CN115576322A - Adaptive cruise control method based on Kalman filtering improved model - Google Patents
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Abstract
The invention discloses a self-adaptive cruise control method based on a Kalman filtering improved model, which comprises the following steps: constructing a workshop state relation model based on longitudinal dynamics of a workshop; constructing a vehicle kinematic model based on the state relationship model and the vehicle motion state; correcting the state variable by using Kalman filtering to obtain a prediction model, and adding vehicle control demand constraint into the prediction model; and correcting the prediction model based on the model prediction error, and acquiring a vehicle control objective function by adopting constrained softening to expand a feasible region. According to the method, the influence of rain and fog weather on an ACC system is reduced by performing noise reduction control on the state variable input into the controller through Kalman filtering; the following prediction model is corrected by utilizing the error between the predicted value and the actual value, so that the robustness of the ACC system is enhanced; the feasible region is enlarged by restraining softening, and the influence of severe weather on an ACC system is reduced.
Description
Technical Field
The invention relates to the technical field of unmanned vehicle trajectory tracking control, in particular to a self-adaptive cruise control method based on a Kalman filtering improved model.
Background
The increase of the automobile holding amount causes frequent traffic accidents, and the accident rate is higher and higher due to misoperation in the driving process. Adaptive Cruise Control (ACC) reduces driver error by automatically adjusting the speed of the vehicle to maintain a safe distance from the vehicle ahead, improves the safety and convenience of vehicle travel, and increases road capacity.
The realization of the functions of the ACC system mostly depends on the correctness of sensing information of the millimeter wave radar, but the performance of the millimeter wave radar is greatly reduced in rainy and foggy weather, so that the ACC system is greatly influenced by the rainy and foggy weather, and the safe distance between the ACC system and a vehicle cannot be effectively identified.
Disclosure of Invention
This section is for the purpose of summarizing some aspects of embodiments of the invention and to briefly introduce some preferred embodiments. In this section, as well as in the abstract and the title of the invention of this application, simplifications or omissions may be made to avoid obscuring the purpose of the section, the abstract and the title, and such simplifications or omissions are not intended to limit the scope of the invention.
The present invention has been made in view of the above-mentioned problems.
Therefore, the technical problem solved by the invention is as follows: how to reduce the influence of bad weather on the adaptive cruise control system.
In order to solve the technical problems, the invention provides the following technical scheme: an adaptive cruise control method based on a Kalman filtering improved model comprises the following steps:
constructing a workshop state relation model based on longitudinal dynamics of a workshop;
constructing a vehicle kinematics model based on the state relationship model and the vehicle motion state;
correcting the state variable by using Kalman filtering to obtain a prediction model, and adding vehicle control demand constraint into the prediction model;
and correcting the prediction model based on the model prediction error, and acquiring a vehicle control objective function by adopting constrained softening to expand a feasible region.
As a preferable aspect of the adaptive cruise control method based on the kalman filter improved model according to the present invention, wherein: the building of the workshop state relation model comprises the following steps:
according to the relative motion state of the vehicle and the front vehicle, a workshop state relation model is constructed and expressed as follows:
d＝x f -x
Δd＝d-d des
v ref ＝v f -v
wherein x represents the position of the vehicle and x f Indicating the position of the leading vehicle; Δ d represents the error in the distance between two vehicles, d represents the actual distance between two vehicles, d des Representing a desired spacing between the two cars; v. of ref Indicating a desired vehicle speed, v, between two vehicles f Indicates the vehicle speed of the preceding vehicle, and v indicates the vehicle speed of the own vehicle.
As a preferable aspect of the adaptive cruise control method based on the kalman filter improved model according to the present invention, wherein: the building of the vehicle kinematic model comprises the following steps:
based on the change of the space pose and the speed of the vehicle along with the time, a state equation of the vehicle is constructed and expressed as follows:
wherein D is r Is the relative displacement of the front vehicle and the vehicle, V r Is the relative speed of the front vehicle and the host vehicle, v is the speed of the host vehicle, a is the acceleration of the host vehicle, and a des To expect acceleration, a f Is the front vehicle acceleration, k is the system gain, τ d Is the time constant and T is the sampling time.
As a preferable aspect of the adaptive cruise control method based on the kalman filter improved model according to the present invention, wherein: the building of the vehicle kinematics model further comprises:
selecting the state quantity of X = [ D ] r V r v a] T The controlled variable is u = a des (ii) a Obtaining a discrete state space equation through linear discretization, and expressing the equation as follows:
x(k+1)＝Ax(k)+Bu(k)+Cω(k)
wherein the content of the first and second substances,
A. b and C are both state space equation coefficient matrixes, and the system state x comprises the relative displacement D of the two workshops r Relative speed V between two workshops r The vehicle speed v and the vehicle acceleration a, the control input u is a desired acceleration, and the measurable disturbance ω is the front vehicle acceleration a f ；
The output variables y (k) are selected to be Δ d and v ref
y(k)＝Dx(k)
Wherein, the first and the second end of the pipe are connected with each other,
is a state space equation coefficient matrix.
As a preferable scheme of the adaptive cruise control method based on the kalman filtering improved model according to the present invention, wherein: the obtaining a prediction model comprises:
updating a state space equation based on the measurement noise and the process noise, expressed as:
x(k+1)＝Ax(k)+Bu(k)+Cω(k)+W(k)
y(k)＝Dx(k)+V(k)
wherein the variance of the process noise matrix W (k) is Q, and the variance of the measurement noise matrix V (k) is R;
the prediction is performed using the one-step covariance of kalman filtering, which is expressed as:
P(k+1|k)＝AP(k|k)A T +GQG T
wherein P (k +1 k) is a covariance matrix of a system at the moment k +1, P (k | k) is a covariance matrix of the system at the moment k, and Q (k) is a system process noise covariance;
performing state updating based on Kalman filtering, and expressing the state updating as follows:
K(k+1|k)＝P(k+1|k)H T [HP(k+1|k)H T +R] -1
P(k+1|k+1)＝[I-K(k+1|k)H]P(k+1|k)
k (K + 1) is Kalman gain and is an intermediate result of filtering, and H is a prediction matrix;
updating the state at the time of k + 1; p (k +1 calc + 1) is the covariance matrix of the system at time k + 1.
As a preferable scheme of the adaptive cruise control method based on the kalman filtering improved model according to the present invention, wherein: the vehicle control demand constraint comprising: and adding safety constraint, economic constraint, following constraint and comfort constraint into the model predictive control algorithm.
As a preferable aspect of the adaptive cruise control method based on the kalman filter improved model according to the present invention, wherein: the modified prediction model comprises: and subtracting the actual state value from the state value predicted by the prediction model to obtain a model prediction error, and correcting the predicted value at the next moment by using the model prediction error to further obtain a final following prediction model.
As a preferable scheme of the adaptive cruise control method based on the kalman filtering improved model according to the present invention, wherein: the final car following prediction model is expressed as:
Y((k+1)|k)＝Ψ(k)ξ(k)+ΘΔU(k)+ΓW(k)+ΦE(k)+Z
where ξ (k) is the current state quantity of the system, Δ U (k) is the control increment in the control time domain, Y, Ψ, Θ, Γ, Φ, and Z are all state space equation coefficient matrixes, N is P Is a prediction time domain; n is a radical of C To control the time domain.
As a preferable aspect of the adaptive cruise control method based on the kalman filter improved model according to the present invention, wherein: the expansion of the feasible region by adopting the constrained softening is represented as:
wherein epsilon is a relaxation factor,
and
the relaxation factors of the upper limit and the lower limit of each constraint are respectively.
As a preferable aspect of the adaptive cruise control method based on the kalman filter improved model according to the present invention, wherein: the vehicle control objective function is expressed as:
J＝‖Γ y ((Y(k+1|k)-R(k+1))‖ 2 +‖Γ u ΔU(k)‖ 2 +ρε 2
in the formula, gamma y Weighting matrices for the prediction output, Γ u To control the weighting matrix of the inputs, R (k + 1) is the reference input and ρ is the penalty factor.
The invention has the beneficial effects that: according to the method, the influence of rain and fog weather on an ACC system is reduced by performing noise reduction control on the state variable input into the controller through Kalman filtering; the following prediction model is corrected by utilizing the error between the predicted value and the actual value, so that the robustness of the ACC system is enhanced; the feasible region is enlarged by restraining softening, and the influence of severe weather on an ACC system is reduced.
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In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings needed to be used in the description of the embodiments will be briefly introduced below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings based on these drawings without inventive exercise. Wherein:
fig. 1 is an overall flowchart of an adaptive cruise control method based on a kalman filtering improved model according to an embodiment of the present invention;
FIG. 2 is a diagram of the longitudinal kinematics of a workshop according to one embodiment of the present invention;
FIG. 3 is a schematic diagram of an improved model predictive control based on Kalman filtering according to an embodiment of the present invention;
fig. 4 is a comparison graph of absolute value results of the distance error between two vehicles controlled by the MPC algorithm and the MPC algorithm modified based on KF according to an embodiment of the present invention.
Detailed Description
In order to make the aforementioned objects, features and advantages of the present invention comprehensible, specific embodiments accompanied with figures are described in detail below, and it is apparent that the described embodiments are a part of the embodiments of the present invention, not all of the embodiments. All other embodiments, which can be obtained by a person skilled in the art without making creative efforts based on the embodiments of the present invention, shall fall within the protection scope of the present invention.
In the following description, numerous specific details are set forth in order to provide a thorough understanding of the present invention, however, the present invention may be practiced otherwise than as specifically described herein, and it will be appreciated by those skilled in the art that the present invention may be practiced without departing from the spirit and scope of the present invention and that the present invention is not limited by the specific embodiments disclosed below.
Furthermore, reference herein to "one embodiment" or "an embodiment" means that a particular feature, structure, or characteristic described in connection with the embodiment is included in at least one implementation of the invention. The appearances of the phrase "in one embodiment" in various places in the specification are not necessarily all referring to the same embodiment, nor are separate or alternative embodiments mutually exclusive of other embodiments.
The present invention will be described in detail with reference to the drawings, wherein the cross-sectional views illustrating the structure of the device are not enlarged partially in general scale for convenience of illustration, and the drawings are only exemplary and should not be construed as limiting the scope of the present invention. In addition, the three-dimensional dimensions of length, width and depth should be included in the actual fabrication.
Meanwhile, in the description of the present invention, it should be noted that the terms "upper, lower, inner and outer" and the like indicate orientations or positional relationships based on the orientations or positional relationships shown in the drawings, and are only for convenience of describing the present invention and simplifying the description, but do not indicate or imply that the referred device or element must have a specific orientation, be constructed in a specific orientation and operate, and thus, cannot be construed as limiting the present invention. Furthermore, the terms first, second, or third are used for descriptive purposes only and are not to be construed as indicating or implying relative importance.
The terms "mounted, connected and connected" in the present invention are to be understood broadly, unless otherwise explicitly specified or limited, for example: can be fixedly connected, detachably connected or integrally connected; they may be mechanically, electrically, or directly connected, or indirectly connected through intervening media, or may be interconnected between two elements. The specific meanings of the above terms in the present invention can be understood in specific cases to those skilled in the art.
Example 1
Referring to fig. 1 to 4, for an embodiment of the present invention, there is provided an adaptive cruise control method based on a kalman filter improved model, including:
s1: and constructing a workshop state relation model based on the longitudinal dynamics of the workshop.
Specifically, as shown in fig. 2, a state relationship model between the host vehicle (experimental vehicle) and the preceding vehicle (target vehicle) is constructed based on the relative motion states of the host vehicle and the preceding vehicle, and is expressed as:
d＝x f -x (1)
Δd＝d-d des (2)
v ref ＝v f -v (3)
wherein x represents the position of the vehicle and x f Indicating the position of the leading vehicle; Δ d represents the error in the distance between two vehicles, d represents the actual distance between two vehicles, d des Representing a desired separation between the two cars; v. of ref Indicating the desired vehicle speed, v, between two vehicles f Indicates the vehicle speed of the preceding vehicle, and v indicates the vehicle speed of the own vehicle.
S2: and constructing a vehicle kinematic model based on the state relation model and the vehicle motion state.
It should be noted that the vehicle motion state includes: the spatial pose, speed, etc. of the vehicle change with time.
Specifically, based on the change of the space pose, the speed and the like of the vehicle along with time, a state equation of the vehicle is constructed and expressed as follows:
wherein D is r Is the relative displacement of the front vehicle and the vehicle, V r Is the relative speed of the front vehicle and the host vehicle, v is the speed of the host vehicle, a is the acceleration of the host vehicle, and a des To expect acceleration, a f Is the front vehicle acceleration, k is the system gain, τ d Is a time constant, T is a sampling timeAnd (3) removing the solvent.
Further, the state quantity is selected as X = [ D ] r V r v a] T The control quantity is selected to be u = a des 。
Through linear discretization, a discrete state space equation can be obtained:
x(k+1)＝Ax(k)+Bu(k)+Cω(k) (5)
wherein the content of the first and second substances,
A. b and C are both state space equation coefficient matrixes, and the system state x comprises the relative displacement D of the two workshops r Relative speed V between two workshops r The vehicle speed v and the vehicle acceleration a, the control input u is a desired acceleration, and the measurable disturbance ω is the front vehicle acceleration a f 。
The output variables y (k) are selected to be Δ d and v ref
y(k)＝Dx(k) (6)
Wherein, the first and the second end of the pipe are connected with each other,
is a state space equation coefficient matrix.
S3: and correcting the state variable by using Kalman filtering to obtain a prediction model, and adding vehicle control demand constraint into the prediction model.
Specifically, the ACC system has measurement noise and process noise, where the measurement noise matrix is V (k), the process noise matrix W (k), the measurement noise matrix variance is R, and the process noise matrix variance is Q.
Further, a new state space equation is obtained based on the measurement noise and the process noise, expressed as:
x(k+1)＝Ax(k)+Bu(k)+Cω(k)+W(k) (7)
y(k)＝Dx(k)+V(k) (8)
wherein the variance of the process noise matrix W (k) is Q and the variance of the measurement noise matrix V (k) is R. Furthermore, a one-step covariance of kalman filtering is used for prediction, which is expressed as:
P(k+1|k)＝AP(k|k)A T +GQG T (9)
wherein P (k +1 k) is the covariance matrix of the system at time k + 1, P (k | k) is the covariance matrix of the system at time k, and Q (k) is the system process noise covariance.
Further, the state update is performed based on kalman filtering, which is expressed as:
K(k+1|k)＝P(k+1|k)H T [HP(k+1|k)H T +R] -1 (10)
P(k+1|k+1)＝[I-K(k+1|k)H]P(k+1|k) (12)
k (K + 1) is Kalman gain and is an intermediate result of filtering, and H is a prediction matrix;
updating the state at the time of k + 1; p (k +1 calc + 1) is the covariance matrix of the system at time k + 1.
It should be noted that attenuation, clutter and noise in rainy and foggy weather can greatly reduce the accuracy of the model predictive control algorithm, and the safety and accuracy of the ACC system in severe weather conditions can be enhanced by correcting the state variable input to the controller by using Kalman filtering.
It should also be noted that the vehicle control demand is a quantitative description of the optimization objectives of the model predictive control algorithm, and that the vehicle control demand constraints include: safety constraints, economic constraints, follow constraints, and comfort constraints.
Further, the safety constraints are expressed as:
d＝x f -x≥d min (13)
wherein d is min The minimum safe distance between two vehicles.
It should be noted that safety is a primary target in a driving process and is a prerequisite of all control, in a driving process, the distance between a vehicle and a front vehicle needs to be paid attention to all the time, the distance between the two vehicles is always kept to be larger than a safe following distance, accidents are avoided, and therefore strict constraint needs to be carried out on the distance between the two vehicles, and safety constraint is introduced into a model prediction control algorithm.
Further, the economic constraint is expressed as:
a min <a<a max (14)
u min <u<u max (15)
in the formula, a min And a max Minimum and maximum acceleration, u, respectively min And u max The minimum value and the maximum value of the control quantity are respectively.
It should be noted that economy is a requirement for the least energy consumption of a vehicle in a driving process, and related researches show that the longitudinal acceleration of the vehicle has a significant influence on the driving economy of the vehicle, and in a following cruise process, the occurrence of frequency speed change is reduced as much as possible, so that the economy of the driving vehicle can be significantly improved, and therefore, in the model predictive control algorithm, the acceleration and the control quantity need to be constrained by introducing economic constraints.
Further, the following constraint is expressed as:
Δd min ≤Δd≤Δd max (16)
Δv min ≤Δv≤Δv max (17)
in the formula,. DELTA.d min And Δ d max The minimum value and the maximum value of the distance error between the vehicles are obtained; Δ v min And Δ v max The maximum and minimum values of the speed error.
It should be noted that the following body of the ACC system is in two aspects of speed following and safe vehicle distance following, the vehicle-to-vehicle distance between the vehicle and the preceding vehicle, the calculated vehicle-to-vehicle distance and the relative vehicle speed between the two vehicles gradually converge to 0, that is, the two vehicles keep a relative stationary state, which is the target of the system following, so that the following constraint needs to be introduced into the model predictive control algorithm to constrain the vehicle-to-vehicle distance error and vehicle speed error, thereby improving the flexibility in the driving process and avoiding the occurrence of accidents.
Further, the comfort constraint is expressed as:
j min ≤j≤j max (18)
Δu min ≤Δu≤Δu max (19)
in the formula, j min And j max A minimum value and a maximum value representing the acceleration change rate; Δ u min And Δ u max The minimum value and the maximum value of the control amount change rate are indicated.
It should be noted that the smaller the absolute values of the acceleration of the vehicle and the rate of change in the acceleration are, the higher the riding comfort is, and therefore, it is necessary to add comfort constraints to the present model predictive control algorithm to constrain the rate of change in the acceleration of the vehicle and the rate of change in the controlled variable.
S4: and correcting the prediction model based on the model prediction error, and acquiring a vehicle control objective function by adopting constrained softening to expand a feasible region.
Specifically, the error between the predicted state value and the actual state value at time k is expressed as:
e(k)＝x(k)-x(k-1|k-1) (20)
in the formula, x (k) is the actual state value, and x (k | k-1) is the predicted state value.
Furthermore, when the predicted value at the next time is corrected by using the model prediction error e (k) at time k, the prediction state at time k is:
x(k+1|k)＝Ax(k)+Bu(k)+Cω(k)+He(k)+W(k) (21)
in the formula (I), the compound is shown in the specification,
to correct the matrix, 0<h i <1,i＝1,2,…n。
It should be noted that the prediction state value is obtained by using kalman filtering, but the uncertainty of the vehicle model is increased due to rainy and foggy weather, so that the error between the prediction state value and the actual state value is increased; and correcting the prediction model, enhancing robustness and reducing errors as far as possible under the rain and fog weather condition.
Furthermore, a final following prediction model equation is obtained and expressed as:
Y((k+1)|k)＝Ψ(k)ξ(k)+ΘΔU(k)+ΓW(k)+ΦE(k)+Z (22)
xi (k) is the current state quantity of the system, Δ U (k) is the control increment in the control time domain, and Y, Ψ, Θ, Γ, Φ, and Z are state space equation coefficient matrices, specifically:
N P is a prediction time domain; n is a radical of C To control the time domain.
Furthermore, the control requirements of the ACC vehicle are weighted and sorted, and the following objective function is finally obtained:
J＝‖Γ y ((Y(k+1|k)-R(k+1))‖ 2 +‖Γ u ΔU(k)‖ 2 (23)
in the formula, gamma y Weighting matrices for the prediction output, Γ u To control the weighting matrix of the inputs, R (k + 1) is the reference input.
Furthermore, a feasible region is expanded by adopting a constraint softening method, specifically:
wherein epsilon is a relaxation factor,
and
the relaxation factors of the upper limit and the lower limit of each constraint are respectively.
It should be noted that due to the influence of severe weather, the hard constraint cannot be satisfied in the face of some emergency conditions, and therefore, the feasible region needs to be enlarged by a constraint softening method.
Further, the ACC vehicle control objective function is updated to obtain a final objective function, expressed as:
J＝‖Γ y ((Y(k+1|k)-R(k+1))‖ 2 +‖Γ u ΔU(k)‖ 2 +ρε 2 (25)
where ρ is a penalty factor.
Example 2
Referring to fig. 1 to 4, an embodiment of the present invention provides an adaptive cruise control method based on a kalman filter improved model, and in order to verify the beneficial effects of the present invention, scientific demonstration is performed through economic efficiency calculation and simulation experiments.
A Carsim & Simulink combined simulation platform is built, and a rain and fog weather scene is simulated by artificially adding noise in millimeter wave radar measurement information in the simulation process.
In Carsim, two vehicles are adopted to simulate an ACC environment, the first vehicle is a front vehicle and runs at an initial speed of 25m/s, the second vehicle is a self vehicle and runs along with the front vehicle, the fixed inter-vehicle distance between the two vehicles is 100m, the sampling time is 120s, wherein the simulation vehicle selects a C-level hatchback vehicle, and the vehicle body parameter setting is shown in Table 1.
TABLE 1 vehicle body parameter settings
In the simulation process, the robustness of the algorithm is verified through the working condition of the front vehicle with the variable vehicle speed, and the effectiveness of the algorithm is verified through comparing whether the MPC algorithm based on Kalman Filtering (KF) improvement exists or not.
The experimental result is shown in fig. 4, wherein the curve with larger fluctuation is the absolute value curve of the distance error between two vehicles controlled by the MPC algorithm, and the curve with smaller fluctuation is the absolute value curve of the distance error between two vehicles controlled by the MPC algorithm based on KF improvement; comparing the absolute values of the error between the distance between the two vehicles controlled by the MPC algorithm and the MPC algorithm based on the KF improvement can find that: the spacing errors under the two schemes can be effectively controlled, but the spacing errors generate larger fluctuation under the condition of only an MPC algorithm, the spacing errors after KF filtering and noise reduction are greatly reduced, and the curve is flatter; therefore, the experiment verifies that the following accuracy of the MPC control algorithm based on KF improvement on the time-varying vehicle speed is greatly improved.
It should be noted that the above-mentioned embodiments are only for illustrating the technical solutions of the present invention and not for limiting, and although the present invention is described in detail with reference to the preferred embodiments, it should be understood by those skilled in the art that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, which should be covered by the claims of the present invention.
Claims (10)
1. An adaptive cruise control method based on a Kalman filtering improved model is characterized by comprising the following steps:
constructing a workshop state relation model based on longitudinal dynamics of a workshop;
constructing a vehicle kinematic model based on the state relationship model and the vehicle motion state;
correcting the state variable by using Kalman filtering to obtain a prediction model, and adding vehicle control demand constraint into the prediction model;
and correcting the prediction model based on the model prediction error, and acquiring a vehicle control objective function by adopting constrained softening to expand a feasible region.
2. The kalman filter improved model-based adaptive cruise control method according to claim 1, characterized by: the building of the workshop state relation model comprises the following steps:
according to the relative motion state of the vehicle and the front vehicle, a vehicle state relation model is established and expressed as follows:
d＝x f -x
Δd＝d-d des
v ref ＝v f -v
wherein x represents the position of the vehicle and x f Indicating the position of the leading vehicle; Δ d represents the error in the distance between two vehicles, d represents the actual distance between two vehicles, d des Representing a desired separation between the two cars; v. of ref Indicating the desired vehicle speed, v, between two vehicles f Indicates the vehicle speed of the preceding vehicle, and v indicates the vehicle speed of the own vehicle.
3. The kalman filter improved model-based adaptive cruise control method according to claim 1 or 2, characterized by: the building of the vehicle kinematic model comprises the following steps:
based on the change of the space pose and the speed of the vehicle along with the time, a state equation of the vehicle is constructed and expressed as follows:
wherein D is r Is the relative displacement of the front vehicle and the vehicle, V r Is the relative speed between the front vehicle and the host vehicle, v is the speed of the host vehicle, a is the acceleration of the host vehicle, and a des To expect acceleration, a f Is the front vehicle acceleration, k is the system gain, τ d Is the time constant and T is the sampling time.
4. The Kalman filter improved model based adaptive cruise control method of claim 3, characterized by: the building of the vehicle kinematic model further comprises:
selecting the state quantity of X = [ D ] r V r v a] T The controlled variable is u = a des (ii) a Obtaining a discrete state space equation by linear discretization, expressed as:
x(k+1)＝Ax(k)+Bu(k)+Cω(k)
wherein the content of the first and second substances,
A. b and C are both state space equation coefficient matrixes, and the system state x comprises the relative displacement D between two workshops r Relative speed V between two vehicles r The vehicle speed v and the vehicle acceleration a, the control input u is a desired acceleration, and the measurable disturbance omega is the front vehicle acceleration a f ；
The output variables y (k) are selected to be Δ d and v ref
y(k)＝Dx(k)
Wherein the content of the first and second substances,
is a state space equation coefficient matrix.
5. The Kalman filter improved model based adaptive cruise control method of claim 4, characterized by: the obtaining of the prediction model comprises:
updating a state space equation based on the measurement noise and the process noise, expressed as:
x(k+1)＝Ax(k)+Bu(k)+Cω(k)+W(k)
y(k)＝Dx(k)+V(k)
wherein the variance of the process noise matrix W (k) is Q, and the variance of the measurement noise matrix V (k) is R;
the prediction is performed by using the one-step covariance of Kalman filtering, which is expressed as:
P(k+1|k)＝AP(k|k)A T +GQG T
wherein P (k +1 k) is a covariance matrix of a system at the moment k +1, P (k | k) is a covariance matrix of the system at the moment k, and Q (k) is a system process noise covariance;
performing state update based on Kalman filtering, expressed as:
K(k+1|k)＝P(k+1|k)H T [HP(k+1|k)H T +R] -1
P(k+1|k+1)＝[I-K(k+1|k)H]P(k+1|k)
k (K + 1) is Kalman gain and is an intermediate result of filtering, and H is a prediction matrix;
updating the state at the time of k + 1; p (k +1 calc + 1) is the covariance matrix of the system at time k + 1.
6. The Kalman filter improved model based adaptive cruise control method of claim 5, characterized by: the vehicle control demand constraint comprising: and adding safety constraint, economic constraint, following constraint and comfort constraint into the model predictive control algorithm.
7. The adaptive cruise control method based on a kalman filter improved model according to any one of claims 4 to 6, characterized in that: the modified prediction model comprises: and subtracting the actual state value from the state value predicted by the prediction model to obtain a model prediction error, and correcting the predicted value at the next moment by using the model prediction error to further obtain a final following prediction model.
8. The Kalman filter improved model based adaptive cruise control method of claim 7, characterized in that: the final car following prediction model is expressed as:
Y((k+1)|k)＝Ψ(k)ξ(k)+ΘΔU(k)+ΓW(k)+ΦE(k)+Z
xi (k) is the current state quantity of the system, delta U (k) is the control increment in the control time domain, Y, psi, theta, gamma, phi and Z are all state space equation coefficient matrixes, N P Is a prediction time domain; n is a radical of C To control the time domain.
9. The kalman filter improved model based adaptive cruise control method according to claim 8, wherein: the expansion of the feasible region by adopting the constrained softening is represented as:
wherein epsilon is a relaxation factor,
and
the relaxation factors of the upper limit and the lower limit of each constraint are respectively.
10. The kalman filter improved model-based adaptive cruise control method according to claim 8 or 9, characterized by: the vehicle control objective function is expressed as:
J＝‖Γ y ((Y(k+1|k)-R(k+1))‖ 2 +‖Γ u ΔU(k)‖ 2 +ρε 2
in the formula, gamma y Weighting matrices for the prediction output, Γ u To control the weighting matrix of the inputs, R (k + 1) is the reference input and ρ is the penalty factor.
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