Detector-free road section traffic operation state sensing method
By constructing spatial distance and feature matrices within the road network and calculating variogram parameters, combined with Copula theory, the problem of missing traffic state data in detector-free road sections was solved, achieving high-precision data filling and improved model interpretability.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- JILIN HIGHROAD RECONNAISSANCE DESIGN INST
- Filing Date
- 2026-03-19
- Publication Date
- 2026-05-15
AI Technical Summary
Existing traffic operation status perception methods suffer from inaccurate spatial correlation characterization and poor model interpretability when dealing with missing data and road sections without detectors.
The spatial distance matrix and traffic characteristic deviation matrix between road segments within the road network are constructed. Intervals are divided using a monotonically increasing distance scale sequence. Variation function parameters are calculated, and traffic data are fitted using various typical variation functions. A conditional probability density model is constructed using Copula theory to achieve traffic state parameter estimation for detector-free road segments.
It reduces reliance on roadside hardware, saves on infrastructure and communication maintenance costs, improves the ability to fill in missing data with high precision, and has broad application prospects and excellent spatial generalization capabilities.
Smart Images
Figure CN122050146A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the technical field of road traffic monitoring, specifically relating to a method for sensing the traffic operation status of road sections without detectors. Background Technology
[0002] In road traffic monitoring systems, sensors such as closed-circuit induction coils, video detectors, and microwave radar are often affected by equipment failures, communication interruptions, and severe weather. Furthermore, limitations in construction and communication maintenance frequently lead to missing traffic status data. Missing data affects the assessment of the real-time operational status of individual road segments and introduces uncertainty into road traffic condition analysis and evaluation.
[0003] In early research, scholars primarily relied on traditional statistical and time series methods for data imputation, including linear interpolation, polynomial fitting, moving averages, and autoregressive models. These methods are computationally simple and fast, making them suitable for short-term and single-segment data gaps. However, they struggle to characterize complex nonlinear relationships and the spatial heterogeneity of traffic conditions within road segments. Therefore, in engineering practice, to address the problem of continuous missing traffic condition data for complex road segments, researchers have introduced machine learning methods. These include algorithms such as random forests, support vector regression (SVR), and gradient boosting trees (XGBoost), which use historical traffic conditions of neighboring road segments, road segment characteristics, and external factors (weather conditions, holidays, and event information) as input to achieve nonlinear traffic condition prediction. These methods, when road data samples are sufficient and feature selection is appropriate, improve the accuracy of missing data recovery. Although the above-mentioned machine learning-based methods have achieved good results in specific scenarios, they still have the following obvious shortcomings: First, these methods are "black box" models, and their calculation and feature processing processes are invisible. Therefore, they lack statistical interpretation of the spatiotemporal changes of traffic flow. Moreover, when facing road sections with no detectors, they are prone to overfitting due to insufficient samples and data imbalance. Summary of the Invention
[0004] The purpose of this invention is to address the aforementioned shortcomings of the prior art by providing a method for perceiving traffic operation status on detector-free road sections, thereby solving the problems of inaccurate spatial correlation characterization and poor model interpretability in existing traffic operation status perception methods when dealing with missing data and detector-free road sections.
[0005] To achieve the above objectives, the technical solution adopted by the present invention is as follows: A method for sensing traffic operation status on detector-free road sections includes the following steps: S1. Based on the traffic characteristic data and spatial location data of detectable road segments within the road network, construct the spatial distance matrix and traffic characteristic deviation matrix between road segments within the road network; S2. Based on a preset monotonically increasing distance scale sequence, the spatial distance matrix is divided into intervals and elements are classified. The corresponding traffic feature deviation values in the traffic feature deviation matrix are indexed simultaneously. The segmented mean of the traffic state parameter difference is calculated to obtain the spatial attribute sequence. S3. Calculate the variation function parameters based on the spatial attribute sequence and the plane coordinates of the road network segments; S4. Various typical variogram functions are used to fit the road network traffic data respectively, and the optimal variogram function is selected based on the minimum loss function. S5. Based on the optimal variogram, construct the spatial covariance matrix and combine it with the preferred optimal marginal distribution. Use the typical maximum likelihood technique to map the measured road network traffic data to a standard Gaussian field to achieve global parameter estimation. Finally, use Copula theory to construct the conditional probability density model of the interpolation point and the neighboring reference points, and obtain the estimated value of the traffic state parameters of the interpolation point through numerical integration.
[0006] Furthermore, S2 specifically includes: Based on the spacing between road segments, a monotonically increasing distance scale sequence is established, and each element in the spatial distance matrix D is assigned to the corresponding distance scale interval of the distance scale sequence. In the middle, based on the traffic feature deviation matrix Spatial distance matrix The same index subscript, from the traffic feature deviation matrix The corresponding traffic feature deviation values are extracted, and the average value of the extracted traffic feature deviation values is calculated segment by segment to obtain the spatial attribute sequence, which is represented as follows: In the formula, For the distance scale sequence, the first Each distance scale value, For the distance scale sequence, the first One distance scale value; This is a mean sequence of traffic condition deviations. This is the mean sequence of actual physical distances within the corresponding interval; , , This represents the mean traffic state deviation within each corresponding distance scale interval; , , This represents the average actual physical distance within each corresponding distance scale interval.
[0007] Furthermore, in step S3, based on the spatial attribute sequence and the planar coordinates of the road network segments, the variation function parameters are calculated, which are expressed as follows: In the formula, For variable range, It is an off-center abutment. It is a nugget of gold; , The plane coordinates of the road network segments; , and These represent taking the maximum, minimum, and median values, respectively.
[0008] Furthermore, S4 includes three typical variogram functions, specifically Gaussian variogram function, exponential variogram function, and spherical variogram function. The three typical variogram functions are used to fit the road network traffic data to calculate the fitting error, the loss function of each typical variogram function is calculated, and the typical variogram function corresponding to the smallest loss function is selected as the optimal variogram function. The loss function is expressed as: In the formula, The fitting loss of the variation function. This represents the total number of distance scale intervals. This represents the autocovariance when the distance is 0. The distance scale is cross-variance at time Let covariance function be used. The first in the mean sequence of traffic state deviations Each element.
[0009] Furthermore, step S5 includes the following sub-steps: S51. Based on the optimal variogram, calculate the spatial covariance matrix for the distance scale; S52. Construct multiple types of edge distribution models, fit each edge distribution model based on measured road network traffic characteristic data, and select the optimal edge distribution model by maximum likelihood estimation. S53. Introduce the typical maximum likelihood technique based on empirical distribution. First, convert the measured traffic feature data into empirical distribution probability. Then, map it to a standard Gaussian field through the inverse Gaussian distribution transformation to obtain field data that conforms to the standard normal distribution. Based on the field data of the standard Gaussian field, complete the joint estimation of the global parameter set from the optimal variogram function and the optimal marginal distribution model. S54. Based on the spatial covariance matrix, the optimal marginal distribution model, the jointly estimated global parameter set, and the field data of the standard Gaussian field, perform spatial interpolation operations on the interpolation points of the detectorless road segment.
[0010] Furthermore, in step S53, based on the field data of the standard Gaussian field, a joint estimation of the global parameter set from the optimal variogram function and the optimal marginal distribution model is completed, which is expressed as: In the formula, The likelihood function value for the global parameters. Let be the set of all parameters to be estimated from the optimal variance function and the optimal marginal distribution model, and let represent the global parameter set; For Copula density function, The marginal cumulative distribution function of traffic state data in each dimension. Dimensions of the observed data For the first Marginal probability density function of traffic state data.
[0011] Furthermore, S54 includes the following sub-steps: S541. Select the detectable road segments that are spatially adjacent to the point to be interpolated as reference points, and calculate the weight coefficients of each reference point based on the covariance function. S542. Combining the global parameter set, reference point traffic data and the optimal edge distribution model, construct the conditional probability density model of the interpolation point using Copula theory. S543. Based on the reference point weight coefficient adjustment optimal edge distribution model, numerical integration is performed on the Gaussian field inverse transform, Copula conditional density function and the fusion formula of the adjusted edge distribution to obtain the estimated value of traffic state parameters of the point to be interpolated.
[0012] Furthermore, in S541, the weighting coefficients of each reference point are expressed as follows: In the formula, The weighting coefficients for the reference points; This is a sequence of distances between the interpolation points and each reference point. Let be the set of parameters for the variation function. This is the distance matrix between reference points.
[0013] Furthermore, in S542, the conditional probability density model of the interpolation point is constructed using Copula theory, which is expressed as: In the formula, Let be the conditional probability density function. For missing observations, For observation samples, The cumulative distribution function of the optimal marginal distribution model. This is the probability density function of the optimal marginal distribution model.
[0014] Furthermore, in S543, based on the weight adjustment of the reference point, the optimal edge distribution model is numerically integrated with the fusion formula of the inverse Gaussian field transform, the Copula conditional density function, and the adjusted edge distribution to obtain the estimated traffic state parameters of the point to be interpolated, which is expressed as: In the formula, These are the estimated traffic state parameters for the points to be interpolated. Let be the inverse Gaussian field transform function. This refers to the marginal distribution after weight adjustment.
[0015] The traffic operation status perception method for detectorless road sections provided by this invention has the following beneficial effects: 1. Reduce reliance on roadside hardware, effectively saving infrastructure and communication maintenance costs; This invention constructs a conditional probability density function based on Copula density, which can effectively utilize traffic state data of surrounding road segments to perform spatial interpolation on blind spot road segments.
[0016] 2. A method for traffic data incomplete that combines analysis of spatial dependence structure and spatial trends is proposed; Existing spatial interpolation studies typically rely solely on spatial correlation for spatial interpolation. However, the complexity of traffic network space means that traffic data does not satisfy the Gaussian stationarity assumption. This invention provides five candidate edge distributions and combines the edge distributions with spatial dependency structures using the Copula function, achieving high-precision data filling for missing data in various scenario modes.
[0017] 3. Possesses excellent spatial generalization ability; This invention is based on a modeling method of pure spatial correlation, which allows it to be extended beyond the fixed physical alignment of a specific highway. By simply recalculating the variation function according to the topology of the new road network, it can be applied to other road segments, demonstrating broad application prospects. Attached Figure Description
[0018] Figure 1 This is a flowchart of the traffic operation status perception method for road sections without detectors in the embodiment.
[0019] Figure 2 The figure shows the variation function curve in the example. Detailed Implementation
[0020] The specific embodiments of the present invention are described below to enable those skilled in the art to understand the present invention. However, it should be understood that the present invention is not limited to the scope of the specific embodiments. For those skilled in the art, various changes are obvious as long as they are within the spirit and scope of the present invention as defined and determined by the appended claims. All inventions utilizing the concept of the present invention are protected.
[0021] The traffic operation status perception method for detectorless road sections in this embodiment specifically includes the following: S1. Based on the traffic characteristic data (such as average vehicle speed, traffic flow or traffic density) and spatial location data (such as the latitude and longitude coordinates of the road segment, the starting and ending points of the road segment or the center point coordinates) of the detectable road segments in the road network, construct the spatial distance matrix D and the traffic characteristic deviation matrix Z between the road segments in the road network. The spatial distance matrix D is represented as: The traffic characteristic deviation matrix Z is represented as: In the formula, Indicates road segment and road sections Spatial distance between road sections; It is a section of road and road sections The difference in traffic characteristic parameters between them.
[0022] S2, Based on a preset monotonically increasing distance scale sequence The spatial distance matrix D is divided into intervals and its elements are classified. The corresponding traffic feature deviation values in the traffic feature deviation matrix are indexed simultaneously. The segmented mean of the traffic state parameter difference is calculated to obtain the spatial attribute sequence. In some embodiments, a monotonically increasing distance scale sequence is set according to the spacing between road segments. , For the distance scale sequence, the first One distance scale value; Divide each element in the spatial distance matrix D into the distance scale intervals corresponding to the distance scale sequence. In the middle, based on the traffic feature deviation matrix Spatial distance matrix The same index subscript, therefore depending on the falling into different The coordinates, from the traffic feature deviation matrix The corresponding traffic feature deviation values can be extracted, and then the spatial relationship between traffic parameters at different distance scales can be quantitatively and statistically analyzed. by For example, suppose In Between these, we can then use the traffic characteristic deviation matrix. Select By performing a mean operation on the extracted values above, we can extract... Spatial properties at the distance scale are as follows: The extracted traffic feature deviation values are averaged piecewise to obtain a spatial attribute sequence, which is represented as follows: In the formula, For the distance scale sequence, the first Each distance scale value, For the distance scale sequence, the first One distance scale value; This is a mean sequence of traffic condition deviations. This is the mean sequence of actual physical distances within the corresponding interval; , , This represents the mean deviation of traffic characteristics within each corresponding distance scale interval; , , This represents the average actual physical distance within each corresponding distance scale interval. This is the function for calculating the mean.
[0023] S3. Calculate the variation function parameters based on the spatial attribute sequence and the plane coordinates of the road network segments; refer to Figure 2 The variogram is often used to describe the relationship between the correlation of state parameters in different spaces and the spatial distance between state parameters. A variogram model relies on the estimation of three core parameters, one of which is... This is called "variable range," which refers to the gradual increase in spatial distance. When this value is 0, it indicates that the spatial correlation drops to 0. The second parameter is... The term "gold nugget" represents the actual measurement error. Therefore, theoretically speaking, It should take the value 0, but in practice, its value ranges between [0, 1]. The third parameter... The term "offset base" indicates a variable range. The corresponding function value.
[0024] The three core parameters of the variation function are calculated as follows: In the formula, For variable range, It is an off-center abutment. It is a nugget of gold; , The plane coordinates of the road network segments; , and These represent taking the maximum, minimum, and median values, respectively.
[0025] S4. Various typical variogram functions are used to fit the road network traffic data respectively, and the optimal variogram function is selected based on the minimum loss function. In some embodiments, three typical variograms are introduced as prior models: Gaussian variogram, exponential variogram, and spherical variogram. Gaussian variograms (Gau) and exponential variograms (Exp) share some similarities in their overall trends, but the difference lies in the fact that, due to the quadratic curve property of the Gaussian variogram, it decays faster, thus reaching its maximum value in a shorter distance than the exponential function. The spherical variogram (Sph), on the other hand, has the characteristic of piecewise mapping; this function varies with its range... As a critical point, once the distance breakthrough When the loss function is zero, its value becomes a constant. Therefore, in practice, the three types of variation functions mentioned above are first used to describe the actual data (road network traffic data), and the corresponding fitting errors are calculated respectively. Finally, the typical variation function that minimizes the loss function is selected as the optimal variation function to represent the current spatial dependency.
[0026] The loss function is expressed as: In the formula, The fitting loss of the variation function. This represents the total number of distance scale intervals. This represents the autocovariance when the distance is 0. The distance scale is cross-variance at time Let covariance function be used. The first in the mean sequence of traffic state deviations Each element.
[0027] S5. Based on the optimal variogram, a spatial covariance matrix is constructed. Combined with the optimized marginal distribution, the measured road network traffic data is mapped to a standard Gaussian field using the typical maximum likelihood technique to achieve global parameter estimation. Finally, the conditional probability density model of the interpolation point and its neighboring reference points is constructed using Copula theory, and the estimated traffic state parameters of the interpolation point are obtained through numerical integration. The specific steps include the following: S51, Based on the optimal variation function , For spatial distance scale variables, The model parameters are the variation function; for the distance scale Calculate its spatial covariance matrix: In the formula, To correspond to the distance scale Spatial covariance matrix, To correspond to the distance scale The spatial distance matrix.
[0028] S52. Construct multiple types of edge distribution models, fit each edge distribution model based on measured road network traffic characteristic data, and select the optimal edge distribution model by maximum likelihood estimation. In some embodiments, five types of marginal distributions were constructed, including the normal / Gaussian distribution (Norm), the generalized extremum distribution (Gev), the Gamma distribution (Gam), the log-normal distribution (Logn), and a Boxcox-based normal marginal distribution. Typically, location and shape parameters, namely the mean u and variance δ, are used to describe the characteristics of most distribution functions. However, some distribution functions have unique or additional parameter representations. For example, GEV depends on specific parameters, where... It is used to characterize the shape of a function; however, in the Gam distribution, it is necessary to determine... Indicates shape parameters, This represents the slope parameter; in a Box-Cox-based normal distribution, in addition to the position and shape parameters... and In addition to the regular parameters, an additional parameter λ is introduced, which is obtained through... Data transformation is performed. Therefore, given the different parameter notations, this embodiment uses a global parameter set. This summarizes the parameters to be estimated for all marginal distributions. Based on measured traffic parameter observations, the parameters of the aforementioned prior distributions can be fitted respectively.
[0029] After calculating and fitting the parameters of the prior distributions separately, the cumulative probability corresponding to each distribution is calculated to evaluate its goodness of fit with the real data. That is, the model with the highest cumulative probability is the marginal distribution of the optimal traffic state parameters. The cumulative probability value is calculated based on the maximum likelihood estimation principle, and the formula is as follows: In the formula, The log-likelihood value is... This represents the total number of samples in the measured traffic characteristic data. Let be the probability density function of the marginal distribution; S53. Introduce the typical maximum likelihood technique based on empirical distribution. First, convert the measured traffic feature data into empirical distribution probability. Then, map it to a standard Gaussian field through the inverse Gaussian distribution transformation to obtain field data that conforms to the standard normal distribution. Based on the field data of the standard Gaussian field, complete the joint estimation of the global parameter set from the optimal variogram function and the optimal marginal distribution model. In parameter estimation, maximum likelihood estimation and marginal distribution inference function method are two commonly used methods. However, both methods are computationally inefficient and require the form of the marginal distribution function to be determined in advance. Therefore, this embodiment introduces the Canonical Maximum Likelihood (CML) technique based on empirical distribution.
[0030] Before performing the CML process, the measured traffic data needs to be converted into "field data" with a specific theoretical distribution field. This invention chooses a Gaussian field with strong universality for data mapping: first, the empirical distribution probability corresponding to the original observed traffic state data is calculated, and then an inverse transformation is performed to obtain the field data. The process is as follows: In the formula, For the first The empirical distribution probability corresponding to each measured traffic condition data point. Let be the inverse Gaussian field transform function. Let be the Gaussian field transformation function. This is the field data after mapping to a standard Gaussian field.
[0031] Subsequently, The probability density function of the dimensional distribution: In the formula, It is the conditional probability density function; This includes measured traffic condition data from various dimensions. For Copula density function, The marginal cumulative distribution function for traffic state data in each dimension; Dimensions of the observed data For the first Marginal probability density function of traffic state data; Based on field data from a standard Gaussian field, a global parameter set from the optimal variogram function and the optimal marginal distribution model is completed. The joint estimate is expressed as: In the formula, The likelihood function value for the global parameters. Let be the set of all parameters to be estimated from the optimal variance function and the optimal marginal distribution model, and let represent the global parameter set; These are the parameters of the optimal variogram to describe spatial dependencies.
[0032] S54. Based on the spatial covariance matrix, the optimal marginal distribution model, the jointly estimated global parameter set, and the field data of the standard Gaussian field, perform spatial interpolation operation on the interpolation points of the detectorless road segment. Spatial interpolation essentially involves establishing a conditional probability density function between missing values and known observations to achieve spatial estimation of missing values. This embodiment utilizes the spatial relationship between the location of missing values and observable locations to fill in missing values, specifically including the following sub-steps: S541. Calculate the weight of the reference point; if Missing observations Therefore, it needs to be the one with the closest spatial distance. Observable samples As a reference point, the distance sequence and spatial distance matrix are extracted by quantizing the distance between the interpolation point and the reference point; based on this, the weight coefficient of each reference point is calculated as follows: In the formula, The weighting coefficients for the reference points; This is a sequence of distances between the interpolation points and each reference point. Let be the set of parameters for the variation function. This is the distance matrix between reference points; and All are dimensional sequence, The spatial search range of the interpolation algorithm is defined. The larger the value, the farther the spatial span of the chosen reference point. Considering the road network topology, the correlation between traffic state parameters of spatially adjacent road segments is more significant, but... If the value is too large, it will introduce noise from distant, unrelated road sections, interfering with the interpolation. Excessively large values can also lead to computational burden. Therefore, this invention specifies... .
[0033] S542. Combining the global parameter set, reference point traffic data, and the optimal edge distribution model, a conditional probability density model for the interpolation points is constructed using Copula theory, which is expressed as: In the formula, For missing observations, For observation samples, The cumulative distribution function of the optimal marginal distribution model. This is the probability density function of the optimal marginal distribution model.
[0034] S543, Order This represents the marginal distribution after weight adjustment; Specifically, based on the weighting coefficients of the reference points, the optimal marginal distribution model is adjusted. Numerical integration is performed on the fusion of the inverse Gaussian field transform, the Copula conditional density function, and the adjusted marginal distribution to obtain the estimated traffic state parameters for the points to be interpolated, expressed as follows: In the formula, Here are the estimated traffic state parameters for the points to be interpolated. This refers to the marginal distribution after weight adjustment.
[0035] Although specific embodiments of the invention have been described in detail with reference to the accompanying drawings, this should not be construed as limiting the scope of protection of this patent. Various modifications and variations that can be made by a person skilled in the art without inventive effort within the scope described in the claims still fall within the scope of protection of this patent.
Claims
1. A method for sensing traffic operation status on detector-free road sections, characterized in that, Includes the following steps: S1. Based on the traffic characteristic data and spatial location data of detectable road segments within the road network, construct the spatial distance matrix and traffic characteristic deviation matrix between road segments within the road network; S2. Based on a preset monotonically increasing distance scale sequence, the spatial distance matrix is divided into intervals and elements are classified. The corresponding traffic feature deviation values in the traffic feature deviation matrix are indexed simultaneously. The segmented mean of the traffic state parameter difference is calculated to obtain the spatial attribute sequence. S3. Calculate the variation function parameters based on the spatial attribute sequence and the plane coordinates of the road network segments; S4. Various typical variogram functions are used to fit the road network traffic data respectively, and the optimal variogram function is selected based on the minimum loss function. S5. Based on the optimal variogram, construct the spatial covariance matrix and combine it with the preferred optimal marginal distribution. Use the typical maximum likelihood technique to map the measured road network traffic data to a standard Gaussian field to achieve global parameter estimation. Finally, use Copula theory to construct the conditional probability density model of the interpolation point and the neighboring reference points, and obtain the estimated value of the traffic state parameters of the interpolation point through numerical integration.
2. The method for sensing traffic operation status on detectorless road sections according to claim 1, characterized in that, S2 specifically includes: Based on the spacing between road segments, a monotonically increasing distance scale sequence is established, and each element in the spatial distance matrix D is assigned to the corresponding distance scale interval of the distance scale sequence. In the middle, based on the traffic feature deviation matrix Spatial distance matrix The same index subscript, from the traffic feature deviation matrix The corresponding traffic feature deviation values are extracted, and the average value of the extracted traffic feature deviation values is calculated segment by segment to obtain the spatial attribute sequence, which is represented as follows: In the formula, For the distance scale sequence, the first Each distance scale value, For the distance scale sequence, the first One distance scale value; This is a mean sequence of traffic condition deviations. This is the mean sequence of actual physical distances within the corresponding interval; , , This represents the mean traffic state deviation within each corresponding distance scale interval; , , This represents the average actual physical distance within each corresponding distance scale interval.
3. The method for sensing traffic operation status on detectorless road sections according to claim 2, characterized in that, In step S3, the variation function parameters are calculated based on the spatial attribute sequence and the planar coordinates of the road network segments, and are expressed as follows: In the formula, For variable range, It is an off-center abutment. It is a nugget of gold; , The plane coordinates of the road network segments; , and These represent taking the maximum, minimum, and median values, respectively.
4. The method for sensing traffic operation status on detectorless road sections according to claim 3, characterized in that, S4 includes three typical variogram functions: Gaussian variogram function, exponential variogram function, and spherical variogram function. The fitting error of the road network traffic data is calculated using the three typical variogram functions respectively, and the loss function of each typical variogram function is calculated. The typical variogram function corresponding to the smallest loss function is selected as the optimal variogram function. The loss function is expressed as: In the formula, The fitting loss of the variation function. This represents the total number of distance scale intervals. This represents the autocovariance when the distance is 0. The distance scale is cross-variance at time Let covariance function be used. The first in the mean sequence of traffic state deviations Each element.
5. The method for sensing traffic operation status on detectorless road sections according to claim 4, characterized in that, S5 includes the following sub-steps: S51. Based on the optimal variogram, calculate the spatial covariance matrix for the distance scale; S52. Construct multiple types of edge distribution models, fit each edge distribution model based on measured road network traffic characteristic data, and select the optimal edge distribution model by maximum likelihood estimation. S53. Introduce the typical maximum likelihood technique based on empirical distribution. First, convert the measured traffic feature data into empirical distribution probability. Then, map it to a standard Gaussian field through the inverse Gaussian distribution transformation to obtain field data that conforms to the standard normal distribution. Based on the field data of the standard Gaussian field, complete the joint estimation of the global parameter set from the optimal variogram function and the optimal marginal distribution model. S54. Based on the spatial covariance matrix, the optimal marginal distribution model, the jointly estimated global parameter set, and the field data of the standard Gaussian field, perform spatial interpolation operations on the interpolation points of the detectorless road segment.
6. The method for sensing traffic operation status on detectorless road sections according to claim 5, characterized in that, In step S53, based on the field data of the standard Gaussian field, a joint estimation of the global parameter set from the optimal variogram function and the optimal marginal distribution model is completed, which is expressed as: In the formula, The likelihood function value for the global parameters. Let be the set of all parameters to be estimated from the optimal variance function and the optimal marginal distribution model, and let represent the global parameter set; For Copula density function, The marginal cumulative distribution function of traffic state data in each dimension. Dimensions of the observed data For the first Marginal probability density function of traffic state data.
7. The method for sensing traffic operation status on detectorless road sections according to claim 6, characterized in that, S54 includes the following sub-steps: S541. Select the detectable road segments that are spatially adjacent to the point to be interpolated as reference points, and calculate the weight coefficients of each reference point based on the covariance function. S542. Combining the global parameter set, reference point traffic data and the optimal edge distribution model, construct the conditional probability density model of the interpolation point using Copula theory. S543. Based on the reference point weight coefficient adjustment optimal edge distribution model, numerical integration is performed on the Gaussian field inverse transform, Copula conditional density function and the fusion formula of the adjusted edge distribution to obtain the estimated traffic state parameters of the point to be interpolated.
8. The method for sensing traffic operation status on detectorless road sections according to claim 7, characterized in that, In S541, the weight coefficients of each reference point are expressed as follows: In the formula, The weighting coefficients for the reference points; This is a sequence of distances between the interpolation points and each reference point. Let be the set of parameters for the variation function. This is the distance matrix between reference points.
9. The method for sensing traffic operation status on detectorless road sections according to claim 7, characterized in that, In S542, the conditional probability density model of the interpolation point is constructed using Copula theory, which is expressed as follows: In the formula, Let be the conditional probability density function. For missing observations, For observation samples, The cumulative distribution function of the optimal marginal distribution model. This is the probability density function of the optimal marginal distribution model.
10. The method for sensing traffic operation status on detectorless road sections according to claim 9, characterized in that, In step S543, the optimal edge distribution model is adjusted based on the weight of the reference point. Numerical integration is performed on the fusion of the inverse Gaussian field transform, the Copula conditional density function, and the adjusted edge distribution to obtain the estimated traffic state parameters of the point to be interpolated, expressed as follows: In the formula, These are the estimated traffic state parameters for the points to be interpolated. Let be the inverse Gaussian field transform function. This refers to the marginal distribution after weight adjustment.