, but the performance of the algorithm can also be accelerated, especially in applications that have strict standards for longitudinal position accuracy. Figure 6 It can also be seen from the cumulative distribution function diagram that at the statistical data level of longitudinal errors, the RSU optimized layout scheme is also better than the other two schemes.

Claims

1. A high-precision positioning method for an RSU-assisted autonomous driving vehicle without GNSS, characterized in that: The following steps are involved: S1. According to the working principle of RSU-assisted vehicle positioning, the influence of RSU layout on the positioning accuracy of static targets is analyzed. By using the geometric precision factor and considering factors such as the vehicle's motion characteristics, the objective function of RSU layout optimization is constructed by minimizing the cumulative geometric precision factor as the optimization goal. S2. According to the location, quantity, communication range and other constraints of RSU, parameterize the scenario model and design constraints suitable for specific actual scenarios; S3, converting the RSU layout optimization problem into a nonlinear optimization problem with constraints, and constructing a nonlinear optimization mathematical model by combining the objective function and the constraints; S4. Initialize the preliminary layout position of RSU, take the coordinates of each RSU as the variable input of the optimization algorithm, use the nonlinear optimization algorithm for iterative calculation, and continuously adjust the RSU position until the optimal RSU layout solution that minimizes the cumulative geometric precision factor is found.

2. A high-precision positioning method for an RSU-assisted autonomous driving vehicle without GNSS, characterized in that: In step S1, the geometric dilution of precision is accumulated as follows: In order to comprehensively evaluate and optimize the performance of the positioning system for autonomous vehicles, it is necessary to introduce a global optimization indicator that can integrate the local geometric precision factor values ​​experienced by the autonomous vehicle on the moving path, that is, the cumulative geometric precision factor. This process is essentially the accumulation and integration of local geometric precision factor values ​​at different geographical locations during vehicle driving, aiming to capture the overall performance and potential fluctuations of positioning accuracy from a macro perspective. In this way, the stability and reliability of the vehicle's positioning system in complex driving routes and dynamic communication environments can be more accurately reflected. The expression of the cumulative geometric precision factor is as follows: Where CGDOP stands for cumulative geometric dilution of precision, u i It means that the vehicle position (x, y) is the starting point coordinate, the i-th RSU position (x i ,y i ) is the vector of the end point coordinates. Similarly, u j It means that the vehicle position (x, y) is the starting point coordinate, the jth RSU position (x j ,y j ) is the vector of the end point coordinates. i and u j It is expressed as follows: or i (x) i -x,y i -and) or j (x) j -x,y j -and) For the convenience of research, it is assumed that the longitudinal coordinate of the vehicle remains unchanged and only moves in a straight line in the lateral direction. l is the total lateral displacement. The lateral displacement of the vehicle is used as the integral variable, and the static geometric precision factor is used as the integrand. Where N(x, y, R) represents the number of RSUs within the communication range of the vehicle, as follows The position of the vehicle is (x, y), and the position of each RSU is (x i ,y i ), where i is the index of the RSU. The communication radius of the vehicle is R, and the number of RSUs that the vehicle can communicate with can be given by the above function expression. Where represents the total number of RSUs in the scene. I(·) is the indicator function, also known as the characteristic function, defined as: I(True)=1 I(False)=0 3. A high-precision positioning method for an RSU-assisted autonomous driving vehicle without GNSS, characterized in that: In step S1, the objective function is as follows: The optimization variable is the coordinates of the N RSUs, and the integral variable is the vehicle horizontal coordinate x. The lower limit of the integral is 0, and the upper limit of the integral is the maximum value L of the vehicle horizontal coordinate displacement.

4. A high-precision positioning method for an RSU-assisted autonomous driving vehicle without GNSS, characterized in that: In step S2, the parameterized scene model is specifically as follows: In this paper, our goal is to design an optimization strategy for deploying a certain number of RSUs in a specific tunnel environment to ensure continuous and high-quality vehicle communication and positioning services. The parameters of the specific scenario are as follows: Environment setting: Consider a tunnel with a total length of L meters, in which a vehicle travels uniformly along a straight path at a constant speed, and its ordinate increases uniformly from 0 meters at the entrance of the tunnel to L meters at the exit. There are fixed-height installation platforms on both sides of the tunnel, located at ordinates Y1 and Y2 respectively. Technical equipment: It is planned to deploy N RSUs, each with a signal coverage radius of R meters, responsible for providing necessary communication services and assisting vehicle positioning. Core goal: Ensure that the vehicle is effectively covered by at least m RSUs at any location in the tunnel, so as to maintain communication continuity and improve positioning accuracy. "Effective coverage" here means that the RSU signal can reach the current location of the vehicle and the coverage range meets the set radius requirements. Performance index: Propose to solve the optimal cumulative geometric precision factor, which is a comprehensive index obtained by integrating all local geometric precision factors (local and immediate geometric precision factors, which are directly affected by the vehicle position and the surrounding RSU layout) along the vehicle's driving path. The smaller the cumulative geometric precision factor value, the more stable and reliable the positioning accuracy is during the entire driving process.

5. A high-precision positioning method for an RSU-assisted autonomous driving vehicle without GNSS, characterized in that: In step S2, the constraints are as follows: Coverage constraint: Ensure that at any position of the vehicle in the tunnel, there are at least m RSUs that can cover that position. This means that for any x, located in [0, L], and a fixed ordinate y, there are at least m RSUs whose Euclidean distances between their horizontal and vertical coordinates and the vehicle position (x, y) do not exceed a given coverage radius R. Mathematically, this can be expressed as: RSU location constraint: Each RSU must be placed within the lateral coordinate range of the tunnel, i.e. x i ∈[0,L] At the same time, their longitudinal coordinates can only choose one of two fixed values, which are the longitudinal coordinates on both sides of the road. yes i ∈[Y1,Y2] Uniqueness constraint: ensure that the layout positions of all RSUs do not overlap, that is, for any two different RSUs (set as i and j), their horizontal coordinates satisfy . x i ≠x j (i≠j) RSU quantity restriction: The total number of deployed RSUs must be strictly equal to a predetermined value N. In other words, there must be exactly N RSUs, neither less nor more than the predetermined N units. N RSU =N These constraints together form the basis of an optimization problem aimed at designing the optimal layout of RSUs to ensure continuous coverage and positioning accuracy of vehicles over the entire tunnel length, while taking into account the feasibility and uniqueness requirements of the deployment.

6. A high-precision positioning method for an RSU-assisted autonomous driving vehicle without GNSS, characterized in that: In step S3, the nonlinear optimization mathematical model is specifically as follows: Objective function: Constraints: x i ∈[0,L] yes i ∈[Y1,Y2] x i ≠x j (i≠j) N RSU =N 7. A high-precision positioning method for an RSU-assisted autonomous driving vehicle without GNSS, characterized in that: In the step S4, In the scenario of RSU position prior constraints, this process aims to improve the layout of RSU through iterative nonlinear optimization strategy. The specific implementation steps are described below, aiming to achieve a more optimized RSU layout scheme, focusing on reducing the cumulative geometric precision factor value, thereby improving positioning accuracy. Initialization phase: First, a set of RSU layout location coordinates is randomly generated, which is used as the starting point of the optimization algorithm. Each coordinate represents a preset geographical location of an RSU. This step aims to explore the possible layout space. Nonlinear optimization intervention: This initial layout is fed into a carefully chosen nonlinear optimization algorithm that uses the relative positions of the RSUs and their potential impact on the overall positioning system accuracy (measured as the cumulative geometric dilution of precision) as evaluation criteria. Evaluation and feedback: After the algorithm runs, it will output a new set of RSU layout positions. At this point, the key is to compare the cumulative geometric precision value of this optimized layout with the cumulative geometric precision value of the initial layout. Decision judgment: If the optimized layout shows a lower cumulative geometric precision factor value, it means that the positioning accuracy has been improved. At this time, the optimization is considered to have achieved the expected goal, the process is terminated, and the current RSU layout position coordinates are used as the final output result. On the contrary, if the optimization does not bring about a significant reduction in the cumulative geometric precision factor value, it means that the current iteration is not optimal. At this time, the layout position obtained by this round of optimization is used as a new input, and the nonlinear optimization algorithm is started again for the next round of iteration. Iteration loop: The above "evaluation and feedback" and "decision-making" steps form a closed loop, which continues until the cumulative geometric precision factor value after optimization is significantly lower than that of the previous round, reaching the preset stopping condition, thereby ensuring that the optimal solution is gradually approached.

8. A computer-readable storage medium, characterized in that: A computer program is stored thereon, and when the computer program is executed by a processor, the method according to any one of claims 1 to 7 is implemented.

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