Urban road network vehicle path estimation method based on deep recursive Logit model

Abstract

The application relates to a kind of urban road network vehicle path estimation methods based on depth recursive Logit model, comprising the following steps: step 1, obtaining the trajectory data of urban road network vehicle;Step 2, initialize iteration round and the parameter of utility function in depth recursive Logit model;Step 3, calculate loss function based on the trajectory data and parameter;Step 4, gradient calculation is carried out, and the update direction is obtained;Step 5, calculate the step of next round, and further update parameter, obtain updated parameter;Step 6, judge whether to reach convergence condition, if yes, then output the updated parameter, if not, then according to the step of next round, return step 2 and carry out iterative calculation until reaching convergence condition;Step 7, according to the optimal parameter, the path of urban road network vehicle is estimated, and estimation result is obtained.Compared with prior art, the application has the advantages of improving the estimation accuracy of vehicle path and the like.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of traffic system state perception, and particularly relates to a city road network vehicle path estimation method based on a deep recursive Logit model. BACKGROUND

[0002] In recent years, route choice modeling has been extensively studied. It can analyze route / trajectory observation data and help people implement link-level traffic planning, management and control in urban traffic systems. The deep recursive Logit model (RL) based on links has more advantages than the selection model based on complete paths: it does not need to construct a complex candidate path set; it can generate more continuous model outputs; and it allows more detailed modeling of link-level features. The specific meaning of the parameter estimation of the RL model is to solve the coefficients of the utility function according to the observed path, which is a function of the link attribute and refers to the immediate utility obtained from entering the adjacent next state (generally referring to a link).

[0003] Due to the complexity brought by the recursive structure, the parameter estimation of the RL model is a core problem. The current parameter estimation of the RL model generally uses the interior point method (outer layer), and the quasi-Newton method can be used in the outer layer to calculate the gradient, and then the parameters are updated step by step to gradually approach the optimal estimation value in each step.

[0004] The inner layer calculation of the RL model parameter estimation is to solve a linear equation set according to the current parameters in each iteration step, and the physical meaning of the solution of the linear equation set is the downstream utility of each link to the destination. If there is no solution to the downstream utility, the model will fail, which will hinder the algorithm from iterating to the optimal parameter solution. The existing methods adopt the idea of limiting the value of the parameters, but these methods often do not start from the sufficient and necessary conditions for solvability, and some methods still cannot guarantee that the linear equation set has a valid unique solution, while some methods give conditions that are too strict, resulting in a reduction in the parameter feasible region and the inability to model more complex route choice behaviors.

[0005] In addition, in the real world, the relationship between utility and each related attribute is often nonlinear, but the existing modeling method of the utility function assumes that it is a linear function, which will limit the ability of the model to model complex paths to some extent. SUMMARY

[0006] The purpose of the present application is to provide a city road network vehicle path estimation method based on a deep recursive Logit model, which improves the accuracy of vehicle path estimation.

[0007] The purpose of the present application can be achieved by the following technical solutions:

[0008] A city road network vehicle path estimation method based on a deep recursive Logit model, comprising the following steps:

[0009] Step 1, obtaining trajectory data of city road network vehicles;

[0010] Step 2, initializing iteration rounds and parameters of a utility function in a deep recursive Logit model, wherein the initial parameters are located in a feasible region, and the utility function is a linear utility function or a nonlinear utility function;

[0011] Step 3, calculating a loss function based on the trajectory data and the parameters;

[0012] Step 4, performing gradient calculation according to the loss function and an L-BFGS algorithm to obtain an update direction;

[0013] Step 5, calculating a step size of a next round according to the update direction and the parameters, and further updating the parameters to obtain updated parameters;

[0014] Step 6, judging whether a convergence condition is reached, if yes, outputting the updated parameters as final optimal parameters, if not, returning to Step 2 for iterative calculation according to the step size of the next round until the convergence condition is reached;

[0015] Step 7, estimating city road network vehicle path selection according to the optimal parameters in the deep recursive Logit model to obtain an estimation result.

[0016] Further, the initial parameters located in the feasible region need to satisfy the following conditions:

[0017] ρ(M) < 1

[0018] In the formula, M is an exponential adjacent utility matrix, which is a variable related to the parameters, and ρ(·) represents the spectral radius of the matrix.

[0019] Further, when the linear utility function is used, the construction process of the loss function includes:

[0020] Defining a linear utility function v(a|k) and an exponential adjacent utility matrix M, wherein M is a variable related to the parameters β, denoted as M(β), and the linear utility function v(a|k) is expressed as:

[0021] v(a|k) = β0+ β1X1+ β b X b +…+ β |B| X |B| = β T X

[0022] In the formula, k is a state, indicating that the vehicle is in a certain road section k, a is an adjacent downstream state, indicating a road section adjacent to the road section k, β0, β1, β b , …, β |B| are parameters, indicating the influence weight of different attributes on utility, X1, X b , …, X |B| are attribute values of the selection a, indicating the road section length and road section passing capacity, M indicates that the state k and the state a have an upstream and downstream adjacent relationship, and the elements of M are M ka indicates the utility value from the state k to the state a, and v(a|k) indicates the utility value of the selection a under the state k.

[0023] According to the trajectory data, a log-likelihood objective function LL(β; ξ * ) is constructed to estimate the parameters by maximizing LL(β; ξ * ), wherein the log-likelihood objective function LL(β; ξ * ) is expressed as:

[0024]

[0025] In the formula, ξ * is trajectory data, N od is the number of observed paths between the start and end points od, T is the maximum number of road sections of each path, is the state transition probability from k t to k t+1 .

[0026] A sufficient and necessary condition ρ(M(β))<1 is introduced, and combined with the log-likelihood objective function LL(β; ξ * ), a final loss function Loss(β; ξ * ; γ) is constructed to estimate the parameters by minimizing Loss(β; ξ * ; γ), wherein the expression of the loss function Loss(β; ξ * ; γ) is:

[0027]

[0028] In the formula, ρ(·) represents the spectral radius of a matrix, and γ is a weight.

[0029] Further, when the linear utility function is used, the obtaining step of the update direction includes:

[0030] Based on the loss function, according to the chain rule of partial derivatives, the following is obtained:

[0031]

[0032] In the formula, Loss is the loss function, β is the parameter, is the state transition probability, v(a|k) is the linear utility function, k is the state, indicating that the vehicle is in a certain road section k, and a is the adjacent downstream state;

[0033] Perform differential calculation on formula (1) to obtain the gradient d′ of parameter β;

[0034] The L-BFGS algorithm is used to perform a second-order correction on the gradient d′ to obtain an updated direction d.

[0035] Furthermore, when the linear utility function is adopted, the step of obtaining the updated parameters includes:

[0036] Perform line search according to the update direction and parameters to obtain the next round step length that meets the conditions. The line search process includes:

[0037] If ρ(M(β i +t·d i ))≥1, then update t=t / 2 until ρ(M(β i +t·d i ))<1, get the final step size of the next round;

[0038] Update the parameters according to the step size and update direction of the next round to obtain the updated parameters β i+1 , expressed as:

[0039] β i+1 =β i +t·d i

[0040] Where, β i+1 is the updated parameter, indicating the parameter of the i+1th round, β i is the parameter of the i-th round, ρ(·) represents the spectral radius of the matrix, t is the step size, d i is the update direction of the i-th round.

[0041] Furthermore, the nonlinear utility function is constructed using a residual neural network, and the specific construction steps include:

[0042] Define the network layer f of the residual neural network (l) (h): For the input vector h of the neural network layer, use the linear weight W (l) 、b (l) Transform h and use the activation function σ (l) Output the final vector result, neural network layer f (l) (h) The expression is:

[0043] f (l) (h)=σ(l) (W (l) h+b (l) )

[0044] wherein, l is the l-th layer network layer;

[0045] defining a residual neural network: according to the network layer f (l) (h) constructing a residual neural network, including an input layer, an intermediate layer and an output layer;

[0046] constructing a nonlinear utility function: for an input vector X of the residual neural network, sequentially passing through the input layer, the intermediate layer and the output layer for transformation, finally taking the scalar utility function output by the output layer as the nonlinear utility function v θ (a|k), the nonlinear utility function v θ (a|k) is expressed as:

[0047] v θ (a|k) = f (out) (h (L) )

[0048] wherein, the transformation expression of the input layer is:

[0049] h (in) = f (in) (X)

[0050] the transformation expression of the intermediate layer is:

[0051] h (1) = f (1) (h (in) )+ h (in) ,..., h (L) = f (L) (h (L-1) )+ h (L-1)

[0052] wherein, θ = {W (in) ,b (in) ,W (l) ,b (l) ,W (out) ,b (out)} is a parameter, W (in) ,b (in) ,W (l) ,b (l) ,W (out) ,b (out) are input layer linear weight, input layer linear bias, intermediate layer linear weight, intermediate layer linear bias, output layer linear weight, output layer linear bias respectively, k is a state, indicating that the vehicle is in a certain road section k, a is an adjacent downstream state, indicating that the road section a adjacent to the road section k, f (out) (h(L) ) is an output vector of an output layer, L is a total number of network layers, f (in) (X) is a calculation result of an input layer, h (in) is a calculation result of an input layer, f (1) (h (in) ) is a calculation result of a first layer intermediate layer, h (1) is a calculation result of a first layer intermediate layer, and an input vector X represents an attribute vector in a nonlinear utility function.

[0053] Further, when the nonlinear utility function is used, the obtaining step of the update direction comprises:

[0054] Based on the loss function, the residual neural network is back-propagated, and further differential calculation is performed to obtain a gradient d' of the parameter θ;

[0055] The L-BFGS algorithm is used to perform second-order correction on the gradient d' to obtain an update direction d.

[0056] Further, when the nonlinear utility function is used, the construction process of the loss function comprises:

[0057] An exponential adjacent utility matrix M is defined, wherein M is a variable related to the parameter θ, and is represented as M(θ);

[0058] According to the trajectory data, a log-likelihood objective function LL(θ;ξ * ) is constructed to estimate the parameter by maximizing LL(θ;ξ * ), wherein the log-likelihood objective function LL(θ;ξ * ) is represented as:

[0059]

[0060] In the formula, ξ * is trajectory data, N od is a number of observed paths between an origin and a destination od, and T is a maximum number of road segments of each path, is a state transition probability from k t to k t+1 .

[0061] A sufficient and necessary condition ρ(M(θ))<1 is introduced, and in combination with the log-likelihood objective function LL(θ;ξ * ), a final loss function Loss(θ;ξ * ;γ) is constructed to estimate the parameter by minimizing Loss(θ;ξ * ;γ), wherein the expression of the loss function Loss(θ;ξ * ;γ) is:

[0062]

[0063] wherein p(·) represents the spectral radius of a matrix, and γ is a weight.

[0064] Further, when the nonlinear utility function is used, the step of obtaining the updated parameter comprises:

[0065] performing a line search according to the update direction and the parameter to obtain a step size of a next round satisfying the condition, and the line search process comprises:

[0066] if p(M(θ i +t·d i ))≥1, updating t=t / 2 until p(M(θ i +t·d i ))<1, and obtaining a final step size of the next round;

[0067] updating the parameter according to the step size of the next round and the update direction to obtain an updated parameter θ i+1 , which is expressed as:

[0068] θ i+1 =θ i +t·d i

[0069] wherein θ i+1 is the updated parameter, θ i represents a parameter of an i+1th round, θ i represents a parameter of an ith round, p(·) represents the spectral radius of a matrix, t is a step size, and d d is an update direction of the ith round.

[0070] Further, the step of obtaining the estimation result comprises:

[0071] given a starting point o and a terminal point d, calculating a state transition probability of a deep recursive Logit model based on the optimal parameter, and estimating a vehicle path result between the starting point and the terminal point;

[0072] wherein the step of constructing the state transition probability comprises:

[0073] in a road section k, a next state a is selected in a downstream adjacent state set A(k) with a probability, a Bellman equation is constructed, and an expression is:

[0074]

[0075] wherein V d (k) is a downstream expected utility from a state k to d, V d (k) is a downstream expected utility from a state a to d, μ is a parameter coefficient of an extreme Gumbel distribution, and Vd (d) is the expected utility from state d to the downstream state, default is 0, is the expected utility, ε(a|k) is the instantaneous utility v ′ is the error component in v(a|k), v(a|k) is the instantaneous utility v ′ is the deterministic component in v(a|k), i.e. the utility function, including linear utility function and nonlinear utility function, k is the state, indicating that the vehicle is at a road segment k, a is the adjacent downstream state, indicating the road segment adjacent to the road segment k;

[0076] It is assumed that ε(a|k) obeys the extreme Gumbel distribution with parameters (0, μ), which is expressed as:

[0077]

[0078] According to formula (1) and (2), we have:

[0079]

[0080] Let The element of the exponential adjacency utility matrix M We have:

[0081]

[0082] In the formula, δ ka is the element of the adjacency matrix δ, is the exponential of the expected utility from state a to d downstream;

[0083] It is assumed that all states k can reach the terminal d with any path and any number of steps, and formula (4) is rewritten as:

[0084] z d = (δ⊙M)z d +b d (5)

[0085] In the formula, b d is a unit vector, z d is the exponential vector of the expected utility from all states to d downstream

[0086] Transforming formula (5), we have:

[0087] z d = (I-δ⊙M) -1 b d (6)

[0088] In the formula, I is a unit vector;

[0089] It is assumed that z d has a unique non-negative solution, and the state transition probability is obtained by solving formula (6), which is expressed as:

[0090]

[0091] In the formula, p d (a|k) is the state transition probability from k to a.

[0092] Compared with the prior art, the present application has the following beneficial effects:

[0093] (1) The present application uses a deep recursive Logit model to simulate the probability of selecting different paths on a road section. In the deep recursive Logit model, a utility function is used to represent the utility value of each selection scheme of a road section, and the parameters in the utility function are used to represent the influence weight of adjacent road sections. The present application updates and calculates the parameters through continuous iteration to obtain the optimal parameters and the optimal influence weight, thereby improving the estimation accuracy of the vehicle path.

[0094] (2) The present application performs parameter estimation calculation based on the necessary and sufficient condition for the solvability of the deep recursive Logit model, which maximizes the feasible region of the parameters and enables the modeling of complex paths.

[0095] (3) The present application uses the universal approximation principle of the arbitrary nonlinear continuous function of the residual neural network to model the nonlinear utility function, which can well improve the ability of the model to model complex paths and improve the estimation accuracy of the vehicle path under the nonlinear utility function.

[0096] (4) Compared with some technologies that change the architecture of the deep recursive Logit model to ensure the solvability of the model, the present application does not change the overall architecture of the original model, and the deep recursive Logit model does not need to construct a complex candidate path set, so the additional computational overhead required is very small. BRIEF DESCRIPTION OF DRAWINGS

[0097] Figure 1 is a method flowchart of the present application;

[0098] Figure 2 is the overall framework of the present application;

[0099] Figure 3 is the relationship of the solvability condition of the present application. DETAILED DESCRIPTION

[0100] The present application will be described in detail below in conjunction with the drawings and specific embodiments. The present embodiment is implemented on the premise of the technical solution of the present application, and detailed implementation modes and specific operation processes are given, but the protection scope of the present application is not limited to the following embodiments.

[0101] The embodiment provides a city road network vehicle path estimation method based on a deep recursive Logit model, and symbols involved in the method include definitions.

[0102] Definition of road network G: Consider a connected, possibly cyclic directed graph G(N, L), where N and L represent the node set and link set in the graph, respectively.

[0103] Definition of state k: According to the majority of deep recursive Logit model theory, the state is defined as the traveler / vehicle being at a certain link k.

[0104] Definition of action / edge k→a: According to the majority of deep recursive Logit model theory, the action / edge is defined as the transition from state k to adjacent downstream state a.

[0105] Definition of adjacency matrix δ: If state k and state a have upstream and downstream adjacent relationship, then the element δ ij =1, otherwise δ ij =0.

[0106] Definition of Origin-Destination: Respectively, the origin link o and the destination link d.

[0107] Definition of immediate utility v ′ (a|k): The utility obtained from state k to adjacent downstream state a. The utility v ′ (a|k) includes a deterministic component v(a|k) and an error component ε(a|k).

[0108] Definition of downstream utility V d (k): The total utility expected to be obtained from state k to destination d (which can be reached through various different paths). The utility from d to d is 0 (boundary condition).

[0109] Definition of the first type of extreme value distribution: Also known as the Gumbel distribution, it is a probability distribution used to describe the distribution of extreme values (such as maximum or minimum) of random variables. In statistics, it is often used to model the occurrence of extreme events, such as the maximum water level of a flood, the maximum magnitude of an earthquake, etc. The probability density function (PDF) of the Gumbel distribution is usually expressed as: where e is the base of the natural logarithm, α is the location parameter, indicating the center of the distribution; μ is the scale parameter, controlling the width of the distribution.

[0110] Definition of exponential adjacency utility matrix M: Where if state k and state a have upstream and downstream adjacent relationship, then the element

[0111] Definition of exponential downstream utility vector z dDefinition of vector z d kth element of z

[0112] State transition probability p d Definition of (a|k): for each given destination d, there is a state transition probability p d (a|k) that represents the probability (between 0 and 1) of transitioning from state k to an adjacent downstream state a.

[0113] In the deep recursive Logit model, the state transition probability is derived from the following three steps / hypotheses.

[0114] (1) Bellman equation: at a road segment k, assume that the decision maker (traveler) chooses the next state a in the set of downstream adjacent states A(k) with probability to maximize the sum of the immediate utility v ′ (k|k) and the expected downstream utility V d (a) to the destination (absorbing state).

[0115]

[0116] where v(a|k) is the utility function, including linear and nonlinear utility functions.

[0117] (2) First-type extreme value distribution: assume that ε(a|k) follows an extreme Gumbel distribution with parameters (0, μ).

[0118] ε(a│k) ~ Gumbel(0, μ) (2)

[0119] According to equations (1) and (2), equation (3) can be obtained.

[0120]

[0121] Let Equation (4) can be obtained.

[0122]

[0123] (3) No path set constraint assumption: assume that all states k can reach d with any path and any number of steps. This assumption is the core assumption of the deep recursive Logit model, avoiding the construction of a complex candidate path set. Therefore, equation (4) can be rewritten in vector form as equation (5). Where b d is a unit vector with a value of 1 on the dth element, and is the Hadamard product.

[0124] z d = (δ⊙M)z d +b d(5)

[0125] Formula (5) can be transformed into formula (6).

[0126] z d =(I-δ⊙M) -1 b d (6)

[0127] If z d There is a unique non-negative solution (the exponential downstream utility must be non-negative to have physical meaning), then the state transition probability p can be solved d (a|k).

[0128]

[0129] From formula (6), we can see that we need to control δ⊙M to ensure that z d There is a unique non-negative solution, and since the adjacency matrix δ is fixed, the elements of M and δ have the same position, and the problem is transformed into controlling M. To facilitate the explanation of the innovation of the present invention, a sufficient condition (8) for solvability in an existing method is introduced for comparison.

[0130]

[0131] The present invention is based on the necessary and sufficient condition (9) for solvability, where ρ(·) means the spectral radius of the matrix.

[0132] ρ(M)<1 (9)

[0133] The relationship between each condition and the solvability of the model is shown in the attached Figure 3 As shown in . It can be concluded that the sufficient condition (7) is too strict and may impose unnecessary restrictions on the value of M, while the necessary and sufficient condition (9) is just right.

[0134] Since the value of M is related to the utility function v(a|k), the parameter estimation process of the RL model will be explained below based on the linearity / nonlinearity of the utility function.

[0135] like Figure 2 As shown, the estimation method of the present invention is combined with the deep recursive Logit model for estimation. The utility function in the deep recursive Logit model can adopt a linear utility function or a nonlinear utility function. By estimating the parameters in the linear or nonlinear utility function, the parameter values ​​are used as the influence weights of different attributes on the utility, thereby estimating a more accurate vehicle path. Figure 1 and Figure 2 , the overall algorithm steps of the estimation method are:

[0136] S1. Obtain vehicle trajectory data on the urban road network;

[0137] S2, initialize model parameters to ensure that they can fall within the feasible region;

[0138] S3, calculate the loss function according to the model parameters and the observed path;

[0139] S4, gradient calculation according to the loss function and L-BFGS algorithm;

[0140] S5, line search according to the gradient and the parameter to obtain a step length that meets the condition;

[0141] S6, update the parameters according to the final step length;

[0142] S7, judge whether the convergence condition is reached, if not, return to S3;

[0143] S8, estimate the vehicle path using the estimated model parameters.

[0144] (I) Parameter estimation method (M1) based on linear utility function RL

[0145] The definition of linear utility function v(a|k) is M, which is related to β, and is denoted as M(β):

[0146]

[0147] According to the above formula, when some observed paths ξ * in the road network are obtained, the log-likelihood objective function LL(β;ξ * ) can be given, and the optimal parameters are estimated by maximizing LL(β;ξ * ).

[0148]

[0149] The invention adds the sufficient and necessary condition (9) to the estimation process. First, for the objective function, the log-bound is used so that when ρ(M) approaches 1, a larger penalty will be obtained, which is a relatively "soft" constraint, and γ is the weight, which can be set according to the needs, or the optimal result is obtained by multiple rounds of iteration. Therefore, the final total objective function is shown in formula (12), and the optimal parameters are estimated by minimizing Loss(β;ξ * ;γ).

[0150]

[0151] In addition to the "soft" constraint, the invention also adds a line search mechanism to the algorithm to ensure that the parameter β of each step meets the condition ρ(M(β))<1.

[0152] According to the above algorithm steps, the steps of estimating using the linear utility function include:

[0153] S1, obtaining urban road network vehicle trajectory data;

[0154] S21, initializing model parameters β 0 , which ensures that it can fall within the feasible region. Specifically, set β1= β2=…= β |B| 0 as 0, and set β0 as a small negative number, for example β0= -10. At this time, the elements on the exponential adjacency utility matrix M will be positive numbers close to 0, and obviously satisfy the sufficient condition (8). According to the relationship between condition (8) and condition (9), it is also obvious to satisfy condition (9), that is, the initial parameters fall within the feasible region;

[0155] S22, initializing the iteration round i = 0;

[0156] S31, initializing the step size t = 1;

[0157] S32, calculating the loss function Loss(β i ; ξ * ; γ) according to the model parameters and the observed path;

[0158] S4, performing gradient calculation according to the loss function and the L-BFGS algorithm to obtain the update direction d i ;

[0159] S5, performing line search (here taking bisection method as an example) according to the gradient and the parameters to obtain a step size that satisfies the condition. The specific method is that if ρ(M(β i +t·d i ))≥1, then update t = t / 2, until ρ(M(β i +t·d i ))<1;

[0160] S6, updating the parameters β i+1 = β i +t·d i according to the final step size;

[0161] S7, judging whether the convergence condition is reached. If the convergence is reached, return β i+1 , otherwise return S22 to update i = i + 1;

[0162] S8, estimating the vehicle path by using the estimated model parameters. Specifically, given the origin and destination od, the state transition probability p d (a|k) calculated according to formula (7), and N paths sampled from the origin o to the destination d, the final path distribution is obtained, that is, the vehicle path estimation result.

[0163] (II) Parameter estimation method (M2) based on nonlinear generalized utility function RL

[0164] For the modeling of nonlinear generalized utility function, according to the universal approximation theorem of neural network for any nonlinear continuous function, the present application adopts the way based on residual neural network.

[0165] Neural network layer f (l) Definition of (h): for an input vector h, the neural network layer uses linear weights W (l) , b (l) to transform h, and then uses an activation function σ (l) to output the final result vector, as formula (13).

[0166]

[0167] Definition of residual neural network: for an input vector X (same meaning as X in formula 9), first transform it through the input layer, as formula (14), then through the intermediate layer, as formula (15), and finally through the output layer transformation, as formula (16). Note that the forward propagation of the intermediate layer will transform the input vector again after adding the input vector itself. The final output is the scalar utility v θ (a|k).

[0168] h (in) = f (in) (X) (14)

[0169] h (1) = f (1) (h (in) )+h (in) ,...,h (L) = f (L) (h (L-1) )+h (L-1) (15)

[0170] v θ (a|k) = f (out) (h (L) ) (16)

[0171] Under the nonlinear utility function v θ (a|k), the construction of the loss function is almost identical to the linear function v(a|k), only the parameter is changed from β to θ, and the log-likelihood formula is shown in formula (17), and (v(a|k) is replaced by v θ (a|k)) is calculated by formula (7). The total loss function is shown in formula (18).

[0172]

[0173]

[0174] The parameters θ that need to be estimated by the nonlinear residual neural network include The algorithm involved is back propagation.

[0175] The update of θ at each step in the parameter estimation process involves the calculation of the gradient of Loss(θ; ξ * ; γ) with respect to the parameters θ, and the algorithm involved is back propagation. The automatic differentiation function of tools or platforms such as PyTorch and MATLAB can be used to calculate the gradient d' of the parameters θ, and the existing L-BFGS algorithm can be used to modify the gradient d' to the second order to speed up the convergence speed, and finally obtain the update direction d.

[0176] S1, obtaining vehicle trajectory data of urban road network;

[0177] S21, initializing model parameters θ 0 to ensure that it can fall within the feasible region. Specifically, W (in) ,b (in) ,W (l) ,b (l) are randomly initialized (cannot be initialized to 0, otherwise the gradient cannot be updated), and W (out) is set to 0, and b (out) is set to a small negative number, for example, b (out) =-10. At this time, the elements on the exponential adjacency utility matrix M will be positive numbers close to 0, and obviously satisfy the sufficient condition (8). According to the relationship between condition (8) and condition (9), it is obvious that condition (9) is also satisfied, that is, the initial parameters fall within the feasible region.

[0178] S22, initializing the iteration round i = 0;

[0179] S31, initializing the step size t = 1;

[0180] S32, calculating the loss function Loss(θ i ; ξ * ; γ) according to the model parameters and the observed path;

[0181] S4, calculating the gradient according to the loss function and the L-BFGS algorithm to obtain the update direction d i ;

[0182] S5, performing line search according to the gradient and the parameters (here, taking bisection as an example), obtaining the step size that satisfies the condition, and the specific method is that if ρ(M(θ i +t·d i ))≥1, then update t = t / 2, until ρ(M(θ i +t·d i ))<1

[0183] S6, update parameter θ according to final step i+1 = θ i + t d i ;

[0184] S7, judge whether to reach convergence condition, if yes, return θ i+1 , otherwise, return S22, update i = i + 1;

[0185] S8, estimate vehicle path by using estimated model parameter, specifically, given origin and destination od, calculate state transition probability p d (a|k) according to formula (7), sample N paths from origin o to destination d, and obtain final path distribution, i.e. vehicle path estimation result.

[0186] Although the preferred embodiments of the present application have been described, those skilled in the art will be able to make additional changes and modifications to these embodiments once they have learned the basic inventive concept. Therefore, the appended claims are intended to be interpreted as including all the preferred embodiments and all the changes and modifications falling within the scope of the present application.

[0187] Obviously, those skilled in the art can make various modifications and variations to the present application without departing from the spirit and scope of the present application. Thus, if these modifications and variations of the present application fall within the scope of the claims of the present application and their equivalent technologies, the present application also intends to include these modifications and variations.

Claims

1.A method for vehicle path estimation of urban road network based on deep recursive Logit model, characterized in that, The method comprises the following steps: Step 1, obtaining trajectory data of vehicles on a city road network; Step 2, initializing an iteration round and parameters of an utility function in a deep recursive Logit model, wherein the initial parameters are located in a feasible region, and the utility function is a linear utility function or a nonlinear utility function; Step 3, calculating a loss function based on the trajectory data and the parameters; Step 4, performing gradient calculation according to the loss function and an L-BFGS algorithm to obtain an update direction; Step 5, calculating a step size of a next round according to the update direction and the parameters, and further updating the parameters to obtain updated parameters; Step 6, judging whether a convergence condition is reached, if yes, outputting the updated parameters as final optimal parameters, if not, returning to Step 2 for iterative calculation according to the step size of the next round until the convergence condition is reached; Step 7, estimating a vehicle path on the city road network based on the optimal parameters in the deep recursive Logit model to obtain an estimation result; When the linear utility function is used, the step of obtaining the updated parameters comprises: performing line search according to the update direction and the parameters to obtain a step size of a next round that meets a condition, and the line search process comprises: If p(M(β i +t·d i ))≥1, update t=t / 2 until p(M(β i +t·d i ))<1, and get the final step size of the next round; updating the parameter according to the step size and the update direction of the next round, to obtain an updated parameter β i+1 is expressed as: β i+1 = β i + t · d i where β i+1 is the updated parameter, β i is the parameter of the i-th iteration, ρ(·) denotes the spectral radius of a matrix, t is the step size, d i is the update direction of the i-th iteration; When the nonlinear utility function is used, the step of obtaining the updated parameters comprises: performing line search according to the update direction and the parameters to obtain a step size of a next round that meets a condition, and the line search process comprises: If p(M(0 i +t·d i ))≥1, update t=t / 2 until p(M(0 i +t·d i ))<1, and get the final step size of the next round. updating the parameter according to the step size and the update direction of the next round, to obtain an updated parameter θ i+1 is represented as: θ i+1 = θ i + t · d i Where θ i+1 is the updated parameter, indicating the parameter of the i+1th round, θ i The parameters of the i-th round, ρ(·) represents the spectral radius of the matrix, t is the step size, d i is the update direction of the i-th round; The step of obtaining the estimation result comprises: given a starting point o and a terminal point d, calculating a state transition probability of the deep recursive Logit model based on the optimal parameters to estimate a vehicle path result between the starting point and the terminal point; wherein the construction step of the state transition probability comprises: in a road section k, setting a next state a in a downstream adjacent state set A(k) to be selected with a probability, constructing a Bellman equation, and the expression is: where V d (k) is the expected utility downstream of state k to d, V d (k) is the expected utility downstream of state a to d, μ is the parameter coefficient of the extreme Gumbel distribution, and V d (d) is the expected utility downstream of state d to d, and is set to 0 by default, is the expected value, and ε(a|k) is the error component of the immediate utility v ′ (a|k) is the deterministic component of the immediate utility v ′ (a|k), i.e., the utility function, including linear utility functions and nonlinear utility functions, k is the state, indicating that the vehicle is on a certain road segment k, and a is the adjacent downstream state, indicating the road segment a adjacent to the road segment k. setting ε(a|k) to follow an extreme Gumbel distribution with parameters (0, μ), and the expression is: ε(a│k)~Gumbel(0,μ)(2) according to the equations (1) and (2), obtaining: Let The elements of the exponential adjacency utility matrix M We obtain: where δ ka is an element of the adjacency matrix δ, is an index of the downstream expected utility of states a through d; setting all states k to be able to reach the terminal point d with any path and any number of steps, and rewriting the equation (4) as: z d = (δ Θ M)z d +b d (5) Where b d is a unit vector, z d is the exponential vector of downstream expected utilities for all states to d transforming the equation (5) to obtain: z d = (I - δ ⊙ M) -1 b d (6) in the equation, I is a unit vector; Set z d There is a unique non-negative solution, and the state transition probability is obtained by solving equation (6), and the expression is: where p d (a|k) is the state transition probability from k to a. 2.The urban road network vehicle path estimation method based on deep recursive Logit model according to claim 1, wherein, the initial parameters located in the feasible region need to meet the following condition: ρ(M)<1 in the equation, M is an exponential adjacent utility matrix, which is a variable related to the parameters, and ρ(·) represents the spectral radius of a matrix. 3.The urban road network vehicle path estimation method based on deep recursive Logit model according to claim 1, characterized in that, When the linear utility function is used, the construction process of the loss function comprises: defining a linear utility function v(a|k) and an exponential adjacent utility matrix M, wherein M is a variable related to the parameters β, and is expressed as M(β), and the linear utility function v(a|k) is expressed as: v(a|k) = β0+ β1X1+ β b X b +…+β |B| X |B| = β T X where k is a state, indicating that the vehicle is in a certain road segment k, a is an adjacent downstream state, indicating the road segment adjacent to road segment k, β0, β1, β b , …, β |B| are parameters, indicating the influence weight of different attributes on utility, X1, X b , …, X |B| are attribute values of the selection a, indicating road length, road capacity, M indicates that there is an upstream and downstream adjacent relationship between state k and state a, and the elements of M are M ka , indicating the utility value from state k to state a, v(a|k) indicates the utility value of selecting a in state k; According to the trajectory data, a log-likelihood objective function LL(β; ξ * ) is constructed to estimate the parameters by maximizing LL(β; ξ * ), wherein the log-likelihood objective function LL(β; ξ * ) is expressed as: wherein ξ * is trajectory data, N od is the number of observed paths between origin and destination od, and T is the maximum number of road segments of each path, is the state transition probability from k t to k t+1 . The sufficient and necessary condition ρ(M(β)) < 1 is introduced, combined with the log-likelihood objective function LL(β; ξ * ), to construct the final loss function Loss(β; ξ * ; γ) to estimate the parameters by minimizing Loss(β; ξ * ; γ), wherein the expression of the loss function Loss(β; ξ * ; γ) is: in the equation, ρ(·) represents the spectral radius of a matrix, and γ is a weight. 4.The urban road network vehicle path estimation method based on deep recursive Logit model according to claim 3, wherein, When the linear utility function is used, the step of obtaining the update direction comprises: based on the loss function, obtaining according to the chain rule of partial derivatives: where Loss is a loss function, and β is a parameter, is the state transition probability, v(a|k) is a linear utility function, k is the state, indicating that the vehicle is on a certain road segment k, and a is the adjacent downstream state; performing differential calculation on the equation (1) to obtain the gradient d' of the parameters β; performing second-order correction on the gradient d' by using an L-BFGS algorithm to obtain an update direction d. 5.The urban road network vehicle path estimation method based on deep recursive Logit model according to claim 1, wherein, The nonlinear utility function is constructed by using a residual neural network, and specific construction steps include: defining a network layer f of a residual neural network (l) (h): for an input vector h of the neural network layer, using linear weights W (l) , b (l) transforming h and utilizing an activation function σ (l) outputting a final vector result, the neural network layer f (l) (h) is expressed as: f (l) (h) = σ (l) (W (l) h+b (l) ) In the formula, l is the lth network layer; defining a residual neural network: according to the network layer f (l) (h) constructing a residual neural network comprising an input layer, an intermediate layer and an output layer; constructing a nonlinear utility function: for an input vector X of the residual neural network, sequentially transforming through an input layer, an intermediate layer and an output layer, and finally taking a scalar utility function output by the output layer as the nonlinear utility function v θ (a|k), the nonlinear utility function v θ (a|k) is represented as: v θ (a|k) = f (out) (h (L) ) The transformation expression of the input layer is: h (in) = f (in) (X) The transformation expression of the intermediate layer is: h (1) = f (1) (h (in) )+ h (in) ,..., h (L) = f (L) (h (L-1) )+ h (L-1) where θ = {W (in) ,b (in) ,W (l) ,b (l) ,W (out) ,b (out)} are parameters, W (in) ,b (in) ,W (l) ,b (l) ,W (out) ,b (out) are input layer linear weights, input layer linear bias, middle layer linear weights, middle layer linear bias, output layer linear weights, output layer linear bias, respectively, k is a state, indicating that the vehicle is in a certain road section k, a is an adjacent downstream state, indicating the road section a adjacent to the road section k, f (out) (h (L) ) is the output vector of the output layer, L is the total number of network layers, f (in) (X) is the calculation result of the input layer, h (in) is the calculation result of the input layer, f (1) (h (in) ) is the calculation result of the first layer middle layer, h (1) is the calculation result of the first layer middle layer, and the input vector X represents the attribute vector in the nonlinear utility function. 6.The urban road network vehicle path estimation method based on deep recursive Logit model according to claim 5, wherein, When the nonlinear utility function is used, the step of obtaining the update direction includes: Based on the loss function, the residual neural network is back propagated, and further differential calculation is performed to obtain the gradient d' of the parameter θ; The L-BFGS algorithm is used to perform second-order correction on the gradient d' to obtain the update direction d. 7.The urban road network vehicle path estimation method based on deep recursive Logit model according to claim 1, wherein, When the nonlinear utility function is used, the construction process of the loss function includes: An exponential adjacency utility matrix M is defined, wherein M is a variable related to the parameter θ, and is expressed as M(θ); According to the trajectory data, a log-likelihood objective function LL(0; 5 * ) is constructed to estimate the parameters by maximizing LL(0; 5 * ), wherein the log-likelihood objective function LL(0; 5 * ) is expressed as: wherein ξ * is trajectory data, N od is the number of observed paths between origin and destination od, and T is the maximum number of road segments of each path, is the state transition probability from k t to k t+1 . A sufficient and necessary condition ρ(M(θ)) < 1 is introduced, combined with the log-likelihood objective function LL(θ; ξ * ), to construct a final loss function Loss(θ; ξ * ; γ) to estimate the parameters by minimizing Loss(θ; ξ * ; γ), where the expression of the loss function Loss(θ; ξ * ; γ) is: In the formula, ρ(·) represents the spectral radius of the matrix, and γ is a weight.

Images