Slope compensation acceleration estimation method based on trajectory data

Abstract

The invention discloses a slope compensation acceleration estimation method based on trajectory data. The slope compensation acceleration estimation method comprises the following steps: 1, acquiring trajectory data of a vehicle running on a slope and a horizontal road section; 2, calibrating the free flow speed of the vehicle by using the trajectory data of the horizontal road section; 3, analyzing the trajectory data of the slope, and constructing an acceleration model of the slope; 4, assuming that the expected acceleration of the horizontal road section and the compensation acceleration of the slope conform to normal distribution, and obtaining the probability density of the observation acceleration, the posterior probability of the compensation acceleration and the joint probability distribution of the two according to the acceleration model; and 5, according to the joint probability distribution, utilizing an expectation maximization algorithm to construct a compensation acceleration estimation model and carrying out iteration to obtain a mean value and a variance of the expectation acceleration of the horizontal road section and a mean value and a variance of the compensation acceleration of the slope. According to the method, the additional vehicle compensation acceleration given by the driver on the slope can be excavated, so that the influence of the driving behavior on the road traffic capacity can be better explained.

Description

Technical Field

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

[0002] Slopes affect the speed of vehicles going uphill or downhill and are common traffic bottlenecks. Typically, drivers adjust the acceleration or braking force of the vehicle by pressing the accelerator pedal 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. In the 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 does not involve how drivers compensate for the effects of gravity on slopes, especially how the compensation behavior is affected by slope characteristics. Therefore, in practice, it can only be speculated based on historical data and road design experience. The main problem at present is how to accurately model the driving behavior of drivers on slopes, and it is very difficult to directly measure the missing data through equipment. Summary of the invention

[0004] The present invention aims to solve the deficiencies of the above-mentioned prior art and proposes a slope compensation acceleration estimation method based on trajectory data, in order to quantify driving behavior according to the measured trajectory and explore the additional compensatory acceleration given to the vehicle by the driver on the slope, so as to better explain the impact of driving behavior on road traffic capacity.

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

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

[0007] Step 1, respectively obtaining the climbing trajectory data of the vehicle starting from the bottom of the slope and driving to the top of the slope and the trajectory data of the vehicle driving on the horizontal 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 observed acceleration of the vehicle on the slope, and use it to build an acceleration model of the slope;

[0010] Step 4: Assuming that the expected acceleration of the horizontal section and the compensation acceleration of 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 compensation acceleration and the joint probability distribution of the two are obtained;

[0011] Step 5: According to 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 of the horizontal section and the mean and variance of the compensation acceleration of the slope.

[0012] The slope compensation acceleration estimation method based on trajectory data described in the present invention is also characterized in that step 2 comprises:

[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 the expected acceleration , the least square 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 comprises:

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

[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, construct the acceleration balance model of the slope using formula (3);

[0022] (3)

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

[0024] Further, the step 4 comprises:

[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 Compensation 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 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 step 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 observed 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 ;

[0033] (6)

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

[0035] (7)

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

[0037] Further, the step 5 comprises:

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

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

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

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

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

[0043] (8)

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

[0045] Step 5.3: For , in [0, ] The compensation acceleration is obtained through equations (4) to (6): Next iteration The conditional probability , the observed acceleration is calculated by formula (7) and compensated acceleration In the The joint distribution probability under 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 true, Assign to Then return to step 5.3 and execute in sequence.

[0055] An 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, wherein a computer program is stored on the computer-readable storage medium, and 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 of the horizontal section and the compensated acceleration of the slope, so as to accurately model 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 of the horizontal section through the Bayesian network model, and can obtain the probability density of the slope observation speed, so as to accurately estimate 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 implementation case, 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, respectively obtaining the climbing trajectory data of the vehicle starting from the bottom of the slope and driving to the top of the slope and the trajectory data of the vehicle driving on the horizontal 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 the expected acceleration , the least square 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 observed acceleration of the vehicle on the slope, and use it to build an acceleration model of the slope;

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

[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, construct the acceleration balance model of the slope using formula (3);

[0073] (3)

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

[0075] Step 4: Assuming that the expected acceleration of the horizontal section and the compensation acceleration of 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 compensation 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 Compensation 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 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 step 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 observed 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 ;

[0084] (6)

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

[0086] (7)

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

[0088] Step 5: According to 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 of the horizontal section and the mean and variance of the compensation acceleration of the slope.

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

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

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

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

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

[0094] (8)

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

[0096] Step 5.3: For , in [0, ] The compensation acceleration is obtained through equations (4) to (6): Next iteration The conditional probability , the observed acceleration is calculated by formula (7) and compensated acceleration In the The joint distribution probability under 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 true, Assign to Then return to step 5.3 and execute 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 on the computer-readable storage medium, and the computer program executes the steps of the above method when executed by a processor.

Claims

1. A slope compensation acceleration estimation method based on trajectory data, characterized in that: The following steps are involved: Step 1, respectively obtaining the climbing trajectory data of the vehicle starting from the bottom of the slope and driving to the top of the slope and the trajectory data of the vehicle driving on the horizontal 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 observed acceleration of the vehicle on the slope, and use it to build an acceleration model of the slope; Step 4: Assuming that the expected acceleration of the horizontal section and the compensation acceleration of 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 compensation acceleration and the joint probability distribution of the two are obtained; Step 5: According to 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 of the horizontal section and the mean and variance of the compensation acceleration of the slope.

2. A slope compensation acceleration estimation method based on trajectory data according to claim 1, characterized in that: The step 2 comprises: 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 the expected acceleration , the least square 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 compensation acceleration estimation method based on trajectory data according to claim 2, characterized in that: The step 3 comprises: Step 3.1, construct the acceleration balance equation of the slope using equation (2); (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, construct the acceleration balance model of the slope using formula (3); (3) In formula (3), is the observed speed of the slope.

4. The slope compensation 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 Compensation acceleration on downhill slope The mean and variance of , T is the time step of trajectory data; Step 4.2: Calculate the time step 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 step 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 observed 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 ; (6) Step 4.6: Calculate the time step by equation (7) Next Compensation acceleration for slopes in the trajectory The conditional probability ; (7) In formula (7), Indicates the compensation acceleration No. The actual value, , for The number of random values ​​​​according to the distribution.

5. The slope compensation 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 , the parameter iteration error is ; Step 5.2: The value range is [0, ]; Initialize the current number of iterations , define The parameter set for the iteration is , in, Indicates The parameters of the acceleration model of the horizontal section in the iteration, Indicates The variance of the expected acceleration of the horizontal section under iterations, Indicates The next iteration time step Compensation of the slope acceleration The mean of Indicates The next iteration time step The variance of the slope-compensated acceleration; Step 5.2: Construct the first The objective function at the iteration : (8) In formula (8), Indicates Compensation acceleration at iteration The conditional probability of Step 5.3: For , in [0, ] The compensation acceleration is obtained through equations (4) to (6): Next iteration The conditional probability , the observed acceleration is calculated by formula (7) and compensated acceleration In the The joint distribution probability under 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 true, Assign to Then return to step 5.3 and execute 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 compensation 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 compensation acceleration estimation method according to any one of claims 1 to 5 are executed.

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