CN111547059A - Distributed driving electric automobile inertia parameter estimation method - Google Patents

Distributed driving electric automobile inertia parameter estimation method Download PDF

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CN111547059A
CN111547059A CN202010325309.3A CN202010325309A CN111547059A CN 111547059 A CN111547059 A CN 111547059A CN 202010325309 A CN202010325309 A CN 202010325309A CN 111547059 A CN111547059 A CN 111547059A
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vehicle
inertia
mass
parameters
tire
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金贤建
杨俊朋
严择圆
王佳栋
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University of Shanghai for Science and Technology
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    • 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
    • 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
    • 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
    • B60W40/105—Speed
    • 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
    • B60W40/107—Longitudinal acceleration
    • 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
    • B60W40/12—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 parameters of the vehicle itself, e.g. tyre models
    • 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
    • B60W40/12—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 parameters of the vehicle itself, e.g. tyre models
    • B60W40/13—Load or weight
    • 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
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    • 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
    • B60W40/12—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 parameters of the vehicle itself, e.g. tyre models
    • B60W40/13—Load or weight
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    • B—PERFORMING OPERATIONS; TRANSPORTING
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    • 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
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    • B—PERFORMING OPERATIONS; TRANSPORTING
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    • 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
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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
    • B60W2530/00—Input parameters relating to vehicle conditions or values, not covered by groups B60W2510/00 or B60W2520/00
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Abstract

The invention relates to a distributed driving electric vehicle inertia parameter estimation method, which comprises the specific steps of firstly considering the change of vehicle inertia parameters caused by uncertain load parameters, establishing a three-degree-of-freedom whole vehicle dynamics model, selecting a nonlinear tire model of a magic formula, designing a state and parameter estimation system of a double-adaptive unscented Kalman filter, and then determining a double-adaptive unscented Kalman filter observer, thereby realizing the estimation of vehicle inertia parameters such as the longitudinal speed of a vehicle, the vehicle mass center and lateral deviation angle and the like, and the vehicle mass, the yaw rotation inertia, the distance from the mass center to the front axle of the vehicle. The method is based on the vehicle dynamics estimation model considering load parameter change, can effectively inhibit the divergence influence of the vehicle state parameter filter by adopting the self-adaptive unscented Kalman filtering method, corrects and predicts the vehicle inertia parameter in real time by utilizing the estimation value of the vehicle state in the double self-adaptive unscented Kalman filter, and has the advantages of high estimation precision and strong reliability.

Description

Distributed driving electric automobile inertia parameter estimation method
Technical Field
The invention belongs to the field of active safety control of distributed driving electric automobiles, and particularly relates to an inertial parameter estimation method of a distributed driving electric automobile.
Background
The electric automobile has great potential of energy conservation and emission reduction, so that the electric automobile becomes a hot spot of the research and development of the energy-saving and environment-friendly automobile technology at present, and the development of the electric automobile becomes the development direction of the automobile industry in the future. However, the increase of the quantity of electric automobiles brings about a plurality of traffic problems, and especially the active safety of vehicles is concerned. In recent years, with the development of electronic information technology and intelligent control technology, many automobile chassis electric control systems capable of effectively improving active safety appear in the modern automobile market: such as anti-lock braking systems (ABS) based on longitudinal control of the vehicle, Traction Control Systems (TCS), and electronic stability systems (ESP) based on lateral control of the vehicle, electric power steering systems (EPS), and direct yaw moment control systems (DYC) based on yaw direction control of the vehicle. To achieve effective and reliable control of these active safety dynamic systems, it is necessary to obtain some critical state parameter information such as vehicle lateral speed, vehicle mass center slip angle, etc. during vehicle driving accurately and reliably.
However, measuring these state parameters requires the installation of expensive on-board sensors, and the reliability of the sensor measurement signals is not fully solved, and these critical states of vehicle operation are difficult to measure directly using standard on-board sensors and can only be observed or estimated. Meanwhile, based on the actual vehicle engineering application visual angle, how to utilize the measurement information of the existing vehicle-mounted sensor and accurately estimate the vehicle state parameter information which is difficult to be directly measured on line is a difficult problem to be solved urgently in the vehicle engineering application.
In current vehicle state estimation studies, most focus on state estimation during vehicle operation, while relatively few studies are being made on vehicle inertial parameter estimation. In fact, the increase of unsprung mass of the distributed-drive electric automobile causes the redistribution of the mass of the whole automobile, and particularly, the uncertainty of load parameters (passenger or cargo loading) causes the change of vehicle inertia parameters including vehicle mass, yaw moment of inertia and vehicle mass center position, and directly influences the handling characteristics, control performance and stability such as lateral stability of a vehicle chassis system, and it is important to observe the information of the inertia parameters of the distributed-drive electric automobile in real time.
In addition, the conventional vehicle nonlinear kalman filter state estimation assumes that the noise statistical characteristic is known and is zero mean white noise, but external and environmental interference exists in the actual vehicle engineering application process, the statistical characteristic of the noise is often unknown, and the noise statistical characteristic under the assumption condition can cause the vehicle state estimation performance to be reduced, even cause estimation divergence. How to avoid estimation failure caused by the acoustic statistical characteristic of uncertain noise in the vehicle state parameter estimation process is also an important problem to be considered.
Disclosure of Invention
The invention aims to provide a distributed driving electric automobile inertia parameter estimation method, which is based on an established vehicle nonlinear dynamics model considering load change, adopts a double-adaptive unscented Kalman filtering algorithm, estimates vehicle inertia parameters such as the whole vehicle mass, the yaw moment of inertia, the distance between a mass center and a front axle of a vehicle and the like in real time on the basis of estimating state quantities such as the vehicle longitudinal speed, the vehicle mass center slip angle and the like, and has the advantages of high precision, strong reliability and the like.
In order to achieve the above object, the present invention provides the following solutions:
a distributed driving electric automobile inertia parameter estimation method adopts a double self-adaptive unscented Kalman filtering algorithm, and specifically comprises the following steps:
(1) and constructing a three-degree-of-freedom vehicle dynamic model considering load parameter uncertainty such as passenger or cargo loading, and establishing a three-degree-of-freedom whole vehicle dynamic model related to vehicle longitudinal speed, vehicle yaw angular velocity, vehicle mass center slip angle, vehicle lateral velocity and acceleration, and whole vehicle mass, yaw moment of inertia and distance from the mass center to a front axle of the vehicle, wherein the three-degree-of-freedom whole vehicle dynamic model comprises vehicle longitudinal motion, vehicle lateral motion and vehicle yaw motion.
In the step (1), the established whole vehicle dynamic equation of the distributed drive electric vehicle including the longitudinal, lateral and yaw motions of the vehicle is as follows:
Figure BDA0002462993050000021
wherein,
Figure BDA0002462993050000022
Figure BDA0002462993050000023
wherein,
Figure BDA0002462993050000024
Figure BDA0002462993050000025
wherein,
Figure BDA0002462993050000026
the position of the center of mass of the model will change, taking into account the change in the load parameters. When the loaded mass center of mass position of the vehicle is corresponding to the coordinate vector of the original coordinate system
Figure BDA0002462993050000027
When load mpAfter loading, the total mass of the vehicle is mn＝me+mp
The yaw moment of inertia at the original centroid after loading is as follows:
Figure BDA0002462993050000028
in the formula IzzoThe yaw moment of inertia when the vehicle is unloaded.
Transverse to the original centre of mass after loadingPendulum moment of inertia:
Figure BDA0002462993050000031
wherein
Figure BDA0002462993050000032
New centroid position coordinates in the original coordinate system:
Figure BDA0002462993050000033
and is
Figure BDA0002462993050000034
Yaw moment of inertia after loading
Figure BDA0002462993050000035
Meanwhile, when the load is changed, the geometric parameters related to the centroid position are correspondingly changed as follows:
Figure BDA0002462993050000036
in the above formula, Vx、VyLongitudinal and lateral velocities of the vehicle's center of mass, respectively; r iszYaw rate of vehicle mass center, β yaw angle of vehicle mass center, me、mp、mnRespectively representing the unloaded mass, the loaded mass and the total mass of the vehicle; fxij、FyijLongitudinal and lateral forces of i and j tires of a vehicle, wherein i ═ f and r; j is l, r. Fw、FfRespectively vehicle air resistance and ground tire rolling resistance; cdIs the air resistance coefficient; ρ is the air density; a. thefThe frontal area of the automobile; a isx、ayLongitudinal and lateral acceleration of the vehicle, respectively; μ is the known road adhesion coefficient;fl、frrespectively the steering angles of the left and right wheels of the front wheel; i iszz、MzRespectively representing yaw rotation of vehicleInertia and vehicle yaw moment; lf、lrThe horizontal distances from the center of mass to the front and rear axles of the vehicle, respectively; bl、brThe horizontal distances from the center of mass to the centers of the left wheel and the right wheel are respectively; m ispIs the load mass of the vehicle; l, B is the horizontal distance between the front and rear axles of the vehicle and the horizontal distance between the left and right wheels of the vehicle; lf0、lr0Respectively the horizontal distances from the front and rear axles to the center of mass of the vehicle when the vehicle is not loaded; x is the number ofp、ypRespectively are coordinate values of the load under the original vehicle coordinate system; x is the number ofn、ynA centroid coordinate when loading the vehicle; bf0、br0The horizontal distances from the left and right wheels to the center of mass when the vehicle is unloaded, respectively.
(2) The method comprises the steps of building a tire model, selecting a Pacejka model to build a nonlinear tire, uniformly expressing longitudinal force, transverse force and the like of the tire by using the same set of composite trigonometric function formula, and having the advantages of strong adaptability and high precision.
The Pacejka model in the step (2) establishes a nonlinear tire as follows:
Figure BDA0002462993050000037
in the above formula, the tire model parameters D, B, C, E are a peak factor, a stiffness factor, a curve shape factor, and a curve curvature factor, respectively; sh、SvThe lateral force and longitudinal force of the tire are calculated as follows:
Figure BDA0002462993050000041
wherein the lateral force to the tire
Figure BDA0002462993050000042
For longitudinal force of tire
Figure BDA0002462993050000043
In the above calculation of the lateral and longitudinal force parameters of the tire, a1,a2,b1,b2Denotes the crest factor calculation coefficient, a3,a4,a5,b3,b4,b5Represents the BCD calculation coefficient, a6,a7,a8,b6,b7,b8Representing the curvature factor calculation coefficient.
(3) And designing a state and parameter estimation system of the double-adaptive unscented Kalman filter according to the built three-degree-of-freedom vehicle dynamics model and the tire model, and simultaneously proving the local observability of the vehicle inertia parameters. The state equation and the observation equation of the state estimation system can be expressed in the following form after discretization:
Figure BDA0002462993050000044
wherein
Figure BDA0002462993050000045
Figure BDA0002462993050000046
Figure BDA0002462993050000047
Figure BDA0002462993050000051
∑Mzi(k-1)＝[Fyfl(k-1)sin(fl(k-1))-Fxfl(k-1)cos(fl(k-1))]bl+[Fxfl(k-1)sin(fl(k-1))+Fyfl(k-1)cos(fl(k-1))]lf+[Fxfr(k-1)cos(fr(k-1))-Fyfr(k-1)sin(fr(k-1))]br+(Fxfr(k-1)sin(fr(k-1))+Fyfr(k-1)cos(fr(k-1))]lf+(Fxrr(k-1)br-Fxrl(k-1)bl)-(Fyrr(k-1)+Fyrl(k-1))lr
In the above state observation system, x (k) ═ rz,Vx,β,ay,Vy]T、θ(k)＝[mn,Izz,lf]TA state vector and a parameter vector of the vehicle nonlinear dynamics observer system, respectively, u (k) ═ cf,wij,Tij]TAnd z (k) ═ rz,ax,ay]TRespectively an input vector and a measurement vector of a vehicle nonlinear dynamics observer system, w (k), v (k) respectively process noise and measurement noise of the system, the two are independent of each other, TsIs the sampling time.
The corresponding parameter estimation system may be further configured to:
Figure BDA0002462993050000052
wherein,
Figure BDA0002462993050000053
in the above parameter estimation system, r (k), e (k) are the process noise and the measurement noise of the system, respectively, and d (k) [ [ r ], (k) ]z,ax,ay]TIs a measurement vector.
The local observability of the inertia parameters is proved by researching the rank of the observability co-distribution matrix of the inertia parameters, and if the observability co-distribution matrix has the column full rank, the inertia parameters are called as local observability. Defining the output vector of the vehicle inertia parameter and the derivative of the output vector as:
Figure BDA0002462993050000054
the observability co-distribution matrix is as follows:
Figure BDA0002462993050000055
wherein the partial derivation of the observability co-distribution matrix is:
Figure BDA0002462993050000056
Figure BDA0002462993050000057
Figure BDA0002462993050000061
Figure BDA0002462993050000062
in the state where the vehicle is running,
Figure BDA0002462993050000063
full rank, then the vehicle inertia parameter θ (k) is [ m ]n,Izz,lf]TThe local area is considerable.
(4) The operation of the double-adaptive unscented Kalman filter observer for the inertial parameters of the distributed driving electric automobile comprises the following steps:
initializing; the values to be initialized are:
Figure BDA0002462993050000064
Pw,Pv,Pr,Pe；
time updating of the time-varying parameters to obtain
Figure BDA0002462993050000065
And
Figure BDA0002462993050000066
constructing sigma point of state, completing time update of state to obtain Xi(k|k-1)、
Figure BDA0002462993050000067
And
Figure BDA0002462993050000068
constructing sigma points of time-varying parameters to obtain thetaj(k-1|k-1)；
Calculating the output estimation of the time-varying parameter according to the sigma point to obtain Dj(k | k-1) and
Figure BDA0002462993050000069
calculating the output estimation of the state according to the sigma point to obtain zi(k | k-1) and
Figure BDA00024629930500000610
calculating Kalman gain of the state to obtain
Figure BDA00024629930500000611
And Lx(k)；
Calculating the Kalman gain of the time-varying parameters to obtain
Figure BDA00024629930500000615
And Lθ(k)；
Respectively completing the measurement update of the state and the time-varying parameters to obtain
Figure BDA00024629930500000613
And
Figure BDA00024629930500000614
respectively completing self-adaptive updating of covariance of noise in state and time-varying parameters to obtain Pw(k-1)、Pv(k)、Pr(k-1) and Pe(k)。
(5) The method comprises the steps of compiling an S function for executing a double-adaptive unscented Kalman filter observer on line, firstly building a Simulink-Carsim distributed drive electric vehicle system state estimation joint simulation platform in a Matlab/Simulink environment, building a distributed drive system of the electric vehicle in an external form because Carsim software does not develop a power source system aiming at a new energy vehicle, building an observer system of the electric vehicle and the like in the Matlab/Simulink, then realizing simulation communication between the Carsim and the Simulink through a Carsim-S function connection interface, and finally realizing estimation of a state and an inertia parameter in the vehicle driving process.
Compared with the prior art, the invention has the following obvious and prominent substantive characteristics and remarkable technical progress:
1. in the process of establishing a vehicle nonlinear dynamics estimation model, the distributed driving electric vehicle inertia parameter estimation dynamics model is established by considering that the load parameters of the distributed driving electric vehicle are uncertain, for example, the inertia parameters of the vehicle, including the mass of the vehicle, the yaw moment of inertia and the change of the position of the center of mass of the vehicle, caused by the loading of passengers or cargos;
2. according to the dynamic tire model of the inertia parameter estimation of the distributed driving electric automobile, the inertia parameter estimation system based on the double-adaptive unscented Kalman filter is designed by utilizing the torque perception information of hub motors of the distributed driving electric automobile which directly drive four wheels by using the hub motors, and the local observability of the inertia parameters of the automobile is simultaneously proved;
3. in the vehicle inertial parameter estimation process, the covariance matrix of the process noise and the measurement noise can be estimated on line by adopting the dual-adaptive unscented Kalman filtering, so that the problems that the filtering estimation performance of the traditional Kalman filter is reduced and even the filtering divergence deviates from the true value due to the fact that the noise statistical characteristic in the estimation process is assumed are solved, and the method has the advantages of high estimation precision and strong reliability.
Drawings
FIG. 1 is a general design framework diagram of a distributed driving electric vehicle inertia parameter estimation method of the present invention.
FIG. 2 is a schematic view of a vehicle dynamics model of the present invention taking into account load parameters.
FIG. 3 is a flow chart of the dual adaptive unscented Kalman filtering algorithm of the present invention.
Detailed Description
The preferred embodiments of the present invention will be described in detail below with reference to the accompanying drawings:
example one
In this embodiment, referring to fig. 1, a method for estimating inertia parameters of a distributed-drive electric vehicle includes the following steps:
s1, establishing a three-degree-of-freedom whole vehicle nonlinear dynamics model including longitudinal, lateral and yaw motions of the vehicle, and considering vehicle dynamics estimation model system changes caused by uncertain load parameters;
s2, building a tire model, and selecting a Pacejka model to build a nonlinear tire;
s3, designing an inertial parameter estimation system framework based on a double-adaptive unscented Kalman filter according to the built three-degree-of-freedom vehicle dynamics model and the tire model, and proving the local observability of the vehicle inertial parameters;
and S4, determining a specific operation method and steps of the dual-adaptive unscented Kalman filter observer based on the inertial parameter estimation system in the step S3, and realizing estimation of vehicle inertial parameters such as vehicle longitudinal speed, vehicle mass center and sideslip angle and the like, and vehicle mass, yaw moment of inertia, distance from the mass center to a front axle of the vehicle.
Example two
This embodiment is substantially the same as the first embodiment, and is characterized in that:
in this embodiment, the equation of the three-degree-of-freedom vehicle dynamics model in step S1 is:
Figure BDA0002462993050000081
wherein,
Figure BDA0002462993050000082
Figure BDA0002462993050000083
Figure BDA0002462993050000084
in the above formula, Vx、VyLongitudinal and lateral velocities of the vehicle's center of mass, respectively; r iszYaw rate of vehicle mass center, β yaw angle of vehicle mass center, mnRepresenting the total mass of the vehicle; fxij、FyijLongitudinal and lateral forces of i and j tires of a vehicle, wherein i ═ f and r; j is l, r; fw、FfRespectively vehicle air resistance and ground tire rolling resistance; cdIs the air resistance coefficient; ρ is the air density; a. thefThe frontal area of the automobile; a isx、ayLongitudinal and lateral acceleration of the vehicle, respectively; μ is the known road adhesion coefficient;fl、frrespectively the steering angles of the left and right wheels of the front wheel; i iszz、MzRespectively representing the vehicle yaw moment of inertia and the vehicle yaw moment; lf、lrThe horizontal distances from the center of mass to the front and rear axles of the vehicle, respectively; bl、brThe horizontal distances from the center of mass to the centers of the left and right wheels, respectively.
The three-degree-of-freedom vehicle dynamics model in the step S1 has changed the position of the center of mass of the model in consideration of the change of the load parameter; the loaded mass center of mass position of the vehicle is assumed to be relative to the coordinate vector of the original coordinate system
Figure BDA0002462993050000085
Load mpAfter loading, the total mass of the vehicle is mn＝me+mpAnd then the yaw moment of inertia at the original centroid after loading is as follows:
Figure BDA0002462993050000086
in the formula IzzoThe yaw moment of inertia when the vehicle is in no load;
yaw moment of inertia at the origin center of mass after loading:
Figure BDA0002462993050000091
wherein
Figure BDA0002462993050000092
New centroid position coordinates in the original coordinate system:
Figure BDA0002462993050000093
and is
Figure BDA0002462993050000094
Yaw moment of inertia after loading
Figure BDA0002462993050000095
Meanwhile, after loading, the relevant geometric parameters are correspondingly changed:
Figure BDA0002462993050000096
in the above formula, mpIs the load mass of the vehicle; i iszzoThe yaw moment of inertia when the vehicle is in no load; l, B is the horizontal distance between the front and rear axles of the vehicle and the horizontal distance between the left and right wheels of the vehicle; lf0、lr0Respectively the horizontal distances from the front and rear axles to the center of mass of the vehicle when the vehicle is not loaded; x is the number ofp、ypRespectively are coordinate values of the load under the original vehicle coordinate system; x is the number ofn、ynA centroid coordinate when loading the vehicle; bf0、br0The horizontal distances from the left and right wheels to the center of mass when the vehicle is unloaded, respectively.
In this embodiment, the Pacejka model in step S2 uses a set of complex trigonometric function formulas to uniformly express the longitudinal force, the lateral force, and the like of the tire in the form of:
Figure BDA0002462993050000097
in the above formula, the tire model parameters D, B, C, E are a peak factor, a stiffness factor, a curve shape factor, and a curve curvature factor, respectively; sh、SvRespectively, the drift of the curve in the horizontal direction and the drift of the curve in the vertical direction, when X is the tire slip angle α, Y is the tire lateral force, when X is the tire longitudinal slip ratio s, Y is the tire longitudinal force;
the lateral and longitudinal forces of the tire are calculated as follows:
Figure BDA0002462993050000098
wherein the lateral force to the tire
Figure BDA0002462993050000101
For longitudinal force of tire
Figure BDA0002462993050000102
In the above calculation of the lateral and longitudinal force parameters of the tire, a1,a2,b1,b2Denotes the crest factor calculation coefficient, a3,a4,a5,b3,b4,b5Represents the BCD calculation coefficient, a6,a7,a8,b6,b7,b8Representing the curvature factor calculation coefficient.
In this embodiment, the state estimation system of the dual adaptive unscented kalman filter in step S3 is:
Figure BDA0002462993050000103
wherein
Figure BDA0002462993050000104
Figure BDA0002462993050000105
Figure BDA0002462993050000106
Figure BDA0002462993050000107
∑Mzi(k-1)＝[Fyfl(k-1)sin(fl(k-1))-Fxfl(k-1)cos(fl(k-1))]bl+[Fxfl(k-1)sin(fl(k-1))+Fyfl(k-1)cos(fl(k-1))]lf+[Fxfr(k-1)cos(fr(k-1))-Fyfr(k-1)sin(fr(k-1))]br+(Fxfr(k-1)sin(fr(k-1))+Fyfr(k-1)cos(fr(k-1))]lf+(Fxrr(k-1)br-Fxrl(k-1)bl)-(Fyrr(k-1)+Fyrl(k-1))lr
In the above state observation system, x (k) ═ rz,Vx,β,ay,Vy]T、θ(k)＝[mn,Izz,lf]TA state vector and a parameter vector of the vehicle nonlinear dynamics observer system, respectively, u (k) ═ cf,wij,Tij]TAnd z (k) ═ rz,ax,ay]TRespectively an input vector and a measurement vector of a vehicle nonlinear dynamics observer system, w (k), v (k) respectively process noise and measurement noise of the system, the two are independent of each other, TsIs the sampling time;
the corresponding dual adaptive unscented kalman filter parameter estimation system may be further configured to:
Figure BDA0002462993050000111
wherein,
Figure BDA0002462993050000112
in the above-described parameter estimation system, r (k)) E (k) is the process noise and the measurement noise of the system, d (k) rz,ax,ay]TIs a measurement vector.
In this embodiment, in step S3, the local observability of the inertial parameter is proved by studying the rank of the observability co-distribution matrix of the inertial parameter, and if the observability co-distribution matrix has a full rank, the inertial parameter is said to be local observability; the process of demonstrating the local observability of the inertial parameters of a vehicle is as follows:
the output vector of the vehicle inertia parameter and the derivative of the output vector are defined as:
Figure BDA0002462993050000113
then its observability co-distribution matrix is:
Figure BDA0002462993050000114
wherein part of the derivation results are:
Figure BDA0002462993050000115
as a result of the above derivation, in the vehicle running state,
Figure BDA0002462993050000116
full rank, then the vehicle inertia parameter θ (k) is [ m ]n,Izz,lf]TThe local area is considerable.
In this embodiment, the specific operation of the dual adaptive unscented kalman filter observer in step S4 includes the following steps:
(1) initialization, the values to be initialized are respectively:
Figure BDA0002462993050000121
Pw,Pv,Pr,Pe；
(2) time updating of the time-varying parameters to obtain
Figure BDA0002462993050000122
And
Figure BDA0002462993050000123
(3) constructing sigma point of state, completing time update of state to obtain Xi(k|k-1)、
Figure BDA0002462993050000124
And
Figure BDA0002462993050000125
(4) constructing sigma points of time-varying parameters to obtain thetaj(k-1|k-1)；
(5) Calculating the output estimation of the time-varying parameter according to the sigma point to obtain Dj(k | k-1) and
Figure BDA0002462993050000126
(6) calculating the output estimation of the state according to the sigma point to obtain zi(k | k-1) and
Figure BDA0002462993050000127
(7) calculating Kalman gain of the state to obtain
Figure BDA0002462993050000128
And Lx(k)；
(8) Calculating the Kalman gain of the time-varying parameters to obtain
Figure BDA0002462993050000129
And Lθ(k)；
(9) Respectively completing the measurement update of the state and the time-varying parameters to obtain
Figure BDA00024629930500001210
And
Figure BDA00024629930500001211
(10) in separately completing state and time-varying parametersAdaptive update of covariance of noise to obtain Pw(k-1)、Pv(k)、Pr(k-1) and Pe(k)。
EXAMPLE III
This embodiment is substantially the same as the previous embodiment, and is characterized in that:
in the embodiment, a distributed driving electric vehicle inertia parameter estimation method is, as shown in fig. 1, a vehicle front wheel steering angle obtained through a vehicle-mounted sensorfAngular velocity w of wheel tireijWheel torque TijVehicle yaw rate rzLongitudinal acceleration axAnd lateral acceleration ayThe information is combined with the double-adaptive unscented Kalman filtering algorithm designed by the vehicle dynamics model with the established relevant degree of freedom to calculate the front wheel steering angle of the vehiclefAngular velocity w of tireijTire torque TijVehicle yaw rate r as a system inputzLongitudinal acceleration axAnd lateral acceleration ayFor systematic measurement, the yaw rate r of the vehicle is realizedzVehicle longitudinal speed VxVehicle mass center slip angle β and vehicle lateral speed VyAnd acceleration ayAnd the mass m of the whole vehiclenYaw moment of inertia IzzDistance l from center of mass to front axle of vehiclefIs estimated.
The estimation method comprises the following specific steps:
1. constructing a vehicle dynamic model with relevant degrees of freedom:
the distributed driving electric vehicle dynamics model considering the load parameters is shown in fig. 2, the origin of the vehicle coordinate system is defined to be located at the center of mass (CG) of the whole vehicle, and the whole vehicle dynamics equation of the distributed driving electric vehicle including the longitudinal, lateral and yaw motions of the vehicle is established as follows:
Figure BDA00024629930500001212
wherein,
Figure BDA0002462993050000131
Figure BDA0002462993050000132
wherein,
Figure BDA0002462993050000133
Figure BDA0002462993050000134
wherein,
Figure BDA0002462993050000135
the position of the centroid of the model has changed taking into account the change in the load parameters. The loaded mass center of mass position of the vehicle is assumed to be relative to the coordinate vector of the original coordinate system
Figure BDA0002462993050000136
Load mpAfter loading, the total mass of the vehicle is mn＝me+mpAnd then the yaw moment of inertia at the original centroid after loading is as follows:
Figure BDA0002462993050000137
in the formula IzzoThe yaw moment of inertia when the vehicle is empty.
By utilizing the parallel axis principle, the loaded yaw moment of inertia at the original centroid can be obtained:
Figure BDA0002462993050000138
further, in the present invention,
Figure BDA0002462993050000139
further, assuming that the height of the mass center of the whole vehicle does not change, the lever principle is utilized to calculate a new position coordinate of the mass center under the original coordinate system:
Figure BDA00024629930500001310
and is
Figure BDA00024629930500001311
To sum up:
Figure BDA00024629930500001312
meanwhile, after loading, the relevant geometric parameters are correspondingly changed into:
Figure BDA0002462993050000141
2. and building a tire model, selecting a Pacejka model to build a nonlinear tire, and uniformly expressing the longitudinal force and the transverse force of the tire by using the same set of composite trigonometric function formula.
The Pacejka model builds nonlinear tires as follows:
Figure BDA0002462993050000142
the lateral and longitudinal forces of the tire are calculated as follows:
Figure BDA0002462993050000143
wherein the lateral force to the tire
Figure BDA0002462993050000144
For longitudinal force of tire
Figure BDA0002462993050000145
In the above calculation of the lateral and longitudinal force parameters of the tire, a1,a2,b1,b2Indicating the peak causeSub-calculation coefficient, a3,a4,a5,b3,b4,b5Represents the BCD calculation coefficient, a6,a7,a8,b6,b7,b8Representing the curvature factor calculation coefficient.
Vertical load of wheel FzijThe calculation is as follows:
Figure BDA0002462993050000146
wheel tire slip angle αijThe calculation is as follows:
Figure BDA0002462993050000151
longitudinal slip s of wheel tyreijThe calculation is as follows:
Figure BDA0002462993050000152
3. establishing a state and parameter estimation system of a double-adaptive unscented Kalman filter and proving the local observability of vehicle inertia parameters:
1) according to the three-degree-of-freedom vehicle dynamics model described above, the state estimation system may be configured to:
Figure BDA0002462993050000153
the method specifically comprises the following steps:
Figure BDA0002462993050000154
Figure BDA0002462993050000155
wherein,
Figure BDA0002462993050000161
Figure BDA0002462993050000162
∑Mzi(k-1)＝[Fyfl(k-1)sin(fl(k-1))-Fxfl(k-1)cos(fl(k-1))]bl+[Fxfl(k-1)sin(fl(k-1))+Fyfl(k-1)cos(fl(k-1))]lf+[Fxfr(k-1)cos(fr(k-1))-Fyfr(k-1)sin(fr(k-1))]br+(Fxfr(k-1)sin(fr(k-1))+Fyfr(k-1)cos(fr(k-1))]lf+(Fxrr(k-1)br-Fxrl(k-1)bl)-(Fyrr(k-1)+Fyrl(k-1))lr
the above formula is middle TsThe sampling time.
The corresponding parameter estimation system may be further configured to:
Figure BDA0002462993050000163
the method specifically comprises the following steps:
Figure BDA0002462993050000164
2) the output vector of the vehicle inertia parameter and the derivative of the output vector are defined as:
Figure BDA0002462993050000165
then its observability co-distribution matrix is:
Figure BDA0002462993050000166
wherein, partial derivation results are:
Figure BDA0002462993050000167
Figure BDA0002462993050000168
Figure BDA0002462993050000169
Figure BDA00024629930500001610
Figure BDA00024629930500001611
as a result of the above derivation, in the vehicle running state,
Figure BDA0002462993050000171
full rank, then the vehicle inertia parameter θ (k) is [ m ]n,Izz,lf]TThe local area is considerable.
4. A double-adaptive unscented kalman filter observer is designed as shown in fig. 3, and the specific algorithm steps are as follows:
1) initializing; the values to be initialized here are:
Figure BDA0002462993050000172
Pw,Pv,Pr,Pe
2) vehicle parameter time update
Calculating a one-step predicted value of the vehicle parameter vector:
Figure BDA0002462993050000173
calculating a one-step vehicle parameter prediction error covariance matrix:
Figure BDA0002462993050000174
3) state-built sigma point and vehicle state time updates
Establishing an initialized 2L +1 sigma point set according to the state mean and covariance of the system state as follows:
Figure BDA0002462993050000175
wherein,
Figure BDA0002462993050000176
in the above formula, L is the dimension of the state vector, λsIn order to be a proportional parameter,
Figure BDA0002462993050000177
is a matrix
Figure BDA0002462993050000178
Column i.
The corresponding weights are:
Figure BDA0002462993050000179
in the above formula, the first and second carbon atoms are,
Figure BDA00024629930500001710
weights for the corresponding mean and variance, αsIs a scale scalar used for controlling the distance of each point to the mean value and satisfies 0.0001 ≦ αs≤1,βsWhich relates to the prior distribution information of the states in the gaussian case, s is a standard parameter, usually 0 or 3-L.
Calculating a sigma point set and a conduction sigma point set of the vehicle state:
Xi(k|k-1)＝f(Xi(k-1|k-1),u(k-1))
calculating a one-step predicted value of the vehicle state vector:
Figure BDA0002462993050000181
calculating a one-step vehicle state prediction error covariance matrix:
Figure BDA0002462993050000182
4) constructing sigma points of time-varying parameters
2l +1 sigma point sets of parameters are constructed according to vehicle parameter information as follows:
Figure BDA0002462993050000183
wherein,
Figure BDA0002462993050000184
where l is the dimension of the estimated parameter vector, λθIn order to be a proportional parameter,
Figure BDA0002462993050000185
is a matrix
Figure BDA0002462993050000186
Column j.
The corresponding weights are:
Figure BDA0002462993050000187
in the above formula, the first and second carbon atoms are,
Figure BDA0002462993050000188
weights for the corresponding mean and variance, αθIs a scale scalar used for controlling the distance of each point to the mean value and satisfies 0.0001 ≦ αθ≤1,βθInvolving a priori distribution information of states in the Gaussian case, sθIs a standard parameter, usually 0 or 3-l.
5) Vehicle parameter measurement update
And further calculating a vehicle parameter measurement sigma point set and a new conduction sigma point set:
Figure BDA0002462993050000189
6) vehicle state measurement update
Further calculating a vehicle state measurement volume point set and a conduction volume point set:
Figure BDA0002462993050000191
7) computing Kalman gain of states
Calculating an innovation covariance matrix:
Figure BDA0002462993050000192
calculating a cross covariance matrix:
Figure BDA0002462993050000193
calculating Kalman filtering nonlinear state observer gain:
Figure BDA0002462993050000194
8) computing Kalman gain of time-varying parameters
Calculating a parameter innovation covariance matrix:
Figure BDA0002462993050000195
calculating a parameter cross covariance matrix:
Figure BDA0002462993050000196
calculating the Kalman filtering nonlinear parameter observer gain:
Figure BDA0002462993050000197
9) separately performing measurement updates of state and time-varying parameters
Updating the state vector at the current moment to obtain the optimal estimation value of the nonlinear vehicle state at the current moment:
Figure BDA0002462993050000198
and simultaneously updating an error covariance matrix:
Figure BDA0002462993050000199
and updating the parameter vector at the current moment to obtain the optimal estimation value of the vehicle parameter at the current moment:
Figure BDA00024629930500001910
and simultaneously updating a parameter error covariance matrix:
Figure BDA00024629930500001911
10) adaptive update of covariance of noise in completion state and time-varying parameters
Adaptive update of state noise covariance:
Figure BDA0002462993050000201
wherein,
Figure BDA0002462993050000202
Figure BDA0002462993050000203
in the above formula, n is the number of sampling times.
Adaptive update of parametric noise covariance:
Figure BDA0002462993050000204
5. a Simulink-Carsim distributed driving electric vehicle inertial parameter estimation simulation platform is built in Matlab/Simulink, wherein a distributed driving system of an electric vehicle is built in an external form, simulation conditions are set in Carsim software, and then joint simulation communication is carried out with the Simulink through a connection interface of a Carsim-S function, so that the inertial parameter estimation of the distributed driving electric vehicle is finally realized.

Claims (7)

1. A distributed driving electric automobile inertia parameter estimation method is characterized by comprising the following steps:
s1, establishing a three-degree-of-freedom whole vehicle nonlinear dynamics model including longitudinal, lateral and yaw motions of the vehicle, and considering vehicle dynamics estimation model system changes caused by uncertain load parameters;
s2, building a tire model, and selecting a Pacejka model to build a nonlinear tire;
s3, designing an inertial parameter estimation system framework based on a double-adaptive unscented Kalman filter according to the built three-degree-of-freedom vehicle dynamics model and the tire model, and proving the local observability of the vehicle inertial parameters;
and S4, determining a specific operation method and steps of the dual-adaptive unscented Kalman filter observer based on the inertial parameter estimation system in the step S3, and realizing estimation of vehicle inertial parameters such as vehicle longitudinal speed, vehicle mass center and sideslip angle and the like, and vehicle mass, yaw moment of inertia, distance from the mass center to a front axle of the vehicle.
2. The distributed-drive electric vehicle inertia parameter estimation method according to claim 1, wherein the equation of the three-degree-of-freedom vehicle dynamics model in step S1 is:
Figure FDA0002462993040000011
wherein,
Figure FDA0002462993040000012
Figure FDA0002462993040000013
Figure FDA0002462993040000014
in the above formula, Vx、VyLongitudinal and lateral velocities of the vehicle's center of mass, respectively; r iszYaw rate of vehicle mass center, β yaw angle of vehicle mass center, mnRepresenting the total mass of the vehicle; fxij、FyijLongitudinal and lateral forces of i and j tires of a vehicle, wherein i ═ f and r; j is l, r; fw、FfRespectively vehicle air resistance and ground tire rolling resistance; cdIs the air resistance coefficient; ρ is the air density; a. thefThe frontal area of the automobile; a isx、ayLongitudinal and lateral acceleration of the vehicle, respectively; μ is the known road adhesion coefficient;fl、frrespectively the steering angles of the left and right wheels of the front wheel; i iszz、MzRespectively representing the vehicle yaw moment of inertia and the vehicle yaw moment; lf、lrThe horizontal distances from the center of mass to the front and rear axles of the vehicle, respectively; bl、brThe horizontal distances from the center of mass to the centers of the left and right wheels, respectively.
3. The distributed-drive electric vehicle inertia parameter estimation method according to claim 1, wherein the three-degree-of-freedom vehicle dynamics model in step S1 has changed the position of the center of mass of the model in consideration of the change of the load parameter; the loaded mass center of mass position of the vehicle is assumed to be relative to the coordinate vector of the original coordinate system
Figure FDA0002462993040000021
Load mpAfter loading, the total mass of the vehicle is mn＝me+mpAnd then the yaw moment of inertia at the original centroid after loading is as follows:
Figure FDA0002462993040000028
in the formula IzzoThe yaw moment of inertia when the vehicle is in no load;
yaw moment of inertia at the origin center of mass after loading:
Figure FDA0002462993040000022
wherein
Figure FDA0002462993040000023
New centroid position coordinates in the original coordinate system:
Figure FDA0002462993040000024
and is
Figure FDA0002462993040000025
Yaw moment of inertia after loading
Figure FDA0002462993040000026
Meanwhile, after loading, the relevant geometric parameters are correspondingly changed:
Figure FDA0002462993040000027
in the above formula, mpIs the load mass of the vehicle; i iszzoThe yaw moment of inertia when the vehicle is in no load; l, B is the horizontal distance between the front and rear axles of the vehicle and the horizontal distance between the left and right wheels of the vehicle; lf0、lr0Respectively the horizontal distances from the front and rear axles to the center of mass of the vehicle when the vehicle is not loaded; x is the number ofp、ypRespectively are coordinate values of the load under the original vehicle coordinate system; x is the number ofn、ynA centroid coordinate when loading the vehicle; bf0、br0The horizontal distances from the left and right wheels to the center of mass when the vehicle is unloaded, respectively.
4. The distributed drive electric vehicle inertial parameter estimation method of claim 1, wherein the steps are performed in the order named
The Pacejka model in S2 uses a set of complex trigonometric function equations to uniformly express the longitudinal force, the lateral force, etc. of the tire in the form of:
Figure FDA0002462993040000031
in the above formula, the tire model parameters D, B, C, E are a peak factor, a stiffness factor, a curve shape factor, and a curve curvature factor, respectively; sh、SvRespectively, the drift of the curve in the horizontal direction and the drift of the curve in the vertical direction, when X is the tire slip angle α, Y is the tire lateral force, when X is the tire longitudinal slip ratio s, Y is the tire longitudinal force;
the lateral and longitudinal forces of the tire are calculated as follows:
Figure FDA0002462993040000032
wherein the lateral force F is applied to the tireyij,
Figure FDA0002462993040000033
For tire longitudinal force Fxij,
Figure FDA0002462993040000034
In the above calculation of the lateral and longitudinal force parameters of the tire, a1,a2,b1,b2Denotes the crest factor calculation coefficient, a3,a4,a5,b3,b4,b5Represents the BCD calculation coefficient, a6,a7,a8,b6,b7,b8Representing the curvature factor calculation coefficient.
5. The method for estimating inertial parameters of a distributed-drive electric vehicle according to claim 1, wherein the state estimation system of the dual adaptive unscented kalman filter in step S3 is:
Figure FDA0002462993040000035
wherein
Figure FDA0002462993040000036
Figure FDA0002462993040000041
Figure FDA0002462993040000042
Figure FDA0002462993040000043
∑Mzi(k-1)＝[Fyfl(k-1)sin(fl(k-1))-Fxfl(k-1)cos(fl(k-1))]bl+[Fxfl(k-1)sin(fl(k-1))+Fyfl(k-1)cos(fl(k-1))]lf+[Fxfr(k-1)cos(fr(k-1))-Fyfr(k-1)sin(fr(k-1))]br+(Fxfr(k-1)sin(fr(k-1))+Fyfr(k-1)cos(fr(k-1))]lf+(Fxrr(k-1)br-Fxrl(k-1)bl)-(Fyrr(k-1)+Fyrl(k-1))lr
In the above state observation system, x (k) ═ rz,Vx,β,ay,Vy]T、θ(k)＝[mn,Izz,lf]TA state vector and a parameter vector of the vehicle nonlinear dynamics observer system, respectively, u (k) ═ cf,wij,Tij]TAnd z (k) ═ rz,ax,ay]TRespectively an input vector and a measurement vector of a vehicle nonlinear dynamics observer system, w (k), v (k) respectively process noise and measurement noise of the system, the two are independent of each other, TsIs the sampling time;
the corresponding dual adaptive unscented kalman filter parameter estimation system may be further configured to:
Figure FDA0002462993040000044
wherein,
Figure FDA0002462993040000045
in the above parameter estimation system, r (k), e (k) are the process noise and the measurement noise of the system, respectively, and d (k) [ [ r ], (k) ]z,ax,ay]TIs a measurement vector.
6. The distributed driving electric vehicle inertia parameter estimation method according to claim 1, wherein the local observability of the inertia parameters is proved by studying the rank of the observability co-distribution matrix of the inertia parameters in the step S3, and if the observability co-distribution matrix has a full rank, the inertia parameters are called local observability; the process of demonstrating the local observability of the inertial parameters of a vehicle is as follows:
the output vector of the vehicle inertia parameter and the derivative of the output vector are defined as:
Figure FDA0002462993040000051
then its observability co-distribution matrix is:
Figure FDA0002462993040000052
wherein part of the derivation results are:
Figure FDA0002462993040000053
as a result of the above derivation, in the vehicle running state,
Figure FDA0002462993040000054
full rank, then the vehicle inertia parameter θ (k) is [ m ]n,Izz,lf]TThe local area is considerable.
7. The method for estimating inertial parameters of a distributed-drive electric vehicle according to claim 1, wherein the operation of the dual-adaptive unscented kalman filter observer in step S4 includes the following steps:
(1) initialization, the values to be initialized are respectively:
Figure FDA0002462993040000055
Pw,Pv,Pr,Pe；
(2) time updating of the time-varying parameters to obtain
Figure FDA0002462993040000056
And
Figure FDA0002462993040000057
(3) constructing sigma point of state, completing time update of state to obtain Xi(k|k-1)、
Figure FDA0002462993040000058
And
Figure FDA0002462993040000059
(4) constructing sigma points of time-varying parameters to obtain thetaj(k-1|k-1)；
(5) Calculating the output estimation of the time-varying parameter according to the sigma point to obtain Dj(k | k-1) and
Figure FDA00024629930400000510
(6) calculating the output estimation of the state according to the sigma point to obtain zi(k | k-1) and
Figure FDA00024629930400000511
(7) calculating Kalman gain of the state to obtain
Figure FDA00024629930400000512
And Lx(k)；
(8) Calculating the Kalman gain of the time-varying parameters to obtain
Figure FDA00024629930400000513
And Lθ(k)；
(9) Respectively completing the measurement update of the state and the time-varying parameters to obtain
Figure FDA00024629930400000514
And
Figure FDA00024629930400000515
(10) respectively completing self-adaptive updating of covariance of noise in state and time-varying parameters to obtain Pw(k-1)、Pv(k)、Pr(k-1) and Pe(k)。
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