A slope compensation acceleration estimation method based on trajectory data

Abstract

The present invention discloses a slope-compensated acceleration estimation method based on trajectory data, comprising the following steps: 1. obtaining trajectory data of a vehicle traveling on a slope and a horizontal section; 2. calibrating the vehicle's free flow speed using the trajectory data of the horizontal section; 3. analyzing the slope trajectory data to construct a slope acceleration model; 4. assuming that the expected acceleration of the horizontal section and the compensated acceleration of the slope conform to a normal distribution, according to the acceleration model, obtaining the probability density of the observed acceleration, the posterior probability of the compensated acceleration, and the joint probability distribution of the two; 5. Based on the joint probability distribution, constructing a compensated acceleration estimation model using an expectation-maximization algorithm and performing iterations to obtain the mean and variance of the expected acceleration of the horizontal section and the mean and variance of the compensated acceleration of the slope. The present invention can identify the additional compensated acceleration given to the vehicle by the driver on a slope, thereby better explaining the impact of driving behavior on road capacity.

Description

Technical Field

[0001] The present invention belongs to the field of intelligent transportation technology, and in particular to a slope compensation acceleration estimation method based on trajectory data. Background Art

[0002] Slopes affect the speed of vehicles going up or downhill and are a common traffic bottleneck. Typically, drivers adjust the acceleration or braking force of the vehicle by pressing the accelerator or brake pedal to compensate for the effects of gravity. Studies have found that drivers tend to overcome half of the effect of gravity on the slope, while truck drivers only compensate for 5% of the loss. During this process, there will be a certain fluctuation in the speed of vehicles on the slope, which reduces the capacity. When the traffic demand is large enough, this fluctuation will generate shock waves in the traffic flow that propagate upstream, causing traffic congestion on the slope. Therefore, the compensation behavior of drivers on slopes is a key factor in determining the formation mechanism of traffic congestion, capacity and instability.

[0003] However, existing research has not addressed how drivers compensate for the effects of gravity on slopes, and in particular, how this compensation behavior is affected by slope characteristics. Therefore, in practice, this can only be estimated based on historical data and road design experience. A major challenge currently is accurately modeling driver behavior on slopes, and directly measuring this missing data using equipment is difficult. Summary of the Invention

[0004] In order to address the shortcomings of the above-mentioned existing technologies, the present invention proposes a slope compensation acceleration estimation method based on trajectory data, in order to quantify driving behavior based on the measured trajectory and explore the additional compensatory acceleration given to the vehicle by the driver on the slope, thereby better explaining the impact of driving behavior on road capacity.

[0005] In order to achieve the above-mentioned object, the present invention adopts the following technical solutions:

[0006] The present invention provides a method for estimating slope-compensated acceleration based on trajectory data, which comprises the following steps:

[0007] Step 1: Obtain the climbing trajectory data of the vehicle starting from the bottom of the slope and traveling to the top of the slope, as well as the trajectory data of the vehicle traveling on the horizontal road section;

[0008] Step 2: calibrate the vehicle free flow speed using the trajectory data of the horizontal section to obtain the vehicle free flow speed on the horizontal section;

[0009] Step 3: Analyze the climbing trajectory data to obtain the vehicle observed acceleration on the slope, and use it to build an acceleration model for the slope;

[0010] Step 4: Assuming that the expected acceleration on the horizontal road section and the compensated acceleration on the slope conform to the normal distribution, according to the acceleration model, the probability density of the vehicle observed acceleration, the posterior probability of the compensated acceleration, and the joint probability distribution of the two are obtained;

[0011] Step 5: Based on the joint probability distribution, the expectation maximization algorithm is used to construct a compensation acceleration estimation model and iterate to obtain the mean and variance of the expected acceleration on the horizontal section and the mean and variance of the compensation acceleration on the slope.

[0012] The slope-compensated acceleration estimation method based on trajectory data according to the present invention is also characterized in that step 2 includes:

[0013] Step 2.1: Use formula (1) to construct the acceleration model of the vehicle on the horizontal road section:

[0014] (1)

[0015] In formula (1), are the parameters of the acceleration model of the horizontal section; is the free flow speed, is the observed speed of the vehicle on the horizontal road section; is the expected acceleration of the horizontal section;

[0016] Step 2.2: Based on the observed speed of the vehicle in the trajectory data of the horizontal section and expected acceleration , the least squares method is used to fit the acceleration model of the horizontal section to obtain the free flow speed of the horizontal section .

[0017] Furthermore, the step 3 includes:

[0018] Step 3.1, use formula (2) to construct the acceleration balance equation of the slope;

[0019] (2)

[0020] In formula (2), is the compensation acceleration of the slope, is the observed acceleration of the vehicle on the slope, is the acceleration due to gravity, is the slope of the slope;

[0021] Step 3.2: Use formula (3) to construct the acceleration balance model of the slope;

[0022] (3)

[0023] In formula (3), is the observed speed of the slope.

[0024] Furthermore, the step 4 includes:

[0025] Step 4.1: Assume that the compensation acceleration of the slope obeys the normal distribution at different time steps, that is, ,in, The time steps Compensated acceleration on downhill slope The mean and variance of , T is the time step of trajectory data;

[0026] Step 4.2: Calculate the time step by formula (4) Next Compensation acceleration for slopes in the trajectory The probability density of :

[0027] (4)

[0028] Step 4.3: Assume that the expected acceleration of the horizontal section at different time steps follows a normal distribution, that is, ,in, and At time steps Expected acceleration on the next level section The mean and variance of

[0029] Step 4.4: Calculate the time step Next Observed acceleration of the slope in the trajectory The probability density of :

[0030] (5)

[0031] In formula (5), For the time step Next Observed acceleration of the slope in the trajectory The corresponding observation speed is , is the number of trajectories;

[0032] Step 4.5: According to Bayesian theory, calculate the time step Next Observed acceleration of the slope in the trajectory and compensated acceleration The joint distribution probability of ;

[0033] (6)

[0034] Step 4.6: Calculate the time step by equation (7) Next Compensation acceleration for slopes in the trajectory The conditional probability of ;

[0035] (7)

[0036] In formula (7), Indicates compensation acceleration No. The actual value, , for The number of random values ​​​​taken according to the distribution.

[0037] Furthermore, the step 5 includes:

[0038] Step 5.1, define the maximum number of iterations as , parameter iteration error is ;

[0039] Step 5.2, let The value range is [0, ];

[0040] Initialize the current number of iterations , define The parameter set for the iteration is ,

[0041] in, Indicates the The parameters of the acceleration model of the horizontal section under iterations, Indicates the The variance of the expected acceleration of the horizontal section under iterations, Indicates the The next time step Compensation acceleration of the slope The mean of Indicates the The next time step The slope of the compensation acceleration variance;

[0042] Step 5.2: Construct the first The objective function under the iteration :

[0043] (8)

[0044] In formula (8), Indicates the Compensation acceleration under iteration The conditional probability of

[0045] Step 5.3: , in [0, ] The compensation acceleration is obtained by equations (4) to (6): Next iteration The conditional probability of , calculate the observed acceleration through formula (7) and compensated acceleration In the The joint distribution probability under the iteration ;

[0046] Step 5.4: Maximize the objective function through formula (9) ;

[0047] (9)

[0048] Step 5.5: Update the first The parameter set for the iteration ;

[0049]

[0050] (10)

[0051] (11)

[0052] (12)

[0053] (13)

[0054] Step 5.5, judgment and Are they both true? If true, then output Next iteration As the final estimation result; if it is not established, Assign to Then return to step 5.3 and execute them in sequence.

[0055] The electronic device of the present invention includes a memory and a processor, wherein the memory is used to store a program that supports the processor to execute the slope compensation acceleration estimation method, and the processor is configured to execute the program stored in the memory.

[0056] The present invention provides a computer-readable storage medium having a computer program stored thereon, wherein the computer program executes the steps of the slope compensation acceleration estimation method when the computer program is executed by a processor.

[0057] Compared with the prior art, the present invention has the following beneficial effects:

[0058] 1. The present invention quantifies the driver's driving behavior on the slope as a compensated acceleration, and splits the actual observed speed of the vehicle on the slope into the expected speed on the horizontal section and the compensated acceleration of the slope, thereby accurately modeling the acceleration model of the vehicle on the slope.

[0059] 2. The present invention constructs the probability distribution of the expected acceleration and slope compensation acceleration on horizontal sections through a Bayesian network model, which can obtain the probability density of the slope observation speed, thereby accurately estimating the driver's compensation acceleration on the slope, overcoming the problem of difficulty in directly measuring missing data. BRIEF DESCRIPTION OF THE DRAWINGS

[0060] Figure 1 This is a flow chart of the slope compensation acceleration estimation of the present invention. DETAILED DESCRIPTION

[0061] In this embodiment, a slope compensation acceleration estimation method based on trajectory data is to use Figure 1 The method shown, taking part of Shanghai Road in Hefei City, Anhui Province as an example, is carried out in the following steps:

[0062] Step 1: Obtain the climbing trajectory data of the vehicle starting from the bottom of the slope and traveling to the top of the slope, as well as the trajectory data of the vehicle traveling on the horizontal road section;

[0063] Step 2: calibrate the vehicle free flow speed using the trajectory data of the horizontal section to obtain the vehicle free flow speed on the horizontal section;

[0064] Step 2.1: Use formula (1) to construct the acceleration model of the vehicle on the horizontal road section:

[0065] (1)

[0066] In formula (1), are the parameters of the acceleration model of the horizontal section; is the free flow speed, is the observed speed of the vehicle on the horizontal road section; is the expected acceleration of the horizontal section;

[0067] Step 2.2: Based on the observed speed of the vehicle in the trajectory data of the horizontal section and expected acceleration , the least squares method is used to fit the acceleration model of the horizontal section to obtain the free flow speed of the horizontal section .

[0068] Step 3: Analyze the climbing trajectory data to obtain the vehicle observed acceleration on the slope, and use it to build an acceleration model for the slope;

[0069] Step 3.1, use formula (2) to construct the acceleration balance equation of the slope;

[0070] (2)

[0071] In formula (2), is the compensation acceleration of the slope, is the observed acceleration of the vehicle on the slope, is the acceleration due to gravity, is the slope of the slope;

[0072] Step 3.2: Use formula (3) to construct the acceleration balance model of the slope;

[0073] (3)

[0074] In formula (3), is the observed speed of the slope.

[0075] Step 4: Assuming that the expected acceleration on the horizontal road section and the compensated acceleration on the slope conform to the normal distribution, according to the acceleration model, the probability density of the vehicle observed acceleration, the posterior probability of the compensated acceleration, and the joint probability distribution of the two are obtained;

[0076] Step 4.1: Assume that the compensation acceleration of the slope obeys the normal distribution at different time steps, that is, ,in, The time steps Compensated acceleration on downhill slope The mean and variance of , T is the time step of trajectory data, and the value of T is 800.

[0077] Step 4.2: Calculate the time step by formula (4) Next Compensation acceleration for slopes in the trajectory The probability density of :

[0078] (4)

[0079] Step 4.3: Assume that the expected acceleration of the horizontal section at different time steps follows a normal distribution, that is, ,in, and At time steps Expected acceleration on the next level section The mean and variance of It is a global unified variable.

[0080] Step 4.4: Calculate the time step Next Observed acceleration of the slope in the trajectory The probability density of :

[0081] (5)

[0082] In formula (5), For the time step Next Observed acceleration of the slope in the trajectory The corresponding observation speed is , is the number of trajectories, according to the measured trajectory data, The value is 100.

[0083] Step 4.5: According to Bayesian theory, calculate the time step Next Observed acceleration of the slope in the trajectory and compensated acceleration The joint distribution probability of ;

[0084] (6)

[0085] Step 4.6: Calculate the time step by equation (7) Next Compensation acceleration for slopes in the trajectory The conditional probability of ;

[0086] (7)

[0087] In formula (7), Indicates compensation acceleration No. The actual value, , for The number of random values ​​​​taken according to the distribution, The value is 20.

[0088] Step 5: Based on the joint probability distribution, the expectation maximization algorithm is used to construct a compensation acceleration estimation model and iterate to obtain the mean and variance of the expected acceleration on the horizontal section and the mean and variance of the compensation acceleration on the slope.

[0089] Step 5.1, define the maximum number of iterations as , parameter iteration error is ;

[0090] Step 5.2, let The value range is [0, ];

[0091] Initialize the current number of iterations , define The parameter set for the iteration is ,

[0092] in, Indicates the The parameters of the acceleration model of the horizontal section under iterations, Indicates the The variance of the expected acceleration of the horizontal section under iterations, Indicates the The next time step Compensation acceleration of the slope The mean of Indicates the The next time step The slope of the compensation acceleration variance.

[0093] Step 5.2: Construct the first The objective function under the iteration :

[0094] (8)

[0095] In formula (8), Indicates the Compensation acceleration under iteration The conditional probability of

[0096] Step 5.3: , in [0, ] The compensation acceleration is obtained by equations (4) to (6): Next iteration The conditional probability of , calculate the observed acceleration through formula (7) and compensated acceleration In the The joint distribution probability under the iteration .

[0097] Step 5.4: Maximize the objective function through formula (9) ;

[0098] (9)

[0099] Step 5.5: Update the first The parameter set for the iteration ;

[0100]

[0101] (10)

[0102] (11)

[0103] (12)

[0104] (13)

[0105] Step 5.5, judgment and Are they both true? If true, then output Next iteration As the final estimation result; if it is not established, Assign to Then return to step 5.3 and execute them in sequence.

[0106] In this embodiment, an electronic device includes a memory and a processor, wherein the memory is used to store a program that supports the processor to execute the above method, and the processor is configured to execute the program stored in the memory.

[0107] In this embodiment, a computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the steps of the above method are executed.

Claims

1. A slope-compensated acceleration estimation method based on trajectory data, characterized in that: The following steps are involved: Step 1: Obtain the climbing trajectory data of the vehicle starting from the bottom of the slope and traveling to the top of the slope, as well as the trajectory data of the vehicle traveling on the horizontal road section; Step 2: calibrate the vehicle free flow speed using the trajectory data of the horizontal section to obtain the vehicle free flow speed on the horizontal section; Step 3: Analyze the climbing trajectory data to obtain the vehicle observed acceleration on the slope, and use it to build an acceleration model for the slope; Step 4: Assuming that the expected acceleration on the horizontal road section and the compensated acceleration on the slope conform to the normal distribution, according to the acceleration model, the probability density of the vehicle observed acceleration, the posterior probability of the compensated acceleration, and the joint probability distribution of the two are obtained; Step 5: Based on the joint probability distribution, the expectation maximization algorithm is used to construct a compensation acceleration estimation model and iterate to obtain the mean and variance of the expected acceleration on the horizontal section and the mean and variance of the compensation acceleration on the slope.

2. The slope-compensated acceleration estimation method based on trajectory data according to claim 1, characterized in that: The step 2 includes: Step 2.1: Use formula (1) to construct the acceleration model of the vehicle on the horizontal road section: (1) In formula (1), are the parameters of the acceleration model of the horizontal section; is the free flow speed, is the observed speed of the vehicle on the horizontal road section; is the expected acceleration of the horizontal section; Step 2.2: Based on the observed speed of the vehicle in the trajectory data of the horizontal section and expected acceleration , the least squares method is used to fit the acceleration model of the horizontal section to obtain the free flow speed of the horizontal section .

3. The slope-compensated acceleration estimation method based on trajectory data according to claim 2, characterized in that: The step 3 includes: Step 3.1, use formula (2) to construct the acceleration balance equation of the slope; (2) In formula (2), is the compensation acceleration of the slope, is the observed acceleration of the vehicle on the slope, is the acceleration due to gravity, is the slope of the slope; Step 3.2: Use formula (3) to construct the acceleration balance model of the slope; (3) In formula (3), is the observed speed of the slope.

4. The slope-compensated acceleration estimation method based on trajectory data according to claim 3, characterized in that: The step 4 comprises: Step 4.1: Assume that the compensation acceleration of the slope obeys the normal distribution at different time steps, that is, ,in, The time steps Compensated acceleration on downhill slope The mean and variance of , T is the time step of trajectory data; Step 4.2: Calculate the time step by formula (4) Next Compensation acceleration for slopes in the trajectory The probability density of : (4) Step 4.3: Assume that the expected acceleration of the horizontal section at different time steps follows a normal distribution, that is, ,in, and At time steps Expected acceleration on the next level section The mean and variance of Step 4.4: Calculate the time step Next Observed acceleration of the slope in the trajectory The probability density of : (5) In formula (5), For the time step Next Observed acceleration of the slope in the trajectory The corresponding observation speed is , is the number of trajectories; Step 4.5: According to Bayesian theory, calculate the time step Next Observed acceleration of the slope in the trajectory and compensated acceleration The joint distribution probability of ; (6) Step 4.6: Calculate the time step by equation (7) Next Compensation acceleration for slopes in the trajectory The conditional probability of ; (7) In formula (7), Indicates compensation acceleration No. The actual value, , for The number of random values ​​​​taken according to the distribution.

5. The slope-compensated acceleration estimation method based on trajectory data according to claim 4, characterized in that: The step 5 comprises: Step 5.1, define the maximum number of iterations as , parameter iteration error is ; Step 5.2, let The value range is [0, ]; Initialize the current number of iterations , define The parameter set for the iteration is , in, Indicates the The parameters of the acceleration model of the horizontal section under iterations, Indicates the The variance of the expected acceleration of the horizontal section under iterations, Indicates the The next time step Compensation acceleration of the slope The mean of Indicates the The next time step The slope of the compensation acceleration variance; Step 5.2: Construct the first The objective function under the iteration : (8) In formula (8), Indicates the Compensation acceleration under iteration The conditional probability of Step 5.3: , in [0, ] The compensation acceleration is obtained by equations (4) to (6): Next iteration The conditional probability of , calculate the observed acceleration through formula (7) and compensated acceleration In the The joint distribution probability under the iteration ; Step 5.4: Maximize the objective function through formula (9) ; (9) Step 5.5: Update the first The parameter set for the iteration ; (10) (11) (12) (13) Step 5.5, judgment and Are they both true? If true, then output Next iteration As the final estimation result; if it is not established, Assign to Then return to step 5.3 and execute them in sequence.

6. An electronic device comprising a memory and a processor, characterized in that: The memory is used to store a program that supports the processor to execute the slope-compensated acceleration estimation method according to any one of claims 1 to 5, and the processor is configured to execute the program stored in the memory.

7. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the slope-compensated acceleration estimation method according to any one of claims 1 to 5 are executed.

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