CN109190811B - Vehicle speed tracking method based on adaptive extended Kalman filtering - Google Patents

Vehicle speed tracking method based on adaptive extended Kalman filtering Download PDF

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CN109190811B
CN109190811B CN201810946898.XA CN201810946898A CN109190811B CN 109190811 B CN109190811 B CN 109190811B CN 201810946898 A CN201810946898 A CN 201810946898A CN 109190811 B CN109190811 B CN 109190811B
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钱丽萍
黄玉蘋
冯安琪
冯旭
吴远
黄亮
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Zhejiang University of Technology ZJUT
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Abstract

A vehicle speed tracking method based on adaptive extended Kalman filtering comprises the following steps: firstly, in an intelligent network traffic system, automatically identifying running vehicles and acquiring related data through a DSRC technology, so as to realize information interaction between a vehicle-mounted system and a roadside unit; secondly, for the collected relevant information, firstly, quantifying the azimuth difference between the roadside unit and the vehicle-mounted system through a quantification formula, secondly, predicting the acceleration through an autoregressive moving average method, and finally, performing speed prediction by using self-adaptive extended Kalman filtering; and finally, broadcasting the processed information to the roadside unit so as to facilitate the information interaction with the vehicle-mounted system next time. The invention provides a vehicle speed tracking method based on adaptive extended Kalman filtering.

Description

Vehicle speed tracking method based on adaptive extended Kalman filtering
Technical Field
The invention belongs to the field of traffic, and particularly relates to a vehicle speed tracking method based on adaptive extended Kalman filtering in an intelligent networked traffic system.
Background
China is the country with the most population in the world, the reform is open, along with the rapid development of the economy of China, the living standard of people is increasingly improved, private cars begin to enter each family, and the traveling of the family is facilitated well. However, the popularization and popularization of vehicles also make the urban traffic environment worsen day by day, and traffic phenomena such as unbalanced traffic flow, traffic congestion, rear collision, side collision and the like occur. Along with the weak infrastructure and the traffic network congestion, the number of road traffic accidents is increasing, and the high incidence of the traffic accidents is sounding an alarm to the whole society, so that the road traffic safety is greatly concerned. In recent years, although the road infrastructure and the traffic network are greatly improved in China, the number of traffic accidents and casualties are reduced, but the total number of accidents and the incidence rate are still high.
Compared with the traditional road traffic system, the intelligent internet traffic system is more prone to a dynamic system in which information interaction is carried out by people, roads, vehicles, road traffic facilities and the like. According to a large amount of statistical research in various countries, it is found that driver error is a main factor causing traffic accidents. Therefore, under the condition that the current road infrastructure can not be improved, the work of acquiring the state information of the vehicles in other lanes of the road, processing and broadcasting the state information to the current vehicle is not slow, so that a driver can better take corresponding remedial measures, and traffic accidents caused by errors of the driver are reduced.
Disclosure of Invention
The invention provides a vehicle speed tracking method based on adaptive extended Kalman filtering, aiming at overcoming the defects of low safety and high vehicle accident probability of the existing information transmission mode between vehicles.
The technical scheme adopted by the invention for solving the technical problems is as follows:
a vehicle speed tracking method based on adaptive extended Kalman filtering comprises the following steps:
1) in an intelligent network traffic system, a vehicle is automatically identified through a DSRC technology, relevant data are obtained, and information interaction between a vehicle-mounted system and a roadside unit is realized, wherein the information interaction comprises the following steps:
step 1.1: when a running vehicle enters the range covered by the directional antenna, the vehicle-mounted system and the roadside unit realize two-way communication through the DSRC technology, so that the two sides can simultaneously transmit information on the storage units of the vehicle-mounted system, wherein the information transmitted by the vehicle-mounted system comprises the current speed, the current position and the time stamp of the vehicle, and the information transmitted by the roadside unit comprises the predicted position of the vehicle on other lanes, the direction in which the vehicle is located, several lanes and the acceleration;
step 1.2: the roadside unit sends the acquired vehicle information to an edge cloud server to perform a series of operation operations;
2) the edge cloud server calculates an azimuth angle and performs corresponding quantization processing according to the azimuth difference between the roadside unit and the vehicle-mounted system, and quantizes the vehicle driving direction according to the position information, wherein the quantization process comprises the following steps:
step 2.1: converting the position information into digital information which is present at a viewing angle, wherein the actual bearing angle of the vehicle
Figure GDA0001842818520000021
The definition with respect to a roadside unit is:
Figure GDA0001842818520000022
Figure GDA0001842818520000031
here, the parameters are defined as follows:
Figure GDA0001842818520000032
an azimuth between the roadside unit and the onboard system at time k;
θk: converting the vehicle position at the moment k into an inverse trigonometric function of the azimuth angle;
σk: bearing error noise caused by signal reflection at time k;
(xk,yk): the current position of the vehicle at time k;
step 2.2: using the center of the crossroad as the origin of coordinates and the angle of opposite direction
Figure GDA0001842818520000033
And performing quantization processing to determine the direction of the vehicle, wherein the quantization formula is as follows:
Figure GDA0001842818520000034
here, the parameters are defined as follows:
bk: quantifying the direction of the intersection at time k;
q (·): a quantization function;
i: direction identification of the crossroad;
step 2.3: to specify the direction information, the lane of the direction is quantized, and the actual bearing angle is determined
Figure GDA0001842818520000035
Rename it to
Figure GDA0001842818520000036
It is recorded as:
Figure GDA0001842818520000037
Figure GDA0001842818520000038
here, the parameters are defined as follows:
Figure GDA0001842818520000041
an azimuth between the roadside unit and the onboard system at time k;
θk': at the moment k, converting the relative position of the vehicle and the roadside unit into an inverse trigonometric function of the azimuth angle;
(xi,yi): the fixed position of the roadside unit in the direction i;
step 2.4: and quantizing the direction of the vehicle for the second time according to the quantization formula to determine the lane of the vehicle.
Figure GDA0001842818520000042
Here, the parameters are defined as follows:
qt: the quantized direction of the lane at time t;
ji: the jth lane in direction i;
n: total number of lanes;
3) assuming that only the latest p +1 vehicle speeds are used for acceleration estimation, the pth acceleration calculation method is:
Figure GDA0001842818520000043
here, the parameters are defined as follows:
Δ τ: a sampling time interval;
Δ v: the difference in velocity between the next time and the previous time;
vk-p: the speed of the trolley at the time t-p;
τk-p: a timestamp of the trolley at the time t-p;
ak-p: the p-th acceleration value;
thereafter, vehicle acceleration prediction is performed by using an autoregressive moving average method according to the p acceleration values, wherein the prediction formula is as follows:
Figure GDA0001842818520000051
here, the parameters are defined as follows:
ak: acceleration of the trolley at the moment k;
p: the autoregressive order, namely the total acceleration;
q: moving average order, i.e., total number of slips;
Figure GDA0001842818520000052
undetermined coefficients other than zero;
ξk: an error term independent at time k;
4) under the condition that a driver does not change a lane, aiming at collected related information, the speed of a running vehicle is predicted by using an adaptive extended Kalman filtering algorithm, wherein a calculation formula of the speed is as follows:
xk＝xk-1+ak-1Δτ；
converting the above formula into a state equation and an observation equation by using a state space model, wherein the equations are as follows:
xk＝f(xk-1)+Wk-1； (1)
zk＝h(xk-1)+Vk-1； (2)
here, the parameters are defined as follows:
xk: the speed of the vehicle at time k;
f (·): a true velocity function, a non-linear function;
h (·): observing a velocity function, which is a non-linear function;
Wk-1: the systematic error at time k-1 follows a Gaussian distribution N (0, Q)k-1) Wherein Q isk-1＝cov(Wk-1)，Qk-1Is the process noise variance at time k-1;
Vk-1: the observed error at time k-1 follows a Gaussian distribution N (0, R)k-1) Wherein R isk-1＝cov(Vk-1)，Rk-1Is the process noise variance at time k-1;
zk: a state observation of the system at time k;
and then, predicting the vehicle speed by using an adaptive extended Kalman filter algorithm according to the state space model, wherein the vehicle position is updated by the following steps:
step 4.1: firstly, the nonlinear functions in the formulas (1) and (2) are subjected to linearization processing, the calculated amount and the model complexity are reduced, namely the nonlinear function f (x)k-1) And h (x)k-1) In filtering prediction value
Figure GDA0001842818520000061
The first order Taylor expansion is performed as follows:
Figure GDA0001842818520000062
Figure GDA0001842818520000063
Figure GDA0001842818520000064
Figure GDA0001842818520000065
here, the parameters are defined as follows:
Φk|k-1: a system state transition matrix from the time k-1 to the time k, wherein k | k-1 is from the time k-1 to the time k; (ii) a
Hk-1: an observation transfer matrix at the k-1 moment;
Δt1: higher order infinitesimal quantities with times higher than one;
Δt2: higher order infinitesimal quantities with times higher than one;
thereafter, ignoring the higher order infinitesimal quantities, and substituting equations (3) and (5) into equations (1) and (2), respectively, yields:
Figure GDA0001842818520000066
Figure GDA0001842818520000067
step 4.2: calculating a priori estimated value, assuming that the current state is at the k-1 moment, and predicting the value at the moment
Figure GDA0001842818520000068
And the true velocity function f (x)k-1) To get rid ofPriori estimated value x for predicting speed of trolley at moment kk|k-1Wherein, in the step (A),
Figure GDA0001842818520000071
k-1| k-1 refers to a value at the time k-1 is calculated based on the time k-1, and what is described when k | k-1 is not a subscript of the state transition matrix means that a value at the time k is calculated based on the time k-1;
step 4.3: calculating the prior error covariance from the posterior error covariance matrix P at time k-1k-1|k-1To predict the prior error covariance matrix P at the current momentk|k-1Wherein, in the step (A),
Figure GDA0001842818520000072
μkis an adaptive forgetting factor;
step 4.4: according to the prior error covariance matrix P at the current momentk|k-1Calculating the Kalman gain KkWherein, in the step (A),
Figure GDA0001842818520000073
step 4.5: according to prior estimated value x of k timek|k-1And the observed value zkObtaining the posterior estimated value x of k timek|kWherein x isk|k＝xk|k-1+Kk(zk-h(xk|k-1))；
Step 4.6: updating a posteriori error covariance matrix Pk|kProvision is made for calculating the prior error covariance matrix at time k +1, where Pk|k＝(I-KkHk)Pk|k-1I is an identity matrix;
step 4.7: k is updated to k +1, and the process returns to the step 4.2 to start a new round of calculation;
5) and finally, the cloud server broadcasts the processed information to the roadside unit so as to facilitate the information interaction with the vehicle-mounted system next time.
Further, in step 4.3, the calculation formula of the adaptive forgetting factor is as follows:
Figure GDA0001842818520000074
Gk＝d(Mk-Hk-1Qk-1Hk-1-Rk-1)；
ek＝zk-h(xk|k-1)；
Figure GDA0001842818520000081
Figure GDA0001842818520000082
Figure GDA0001842818520000083
here, the parameters are defined as follows:
max {. cndot ]: taking the maximum value after comparison;
α: the correction coefficient can forcibly improve the tracking performance of the filter;
Gk,ξk: intermediate derivation variables, no actual physical meaning;
ek: innovation, i.e. the difference between the true observed value and the estimated output value at time k;
u: maximum tolerable error;
d: when the innovation exceeds the maximum tolerable error, the value of the adaptive factor is reduced by reducing the weight factor, and finally the error is reduced;
Mk: innovation covariance matrix at time k.
Further, in the step 1), in the intelligent internet traffic system, the roadside units are installed on traffic lights of the crossroads and are attached with the cloud server and the directional antenna, wherein the emission angle of the routing antenna is 60 degrees, so that the roadside units can better perform information interaction with a vehicle-mounted system in a vehicle.
Furthermore, in step 1.2, the data in the server is cleared every other week in consideration of the limited storage capacity of the edge cloud server.
The technical conception of the invention is as follows: firstly, in an intelligent network traffic system, a vehicle is automatically identified through a DSRC technology, and relevant data are acquired, so that information interaction between a vehicle-mounted system and a roadside unit is realized. Secondly, quantifying the azimuth difference between the roadside unit and the vehicle-mounted system by using a quantification formula according to the collected related information; predicting the acceleration by using an autoregressive moving average method; and (5) carrying out speed prediction by using the adaptive extended Kalman filtering. And finally, broadcasting the processed information to the roadside unit so as to facilitate the information interaction with the vehicle-mounted system next time.
The invention has the advantages that 1, the lanes in which the current vehicle is positioned can be clearly known through quantifying the azimuth difference between the roadside unit and the vehicle-mounted system. 2. The prediction of the acceleration and the position is realized by combining an autoregressive moving average method and an adaptive extended Kalman filtering method, and the result is transmitted to the driver, so that the driver can make proper judgment and behavior according to the relevant information of the vehicle and own experience, and the occurrence rate of traffic accidents is effectively reduced.
Drawings
Fig. 1 is a schematic diagram of mobile internet traffic system information interaction.
Detailed Description
The present invention is described in further detail below with reference to the attached drawing figures.
Referring to fig. 1, a vehicle speed tracking method based on quantization adaptive extended kalman filtering, the invention is based on an information interaction model under DSRC technology communication (as shown in fig. 1). In an intelligent internet traffic system, firstly, azimuth differences between a roadside unit and a vehicle-mounted system are quantized through a quantization formula, secondly, acceleration is predicted through an autoregressive moving average method, and finally, position prediction is performed through adaptive extended Kalman filtering, wherein the vehicle speed tracking method comprises the following steps:
1) in an intelligent network traffic system, a vehicle is automatically identified through a DSRC technology, relevant data are obtained, and information interaction between a vehicle-mounted system and a roadside unit is realized, wherein the information interaction comprises the following steps:
step 1.1: when a running vehicle enters the range covered by the directional antenna, the vehicle-mounted system and the roadside unit realize two-way communication through the DSRC technology, so that the two sides can simultaneously transmit information on the storage units of the vehicle-mounted system, wherein the information transmitted by the vehicle-mounted system comprises the current speed, the current position and the time stamp of the vehicle, and the information transmitted by the roadside unit comprises the predicted position of the vehicle on other lanes, the direction in which the vehicle is located, several lanes and the acceleration;
step 1.2: the roadside unit sends the acquired vehicle information to the edge cloud server to perform a series of operation operations, and the data in the server is cleared every other week in consideration of the limited storage capacity of the edge cloud server;
2) the edge cloud server calculates an azimuth angle and performs corresponding quantization processing according to the azimuth difference between the roadside unit and the vehicle-mounted system, and quantizes the vehicle driving direction according to the position information, wherein the quantization process comprises the following steps:
step 2.1: converting the position information into digital information which is present at a viewing angle, wherein the actual bearing angle of the vehicle
Figure GDA0001842818520000101
The definition with respect to a roadside unit is:
Figure GDA0001842818520000102
Figure GDA0001842818520000103
here, the parameters are defined as follows:
Figure GDA0001842818520000104
an azimuth between the roadside unit and the onboard system at time k;
θk: converting the vehicle position at the moment k into an inverse trigonometric function of the azimuth angle;
σk: bearing error noise caused by signal reflection at time k;
(xk,yk): the current position of the vehicle at time k;
step 2.2: using the center of the crossroad as the origin of coordinates and the angle of opposite direction
Figure GDA0001842818520000111
And performing quantization processing to determine the direction of the vehicle, wherein the quantization formula is as follows:
Figure GDA0001842818520000112
here, the parameters are defined as follows:
bk: quantifying the direction of the intersection at time k;
q (·): a quantization function;
i: direction identification of the crossroad;
step 2.3: to specify the direction information, the lane of the direction is quantized, and the actual bearing angle is determined
Figure GDA0001842818520000113
Rename it to
Figure GDA0001842818520000114
It is recorded as:
Figure GDA0001842818520000115
Figure GDA0001842818520000116
here, the parameters are defined as follows:
Figure GDA0001842818520000117
an azimuth between the roadside unit and the onboard system at time k;
θk': at the moment k, converting the relative position of the vehicle and the roadside unit into an inverse trigonometric function of the azimuth angle;
(xi,yi): the fixed position of the roadside unit in the direction i;
step 2.4: according to the quantization formula, performing second quantization on the direction of the vehicle to determine the lane of the vehicle;
Figure GDA0001842818520000118
here, the parameters are defined as follows:
qt: the quantized direction of the lane at time t;
ji: the jth lane in direction i;
n: total number of lanes;
3) assuming that only the latest p +1 vehicle speeds are used for acceleration estimation, the pth acceleration calculation method is:
Figure GDA0001842818520000121
here, the parameters are defined as follows:
Δ τ: a sampling time interval;
Δ v: the difference in velocity between the next time and the previous time;
vk-p: the speed of the trolley at the time t-p;
τk-p: a timestamp of the trolley at the time t-p;
ak-p: the p-th acceleration value;
thereafter, vehicle acceleration prediction is performed by using an autoregressive moving average method according to the p acceleration values, wherein the prediction formula is as follows:
Figure GDA0001842818520000122
here, the parameters are defined as follows:
ak: acceleration of the trolley at the moment k;
p: the autoregressive order, namely the total acceleration;
q: moving average order, i.e., total number of slips;
Figure GDA0001842818520000123
undetermined coefficients other than zero;
ξk: an error term independent at time k;
4) under the condition that a driver does not change a lane, aiming at collected related information, the speed of a running vehicle is predicted by using an adaptive extended Kalman filtering algorithm, wherein a calculation formula of the speed is as follows:
xk＝xk-1+ak-1Δτ；
converting the above formula into a state equation and an observation equation by using a state space model, wherein the equations are as follows:
xk＝f(xk-1)+Wk-1； (1)
zk＝h(xk-1)+Vk-1； (2)
here, the parameters are defined as follows:
xk: the speed of the vehicle at time k;
f (·): a true velocity function, a non-linear function;
h (·): observing a velocity function, which is a non-linear function;
Wk-1: the systematic error at time k-1 follows a Gaussian distribution N (0, Q)k-1) Wherein Q isk-1＝cov(Wk-1)，Qk-1Is the process noise variance at time k-1;
Vk-1: the observed error at time k-1 follows a Gaussian distribution N (0, R)k-1) Wherein R isk-1＝cov(Vk-1)，Rk-1Is the process noise variance at time k-1;
zk: a state observation of the system at time k;
and then, predicting the vehicle speed by using an adaptive extended Kalman filter algorithm according to the state space model, wherein the vehicle position is updated by the following steps:
step 4.1: firstly, the nonlinear functions in the formulas (1) and (2) are subjected to linearization processing, the calculated amount and the model complexity are reduced, namely the nonlinear function f (x)k-1) And h (x)k-1) In filtering prediction value
Figure GDA0001842818520000131
The first order Taylor expansion is performed as follows:
Figure GDA0001842818520000132
Figure GDA0001842818520000133
Figure GDA0001842818520000134
Figure GDA0001842818520000141
here, the parameters are defined as follows:
Φk|k-1: a system state transition matrix from the time k-1 to the time k, wherein k | k-1 is from the time k-1 to the time k; (ii) a
Hk-1: an observation transfer matrix at the k-1 moment;
Δt1: higher order infinitesimal quantities with times higher than one;
Δt2: higher order infinitesimal quantities with times higher than one;
thereafter, ignoring the higher order infinitesimal quantities, and substituting equations (3) and (5) into equations (1) and (2), respectively, yields:
Figure GDA0001842818520000142
Figure GDA0001842818520000143
step 4.2: calculating a priori estimated value, assuming that the current state is at the k-1 moment, and predicting the value at the moment
Figure GDA0001842818520000144
And the true velocity function f (x)k-1) Priori estimated value x for predicting speed of trolley at moment kk|k-1Wherein, in the step (A),
Figure GDA0001842818520000145
k-1| k-1 refers to a value at the time k-1 is calculated based on the time k-1, and what is described when k | k-1 is not a subscript of the state transition matrix means that a value at the time k is calculated based on the time k-1;
step 4.3: calculating the prior error covariance from the posterior error covariance matrix P at time k-1k-1|k-1To predict the prior error covariance matrix P at the current momentk|k-1Wherein, in the step (A),
Figure GDA0001842818520000146
μkis an adaptive forgetting factor;
step 4.4: according to the prior error covariance matrix P at the current momentk|k-1Calculating the Kalman gain KkWherein, in the step (A),
Figure GDA0001842818520000147
step 4.5: according to prior estimated value x of k timek|k-1And the observed value zkObtaining the posterior estimated value x of k timek|kWherein x isk|k＝xk|k-1+Kk(zk-h(xk|k-1))；
Step 4.6: updating a posteriori error covariance matrix Pk|kProvision is made for calculating the prior error covariance matrix at time k +1, where Pk|k＝(I-KkHk)Pk|k-1I is an identity matrix;
step 4.7: k is updated to k +1, and the process returns to the step 4.2 to start a new round of calculation;
5) finally, the cloud server broadcasts the processed information (predicted speed of the vehicle, which direction it is in, several lanes and acceleration) to the roadside units for the next information interaction with the on-board system.
Further, in step 4.3, the calculation formula of the adaptive forgetting factor is as follows:
Figure GDA0001842818520000151
Gk＝d(Mk-Hk-1Qk-1Hk-1-Rk-1)；
ek＝zk-h(xk|k-1)；
Figure GDA0001842818520000152
Figure GDA0001842818520000153
Figure GDA0001842818520000154
here, the parameters are defined as follows:
max {. cndot ]: taking the maximum value after comparison;
α: the correction coefficient can forcibly improve the tracking performance of the filter;
Gk,ξk: intermediate derivation variables, no actual physical meaning;
ek: innovation, i.e. the difference between the true observed value and the estimated output value at time k;
u: maximum tolerable error;
d: when the innovation exceeds the maximum tolerable error, the value of the adaptive factor is reduced by reducing the weight factor, and finally the error is reduced;
Mk: innovation covariance matrix at time k.
Further, in the step 1), in the intelligent internet traffic system, the roadside units are installed on traffic lights of the crossroads and are attached with the cloud server and the directional antenna, wherein the emission angle of the routing antenna is 60 degrees, so that the roadside units can better perform information interaction with a vehicle-mounted system in a vehicle.

Claims (4)

1. A vehicle speed tracking method based on adaptive extended Kalman filtering is characterized by comprising the following steps:
1) in an intelligent network traffic system, a vehicle is automatically identified through a DSRC technology, relevant data are obtained, and information interaction between a vehicle-mounted system and a roadside unit is realized, wherein the information interaction comprises the following steps:
step 1.1: when a running vehicle enters the range covered by the directional antenna, the vehicle-mounted system and the roadside unit realize two-way communication through the DSRC technology, so that the two sides can simultaneously transmit information on the storage units of the vehicle-mounted system, wherein the information transmitted by the vehicle-mounted system comprises the current speed, the current position and the time stamp of the vehicle, and the information transmitted by the roadside unit comprises the predicted position of the vehicle on other lanes, the direction in which the vehicle is located, several lanes and the acceleration;
step 1.2: the roadside unit sends the acquired vehicle information to an edge cloud server to perform a series of operation operations;
2) the edge cloud server calculates an azimuth angle and performs corresponding quantization processing according to the azimuth difference between the roadside unit and the vehicle-mounted system, and quantizes the vehicle driving direction according to the position information, wherein the quantization process comprises the following steps:
step 2.1: converting the position information into digital information existing in a viewing angle, wherein an azimuth angle between a roadside unit and an on-board system of the vehicle at time k
Figure FDA0003104100420000011
The definition with respect to a roadside unit is:
Figure FDA0003104100420000012
Figure FDA0003104100420000021
here, the parameters are defined as follows:
Figure FDA0003104100420000022
an azimuth between the roadside unit and the onboard system at time k;
θk: converting the vehicle position at the moment k into an inverse trigonometric function of the azimuth angle;
σk: bearing error noise caused by signal reflection at time k;
(xk,yk): the current position of the vehicle at time k;
step 2.2: using the center of the crossroad as the origin of coordinates, aiming at the azimuth angle between the roadside unit and the vehicle-mounted system at the moment k
Figure FDA0003104100420000023
And performing quantization processing to determine the direction of the vehicle, wherein the quantization formula is as follows:
Figure FDA0003104100420000024
here, the parameters are defined as follows:
bk: quantifying the direction of the intersection at time k;
q (·): a quantization function;
i: direction identification of the crossroad;
step 2.3: in order to realize the concretization of the direction information, the lane of the direction is quantized, and the azimuth angle between the roadside unit and the vehicle-mounted system at the time of k
Figure FDA0003104100420000025
Rename it to
Figure FDA0003104100420000026
It is recorded as:
Figure FDA0003104100420000031
Figure FDA0003104100420000032
here, the parameters are defined as follows:
Figure FDA0003104100420000033
an azimuth between the roadside unit and the onboard system at time k;
θk': at the moment k, converting the relative position of the vehicle and the roadside unit into an inverse trigonometric function of the azimuth angle;
(xi,yi): the fixed position of the roadside unit in the direction i;
step 2.4: according to the quantization formula, performing second quantization on the direction of the vehicle to determine the lane of the vehicle;
Figure FDA0003104100420000034
here, the parameters are defined as follows:
qt: the quantized direction of the lane at time t;
ji: the jth lane in direction i;
n: total number of lanes;
3) assuming that only the latest p +1 vehicle speeds are used for acceleration estimation, the pth acceleration calculation method is:
Figure FDA0003104100420000035
here, the parameters are defined as follows:
Δ τ: a sampling time interval;
Δ v: the difference in velocity between the next time and the previous time;
vk-p: the speed of the trolley at the time t-p;
τk-p: a timestamp of the trolley at the time t-p;
ak-p: the p-th acceleration value;
thereafter, vehicle acceleration prediction is performed by using an autoregressive moving average method according to the p acceleration values, wherein the prediction formula is as follows:
Figure FDA0003104100420000041
here, the parameters are defined as follows:
ak: acceleration of the trolley at the moment k;
p: the autoregressive order, namely the total acceleration;
q: moving average order, i.e., total number of slips;
Figure FDA0003104100420000042
undetermined coefficients other than zero;
ξk: an error term independent at time k;
4) under the condition that a driver does not change a lane, aiming at collected related information, the speed of a running vehicle is predicted by using an adaptive extended Kalman filtering algorithm, wherein a calculation formula of the speed is as follows:
xk＝xk-1+ak-1Δτ；
converting the above formula into a state equation and an observation equation by using a state space model, wherein the equations are as follows:
xk＝f(xk-1)+Wk-1； (1)
zk＝h(xk-1)+Vk-1； (2)
here, the parameters are defined as follows:
xk: the speed of the vehicle at time k;
f (·): a true velocity function, a non-linear function;
h (·): observing a velocity function, which is a non-linear function;
Wk-1: the systematic error at time k-1 follows a Gaussian distribution N (0, Q)k-1) Wherein, in the step (A),
Qk-1＝cov(Wk-1)，Qk-1is the process noise variance at time k-1;
Vk-1: the observed error at time k-1 follows a Gaussian distribution N (0, R)k-1) Wherein, in the step (A),
Rk-1＝cov(Vk-1)，Rk-1is the process noise variance at time k-1;
zk: a state observation of the system at time k;
and then, predicting the vehicle speed by using an adaptive extended Kalman filter algorithm according to the state space model, wherein the vehicle position is updated by the following steps:
step 4.1: firstly, non-lines in the formulas (1) and (2)The linear function is subjected to linearization treatment to reduce the calculation amount and the model complexity, namely the nonlinear function f (x)k-1) And h (x)k-1) In filtering prediction value
Figure FDA0003104100420000051
The first order Taylor expansion is performed as follows:
Figure FDA0003104100420000052
Figure FDA0003104100420000053
Figure FDA0003104100420000054
Figure FDA0003104100420000055
here, the parameters are defined as follows:
Φk|k-1: a system state transition matrix from the time k-1 to the time k, wherein k | k-1 is from the time k-1 to the time k;
Hk-1: an observation transfer matrix at the k-1 moment;
Δt1: higher order infinitesimal quantities with times higher than one;
Δt2: higher order infinitesimal quantities with times higher than one;
thereafter, ignoring the higher order infinitesimal quantities, and substituting equations (3) and (5) into equations (1) and (2), respectively, yields:
Figure FDA0003104100420000056
Figure FDA0003104100420000061
step 4.2: calculating a priori estimated value, assuming that the current state is at the k-1 moment, and predicting the value at the moment
Figure FDA0003104100420000062
And the true velocity function f (x)k-1) Priori estimated value x for predicting speed of trolley at moment kk|k-1Wherein, in the step (A),
Figure FDA0003104100420000063
k-1| k-1 refers to a value at the time k-1 is calculated based on the time k-1, and what is described when k | k-1 is not a subscript of the state transition matrix means that a value at the time k is calculated based on the time k-1;
step 4.3: calculating the prior error covariance from the posterior error covariance matrix P at time k-1k-1|k-1To predict the prior error covariance matrix P at the current momentk|k-1Wherein, in the step (A),
Figure FDA0003104100420000064
μkis an adaptive forgetting factor;
step 4.4: according to the prior error covariance matrix P at the current momentk|k-1Calculating the Kalman gain KkWherein, in the step (A),
Figure FDA0003104100420000065
step 4.5: according to prior estimated value x of k timek|k-1And the observed value zkObtaining the posterior estimated value x of k timek|kWherein x isk|k＝xk|k-1+Kk(zk-h(xk|k-1))；
Step 4.6: updating a posteriori error covariance matrix Pk|kProvision is made for calculating the prior error covariance matrix at time k +1, where Pk|k＝(I-KkHk)Pk|k-1I isAn identity matrix;
step 4.7: k is updated to k +1, and the process returns to the step 4.2 to start a new round of calculation;
5) and finally, the cloud server broadcasts the processed information to the roadside unit so as to facilitate the information interaction with the vehicle-mounted system next time.
2. The vehicle speed tracking method based on the adaptive extended kalman filter according to claim 1, wherein: in the step 4.3, the calculation formula of the adaptive forgetting factor is as follows:
Figure FDA0003104100420000071
Gk＝d(Mk-Hk-1Qk-1Hk-1-Rk-1)；
ek＝zk-h(xk|k-1)；
Figure FDA0003104100420000072
Figure FDA0003104100420000073
Figure FDA0003104100420000074
here, the parameters are defined as follows:
max {. cndot ]: taking the maximum value after comparison;
α: the correction coefficient can forcibly improve the tracking performance of the filter;
Gk,ξk: intermediate derivation variables, no actual physical meaning;
ek: innovation, i.e. between true observed and estimated output at time kA difference of (d);
u: maximum tolerable error;
d: when the innovation exceeds the maximum tolerable error, the value of the adaptive factor is reduced by reducing the weight factor, and finally the error is reduced;
Mk: innovation covariance matrix at time k.
3. The vehicle speed tracking method based on the adaptive extended kalman filter according to claim 1 or 2, characterized in that: in the step 1), in the intelligent network traffic system, the roadside units are installed on traffic lights of the crossroad and are attached with the cloud server and the directional antenna, wherein the emission angle of the routing antenna is 60 degrees, so that the roadside units can better perform information interaction with a vehicle-mounted system in a vehicle.
4. The vehicle speed tracking method based on the adaptive extended kalman filter according to claim 1 or 2, characterized in that: in step 1.2, the data in the server is cleared every other week in consideration of the limited storage capacity of the edge cloud server.
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