CN108162976A - A kind of vehicle running state method of estimation based on sparse grid quadrature Kalman filtering - Google Patents

A kind of vehicle running state method of estimation based on sparse grid quadrature Kalman filtering Download PDF

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CN108162976A
CN108162976A CN201711389922.6A CN201711389922A CN108162976A CN 108162976 A CN108162976 A CN 108162976A CN 201711389922 A CN201711389922 A CN 201711389922A CN 108162976 A CN108162976 A CN 108162976A
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vehicle
state
kalman filtering
longitudinal
sparse grid
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陈建锋
曹杰
汤传业
黄浩乾
孙坚添
郭聪聪
孙晓东
陈龙
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Jiangsu University
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    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B60—VEHICLES IN GENERAL
    • B60W—CONJOINT CONTROL OF VEHICLE SUB-UNITS OF DIFFERENT TYPE OR DIFFERENT FUNCTION; CONTROL SYSTEMS SPECIALLY ADAPTED FOR HYBRID VEHICLES; ROAD VEHICLE DRIVE CONTROL SYSTEMS FOR PURPOSES NOT RELATED TO THE CONTROL OF A PARTICULAR SUB-UNIT
    • B60W40/00—Estimation or calculation of non-directly measurable driving parameters for road vehicle drive control systems not related to the control of a particular sub unit, e.g. by using mathematical models
    • B60W40/10—Estimation or calculation of non-directly measurable driving parameters for road vehicle drive control systems not related to the control of a particular sub unit, e.g. by using mathematical models related to vehicle motion
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/10—Geometric CAD
    • G06F30/15—Vehicle, aircraft or watercraft design
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B60—VEHICLES IN GENERAL
    • B60W—CONJOINT CONTROL OF VEHICLE SUB-UNITS OF DIFFERENT TYPE OR DIFFERENT FUNCTION; CONTROL SYSTEMS SPECIALLY ADAPTED FOR HYBRID VEHICLES; ROAD VEHICLE DRIVE CONTROL SYSTEMS FOR PURPOSES NOT RELATED TO THE CONTROL OF A PARTICULAR SUB-UNIT
    • B60W50/00—Details of control systems for road vehicle drive control not related to the control of a particular sub-unit, e.g. process diagnostic or vehicle driver interfaces
    • B60W2050/0001—Details of the control system
    • B60W2050/0019—Control system elements or transfer functions
    • B60W2050/0028—Mathematical models, e.g. for simulation
    • B60W2050/0031—Mathematical model of the vehicle
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2111/00—Details relating to CAD techniques
    • G06F2111/10—Numerical modelling
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
    • G06F2119/06—Power analysis or power optimisation

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  • Mechanical Engineering (AREA)
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  • Mathematical Physics (AREA)
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Abstract

The invention discloses a kind of vehicle running state methods of estimation based on sparse grid quadrature Kalman filtering, rely on the seven freedom vehicle movement model of selection, based on the quadrature kalman filter method for combining sparse grid theory, it chooses multidimensional integral point, carry out time update and measure to update, estimate the longitudinal speed, lateral speed, side slip angle of vehicle.State of motion of vehicle method for parameter estimation proposed by the present invention has the characteristics that with high accuracy, while precision of state estimation is improved, can also effectively improve the real-time of state estimation.

Description

A kind of vehicle running state method of estimation based on sparse grid quadrature Kalman filtering
Technical field
The invention belongs to system state estimation field more particularly to a kind of vehicles based on sparse grid quadrature Kalman filtering Transport condition method of estimation.
Background technology
With the deep development of vehicle active safety technologies, the accurate acquisition of vehicle itself transport condition is more and more important. Due to the limitation of sensor technology and vehicle cost, the vehicle running state estimation based on model prediction has become the hot spot of research One of.
Mainly include Extended Kalman filter (Extended currently based on the vehicle state estimation method of model prediction Kalman Filter, EKF), Unscented kalman filtering (Unscented Kalman Filter, UKF), volume Kalman filtering (Cubature Kalman Filters, CKF), particle filter (Particle Filter, PF) etc., wherein spreading kalman are filtered Nonlinear system approximation is converted into linear system by wave by Taylor series expansion, and when mission nonlinear is stronger, error is larger； Unscented kalman filtering carries out UT transformation, avoids the approximation to nonlinear system by the selections of Sigma points, and precision is higher, But calculation amount is larger；The precision of volume Kalman filtering is suitable with Unscented kalman filtering, but required sampled point is less；Particle Filtering accuracy is higher, but there are the problems such as the exhaustion of particle sample and poor real-time.
Quadrature Kalman filtering (Quadrature Filter, QF) is a kind of nonlinear filter, and estimated accuracy is higher than EKF, UKF, CKF, but real-time is poor, because its calculation amount can exponentially rise with the increase of state dimension.In recent years, Sparse grid theory has obtained quick development, and the calculation amount of quadrature Kalman filtering can be effectively reduced using this method, and then Apply to vehicle state estimation field.
Invention content
The present invention provides one kind to be based on sparse grid quadrature Kalman filtering (Sparse Grid Quadrature Filter, SGQF) vehicle running state method of estimation, it is intended to improve the precision of vehicle state estimation, make quadrature Kalman filter Wave theory effectively applies to vehicle state estimation field.
The technical scheme is that：
A kind of vehicle running state method of estimation based on sparse grid quadrature Kalman filtering, includes the following steps：
Step (1), establishes seven freedom vehicle dynamic model；
Assuming that pavement conditions variation is slow, vehicle longitudinal movement, lateral movement, weaving and time of four tires are considered Transhipment is dynamic, establishes following seven freedom auto model：
Wherein, vxFor longitudinal speed, vyFor lateral speed, axFor longitudinal acceleration, ayFor side acceleration, r is yaw angle Speed, a are distance of the barycenter away from front axle, and b is distance of the barycenter away from rear axle, and δ is front wheel angle, and m is the quality of vehicle, lFIt is preceding Take turns wheelspan, lRFor rear track, Fx1、Fx2、Fx3、Fx4Before respectively left front, right, left back, right rear fire longitudinal force, Fy1、Fy2、 Fy3、Fy4Before respectively left front, right, left back, right rear fire lateral force, IzIt is vehicle around the rotary inertia of z-axis, MzFor around z-axis Torque.
Step (2) based on sparse grid quadrature kalman filtering theory, chooses multidimensional integral point, initialization, carries out the time Update is updated with measuring, and estimates the longitudinal speed, lateral speed, side slip angle of vehicle.
The selection of multidimensional integral point：
With longitudinal velocity vx, side velocity vy, yaw velocity r, longitudinal acceleration ax, side acceleration ayAnd vehicle is around z Shaft torque MzFor quantity of state x=[vx,vy,r,ax,ay,Mz]T, quantity of state dimension n=6, precision level L=2, then multidimensional integral point ξiAnd its weight wiShown in specific as follows：
Initialization procedure：
Using front wheel angle, four-wheel wheel speed as input u=[δ, ω1,ω2,ω3,ω4,]T, with longitudinal acceleration ax, it is lateral plus Speed ayAnd yaw velocity r is observed quantity z=[ax,ay,r]T, longitudinal velocity vx, side velocity vy, yaw velocity r, longitudinal direction Acceleration ax, side acceleration ayAnd vehicle is around z-axis torque MzFor quantity of state x=[vx,vy,r,ax,ay,Mz]T；If the shape of system State initial value x0=[vx0,0,0,0,0,0]T, error co-variance matrix initial value is P0；
Time, newer process was：
1. to error co-variance matrix decomposed Pk-1|k-1=SST, wherein S is Orthogonal Decomposition matrix, and k is current time；
2. calculate sampled pointWherein ζiPoint used by for this method,When being current Quarter state moment matrix；
3. status predication：
A. tire force is predicted
F~f (Ok-1|k-1)
In formula,It represents respectively Matrix γiThe first column element of the first row, second the first column element of row, the first column element of the third line, the first column element of fourth line, The first column element of fifth line；
B. state quantity prediction
Gained sampled point substitution seven freedom auto model is obtained into state-transition matrix；
Point is converted to：
In formula, T is the sampling time；
Then state is updated to：
4. status predication error covarianceQ in formula For system noise covariance matrix,Matrix is updated for state；
Measuring newer process is：
1. resamplingPk|k-1=SST；
2. observation predictionTo observe predictor matrix；
Using longitudinal acceleration, side acceleration and yaw velocity as observed quantity, observational equation is：
3. predict observation error covarianceR is in formula Observation noise covariance matrix；
4. calculate cross covariance
5. calculate kalman gain
6. state updates
7. state covariance updates
Beneficial effects of the present invention：The present invention proposes a kind of vehicle traveling based on sparse grid quadrature Kalman filtering Method for estimating state will combine the quadrature kalman filter method of sparse grid theory and estimate applied to vehicle status parameters, It can effectively improve the real-time of state estimation while precision of state estimation is improved, be the hair of vehicle active safety technologies Exhibition provides beneficial support.
Description of the drawings
Fig. 1 is a kind of vehicle running state method of estimation based on sparse grid quadrature Kalman filtering proposed by the present invention Flow chart；
Fig. 2 is seven freedom vehicle dynamic model；
Fig. 3 compares figure for vehicular longitudinal velocity estimated value；
Fig. 4 compares figure for the lateral velocity estimation value of vehicle；
Fig. 5 compares figure for vehicle centroid side drift angle estimated value.
Specific embodiment
The invention will be further described in the following with reference to the drawings and specific embodiments.
As shown in Figure 1, the vehicle running state method of estimation based on sparse grid quadrature Kalman filtering, including following step Suddenly：
1. establish vehicle dynamic model
The present embodiment considers the rotary motion of vehicle longitudinal movement, lateral movement, weaving and four tires (assuming that road Known to noodles part), seven freedom vehicle dynamic model is established, as shown in Figure 2.In figure, x-axis be longitudinal direction of car travel direction, y Axis be the lateral travel direction of vehicle, vxFor longitudinal speed, vyFor lateral speed, r is yaw velocity, and β is side slip angle, and a is Distance of the barycenter away from front axle, b are distance of the barycenter away from rear axle, and δ is front wheel angle, lFFor front tread, lRFor rear track, Fx1、Fx2、Fx3、Fx4Before respectively left front, right, left back, right rear fire longitudinal force, Fy1、Fy2、Fy3、Fy4It is respectively left front, right Before, left back, right rear fire lateral force, Mz1、Mz2、Mz3、Mz4Before respectively left front, right, left back, right rear fire around z-axis turn Square.
In formula, IzBe vehicle around the rotary inertia of z-axis, m is the quality of vehicle, MzFor the torque around z-axis.
Tire force in above formula is obtained by Dugoff tire models, and Dugoff tire models and its parameter calculation formula are such as Under：
In formula, u is surface friction coefficient, FzFor vertical load suffered by tire, cx、cyIt is firm for longitudinal tire stiffness, lateral deviation Degree, α are slip angle of tire, and λ is tire straight skidding rate, and i=1,2,3,4 represent the near front wheel, off-front wheel, left rear wheel, the right side respectively Trailing wheel, ε are speed impact factor；
In formula, ReFor tire effective radius, ω is tire rotational speed, vwProlong the speed in its section direction for wheel center；
In formula, h is vehicle centroid height, and g is acceleration of gravity, FSZFor static tire vertical load；
Based on Dugoff tire models and its parameter calculation formula, the tire is longitudinally, laterally abbreviated as with joint efforts：F~f (O), O=[vx,xy,r,ax,ay,u,δ,ω1,ω2,ω3,ω4]T。
2. vehicle state estimation is realized based on sparse grid quadrature kalman filtering theory
(1) multidimensional integral point is chosen
1. determine one-dimensional integration point set and its weight
The present embodiment chooses Gauss-Hermite criterion configuration one-dimensional point and its weight, single argument integration point set It is as shown in table 1 below.
Table 1Gauss-Hermite one-dimensionals point and its weight
2. determine one-dimensional integral accuracy level set
One-dimensional integral accuracy level set is：
In formula, q is auxiliary variable, meets L-n≤q≤L-1, and L is precision level；N is quantity of state dimension；ikIt is accumulated for one-dimensional Divide precision level；ik∈ Ξ,
The present embodiment is with longitudinal velocity, side velocity, yaw velocity, longitudinal acceleration, side acceleration and vehicle around z Shaft torque is state vector x=[vx,vy,r,ax,ay,Mz]T, precision level L=2 is chosen in quantity of state dimension n=6；According to sparse Grid multidimensional integral point Allocation Theory, obtains one-dimensional integral accuracy level set
3. determine each point and its weight
Tensor product of the multidimensional integral point for six one-dimensional points in the present embodiment, if the point is a new point, Its weight is：
In formula, w is the weight of point；
If the point is existing, weight is updated to：
During with q=0, take and illustrate for six one-dimensional integral accuracies horizontal (1,1,1,1,1,1)：
When one-dimensional integral accuracy level set isWhen, the tensor product of one-dimensional integration point set is A sextuple point ξ can be generated1=[0,0,0,0,0,0]T；Its weight is 1, if point is still obtained by follow-up [0,0,0,0, 0,0]T, then weight is updated.
The present embodiment multidimensional integral point ξiAnd its weight wiShown in specific as follows：
In formula, work as i=2 ..., when 7, -1 in ξiFirst row to the 6th row variation, during such as i=2, ξ2=[- 1,0,0,0, 0,0]T, during i=3, ξ3=[0, -1,0,0,0,0]T。
(2) it initializes
The present embodiment is using front wheel angle, four-wheel wheel wheel speed as input u=[δ, ω1,ω2,ω3,ω4,]T, with longitudinal acceleration Degree, side acceleration and yaw velocity are observed quantity z=[ax,ay,r]T, it is longitudinal velocity, side velocity, yaw velocity, vertical To acceleration, side acceleration and vehicle around z-axis torque be state vector x=[vx,vy,r,ax,ay,Mz]T；If the state of system Initial value x0=[vx0,0,0,0,0,0]T, error co-variance matrix initial value is P0。
(3) time updates
1. error co-variance matrix is decomposed
Pk-1|k-1=SST (12)
Wherein, S is Orthogonal Decomposition matrix, and k is current time；
2. calculate sampled point
In formula, ξiPoint used by for the present embodiment；
3. status predication
A. tire force is predicted
In formula,It represents respectively Matrix γiThe first column element of the first row, second the first column element of row, the first column element of the third line, the first column element of fourth line, The first column element of fifth line；
B. state quantity prediction
Gained sampled point substitution seven freedom auto model is obtained into state-transition matrix：
Point is converted to：
In formula, T is the sampling time；
Then state is updated to：
4. status predication error covariance
In formula, Q is system noise covariance matrix；
(4) update is measured
1. resampling
2. observation prediction
Using longitudinal acceleration, side acceleration and yaw velocity as observed quantity, observational equation is the present embodiment：
3. predict observation error covariance
In formula, R is observation noise covariance matrix；
4. calculate cross covariance
5. calculate kalman gain
6. state updates
7. state covariance updates
It, can be effectively using sparse grid quadrature Kalman Filter Estimation method based on seven free vehicle dynamic models Estimate longitudinal speed, side velocity and the vehicle centroid side drift angle of vehicle.
3. simulating, verifying：
The present embodiment carries method for estimating state, the vehicle parameter of use by the verification of Carsim/Matlab associative simulations As shown in table 2.
2 whole-car parameters of table
Auto model parameter Numerical value
Complete vehicle quality m/kg 1416
Barycenter is to front axle distance a/m 1.016
Barycenter is to rear axle distance b/m 1.562
Height of center of mass h/m 0.54
Yaw rotation inertia Iz/kg·m2 1523
Front tread lF/m 1.539
Rear track lR/m 1.539
Tire effective radius Re/m 0.31
For the validity of verification the present embodiment institute extracting method, two-track line operating mode emulation experiment, the emulation of two-track line operating mode are carried out Parameter setting：Speed is constant for 45km/h, coefficient of road adhesion μ=0.85, sampling time 0.01s.Quantity of state initial value x0= [45/3.6,0,0,0,0,0]T, Q=100 × I8×8, R=I3×3.Gained vehicular longitudinal velocity, side velocity, side slip angle are estimated Evaluation is as shown in Fig. 3, Fig. 4, Fig. 5, by simulation result it will be evident that the present embodiment uses method relative to spreading kalman Filtering method, precision are greatly improved, i.e., SGQF estimated values are more nearly with Carsim output valves.
Although an embodiment of the present invention has been shown and described, it will be understood by those skilled in the art that：Not In the case of being detached from the principle of the present invention and objective a variety of change, modification, replacement and modification can be carried out to these embodiments, this The range of invention is limited by claim and its equivalent.

Claims (8)

1. a kind of vehicle running state method of estimation based on sparse grid quadrature Kalman filtering, which is characterized in that including with Lower step：
Step (1), establishes seven freedom vehicle dynamic model；
Step (2) based on sparse grid quadrature kalman filtering theory, chooses multidimensional integral point, initialization, carries out time update It is updated with measuring, estimates the longitudinal speed, lateral speed, side slip angle of vehicle.
2. a kind of vehicle running state estimation side based on sparse grid quadrature Kalman filtering according to claim 1 Method, which is characterized in that in the step (1), the foundation of seven freedom vehicle dynamic model：
Assuming that pavement conditions variation is slow, the revolution fortune of vehicle longitudinal movement, lateral movement, weaving and four tires is considered It is dynamic, establish following seven freedom auto model：
Wherein, vxFor longitudinal speed, vyFor lateral speed, axFor longitudinal acceleration, ayFor side acceleration, r is yaw velocity, A is distance of the barycenter away from front axle, and b is distance of the barycenter away from rear axle, and δ is front wheel angle, and m is the quality of vehicle, lFFor front-wheel wheel Away from lRFor rear track, Fx1、Fx2、Fx3、Fx4Before respectively left front, right, left back, right rear fire longitudinal force, Fy1、Fy2、Fy3、 Fy4Before respectively left front, right, left back, right rear fire lateral force, IzIt is vehicle around the rotary inertia of z-axis, MzFor turning around z-axis Square.
3. a kind of vehicle running state estimation side based on sparse grid quadrature Kalman filtering according to claim 1 Method, which is characterized in that in the step (2), the selection of multidimensional integral point：
With longitudinal velocity vx, side velocity vy, yaw velocity r, longitudinal acceleration ax, side acceleration ayAnd vehicle turns around z-axis Square MzFor quantity of state x=[vx,vy,r,ax,ay,Mz]T, quantity of state dimension n=6, precision level L=2, then multidimensional integral point ξiAnd Its weight wiShown in specific as follows：
4. a kind of vehicle running state estimation side based on sparse grid quadrature Kalman filtering according to claim 1 Method, which is characterized in that in the step (2), initialization procedure：
Using front wheel angle, four-wheel wheel speed as input u=[δ, ω1,ω2,ω3,ω4,]T, with longitudinal acceleration ax, side acceleration ayAnd yaw velocity r is observed quantity z=[ax,ay,r]T, longitudinal velocity vx, side velocity vy, yaw velocity r, longitudinal direction accelerate Spend ax, side acceleration ayAnd vehicle is around z-axis torque MzFor quantity of state x=[vx,vy,r,ax,ay,Mz]T；If at the beginning of the state of system Value x0=[vx0,0,0,0,0,0]T, error co-variance matrix initial value is P0。
5. a kind of vehicle running state estimation based on sparse grid quadrature Kalman filtering according to claim 3 or 4 Method, which is characterized in that in the step (2), the time newer process is：
1. to error co-variance matrix decomposed Pk-1|k-1=SST, wherein S is Orthogonal Decomposition matrix, and k is current time；
2. calculate sampled pointWherein ζiPoint used by for this method,For current time state Moment matrix；
3. status predication：Tire force is predicted and state quantity prediction；
4. status predication error covarianceQ is is in formula System noise covariance matrix,Matrix is updated for state.
6. a kind of vehicle running state estimation side based on sparse grid quadrature Kalman filtering according to claim 5 Method, which is characterized in that the process of the status predication is：
A. tire force is predicted
F~f (Ok-1|k-1)
In formula,Representing matrix respectively γiThe first column element of the first row, second the first column element of row, the first column element of the third line, the first column element of fourth line, the 5th The first column element of row.
B. state quantity prediction
Gained sampled point substitution seven freedom auto model is obtained into state-transition matrix；
Point is converted to：
In formula, T is the sampling time；
Then state is updated to：
7. a kind of vehicle running state estimation side based on sparse grid quadrature Kalman filtering according to claim 5 Method, which is characterized in that in the step (2), the newer process of measurement is：
1. resampling
2. observation prediction To observe predictor matrix；
3. predict observation error covarianceR makes an uproar for observation in formula Sound covariance matrix；
4. calculate cross covariance
5. calculate kalman gain
6. state updates
7. state covariance updates
8. a kind of vehicle running state estimation side based on sparse grid quadrature Kalman filtering according to claim 7 Method, which is characterized in that the process of the observation prediction：
Using longitudinal acceleration, side acceleration and yaw velocity as observed quantity, observational equation is：
CN201711389922.6A 2017-12-21 2017-12-21 A kind of vehicle running state method of estimation based on sparse grid quadrature Kalman filtering Pending CN108162976A (en)

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Cited By (12)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN109606378A (en) * 2018-11-19 2019-04-12 江苏大学 Vehicle running state estimation method towards non-Gaussian noise environment
CN110532590A (en) * 2019-07-12 2019-12-03 南京航空航天大学 A kind of vehicle state estimation method based on adaptive volume particle filter
CN110532590B (en) * 2019-07-12 2023-06-13 南京航空航天大学 Vehicle state estimation method based on self-adaptive volume particle filtering
CN110497916A (en) * 2019-08-15 2019-11-26 太原科技大学 Vehicle driving state estimation method based on BP neural network
CN110497915A (en) * 2019-08-15 2019-11-26 太原科技大学 A kind of vehicle driving state estimation method based on Weighted Fusion algorithm
CN110884499A (en) * 2019-12-19 2020-03-17 北京理工大学 Method and system for determining vehicle mass center slip angle
CN110884499B (en) * 2019-12-19 2021-03-19 北京理工大学 Method and system for determining vehicle mass center slip angle
CN111475912A (en) * 2020-02-11 2020-07-31 北京理工大学 Joint prediction method and system for longitudinal and lateral vehicle speeds of vehicle
CN111475912B (en) * 2020-02-11 2022-07-08 北京理工大学 Joint prediction method and system for longitudinal and lateral vehicle speeds of vehicle
WO2022193940A1 (en) * 2021-03-18 2022-09-22 北京航迹科技有限公司 Vehicle speed measurement method and apparatus, vehicle-mounted computer device and storage medium
CN113276862A (en) * 2021-06-21 2021-08-20 智新控制系统有限公司 Vehicle driving state estimation method
WO2023087202A1 (en) * 2021-11-18 2023-05-25 华为技术有限公司 Motion state estimation method and apparatus

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