CN107878462A - Speed prediction method and apparatus - Google Patents
Speed prediction method and apparatus Download PDFInfo
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- CN107878462A CN107878462A CN201610875080.4A CN201610875080A CN107878462A CN 107878462 A CN107878462 A CN 107878462A CN 201610875080 A CN201610875080 A CN 201610875080A CN 107878462 A CN107878462 A CN 107878462A
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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
- B60W40/105—Speed
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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
- B60W2520/00—Input parameters relating to overall vehicle dynamics
- B60W2520/10—Longitudinal speed
- B60W2520/105—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
- B60W2520/00—Input parameters relating to overall vehicle dynamics
- B60W2520/28—Wheel 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
- B60W2720/00—Output or target parameters relating to overall vehicle dynamics
- B60W2720/10—Longitudinal speed
Abstract
This disclosure relates to a kind of speed prediction method and apparatus, this method include:Obtain wheel speed sample set and longitudinal acceleration of N number of wheel in current period of vehicle;Dynamic prediction model is established according to the wheel speed sample set and longitudinal acceleration of current period, and the error correction parameter obtained according to a upper cycle is modified to dynamic prediction model;State space vector is obtained according to default state-space model and wheel speed sample set;According to the longitudinal acceleration of state space vector and current period, the speed prediction value of revised dynamic prediction model acquisition current period is utilized;According to current period and the speed prediction value of M cycle acquisition, the reference obtained with current period and M cycle before takes turns wheel speed measured value, obtains error sample set;Error correction parameter for next cycle is obtained according to error sample set, for the calculating in next cycle.The disclosure can improve the degree of accuracy of speed prediction, reduce error.
Description
Technical field
This disclosure relates to field of measuring technique, in particular it relates to a kind of speed prediction method and apparatus.
Background technology
With automobile, role is more and more important in daily life, and the raising of automobile various aspects of performance is just
The prediction of the problem of extremely being paid close attention into everybody, especially the automobile speed under the several scenes such as traveling, braking, sideslip, prediction
Speed to realizing that Vehicle Electronic Control is very important state parameter, and the speed prediction method used at present is generally root
Four wheel wheel speeds are gathered according to wheel speed sensors, the acceleration magnitude of four wheels is tried to achieve and estimates four corresponding cars of wheel
Speed, judge it is damped condition or driving operating mode further according to wheel acceleration magnitude, the corresponding speed of four wheels is chosen according to different operating modes
In maximum or minimum value as predicted value, the information of four wheel speeds is not made full use of, simultaneously because vehicle is being run over
Cheng Zhong, accelerate and often produce the excessive phenomenon of the slip rates such as sliding, idle running, sideslip when braking, easily cause what speed calculated
Error is larger.
The content of the invention
The purpose of the disclosure is to provide a kind of speed prediction method and apparatus, low for solving traditional speed-measuring method versatility
And error it is larger the problem of.
To achieve these goals, according to the first aspect of the embodiment of the present disclosure, there is provided a kind of speed prediction method, it is described
Method includes:Wheel speed sample set of N number of wheel in current period of vehicle is obtained, and the vehicle is in the current period
Longitudinal acceleration, wherein N is positive integer;
Dynamic prediction is established according to the longitudinal acceleration of the wheel speed sample set of the current period and the current period
Model, and the dynamic prediction model was carried out according to the error correction parameter for the current period that a upper cycle obtains
Amendment;
State space vector is obtained according to default state-space model and the wheel speed sample set;
According to the state space is vectorial and the longitudinal acceleration of the current period, revised dynamic prediction is utilized
Model obtains the speed prediction value of the current period;
The speed prediction value that M cycle obtains according to the speed prediction value of the current period and before, work as with described
The reference wheel wheel speed measured value that the reference wheel wheel speed measured value in preceding cycle and the M cycle obtain, obtains error sample set
Close;
Error correction parameter for next cycle is obtained according to the error sample set, and utilizes and is used for next cycle
Error correction parameter carry out the calculating in next cycle, wherein from N number of wheel of the acquisition vehicle current period wheel speed
Sample set, and the vehicle obtain in the longitudinal acceleration of the current period to described according to the error sample set
Error correction parameter for next cycle is a cycle.
Optionally, it is described obtain vehicle N number of wheel current period wheel speed sample set, and the vehicle work as
The longitudinal acceleration in preceding cycle, including:
Obtain multiple wheel speed signals of N number of wheel of the vehicle gathered in preset duration;
The multiple wheel speed signal is filtered, multiple wheel speed signals after being filtered;
According to the wheel speed signal of multiple default sample conditions of wheel speed signal selection satisfaction after the filtering, the wheel is obtained
Fast sample set;
Obtain and accelerated by the vehicle that the acceleration transducer of the vehicle gathers in the longitudinal direction of the current period
Measured value is spent, and the longitudinal acceleration measured value of the current period is filtered by default filtering algorithm, obtains institute
State current period longitudinal acceleration.
Optionally, it is described to be built according to the wheel speed sample set of the current period and the longitudinal acceleration of the current period
Vertical dynamic prediction model, including:
Obtained according to the speed prediction value in the wheel speed sample set in a upper cycle and a upper cycle described N number of
Wheel on described the wheel speed in a cycle and it is described on a cycle speed prediction value deviation;
Obtain the wheel acceleration of N number of wheel respectively according to the wheel speed sample set of the current period;
According to the wheel speed sample set of the current period, the deviation, the wheel acceleration of N number of wheel and described
The longitudinal acceleration of current period establishes dynamic prediction model.
Optionally, the error correction parameter obtained according to the error sample set for next cycle, including:
The error prediction model of the current period is established according to the error sample set;
The error correction parameter for being used for next cycle is obtained using the error prediction model.
Optionally, the speed prediction value according to the current period and the speed prediction that M cycle obtains before
Value, the reference speed measured value obtained with the reference speed measured value of the current period and the M cycle, obtains error
Sample set, including:
The current period is obtained respectively and in the M cycle, the speed prediction value in each cycle with reference to wheel with taking turns
The error of fast measured value, obtain multiple errors;
The some or all of error in the multiple error is selected to obtain the error sample set as error sample
Close.
Optionally, the dynamic prediction model includes:
Wherein,Represent respectively the cycle of kth -1 the near front wheel wheel speed and speed prediction value it
Between deviation, the deviation between the left rear wheel wheel speed in the cycle of kth -1 and speed prediction value, the off-front wheel wheel speed in the cycle of kth -1 with
Deviation between the off hind wheel wheel speed and speed prediction value of deviation, the cycle of kth -1 between speed prediction value,The near front wheel wheel speed in the expression cycle of kth -1, off-front wheel wheel speed, left rear wheel wheel speed, the right side respectively
Trailing wheel wheel speed,The near front wheel wheel speed, off-front wheel wheel speed, left rear wheel in kth cycle are represented respectively
Wheel speed, off hind wheel wheel speed, VkFor the speed prediction value in kth cycle,The near front wheel wheel acceleration in kth cycle is represented,Table
Show the off-front wheel wheel acceleration in kth cycle,The left rear wheel wheel acceleration in kth cycle is represented,Represent the right side in kth cycle
Rear wheel rotation acceleration, axkThe longitudinal acceleration of the vehicle in kth cycle is represented, Δ represents wheel acceleration and longitudinal acceleration
The threshold value of difference.
Optionally, the state space vector is the vector using the wheel speed of N number of wheel as element, the state space
Model includes:
Wherein,The cycle of kth+1 and the wheel speed value of any wheel of kth cycle vehicle, λ are represented respectively1、λ2Table
Show parameter value, and meet λ1+λ2=1, Δ represents the deviation threshold of the state space vector in two neighboring cycle.
Optionally, the error prediction model includes:
xk=xk-1+vk
Wherein, xkThe error correction values in kth cycle are represented,The predicted value of the error correction values in kth cycle is represented,Table
Show the estimate of the error correction values in kth cycle, Q represents process noise covariance, zkRepresent the error actual value in kth cycle, R
Measurement noise covariance is represented,The evaluated error covariance in kth cycle is represented,Represent the prediction error association side in kth cycle
Difference, KkThe kalman gain in kth cycle is represented, I represents unit matrix.
Optionally, the filtering algorithm includes:
Wherein,Kth cycle and the longitudinal acceleration measured value of the vehicle in the cycle of kth -1 are represented respectively,
axkRepresent the longitudinal acceleration value in kth cycle.
According to the second aspect of the embodiment of the present disclosure, there is provided a kind of speed prediction device, described device include:Obtain mould
Block, forecast model establish module, state space vector acquisition module, speed prediction module, error acquisition module and corrected parameter
Acquisition module;
The acquisition module, for obtaining wheel speed sample set of N number of wheel in current period of vehicle, and the car
The current period longitudinal acceleration, wherein N is positive integer;
The forecast model establishes module, for the wheel speed sample set according to the current period and the current period
Longitudinal acceleration establish dynamic prediction model, and the error correction for being used for the current period ginseng obtained according to a upper cycle
It is several that the dynamic prediction model is modified;
The state space vector acquisition module, for according to default state-space model and the wheel speed sample set
Close and obtain state space vector;
The speed prediction module, for vectorial and the longitudinal direction of the current period accelerates according to the state space
Degree, the speed prediction value of the current period is obtained using revised dynamic prediction model;
The error acquisition module, for the speed prediction value according to the current period and before M cycle obtain
Speed prediction value, take turns wheel speed measured value with the reference of the current period and reference wheel wheel speed that the M cycle obtains
Measured value, error sample set is obtained, wherein M is nonnegative integer;
The corrected parameter acquisition module, repaiied for being obtained according to the error sample set for the error in next cycle
Positive parameter, and utilize the calculating that next cycle is carried out for the error correction parameter in next cycle, wherein from the acquisition vehicle
N number of wheel current period wheel speed sample set, and the vehicle the current period longitudinal acceleration to institute
State that to be obtained according to the error sample set for the error correction parameter in next cycle be a cycle.
Optionally, the acquisition module includes:Signal acquisition module, filtration module, sample set acquisition module and acceleration
Spend acquisition module;
The signal acquisition module, multiple wheel speed signals of N number of wheel of the vehicle for obtaining collection;
The filtration module, for being filtered to the multiple wheel speed signal, multiple wheel speed signals after being filtered;
The sample set acquisition module, for according to multiple default samples of wheel speed signal selection satisfaction after the filtering
The wheel speed signal of condition, obtain the wheel speed sample set;
The acceleration acquisition module, the vehicle that the acceleration transducer for obtaining by the vehicle gathers exist
The longitudinal acceleration measured value of the current period, and the longitudinal acceleration by default filtering algorithm to the current period
Measured value is filtered, and obtains the current period longitudinal acceleration.
Optionally, the forecast model is established module and included:Deviation acquisition module, wheel acceleration acquisition module and modeling mould
Block;
The deviation acquisition module, for the wheel speed sample set according to the upper cycle and a upper cycle
Speed prediction value obtain N number of wheel on described the wheel speed in a cycle with it is described on a cycle speed prediction value it is inclined
Difference;
The wheel acceleration acquisition module, it is described N number of for being obtained respectively according to the wheel speed sample set of the current period
The wheel acceleration of wheel;
The modeling module, for the wheel speed sample set according to the current period, the deviation, N number of wheel
Wheel acceleration and the longitudinal acceleration of the current period establish dynamic prediction model.
Optionally, the corrected parameter acquisition module includes:
Error model establishes module, for establishing the error prediction mould of the current period according to the error sample set
Type;
Parameter acquisition module, join for utilizing the error prediction model to obtain the error correction for next cycle
Number.
Optionally, the error acquisition module includes:
Error calculating module, for obtaining the current period respectively and in the M cycle, the speed in each cycle
Predicted value and the error with reference to wheel wheel speed measured value, obtain multiple errors;
Error screening sample module, for selecting some or all of error in the multiple error as error sample
This, obtains the error sample set.
Optionally, the dynamic prediction model includes:
Wherein,Represent respectively the cycle of kth -1 the near front wheel wheel speed and speed prediction value it
Between deviation, the deviation between the left rear wheel wheel speed in the cycle of kth -1 and speed prediction value, the off-front wheel wheel speed in the cycle of kth -1 with
Deviation between the off hind wheel wheel speed and speed prediction value of deviation, the cycle of kth -1 between speed prediction value,The near front wheel wheel speed in the expression cycle of kth -1, off-front wheel wheel speed, left rear wheel wheel speed, the right side respectively
Trailing wheel wheel speed,The near front wheel wheel speed, off-front wheel wheel speed, left rear wheel in kth cycle are represented respectively
Wheel speed, off hind wheel wheel speed, VkFor the speed prediction value in kth cycle,The near front wheel wheel acceleration in kth cycle is represented,Table
Show the off-front wheel wheel acceleration in kth cycle,The left rear wheel wheel acceleration in kth cycle is represented,Represent the right side in kth cycle
Rear wheel rotation acceleration, axkThe longitudinal acceleration of the vehicle in kth cycle is represented, Δ represents wheel acceleration and longitudinal acceleration
The threshold value of difference.
Optionally, the state space vector is the vector using the wheel speed of N number of wheel as element, the state space
Model includes:
Wherein,The cycle of kth+1 and the wheel speed value of any wheel of kth cycle vehicle, λ are represented respectively1、λ2Table
Show parameter value, and meet λ1+λ2=1, Δ represents the deviation threshold of the state space vector in two neighboring cycle.
Optionally, the error prediction model includes:
xk=xk-1+vk
Wherein, xkThe error correction values in kth cycle are represented,The predicted value of the error correction values in kth cycle is represented,Table
Show the estimate of the error correction values in kth cycle, Q represents process noise covariance, zkRepresent the error actual value in kth cycle, R
Measurement noise covariance is represented,The evaluated error covariance in kth cycle is represented,Represent the prediction error association side in kth cycle
Difference, KkThe kalman gain in kth cycle is represented, I represents unit matrix.
Optionally, the filtering algorithm includes:
Wherein,Kth cycle and the longitudinal acceleration measured value of the vehicle in the cycle of kth -1 are represented respectively,
axkRepresent the longitudinal acceleration value in kth cycle.
Pass through above-mentioned technical proposal, the wheel speed for combining whole wheels are modeled, and are gone for vehicle and are run over
Various scenes in journey, the versatility easily occurred during wheel speed calculation speed using single wheel in the prior art can be avoided
Low, the problem of error is larger, therefore versatility can be improved, meanwhile, the technical scheme that the disclosure is provided being capable of real-time update
For predicting the model of speed, so as to the interference that brings of wheel speed error during effectively reducing braking, breakking away, prediction is improved
The degree of accuracy, reduce error.
Other feature and advantage of the disclosure will be described in detail in subsequent specific embodiment part, it should be understood that
, the general description and following detailed description of the above are only exemplary and explanatory, can not limit the disclosure.
Brief description of the drawings
Accompanying drawing is for providing further understanding of the disclosure, and a part for constitution instruction, with following tool
Body embodiment is used to explain the disclosure together, but does not form the limitation to the disclosure.In the accompanying drawings:
Fig. 1 is a kind of flow chart of speed prediction method according to an exemplary embodiment;
Fig. 2 is the flow chart of another speed prediction method according to an exemplary embodiment;
Fig. 3 is the flow chart of another speed prediction method according to an exemplary embodiment;
Fig. 4 is the flow chart of another speed prediction method according to an exemplary embodiment;
Fig. 5 is the flow chart of another speed prediction method according to an exemplary embodiment;
Fig. 6 is a kind of vehicle electronic system structural representation according to an exemplary embodiment;
Fig. 7 is a kind of block diagram of speed prediction device according to an exemplary embodiment;
Fig. 8 is a kind of block diagram of acquisition module according to an exemplary embodiment;
Fig. 9 is the block diagram that a kind of forecast model according to an exemplary embodiment establishes module;
Figure 10 is a kind of block diagram of corrected parameter acquisition module according to an exemplary embodiment;
Figure 11 is a kind of block diagram of error acquisition module according to an exemplary embodiment.
Embodiment
The embodiment of the disclosure is described in detail below in conjunction with accompanying drawing, its example is illustrated in the accompanying drawings.Under
When the description in face is related to accompanying drawing, unless otherwise indicated, the same numbers in different accompanying drawings represent same or analogous key element.Below
Embodiment described in exemplary embodiment does not represent all embodiments consistent with the disclosure.On the contrary, they
Only it is the example of the apparatus and method consistent with some aspects being described in detail in such as appended claims, the disclosure.
Before the speed prediction method and apparatus explanation provided the disclosure, first to involved by each embodiment of the disclosure
Application scenarios are introduced.The application scenarios can be any one vehicle, such as automobile, the automobile be not limited to orthodox car,
Pure electric automobile or mixed electrical automobile, other kinds of motor vehicle or non-motor vehicle are in addition can be applicable to, in this public affairs
Open in each embodiment, illustrated so that vehicle is automobile as an example.
Fig. 1 is a kind of flow chart of speed prediction method according to an exemplary embodiment, as shown in figure 1, the party
Method includes:
Step 101, wheel speed sample set of N number of wheel in current period of vehicle is obtained, and vehicle is in current period
Longitudinal acceleration, wherein N is positive integer.
Example, N number of wheel of vehicle can be whole wheels of vehicle, and by taking automobile as an example, usual automobile is provided with 4
Wheel, therefore in the present embodiment, N can be 4.
Step 102, dynamic prediction is established according to the longitudinal acceleration of the wheel speed sample set of current period and current period
Model, and the error correction parameter for current period obtained according to a upper cycle is modified to dynamic prediction model.
Wherein, the output of the dynamic prediction model is the speed prediction value of the vehicle, therefore the dynamic prediction model can be managed
Solve for be wheel speed and longitudinal acceleration using above-mentioned N number of wheel as variable, using speed prediction value as output function model,
And in the dynamic prediction model coefficient of each wheel wheel speed can according to each wheel a upper cycle wheel speed with it is upper
The deviation of one cycle speed prediction value obtains.
Wherein, the error correction parameter for current period that a upper cycle obtains just refers to once perform step upper
The error correction parameter obtained during 101-106.
Step 103, state space vector is obtained according to default state-space model and wheel speed sample set.
Wherein, state space vector is the vector using the wheel speed of N number of wheel as element, using 4 wheels of general vehicle as
, contain the near front wheel wheel speed, left rear wheel wheel speed in state space vector.Off-front wheel wheel speed and off hind wheel wheel speed.Due to vehicle
Running environment complexity, for gathering the process circuit of wheel speed inevitably by by the strong electromagnetic in the external world, from
And the moment distortion of wheel speed signal may be caused, therefore can be by default state-space model to being obtained in step 101
Wheel speed sample set is handled, and can be obtained respectively in the case of wheel speed distortion and the non-distortion of wheel speed by the state-space model
The accurate wheel speed of N number of wheel is obtained, so as to obtain state space vector.
Therefore, the state space vector is the vector using the wheel speed of N number of wheel as element, can be according to following formula
Can calculates the wheel speed of each wheel, and so as to obtain state space vector, the state-space model can include:
Wherein,The cycle of kth+1 and the wheel speed value of any wheel of kth cycle vehicle, λ are represented respectively1、λ2Table
Show parameter value, and meet λ1+λ2=1, Δ represents the deviation threshold of the state space vector in two neighboring cycle.Wherein, λ1、λ2
Specific value need to be obtained according to Experimental Calibration, such as can be with empirically determined λ1=3/4, λ2=1/4.
Step 104, according to the longitudinal acceleration of state space vector and current period, revised dynamic prediction is utilized
Model obtains the speed prediction value of current period.
Step 105, the speed prediction value that M cycle obtains according to the speed prediction value of current period and before, with working as
The reference wheel wheel speed measured value that the reference wheel wheel speed measured value in preceding cycle and M cycle obtain, obtains error sample set, its
Middle M is nonnegative integer.
Example, M value can be set according to the actual requirements, and M value is higher, represent to include in error sample set
Error sample it is more, be more beneficial for improve error correction parameter accuracy, it can be mentioned that data volume too conference is led
Cause memory space excessive, committed memory amount, and do not have real-time;And the error sample set included in error sample set is too
It is few, then error prediction value deviation can be caused larger, availability reduces, therefore M specific value can be come really according to the actual requirements
It is fixed.
In each embodiment of the disclosure, used with reference to the amendment that wheel wheel speed measured value is only used for speed prediction.Show
The maximum of each wheel wheel speed when example with reference to wheel wheel speed measured value can be driving operating mode, to be each during damped condition
The minimum value of wheel wheel speed, the average of the maximum wheel speed of left and right vehicle wheel both sides is commonly may be referred to when turning and christiania, driven
The average of the minimum wheel speed of left and right vehicle wheel both sides is may be referred to when turn is curved.
Step 106, the error correction parameter for next cycle is obtained according to error sample set.And it is possible to utilize
The error correction parameter for being used for next cycle carries out the calculating in next cycle.
Wherein, it is a cycle from step 101 to step 106.
Fig. 2 is the flow chart of another speed prediction method according to an exemplary embodiment, as shown in Fig. 2 step
N number of wheel of acquisition vehicle described in rapid 101 is in the wheel speed sample set of current period, and vehicle is in the longitudinal direction of current period
The step of acceleration, may comprise steps of:
Step 1011, multiple wheel speed signals of N number of wheel of the vehicle are obtained.
Step 1012, multiple wheel speed signals are filtered, multiple wheel speed signals after being filtered.
Step 1013, the wheel speed signal of default sample conditions is met according to multiple wheel speed signal selections after the filtering, is obtained
Wheel speed sample set.
Example, the wheel speed of each wheel in vehicle travel process can be monitored by wheel detector, when wheel rotates
When, generation is transferred to the electronic control assembly of vehicle with rotary body phase identical pulse signal as wheel speed signal.By this
Method electronic assembly can receive multiple wheel speed signals of whole wheels, then be filtered processing to these wheel speed signals,
And therefrom selection meets the wheel speed signal of sample conditions, obtains wheel speed sample set, includes vehicle in the wheel speed sample set
Each wheel wheel speed.
Step 1014, the longitudinal acceleration in current period by the vehicle that the acceleration transducer of vehicle gathers is obtained
Measured value, and the longitudinal acceleration measured value of current period is filtered by default filtering algorithm, obtain current period
Longitudinal acceleration.Wherein, step 1011 is to 1013, and step 1014 can perform simultaneously.
Example, the preset algorithm can be Kalman (kalman) filtering, limit filtration etc., by taking limit filtration as an example,
The filtering algorithm can include:
Wherein,Kth cycle and the longitudinal acceleration measured value of the vehicle in the cycle of kth -1, ax are represented respectivelyk
Represent the longitudinal acceleration value in kth cycle, δ0Represent the threshold value of the longitudinal acceleration difference in two neighboring cycle.It can understand
For due to the complexity of the running environment of vehicle, for gathering the process circuit of wheel speed inevitably by by the strong of the external world
Electromagnetic interference, so as to cause the moment distortion of wheel speed signal, therefore obtaining the longitudinal acceleration measured value of current period
Afterwards, it is necessary to determine whether to be modified the longitudinal acceleration measured value of current period, its judgement can be according to current period
The difference of longitudinal acceleration measured value in longitudinal acceleration measured value and a upper cycle whether be less than threshold value δ0, when the difference is small
In threshold value δ0When, illustrating the longitudinal acceleration measured value of current period does not have distortion, can be directly as the vehicle of current period
Longitudinal acceleration, when the difference is more than threshold value δ0When, it is believed that the longitudinal acceleration measured value distortion of current period, then need
To be modified by above-mentioned filtering algorithm.
Fig. 3 is the flow chart of another speed prediction method according to an exemplary embodiment, as shown in figure 3, step
Described in rapid 102 dynamic prediction model is established according to the wheel speed sample set of current period and the longitudinal acceleration of current period can
To comprise the following steps:
Step 1021, N number of car was obtained according to the speed prediction value in the wheel speed sample set in a upper cycle and a upper cycle
Wheel is in the wheel speed in a upper cycle and the deviation of the speed prediction value in a upper cycle.
Step 1022, the wheel acceleration of N number of wheel is obtained respectively according to the wheel speed sample set of current period.
Step 1023, according to the wheel speed of the wheel speed sample set of current period, N number of wheel in a upper cycle and a upper cycle
The deviation of speed prediction value, the longitudinal acceleration of the wheel acceleration of N number of wheel and current period establish dynamic prediction model.
Wherein, the dynamic prediction model can be understood as using the wheel speed of above-mentioned N number of wheel and longitudinal acceleration as
Variable, the function model using speed prediction value as output, and the coefficient of each wheel wheel speed can in the dynamic prediction model
With what is obtained according to each wheel in the wheel speed in a upper cycle and the deviation of upper cycle speed prediction value.
Example, by taking the automobile of 4 wheels as an example, the dynamic prediction model can be expressed as:
Wherein,Represent respectively the cycle of kth -1 the near front wheel wheel speed and speed prediction value it
Between deviation, the deviation between the left rear wheel wheel speed in the cycle of kth -1 and speed prediction value, the off-front wheel wheel speed in the cycle of kth -1 with
Deviation between the off hind wheel wheel speed and speed prediction value of deviation, the cycle of kth -1 between speed prediction value,The near front wheel wheel speed in the expression cycle of kth -1, off-front wheel wheel speed, left rear wheel wheel speed, the right side respectively
Trailing wheel wheel speed,The near front wheel wheel speed, off-front wheel wheel speed, left rear wheel in kth cycle are represented respectively
Wheel speed, off hind wheel wheel speed, VkFor the speed prediction value in kth cycle,The near front wheel wheel acceleration in kth cycle is represented,Table
Show the off-front wheel wheel acceleration in kth cycle,The left rear wheel wheel acceleration in kth cycle is represented,Represent the right side in kth cycle
Rear wheel rotation acceleration, axkThe longitudinal acceleration of the vehicle in kth cycle is represented, Δ represents wheel acceleration and longitudinal acceleration difference
Threshold value.
It is understood that in 5 formula for speed prediction that above-mentioned dynamic prediction model is provided, specifically
Speed prediction is carried out using which, can be according to the wheel acceleration difference with longitudinal acceleration, and above-mentioned dynamic respectively of 4 wheels
Rule of judgment shown in state forecast model determines.
Optionally, Fig. 4 is the flow chart of another speed prediction method according to an exemplary embodiment, such as Fig. 4
It is shown, described in step 105 according to the speed prediction value of current period and M cycle obtains before speed prediction value, with
The reference speed measured value that the reference speed measured value of current period and M cycle obtain, obtaining error sample set can be with
Comprise the following steps:
Step 1051, current period is obtained respectively and in M cycle, the speed prediction value in each cycle with reference to wheel with taking turns
The error of fast measured value, obtain multiple errors.
Error i.e. between the reference wheel wheel speed measured value of the speed prediction value of acquisition current period and current period, upper one
The speed prediction value in cycle and the reference wheel wheel speed measured value in a upper cycle, by that analogy, until before obtaining current period
The error in m-th cycle, so as to obtain multiple errors.
Step 1052, some or all of error in multiple errors is selected to obtain error sample set as error sample
Close.
Optionally, Fig. 5 is the flow chart of another speed prediction method according to an exemplary embodiment, such as Fig. 5
It is shown, error correction parameter for next cycle is obtained according to error sample set described in step 106, and under utilizing and being used for
The calculating that the error correction parameter in one cycle carries out next cycle can be included with following steps:
Step 1061, the error prediction model of current period is established according to error sample set.
The error prediction model that current period is established according to error sample set is appreciated that as according to error sample set
In multiple errors be fitted the error prediction model of current period.It is noted that due to that will be obtained in each cycle
Current period and in the preceding M cycle, the speed prediction value in each cycle and the error with reference to wheel wheel speed measured value, therefore every
The element that the individual cycle is obtained in error sample set all (can be understood as adding the error of current period, and removes it in renewal
The error of time earliest a cycle in the preceding M cycle), therefore error prediction model can be made also to keep real-time update.
Step 1062, the error correction parameter for next cycle is obtained using error prediction model.
Example, according to error sample set establish error prediction model can by interpolation, fitting, Kalman Algorithm,
The methods of Luenberger observer, here by taking Kalman Algorithm as an example, the error prediction model can include:
xk=xk-1+vk
Wherein, xkThe error correction values in kth cycle are represented,The predicted value of the error correction values in kth cycle is represented,Table
Show the estimate of the error correction values in kth cycle, Q represents process noise covariance, zkRepresent the error actual value in kth cycle, R
Measurement noise covariance is represented,The evaluated error covariance in kth cycle is represented,Represent the prediction error association side in kth cycle
Difference, KkThe kalman gain in kth cycle is represented, I represents unit matrix.
Above-mentioned method is illustrated when so that the vehicle of speed to be predicted being four-wheel car as an example, and Fig. 6 is according to one
A kind of vehicle electronic system structural representation shown in exemplary embodiment, as shown in fig. 6, the electronic control system bag of the vehicle
Include:Electronic control assembly and hydraulic assembly, the electronic control assembly include computing unit, control unit and monitoring unit etc., liquid
Pressure assembly master cylinder is connected, brake pedal connection master cylinder, and the magnetic valve in the hydraulic assembly is controlled by the control unit, and the system is also
Including acceleration transducer, and the wheel speed sensors that respectively four wheels are set.It is one from step 101 to step 106
Cycle T (completes the time required for step 101 to step 106).
The wheel speed signal of four wheels of automobile can be gathered by wheel speed sensors, and the wheel speed signal of four wheels is entered
Row filtering process, the filtering algorithm can be digital averaging filtering, first-order lag filtering or limit filtration, can effectively remove dry
Disturb.One sample conditions of setting screen to filtered wheel speed signal, obtain wheel speed sample set { ωn}.Wherein sample
The acquisition of condition, such as a fixed threshold value can be chosen according to a large amount of empirical datas obtained in the daily traveling of automobile,
An or moveable value window.Meanwhile the longitudinal acceleration of the vehicle gathered by acceleration transducer, obtain vehicle
The method of longitudinal acceleration can be described above shown in step 1014.Then computing unit can be by obtaining wheel speed sample set
{ωnAnd longitudinal acceleration establish dynamic prediction model, it establishes process as shown in step 1023, the dynamic prediction model it is defeated
Go out is (to be expressed as T in the current kth cycle to vehiclek) travel speed YkSpeed prediction value, wherein k, n is positive integer, k
Initial value be less than n for 1, i.Then T (can be expressed as according to a upper cycle, the i.e. cycle of kth -1k-1) obtained error correction
Parameter is modified to the dynamic prediction model, and by obtained state space vector, and longitudinal acceleration is as the amendment
The input of dynamic prediction model afterwards, so as to calculate current cycle TkSpeed prediction value Yk.Wherein, when k is 1, i.e.,
During a cycle, due to a no upper cycle, therefore the error correction parameter in a upper cycle is 0, corresponding dynamic prediction mould
Type does not also update.It is then possible to according to acquisition current period TkAnd the dynamic in each cycle in the k-1 cycle before is pre-
The speed prediction value of model output and the error with reference to wheel wheel speed measured value are surveyed, so as to obtain k error, and selects this k by mistake
Some or all of error in difference is as error sample, so as to obtain error sample set.So as to according to error sample
Current period T is established in setkError prediction model, and obtained using error prediction model for next cycle, i.e. the week of kth+1
Phase (is expressed as Tk+1) error correction parameter, the parameter error corrected parameter can be used for next cycle Tk+1Step 101 to
Step 106, i.e., basis is used for next cycle Tk+1Error correction parameter, next time perform step 101 to step 106 when repair
Orthokinesis forecast model, so as to obtain next cycle T using revised dynamic prediction modelk+1Speed prediction value Yk+1.Can
See, perform step 101 to 106 by constantly circulating, you can obtain the current speed prediction value of vehicle in real time, and pass through
Each amendment of the cycle to dynamic prediction model, can make it that speed prediction value is more and more accurate.
Wherein, speed prediction value can feed back to the electronic control module of vehicle, can be the driving of vehicle, braking, turn
The control of curved and electronic stability provides reliable reference information.
In summary, the disclosure combines the wheel speed of whole wheels and is modeled, and goes for vehicle travel process
In various scenes, the versatility easily occurred during wheel speed calculation speed using single wheel in the prior art can be avoided
Low, the problem of error is larger, therefore versatility can be improved, meanwhile, the technical scheme that the disclosure is provided being capable of real-time update
For predicting the model of speed, so as to the interference that brings of wheel speed error during effectively reducing braking, breakking away, prediction is improved
The degree of accuracy, reduce error.
Fig. 7 is a kind of block diagram of speed prediction device according to an exemplary embodiment, as shown in fig. 7, the device
Including:Acquisition module 401, forecast model establish module 402, state space vector acquisition module 403, speed prediction module 404,
Error acquisition module 405 and corrected parameter acquisition module 406;
Acquisition module 401, for obtaining wheel speed sample set of N number of wheel in current period of vehicle, and vehicle exists
The longitudinal acceleration of current period, wherein N are positive integer.
Forecast model establishes module 402, adds for the wheel speed sample set according to current period and the longitudinal direction of current period
Speed establishes dynamic prediction model, and the error correction parameter for current period obtained according to a upper cycle is to dynamic prediction
Model is modified.
State space vector acquisition module 403, for being obtained according to default state-space model and wheel speed sample set
Take state space vectorial.
Speed prediction module 404, for the longitudinal acceleration according to state space vector and current period, utilize amendment
Dynamic prediction model afterwards obtains the speed prediction value of current period.
Error acquisition module 405, the speed that M cycle obtains for the speed prediction value according to current period and before
Predicted value, the reference wheel wheel speed measured value that wheel speed measured value is taken turns in the reference with current period and M cycle obtains, obtains error
Sample set, wherein M are nonnegative integer.
Corrected parameter acquisition module 406, for obtaining the error correction ginseng for next cycle according to error sample set
Number, and the calculating that next cycle is carried out for the error correction parameter in next cycle is utilized, wherein N number of wheel from acquisition vehicle
Obtained in the wheel speed sample set of current period, and vehicle in the longitudinal acceleration of current period to according to error sample set
Error correction parameter for next cycle is a cycle.
Optionally, Fig. 8 is a kind of block diagram of acquisition module according to an exemplary embodiment, as shown in figure 8, obtaining
Module 401 can include:
Signal acquisition module 4011, multiple wheel speed signals of N number of wheel for obtaining vehicle.
Filtration module 4012, for being filtered to multiple wheel speed signals, multiple wheel speed signals after being filtered.
Sample set acquisition module 4013, for meeting default sample conditions according to multiple wheel speed signal selections after the filtering
Wheel speed signal, obtain wheel speed sample set.
Acceleration acquisition module 4014, the vehicle that the acceleration transducer for obtaining by vehicle gathers is in current period
Longitudinal acceleration measured value, and the longitudinal acceleration measured value of current period is filtered by default filtering algorithm,
Obtain current period longitudinal acceleration.
Optionally, Fig. 9 is the block diagram that a kind of forecast model according to an exemplary embodiment establishes module, such as Fig. 9
Shown, forecast model, which establishes module 402, to be included:Deviation acquisition module 4021, wheel acceleration acquisition module 4022 and modeling
Module 4023.
Deviation acquisition module 4021, for the wheel speed sample set according to a upper cycle and the speed prediction in a upper cycle
Value obtained N number of wheel in the wheel speed in a upper cycle and the deviation of the speed prediction value in a upper cycle;
Acceleration acquisition module 4022 is taken turns, for obtaining the wheel of N number of wheel respectively according to the wheel speed sample set of current period
Acceleration;
Modeling module 4023, for the wheel speed sample set according to current period, the deviation, N number of wheel wheel acceleration
And the longitudinal acceleration of current period establishes dynamic prediction model.
Optionally, Figure 10 is a kind of block diagram of corrected parameter acquisition module according to an exemplary embodiment, is such as schemed
Shown in 10, corrected parameter acquisition module 406 can include:
Error model establishes module 4061, for establishing the error prediction model of current period according to error sample set.
Parameter acquisition module 4062, for obtaining the error correction parameter for next cycle using error prediction model.
Optionally, Figure 11 is a kind of block diagram of error acquisition module according to an exemplary embodiment, such as Figure 11 institutes
Show, error acquisition module 405 can include:
Error calculating module 4051, for obtaining current period respectively and in M cycle, the speed prediction in each cycle
Value and the error with reference to wheel wheel speed measured value, obtain multiple errors.
Error screening sample module 4052, for selecting some or all of error in multiple errors as error sample
This, obtains error sample set.
Optionally, the dynamic prediction model can include:
Wherein,Represent respectively the cycle of kth -1 the near front wheel wheel speed and speed prediction value it
Between deviation, the deviation between the left rear wheel wheel speed in the cycle of kth -1 and speed prediction value, the off-front wheel wheel speed in the cycle of kth -1 with
Deviation between the off hind wheel wheel speed and speed prediction value of deviation, the cycle of kth -1 between speed prediction value,The near front wheel wheel speed in the expression cycle of kth -1, off-front wheel wheel speed, left rear wheel wheel speed, the right side respectively
Trailing wheel wheel speed,The near front wheel wheel speed, off-front wheel wheel speed, left rear wheel in kth cycle are represented respectively
Wheel speed, off hind wheel wheel speed, VkFor the speed prediction value in kth cycle,The near front wheel wheel acceleration in kth cycle is represented,Table
Show the off-front wheel wheel acceleration in kth cycle,The left rear wheel wheel acceleration in kth cycle is represented,Represent the right side in kth cycle
Rear wheel rotation acceleration, axkThe longitudinal acceleration of the vehicle in kth cycle is represented, Δ represents wheel acceleration and longitudinal acceleration difference
Threshold value.
Optionally, the state space vector is the vector using the wheel speed of N number of wheel as element, and the state-space model can be with
Including:
Wherein,The cycle of kth+1 and the wheel speed value of any wheel of kth cycle vehicle, λ are represented respectively1、λ2Table
Show parameter value, and meet λ1+λ2=1, Δ represents the deviation threshold of the state space vector in two neighboring cycle.
Optionally, the error prediction model can include:
xk=xk-1+vk
Wherein, xkThe error correction values in kth cycle are represented,The predicted value of the error correction values in kth cycle is represented,Table
Show the estimate of the error correction values in kth cycle, Q represents process noise covariance, zkRepresent the error actual value in kth cycle, R
Measurement noise covariance is represented,The evaluated error covariance in kth cycle is represented,Represent the prediction error association side in kth cycle
Difference, KkThe kalman gain in kth cycle is represented, I represents unit matrix.
Optionally, the filtering algorithm for being used to obtain vehicle acceleration can include:
Wherein,Kth cycle and the longitudinal acceleration measured value of the vehicle in the cycle of kth -1, ax are represented respectivelyk
Represent the longitudinal acceleration value in kth cycle.
Wherein, illustrating for above-mentioned modules realization of functions has been carried out in detail in above method embodiment
Description, here is omitted.
In summary, the disclosure can avoid not making full use of the information of four wheel speeds in the prior art, versatility is low,
The problem of error is larger, therefore versatility can be improved, meanwhile, the technical scheme that the disclosure is provided being capable of real-time update prediction
The model of speed, so as to the interference that brings of wheel speed error during effectively reducing braking, breakking away, improve the accurate of prediction
Degree, reduce error.
Those skilled in the art will readily occur to other embodiment party of the disclosure after considering specification and putting into practice the disclosure
Case.The application is intended to any modification, purposes or the adaptations of the disclosure, these modifications, purposes or adaptability
Change follows the general principle of the disclosure and including the undocumented common knowledge in the art of the disclosure or usual skill
Art means.Description and embodiments are considered only as exemplary, and the true scope of the disclosure and spirit are pointed out by claim.
It should be appreciated that the precision architecture that the disclosure is not limited to be described above and is shown in the drawings, and
And various modifications and changes can be being carried out without departing from the scope, it can also enter between a variety of embodiments of the disclosure
Row any combination, as long as it without prejudice to the thought of the disclosure, it should equally be considered as disclosure disclosure of that.The disclosure
Scope is only limited by appended claim.
Claims (18)
- A kind of 1. speed prediction method, it is characterised in that methods described includes:Wheel speed sample set of N number of wheel in current period of vehicle, and the vehicle are obtained in the vertical of the current period To acceleration, wherein N is positive integer;Dynamic prediction model is established according to the longitudinal acceleration of the wheel speed sample set of the current period and the current period, And the error correction parameter for the current period obtained according to a upper cycle is modified to the dynamic prediction model;State space vector is obtained according to default state-space model and the wheel speed sample set;According to the state space is vectorial and the longitudinal acceleration of the current period, revised dynamic prediction model is utilized Obtain the speed prediction value of the current period;The speed prediction value that M cycle obtains according to the speed prediction value of the current period and before, with the current week The reference wheel wheel speed measured value that the reference wheel wheel speed measured value of phase and the M cycle obtain, obtains error sample set, its Middle M is nonnegative integer;Error correction parameter for next cycle is obtained according to the error sample set, and utilizes the mistake for next cycle Poor corrected parameter carries out the calculating in next cycle, wherein from N number of wheel of the acquisition vehicle current period wheel speed sample Set, and the vehicle are used in longitudinal acceleration to described obtained according to the error sample set of the current period The error correction parameter in next cycle is a cycle.
- 2. according to the method for claim 1, it is characterised in that wheel of the N number of wheel for obtaining vehicle in current period Fast sample set, and the vehicle is in the longitudinal acceleration of current period, including:Obtain multiple wheel speed signals of N number of wheel of the vehicle gathered in preset duration;The multiple wheel speed signal is filtered, multiple wheel speed signals after being filtered;According to the wheel speed signal of multiple default sample conditions of wheel speed signal selection satisfaction after the filtering, the wheel speed sample is obtained This set;Obtain real in the longitudinal acceleration of the current period by the vehicle that the acceleration transducer of the vehicle gathers Measured value, and the longitudinal acceleration measured value of the current period is filtered by default filtering algorithm, obtain described work as Preceding cycle longitudinal acceleration.
- 3. method according to claim 1 or 2, it is characterised in that the wheel speed sample set according to the current period Close and the longitudinal acceleration of the current period establishes dynamic prediction model, including:N number of wheel is obtained according to the speed prediction value in the wheel speed sample set in a upper cycle and a upper cycle On described the wheel speed in a cycle and it is described on a cycle speed prediction value deviation;Obtain the wheel acceleration of N number of wheel respectively according to the wheel speed sample set of the current period;According to the wheel speed sample set of the current period, the deviation, the wheel acceleration of N number of wheel and described current The longitudinal acceleration in cycle establishes dynamic prediction model.
- 4. according to the method for claim 1, it is characterised in that described to be obtained according to the error sample set for next The error correction parameter in cycle, including:The error prediction model of the current period is established according to the error sample set;The error correction parameter for being used for next cycle is obtained using the error prediction model.
- 5. according to the method for claim 1, it is characterised in that the speed prediction value according to the current period and The speed prediction value that M cycle obtains before, is obtained with the reference speed measured value of the current period and the M cycle Reference speed measured value, obtain error sample set, including:The current period is obtained respectively and in the M cycle, the speed prediction value and reference wheel wheel speed in each cycle are real The error of measured value, obtain multiple errors;The some or all of error in the multiple error is selected to obtain the error sample set as error sample.
- 6. according to the method described in claim any one of 1-5, it is characterised in that the dynamic prediction model includes:<mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msup> <mi>V</mi> <mi>k</mi> </msup> <mo>=</mo> <mfrac> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>F</mi> <mi>L</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> <mrow> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>F</mi> <mi>L</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> <mo>+</mo> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>F</mi> <mi>R</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> <mo>+</mo> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>R</mi> <mi>L</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> <mo>+</mo> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>R</mi> <mi>R</mi> </mrow> 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<mi>V</mi> <mi>k</mi> </msup> <mo>=</mo> <mfrac> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>F</mi> <mi>L</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> <mrow> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>F</mi> <mi>L</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> <mo>+</mo> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>F</mi> <mi>R</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> <mo>+</mo> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>R</mi> <mi>L</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> <mo>+</mo> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>R</mi> <mi>R</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> </mrow> </mfrac> <mrow> <mo>(</mo> <msubsup> <mi>V</mi> <mrow> <mi>w</mi> <mi>s</mi> <mi>F</mi> <mi>L</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <mo>+</mo> <msup> <mi>ax</mi> <mi>k</mi> </msup> <mo>*</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>+</mo> <mfrac> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>F</mi> <mi>R</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> <mrow> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>F</mi> <mi>L</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> <mo>+</mo> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>F</mi> <mi>R</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> <mo>+</mo> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>R</mi> <mi>L</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> <mo>+</mo> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>R</mi> <mi>R</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> </mrow> </mfrac> <msubsup> <mi>V</mi> <mrow> <mi>w</mi> <mi>s</mi> <mi>F</mi> <mi>R</mi> </mrow> <mi>k</mi> </msubsup> <mo>+</mo> <mfrac> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>R</mi> <mi>L</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> <mrow> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>F</mi> <mi>L</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> <mo>+</mo> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>F</mi> <mi>R</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> <mo>+</mo> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>R</mi> <mi>L</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> <mo>+</mo> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>R</mi> <mi>R</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> </mrow> </mfrac> <msubsup> <mi>V</mi> <mrow> <mi>w</mi> <mi>s</mi> <mi>R</mi> <mi>L</mi> </mrow> <mi>k</mi> </msubsup> <mo>+</mo> <mfrac> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>R</mi> <mi>R</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> <mrow> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>F</mi> <mi>L</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> <mo>+</mo> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>F</mi> <mi>R</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> <mo>+</mo> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>R</mi> <mi>L</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> <mo>+</mo> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>R</mi> <mi>R</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> </mrow> </mfrac> <msubsup> <mi>V</mi> <mrow> <mi>w</mi> <mi>s</mi> <mi>R</mi> <mi>R</mi> </mrow> <mi>k</mi> </msubsup> <mo>,</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>i</mi> <mi>f</mi> <mrow> <mo>(</mo> <mo>|</mo> <msubsup> <mi>av</mi> <mrow> <mi>F</mi> <mi>L</mi> </mrow> <mi>k</mi> </msubsup> <mo>-</mo> <msup> <mi>ax</mi> <mi>k</mi> </msup> <mo>|</mo> <mo>></mo> <mi>&Delta;</mi> <mo>,</mo> <mo>|</mo> <msubsup> <mi>av</mi> <mrow> <mi>F</mi> <mi>R</mi> </mrow> <mi>k</mi> </msubsup> <mo>-</mo> <msup> <mi>ax</mi> <mi>k</mi> </msup> <mo>|</mo> <mo>&le;</mo> <mi>&Delta;</mi> <mo>,</mo> <mo>|</mo> <msubsup> <mi>av</mi> <mrow> <mi>R</mi> <mi>L</mi> </mrow> <mi>k</mi> </msubsup> <mo>-</mo> <msup> <mi>ax</mi> <mi>k</mi> </msup> <mo>|</mo> <mo>&le;</mo> <mi>&Delta;</mi> <mo>,</mo> <mo>|</mo> <msubsup> <mi>av</mi> <mrow> <mi>R</mi> <mi>R</mi> </mrow> <mi>k</mi> </msubsup> <mo>-</mo> <msup> <mi>ax</mi> <mi>k</mi> </msup> <mo>|</mo> <mo>&le;</mo> <mi>&Delta;</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msup> <mi>V</mi> <mi>k</mi> </msup> <mo>=</mo> <mfrac> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>F</mi> <mi>L</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> <mrow> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>F</mi> <mi>L</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> <mo>+</mo> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>F</mi> <mi>R</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> <mo>+</mo> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>R</mi> <mi>L</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> <mo>+</mo> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>R</mi> <mi>R</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> </mrow> </mfrac> <msubsup> <mi>V</mi> <mrow> <mi>w</mi> <mi>s</mi> <mi>F</mi> <mi>L</mi> </mrow> <mi>k</mi> </msubsup> <mo>+</mo> <mfrac> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>F</mi> <mi>R</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> <mrow> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>F</mi> <mi>L</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> <mo>+</mo> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>F</mi> <mi>R</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> <mo>+</mo> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>R</mi> <mi>L</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> <mo>+</mo> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>R</mi> <mi>R</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> </mrow> </mfrac> <mrow> <mo>(</mo> <msubsup> <mi>V</mi> <mrow> <mi>w</mi> <mi>s</mi> <mi>F</mi> <mi>R</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <mo>+</mo> <msup> <mi>ax</mi> <mi>k</mi> </msup> <mo>*</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>+</mo> <mfrac> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>R</mi> <mi>L</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> <mrow> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>F</mi> <mi>L</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> <mo>+</mo> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>F</mi> <mi>R</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> <mo>+</mo> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>R</mi> <mi>L</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> <mo>+</mo> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>R</mi> <mi>R</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> </mrow> </mfrac> <msubsup> <mi>V</mi> <mrow> <mi>w</mi> <mi>s</mi> <mi>R</mi> <mi>L</mi> </mrow> <mi>k</mi> </msubsup> <mo>+</mo> <mfrac> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>R</mi> <mi>R</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> <mrow> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>F</mi> <mi>L</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> <mo>+</mo> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>F</mi> <mi>R</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> <mo>+</mo> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>R</mi> <mi>L</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> <mo>+</mo> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>R</mi> <mi>R</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> </mrow> </mfrac> <msubsup> <mi>V</mi> <mrow> <mi>w</mi> <mi>s</mi> <mi>R</mi> <mi>R</mi> </mrow> <mi>k</mi> </msubsup> <mo>,</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>i</mi> <mi>f</mi> <mrow> <mo>(</mo> <mo>|</mo> <msubsup> <mi>av</mi> <mrow> <mi>F</mi> <mi>L</mi> </mrow> <mi>k</mi> </msubsup> <mo>-</mo> <msup> <mi>ax</mi> <mi>k</mi> </msup> <mo>|</mo> <mo>&le;</mo> <mi>&Delta;</mi> <mo>,</mo> <mo>|</mo> <msubsup> <mi>av</mi> <mrow> <mi>F</mi> <mi>R</mi> </mrow> <mi>k</mi> </msubsup> <mo>-</mo> <msup> <mi>ax</mi> <mi>k</mi> </msup> <mo>|</mo> <mo>></mo> <mi>&Delta;</mi> <mo>,</mo> <mo>|</mo> <msubsup> <mi>av</mi> <mrow> <mi>R</mi> <mi>L</mi> </mrow> <mi>k</mi> </msubsup> <mo>-</mo> <msup> <mi>ax</mi> <mi>k</mi> </msup> <mo>|</mo> <mo>&le;</mo> <mi>&Delta;</mi> <mo>,</mo> <mo>|</mo> <msubsup> <mi>av</mi> <mrow> <mi>R</mi> <mi>R</mi> </mrow> <mi>k</mi> </msubsup> <mo>-</mo> <msup> <mi>ax</mi> <mi>k</mi> </msup> <mo>|</mo> <mo>&le;</mo> <mi>&Delta;</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msup> <mi>V</mi> <mi>k</mi> </msup> <mo>=</mo> <mfrac> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>F</mi> <mi>L</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> <mrow> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>F</mi> <mi>L</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> <mo>+</mo> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>F</mi> <mi>R</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> <mo>+</mo> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>R</mi> <mi>L</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> <mo>+</mo> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>R</mi> <mi>R</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> </mrow> </mfrac> <msubsup> <mi>V</mi> <mrow> <mi>w</mi> <mi>s</mi> <mi>F</mi> <mi>L</mi> </mrow> <mi>k</mi> </msubsup> <mo>+</mo> <mfrac> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>F</mi> <mi>R</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> <mrow> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>F</mi> <mi>L</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> <mo>+</mo> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>F</mi> <mi>R</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> <mo>+</mo> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>R</mi> <mi>L</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> <mo>+</mo> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>R</mi> <mi>R</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> </mrow> </mfrac> <msubsup> <mi>V</mi> <mrow> <mi>w</mi> <mi>s</mi> <mi>F</mi> <mi>R</mi> </mrow> <mi>k</mi> </msubsup> <mo>+</mo> <mfrac> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>R</mi> <mi>L</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> <mrow> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>F</mi> <mi>L</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> <mo>+</mo> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>F</mi> <mi>R</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> <mo>+</mo> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>R</mi> <mi>L</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> <mo>+</mo> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>R</mi> <mi>R</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> </mrow> </mfrac> <mrow> <mo>(</mo> <msubsup> <mi>V</mi> <mrow> <mi>w</mi> <mi>s</mi> <mi>R</mi> <mi>L</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <mo>+</mo> <msup> <mi>ax</mi> <mi>k</mi> </msup> <mo>*</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>+</mo> <mfrac> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>R</mi> <mi>R</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> <mrow> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>F</mi> <mi>L</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> <mo>+</mo> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>F</mi> <mi>R</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> <mo>+</mo> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>R</mi> <mi>L</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> <mo>+</mo> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>R</mi> <mi>R</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> </mrow> </mfrac> <msubsup> <mi>V</mi> <mrow> <mi>w</mi> <mi>s</mi> <mi>R</mi> <mi>R</mi> </mrow> <mi>k</mi> </msubsup> <mo>,</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>i</mi> <mi>f</mi> <mrow> <mo>(</mo> <mo>|</mo> <msubsup> <mi>av</mi> <mrow> <mi>F</mi> <mi>L</mi> </mrow> <mi>k</mi> </msubsup> <mo>-</mo> <msup> <mi>ax</mi> <mi>k</mi> </msup> <mo>|</mo> <mo>&le;</mo> <mi>&Delta;</mi> <mo>,</mo> <mo>|</mo> <msubsup> <mi>av</mi> <mrow> <mi>F</mi> <mi>R</mi> </mrow> <mi>k</mi> </msubsup> <mo>-</mo> <msup> <mi>ax</mi> <mi>k</mi> </msup> <mo>|</mo> <mo>&le;</mo> <mi>&Delta;</mi> <mo>,</mo> <mo>|</mo> <msubsup> <mi>av</mi> <mrow> <mi>R</mi> <mi>L</mi> </mrow> <mi>k</mi> </msubsup> <mo>-</mo> <msup> <mi>ax</mi> <mi>k</mi> </msup> <mo>|</mo> <mo>></mo> <mi>&Delta;</mi> <mo>,</mo> <mo>|</mo> <msubsup> <mi>av</mi> <mrow> <mi>R</mi> <mi>R</mi> </mrow> <mi>k</mi> </msubsup> <mo>-</mo> <msup> <mi>ax</mi> <mi>k</mi> </msup> <mo>|</mo> <mo>&le;</mo> <mi>&Delta;</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msup> <mi>V</mi> <mi>k</mi> </msup> <mo>=</mo> <mfrac> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>F</mi> <mi>L</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> <mrow> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>F</mi> <mi>L</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> <mo>+</mo> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>F</mi> <mi>R</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> <mo>+</mo> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>R</mi> <mi>L</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> <mo>+</mo> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>R</mi> <mi>R</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> </mrow> </mfrac> <msubsup> <mi>V</mi> <mrow> <mi>w</mi> <mi>s</mi> <mi>F</mi> <mi>L</mi> </mrow> <mi>k</mi> </msubsup> <mo>+</mo> <mfrac> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>F</mi> <mi>R</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> <mrow> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>F</mi> <mi>L</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> <mo>+</mo> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>F</mi> <mi>R</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> <mo>+</mo> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>R</mi> <mi>L</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> <mo>+</mo> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>R</mi> <mi>R</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> </mrow> </mfrac> <msubsup> <mi>V</mi> <mrow> <mi>w</mi> <mi>s</mi> <mi>F</mi> <mi>R</mi> </mrow> <mi>k</mi> </msubsup> <mo>+</mo> <mfrac> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>R</mi> <mi>L</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> <mrow> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>F</mi> <mi>L</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> <mo>+</mo> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>F</mi> <mi>R</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> <mo>+</mo> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>R</mi> <mi>L</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> <mo>+</mo> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>R</mi> <mi>R</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> </mrow> </mfrac> <msubsup> <mi>V</mi> <mrow> <mi>w</mi> <mi>s</mi> <mi>R</mi> <mi>L</mi> </mrow> <mi>k</mi> </msubsup> <mo>+</mo> <mfrac> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>R</mi> <mi>R</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> <mrow> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>F</mi> <mi>L</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> <mo>+</mo> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>F</mi> <mi>R</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> <mo>+</mo> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>R</mi> <mi>L</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> <mo>+</mo> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>R</mi> <mi>R</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> </mrow> </mfrac> <mrow> <mo>(</mo> <msubsup> <mi>V</mi> <mrow> <mi>w</mi> <mi>s</mi> <mi>R</mi> <mi>R</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <mo>+</mo> <msup> <mi>ax</mi> <mi>k</mi> </msup> <mo>*</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>,</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>i</mi> <mi>f</mi> <mrow> <mo>(</mo> <mo>|</mo> <msubsup> <mi>av</mi> <mrow> <mi>F</mi> <mi>L</mi> </mrow> <mi>k</mi> </msubsup> <mo>-</mo> <msup> <mi>ax</mi> <mi>k</mi> </msup> <mo>|</mo> <mo>&le;</mo> <mi>&Delta;</mi> <mo>,</mo> <mo>|</mo> <msubsup> <mi>av</mi> <mrow> <mi>F</mi> <mi>R</mi> </mrow> <mi>k</mi> </msubsup> <mo>-</mo> <msup> <mi>ax</mi> <mi>k</mi> </msup> <mo>|</mo> <mo>&le;</mo> <mi>&Delta;</mi> <mo>,</mo> <mo>|</mo> <msubsup> <mi>av</mi> <mrow> <mi>R</mi> <mi>L</mi> </mrow> <mi>k</mi> </msubsup> <mo>-</mo> <msup> <mi>ax</mi> <mi>k</mi> </msup> <mo>|</mo> <mo>&le;</mo> <mi>&Delta;</mi> <mo>,</mo> <mo>|</mo> <msubsup> <mi>av</mi> <mrow> <mi>R</mi> <mi>R</mi> </mrow> <mi>k</mi> </msubsup> <mo>-</mo> <msup> <mi>ax</mi> <mi>k</mi> </msup> <mo>|</mo> <mo>></mo> <mi>&Delta;</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced>Wherein,Respectively represent the cycle of kth -1 the near front wheel wheel speed and speed prediction value between deviation, Deviation, the off-front wheel wheel speed in the cycle of kth -1 and speed prediction value between the left rear wheel wheel speed and speed prediction value in the cycle of kth -1 Between deviation, the deviation between the off hind wheel wheel speed in the cycle of kth -1 and speed prediction value, The near front wheel wheel speed, off-front wheel wheel speed, left rear wheel wheel speed, the off hind wheel wheel speed in the cycle of kth -1 are represented respectively,The near front wheel wheel speed in expression kth cycle, off-front wheel wheel speed, left rear wheel wheel speed, off hind wheel respectively Wheel speed, VkFor the speed prediction value in kth cycle,The near front wheel wheel acceleration in kth cycle is represented,Represent the kth cycle Off-front wheel wheel acceleration,The left rear wheel wheel acceleration in kth cycle is represented,Represent that the off hind wheel wheel in kth cycle accelerates Degree, axkThe longitudinal acceleration of the vehicle in kth cycle is represented, Δ represents wheel acceleration and the threshold value of longitudinal acceleration difference.
- 7. according to the method described in claim any one of 1-5, it is characterised in that the state space vector is with described N number of The wheel speed of wheel is the vector of element, and the state-space model includes:<mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <msubsup> <mi>V</mi> <mrow> <mi>w</mi> <mi>s</mi> </mrow> <mrow> <mi>k</mi> <mo>+</mo> <mn>1</mn> </mrow> </msubsup> <mo>=</mo> <msubsup> <mi>V</mi> <mrow> <mi>w</mi> <mi>s</mi> </mrow> <mrow> <mi>k</mi> <mo>+</mo> <mn>1</mn> </mrow> </msubsup> <mo>,</mo> <mi>i</mi> <mi>f</mi> <mo>|</mo> <msubsup> <mi>V</mi> <mrow> <mi>w</mi> <mi>s</mi> </mrow> <mrow> <mi>k</mi> <mo>+</mo> <mn>1</mn> </mrow> </msubsup> <mo>-</mo> <msubsup> <mi>V</mi> <mrow> <mi>w</mi> <mi>s</mi> </mrow> <mi>k</mi> </msubsup> <mo>|</mo> <mo><</mo> <mi>&Delta;</mi> </mtd> </mtr> <mtr> <mtd> <msubsup> <mi>V</mi> <mrow> <mi>w</mi> <mi>s</mi> </mrow> <mrow> <mi>k</mi> <mo>+</mo> <mn>1</mn> </mrow> </msubsup> <mo>=</mo> <msub> <mi>&lambda;</mi> <mn>1</mn> </msub> <mo>*</mo> <msubsup> <mi>V</mi> <mrow> <mi>w</mi> <mi>s</mi> </mrow> <mi>k</mi> </msubsup> <mo>+</mo> <msub> <mi>&lambda;</mi> <mn>2</mn> </msub> <mo>*</mo> <msubsup> <mi>V</mi> <mrow> <mi>w</mi> <mi>s</mi> </mrow> <mrow> <mi>k</mi> <mo>+</mo> <mn>1</mn> </mrow> </msubsup> <mo>,</mo> <mi>i</mi> <mi>f</mi> <mo>|</mo> <msubsup> <mi>V</mi> <mrow> <mi>w</mi> <mi>s</mi> </mrow> <mrow> <mi>k</mi> <mo>+</mo> <mn>1</mn> </mrow> </msubsup> <mo>-</mo> <msubsup> <mi>V</mi> <mrow> <mi>w</mi> <mi>s</mi> </mrow> <mi>k</mi> </msubsup> <mo>|</mo> <mo>></mo> <mo>=</mo> <mi>&Delta;</mi> </mtd> </mtr> </mtable> </mfenced>Wherein,The cycle of kth+1 and the wheel speed value of any wheel of kth cycle vehicle, λ are represented respectively1、λ2Represent ginseng Numerical value, and meet λ1+λ2=1, Δ represents the deviation threshold of the state space vector in two neighboring cycle.
- 8. according to the method for claim 4, it is characterised in that the error prediction model includes:xk=xk-1+vk<mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msubsup> <mi>x</mi> <mi>k</mi> <mo>-</mo> </msubsup> <mo>=</mo> <msub> <mover> <mi>x</mi> <mo>^</mo> </mover> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msubsup> <mi>p</mi> <mi>k</mi> <mo>-</mo> </msubsup> <mo>=</mo> <msub> <mover> <mi>p</mi> <mo>^</mo> </mover> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>+</mo> <mi>Q</mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>K</mi> <mi>k</mi> </msub> <mo>=</mo> <msubsup> <mi>p</mi> <mi>k</mi> <mo>-</mo> </msubsup> <msup> <mrow> <mo>(</mo> <msubsup> <mi>p</mi> <mi>k</mi> <mo>-</mo> </msubsup> <mo>+</mo> <mi>R</mi> <mo>)</mo> </mrow> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mover> <mi>x</mi> <mo>^</mo> </mover> <mi>k</mi> </msub> <mo>=</mo> <msubsup> <mi>x</mi> <mi>k</mi> <mo>-</mo> </msubsup> <mo>+</mo> <msub> <mi>K</mi> <mi>k</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>z</mi> <mi>k</mi> </msub> <mo>-</mo> <msubsup> <mi>x</mi> <mi>k</mi> <mo>-</mo> </msubsup> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mover> <mi>p</mi> <mo>^</mo> </mover> <mi>k</mi> </msub> <mo>=</mo> <mrow> <mo>(</mo> <mi>I</mi> <mo>-</mo> <msub> <mi>K</mi> <mi>k</mi> </msub> <mo>)</mo> </mrow> <msubsup> <mi>p</mi> <mi>k</mi> <mo>-</mo> </msubsup> </mrow> </mtd> </mtr> </mtable> </mfenced>Wherein, xkThe error correction values in kth cycle are represented,The predicted value of the error correction values in kth cycle is represented,Represent kth The estimate of the error correction values in cycle, Q represent process noise covariance, zkThe error actual value in kth cycle is represented, R is represented Measurement noise covariance,The evaluated error covariance in kth cycle is represented,Represent the predicting covariance in kth cycle, Kk The kalman gain in kth cycle is represented, I represents unit matrix.
- 9. according to the method for claim 2, it is characterised in that the filtering algorithm includes:<mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mi>a</mi> <msup> <mi>x</mi> <mi>k</mi> </msup> <mo>=</mo> <mi>a</mi> <msubsup> <mi>x</mi> <mn>1</mn> <mi>k</mi> </msubsup> <mo>,</mo> <mi>i</mi> <mi>f</mi> <mo>|</mo> <mi>a</mi> <msubsup> <mi>x</mi> <mn>1</mn> <mi>k</mi> </msubsup> <mo>-</mo> <mi>a</mi> <msubsup> <mi>x</mi> <mn>1</mn> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <mo>|</mo> <mo><</mo> <msub> <mi>&delta;</mi> <mn>0</mn> </msub> </mtd> </mtr> <mtr> <mtd> <mrow> <msup> <mi>ax</mi> <mi>k</mi> </msup> <mo>=</mo> <msubsup> <mi>ax</mi> <mn>1</mn> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <mo>+</mo> <msub> <mi>&delta;</mi> <mn>0</mn> </msub> <mo>,</mo> <mi>i</mi> <mi>f</mi> <mrow> <mo>(</mo> <msubsup> <mi>ax</mi> <mn>1</mn> <mi>k</mi> </msubsup> <mo>-</mo> <msubsup> <mi>ax</mi> <mn>1</mn> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <mo>)</mo> </mrow> <mo>></mo> <msub> <mi>&delta;</mi> <mn>0</mn> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msup> <mi>ax</mi> <mi>k</mi> </msup> <mo>=</mo> <msubsup> <mi>ax</mi> <mn>1</mn> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <mo>-</mo> <msub> <mi>&delta;</mi> <mn>0</mn> </msub> <mo>,</mo> <mi>i</mi> <mi>f</mi> <mrow> <mo>(</mo> <msubsup> <mi>ax</mi> <mn>1</mn> <mi>k</mi> </msubsup> <mo>-</mo> <msubsup> <mi>ax</mi> <mn>1</mn> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <mo>)</mo> </mrow> <mo><</mo> <mo>-</mo> <msub> <mi>&delta;</mi> <mn>0</mn> </msub> </mrow> </mtd> </mtr> </mtable> </mfenced>Wherein,Kth cycle and the longitudinal acceleration measured value of the vehicle in the cycle of kth -1, ax are represented respectivelyk Represent the longitudinal acceleration value in kth cycle, δ0Represent the threshold value of the longitudinal acceleration difference in two neighboring cycle.
- 10. a kind of speed prediction device, it is characterised in that described device includes:Acquisition module, forecast model establish module, shape State space vector acquisition module, speed prediction module, error acquisition module and corrected parameter acquisition module;The acquisition module, for obtaining wheel speed sample set of N number of wheel in current period of vehicle, and the vehicle exists The longitudinal acceleration of the current period, wherein N are positive integer;The forecast model establishes module, for the vertical of the wheel speed sample set according to the current period and the current period Dynamic prediction model, and the error correction parameter pair for the current period obtained according to a upper cycle are established to acceleration The dynamic prediction model is modified;The state space vector acquisition module, for being obtained according to default state-space model and the wheel speed sample set Take state space vectorial;The speed prediction module, for according to the state space is vectorial and the longitudinal acceleration of the current period, profit The speed prediction value of the current period is obtained with revised dynamic prediction model;The error acquisition module, the car that M cycle obtains for the speed prediction value according to the current period and before Fast predicted value, the reference wheel wheel speed actual measurement that wheel speed measured value is taken turns in the reference with the current period and the M cycle obtains Value, error sample set is obtained, wherein M is nonnegative integer;The corrected parameter acquisition module, for obtaining the error correction ginseng for next cycle according to the error sample set Number, and the calculating that next cycle is carried out for the error correction parameter in next cycle is utilized, wherein obtaining the N number of of vehicle from described Wheel current period wheel speed sample set, and the vehicle the current period longitudinal acceleration to the basis It is a cycle that the error sample set, which is obtained for the error correction parameter in next cycle,.
- 11. device according to claim 10, it is characterised in that the acquisition module includes:Signal acquisition module, filtering Module, sample set acquisition module and acceleration acquisition module;The signal acquisition module, multiple wheel speed signals of N number of wheel of the vehicle for obtaining collection;The filtration module, for being filtered to the multiple wheel speed signal, multiple wheel speed signals after being filtered;The sample set acquisition module, for according to multiple default sample conditions of wheel speed signal selection satisfaction after the filtering Wheel speed signal, obtain the wheel speed sample set;The acceleration acquisition module, the vehicle that the acceleration transducer for obtaining by the vehicle gathers is described The longitudinal acceleration measured value of current period, and the longitudinal acceleration of the current period is surveyed by default filtering algorithm Value is filtered, and obtains the current period longitudinal acceleration.
- 12. the device according to claim 10 or 11, it is characterised in that the forecast model, which establishes module, to be included:Deviation Acquisition module, wheel acceleration acquisition module and modeling module;The deviation acquisition module, for the wheel speed sample set according to the upper cycle and the speed in a upper cycle Predicted value obtain N number of wheel on described the wheel speed in a cycle and it is described on a cycle speed prediction value deviation;The wheel acceleration acquisition module, for obtaining N number of wheel respectively according to the wheel speed sample set of the current period Wheel acceleration;The modeling module, for the wheel speed sample set according to the current period, the deviation, N number of wheel wheel The longitudinal acceleration of acceleration and the current period establishes dynamic prediction model.
- 13. device according to claim 10, it is characterised in that the corrected parameter acquisition module includes:Error model establishes module, for establishing the error prediction model of the current period according to the error sample set;Parameter acquisition module, for utilizing the error prediction model to obtain the error correction parameter for being used for next cycle.
- 14. device according to claim 10, it is characterised in that the error acquisition module includes:Error calculating module, for obtaining the current period respectively and in the M cycle, the speed prediction in each cycle Value and the error with reference to wheel wheel speed measured value, obtain multiple errors;Error screening sample module, for selecting some or all of error in the multiple error to be obtained as error sample To the error sample set.
- 15. according to the device described in claim any one of 10-14, it is characterised in that the dynamic prediction model includes:<mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msup> <mi>V</mi> <mi>k</mi> </msup> <mo>=</mo> <mfrac> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>F</mi> <mi>L</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> <mrow> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>F</mi> <mi>L</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> <mo>+</mo> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>F</mi> <mi>R</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> <mo>+</mo> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>R</mi> <mi>L</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> <mo>+</mo> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>R</mi> <mi>R</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> </mrow> </mfrac> <msubsup> <mi>V</mi> <mrow> <mi>w</mi> <mi>s</mi> <mi>F</mi> <mi>L</mi> </mrow> <mi>k</mi> </msubsup> <mo>+</mo> <mfrac> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>F</mi> <mi>R</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> <mrow> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>F</mi> <mi>L</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> <mo>+</mo> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>F</mi> <mi>R</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> <mo>+</mo> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>R</mi> <mi>L</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> <mo>+</mo> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>R</mi> <mi>R</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> </mrow> </mfrac> <msubsup> <mi>V</mi> <mrow> <mi>w</mi> <mi>s</mi> <mi>F</mi> <mi>R</mi> </mrow> <mi>k</mi> </msubsup> <mo>+</mo> <mfrac> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>R</mi> <mi>L</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> <mrow> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>F</mi> <mi>L</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> <mo>+</mo> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>F</mi> <mi>R</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> <mo>+</mo> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>R</mi> <mi>L</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> <mo>+</mo> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>R</mi> <mi>R</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> </mrow> </mfrac> <msubsup> <mi>V</mi> <mrow> <mi>w</mi> <mi>s</mi> <mi>R</mi> <mi>L</mi> </mrow> <mi>k</mi> </msubsup> <mo>+</mo> <mfrac> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>R</mi> <mi>R</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> <mrow> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>F</mi> <mi>L</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> <mo>+</mo> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>F</mi> <mi>R</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> <mo>+</mo> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>R</mi> <mi>L</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> <mo>+</mo> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>R</mi> <mi>R</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> </mrow> </mfrac> <msubsup> <mi>V</mi> <mrow> <mi>w</mi> <mi>s</mi> <mi>R</mi> <mi>R</mi> </mrow> <mi>k</mi> </msubsup> <mo>,</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>i</mi> <mi>f</mi> <mrow> <mo>(</mo> <mo>|</mo> <msubsup> <mi>av</mi> <mrow> <mi>F</mi> <mi>L</mi> </mrow> <mi>k</mi> </msubsup> <mo>-</mo> <msup> <mi>ax</mi> <mi>k</mi> </msup> <mo>|</mo> <mo>&le;</mo> <mi>&Delta;</mi> <mo>,</mo> <mo>|</mo> <msubsup> <mi>av</mi> <mrow> <mi>F</mi> <mi>R</mi> </mrow> <mi>k</mi> </msubsup> <mo>-</mo> <msup> <mi>ax</mi> <mi>k</mi> </msup> <mo>|</mo> <mo>&le;</mo> <mi>&Delta;</mi> <mo>,</mo> <mo>|</mo> <msubsup> <mi>av</mi> <mrow> <mi>R</mi> <mi>L</mi> </mrow> <mi>k</mi> </msubsup> <mo>-</mo> <msup> <mi>ax</mi> <mi>k</mi> </msup> <mo>|</mo> <mo>&le;</mo> <mi>&Delta;</mi> <mo>,</mo> <mo>|</mo> <msubsup> <mi>av</mi> <mrow> <mi>R</mi> <mi>R</mi> </mrow> <mi>k</mi> </msubsup> <mo>-</mo> <msup> <mi>ax</mi> <mi>k</mi> </msup> <mo>|</mo> <mo>&le;</mo> <mi>&Delta;</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msup> <mi>V</mi> <mi>k</mi> </msup> <mo>=</mo> <mfrac> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>F</mi> <mi>L</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> <mrow> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>F</mi> <mi>L</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> <mo>+</mo> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>F</mi> <mi>R</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> <mo>+</mo> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>R</mi> <mi>L</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> <mo>+</mo> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>R</mi> <mi>R</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> </mrow> </mfrac> <mrow> <mo>(</mo> <msubsup> <mi>V</mi> <mrow> <mi>w</mi> <mi>s</mi> <mi>F</mi> <mi>L</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <mo>+</mo> <msup> <mi>ax</mi> <mi>k</mi> </msup> <mo>*</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>+</mo> <mfrac> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>F</mi> <mi>R</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> <mrow> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>F</mi> <mi>L</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> <mo>+</mo> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>F</mi> <mi>R</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> <mo>+</mo> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>R</mi> <mi>L</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> <mo>+</mo> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>R</mi> <mi>R</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> </mrow> </mfrac> <msubsup> <mi>V</mi> <mrow> <mi>w</mi> <mi>s</mi> <mi>F</mi> <mi>R</mi> </mrow> <mi>k</mi> </msubsup> <mo>+</mo> <mfrac> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>R</mi> <mi>L</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> <mrow> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>F</mi> <mi>L</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> <mo>+</mo> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>F</mi> <mi>R</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> <mo>+</mo> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>R</mi> <mi>L</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> <mo>+</mo> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>R</mi> <mi>R</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> </mrow> </mfrac> <msubsup> <mi>V</mi> <mrow> <mi>w</mi> <mi>s</mi> <mi>R</mi> <mi>L</mi> </mrow> <mi>k</mi> </msubsup> <mo>+</mo> <mfrac> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>R</mi> <mi>R</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> <mrow> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>F</mi> <mi>L</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> <mo>+</mo> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>F</mi> <mi>R</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> <mo>+</mo> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>R</mi> <mi>L</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> <mo>+</mo> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>R</mi> <mi>R</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> </mrow> </mfrac> <msubsup> <mi>V</mi> <mrow> <mi>w</mi> <mi>s</mi> <mi>R</mi> <mi>R</mi> </mrow> <mi>k</mi> </msubsup> <mo>,</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>i</mi> <mi>f</mi> <mrow> <mo>(</mo> <mo>|</mo> <msubsup> <mi>av</mi> <mrow> <mi>F</mi> <mi>L</mi> </mrow> <mi>k</mi> </msubsup> <mo>-</mo> <msup> <mi>ax</mi> <mi>k</mi> </msup> <mo>|</mo> <mo>></mo> <mi>&Delta;</mi> <mo>,</mo> <mo>|</mo> <msubsup> <mi>av</mi> <mrow> <mi>F</mi> <mi>R</mi> </mrow> <mi>k</mi> </msubsup> <mo>-</mo> <msup> <mi>ax</mi> <mi>k</mi> </msup> <mo>|</mo> <mo>&le;</mo> <mi>&Delta;</mi> <mo>,</mo> <mo>|</mo> <msubsup> <mi>av</mi> <mrow> <mi>R</mi> <mi>L</mi> </mrow> <mi>k</mi> </msubsup> <mo>-</mo> <msup> <mi>ax</mi> <mi>k</mi> </msup> <mo>|</mo> <mo>&le;</mo> <mi>&Delta;</mi> <mo>,</mo> <mo>|</mo> <msubsup> <mi>av</mi> <mrow> <mi>R</mi> <mi>R</mi> </mrow> <mi>k</mi> </msubsup> <mo>-</mo> <msup> <mi>ax</mi> <mi>k</mi> </msup> <mo>|</mo> <mo>&le;</mo> <mi>&Delta;</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msup> <mi>V</mi> <mi>k</mi> </msup> <mo>=</mo> <mfrac> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>F</mi> <mi>L</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> <mrow> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>F</mi> <mi>L</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> <mo>+</mo> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>F</mi> <mi>R</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> <mo>+</mo> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>R</mi> <mi>L</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> <mo>+</mo> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>R</mi> <mi>R</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> </mrow> </mfrac> <msubsup> <mi>V</mi> <mrow> <mi>w</mi> <mi>s</mi> <mi>F</mi> <mi>L</mi> </mrow> <mi>k</mi> </msubsup> <mo>+</mo> <mfrac> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>F</mi> <mi>R</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> <mrow> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>F</mi> <mi>L</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> <mo>+</mo> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>F</mi> <mi>R</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> <mo>+</mo> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>R</mi> <mi>L</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> <mo>+</mo> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>R</mi> <mi>R</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> </mrow> </mfrac> <mrow> <mo>(</mo> <msubsup> <mi>V</mi> <mrow> <mi>w</mi> <mi>s</mi> <mi>F</mi> <mi>R</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <mo>+</mo> <msup> <mi>ax</mi> <mi>k</mi> </msup> <mo>*</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>+</mo> <mfrac> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>R</mi> <mi>L</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> <mrow> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>F</mi> <mi>L</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> <mo>+</mo> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>F</mi> <mi>R</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> <mo>+</mo> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>R</mi> <mi>L</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> <mo>+</mo> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>R</mi> <mi>R</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> </mrow> </mfrac> <msubsup> <mi>V</mi> <mrow> <mi>w</mi> <mi>s</mi> <mi>R</mi> <mi>L</mi> </mrow> <mi>k</mi> </msubsup> <mo>+</mo> <mfrac> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>R</mi> <mi>R</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> <mrow> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>F</mi> <mi>L</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> <mo>+</mo> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>F</mi> <mi>R</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> <mo>+</mo> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>R</mi> <mi>L</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> <mo>+</mo> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>R</mi> <mi>R</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> </mrow> </mfrac> <msubsup> <mi>V</mi> <mrow> <mi>w</mi> <mi>s</mi> <mi>R</mi> <mi>R</mi> </mrow> <mi>k</mi> </msubsup> <mo>,</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>i</mi> <mi>f</mi> <mrow> <mo>(</mo> <mo>|</mo> <msubsup> <mi>av</mi> <mrow> <mi>F</mi> <mi>L</mi> </mrow> <mi>k</mi> </msubsup> <mo>-</mo> <msup> <mi>ax</mi> <mi>k</mi> </msup> <mo>|</mo> <mo>&le;</mo> <mi>&Delta;</mi> <mo>,</mo> <mo>|</mo> <msubsup> <mi>av</mi> <mrow> <mi>F</mi> <mi>R</mi> </mrow> <mi>k</mi> </msubsup> <mo>-</mo> <msup> <mi>ax</mi> <mi>k</mi> </msup> <mo>|</mo> <mo>></mo> <mi>&Delta;</mi> <mo>,</mo> <mo>|</mo> <msubsup> <mi>av</mi> <mrow> <mi>R</mi> <mi>L</mi> </mrow> <mi>k</mi> </msubsup> <mo>-</mo> <msup> <mi>ax</mi> <mi>k</mi> </msup> <mo>|</mo> <mo>&le;</mo> <mi>&Delta;</mi> <mo>,</mo> <mo>|</mo> <msubsup> <mi>av</mi> <mrow> <mi>R</mi> <mi>R</mi> </mrow> <mi>k</mi> </msubsup> <mo>-</mo> <msup> <mi>ax</mi> <mi>k</mi> </msup> <mo>|</mo> <mo>&le;</mo> <mi>&Delta;</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msup> <mi>V</mi> <mi>k</mi> </msup> <mo>=</mo> <mfrac> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>F</mi> <mi>L</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> <mrow> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>F</mi> <mi>L</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> <mo>+</mo> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>F</mi> <mi>R</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> <mo>+</mo> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>R</mi> <mi>L</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> <mo>+</mo> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>R</mi> <mi>R</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> </mrow> </mfrac> <msubsup> <mi>V</mi> <mrow> <mi>w</mi> <mi>s</mi> <mi>F</mi> <mi>L</mi> </mrow> <mi>k</mi> </msubsup> <mo>+</mo> <mfrac> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>F</mi> <mi>R</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> <mrow> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>F</mi> <mi>L</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> <mo>+</mo> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>F</mi> <mi>R</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> <mo>+</mo> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>R</mi> <mi>L</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> <mo>+</mo> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>R</mi> <mi>R</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> </mrow> </mfrac> <msubsup> <mi>V</mi> <mrow> <mi>w</mi> <mi>s</mi> <mi>F</mi> <mi>R</mi> </mrow> <mi>k</mi> </msubsup> <mo>+</mo> <mfrac> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>R</mi> <mi>L</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> <mrow> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>F</mi> <mi>L</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> <mo>+</mo> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>F</mi> <mi>R</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> <mo>+</mo> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>R</mi> <mi>L</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> <mo>+</mo> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>R</mi> <mi>R</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> </mrow> </mfrac> <mrow> <mo>(</mo> <msubsup> <mi>V</mi> <mrow> <mi>w</mi> <mi>s</mi> <mi>R</mi> <mi>L</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <mo>+</mo> <msup> <mi>ax</mi> <mi>k</mi> </msup> <mo>*</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>+</mo> <mfrac> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>R</mi> <mi>R</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> <mrow> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>F</mi> <mi>L</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> <mo>+</mo> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>F</mi> <mi>R</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> <mo>+</mo> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>R</mi> <mi>L</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> <mo>+</mo> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>R</mi> <mi>R</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> </mrow> </mfrac> <msubsup> <mi>V</mi> <mrow> <mi>w</mi> <mi>s</mi> <mi>R</mi> <mi>R</mi> </mrow> <mi>k</mi> </msubsup> <mo>,</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>i</mi> <mi>f</mi> <mrow> <mo>(</mo> <mo>|</mo> <msubsup> <mi>av</mi> <mrow> <mi>F</mi> <mi>L</mi> </mrow> <mi>k</mi> </msubsup> <mo>-</mo> <msup> <mi>ax</mi> <mi>k</mi> </msup> <mo>|</mo> <mo>&le;</mo> <mi>&Delta;</mi> <mo>,</mo> <mo>|</mo> <msubsup> <mi>av</mi> <mrow> <mi>F</mi> <mi>R</mi> </mrow> <mi>k</mi> </msubsup> <mo>-</mo> <msup> <mi>ax</mi> <mi>k</mi> </msup> <mo>|</mo> <mo>&le;</mo> <mi>&Delta;</mi> <mo>,</mo> <mo>|</mo> <msubsup> <mi>av</mi> <mrow> <mi>R</mi> <mi>L</mi> </mrow> <mi>k</mi> </msubsup> <mo>-</mo> <msup> <mi>ax</mi> <mi>k</mi> </msup> <mo>|</mo> <mo>></mo> <mi>&Delta;</mi> <mo>,</mo> <mo>|</mo> <msubsup> <mi>av</mi> <mrow> <mi>R</mi> <mi>R</mi> </mrow> <mi>k</mi> </msubsup> <mo>-</mo> <msup> <mi>ax</mi> <mi>k</mi> </msup> <mo>|</mo> <mo>&le;</mo> <mi>&Delta;</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msup> <mi>V</mi> <mi>k</mi> </msup> <mo>=</mo> <mfrac> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>F</mi> <mi>L</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> <mrow> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>F</mi> <mi>L</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> <mo>+</mo> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>F</mi> <mi>R</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> <mo>+</mo> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>R</mi> <mi>L</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> <mo>+</mo> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>R</mi> <mi>R</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> </mrow> </mfrac> <msubsup> <mi>V</mi> <mrow> <mi>w</mi> <mi>s</mi> <mi>F</mi> <mi>L</mi> </mrow> <mi>k</mi> </msubsup> <mo>+</mo> <mfrac> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>F</mi> <mi>R</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> <mrow> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>F</mi> <mi>L</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> <mo>+</mo> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>F</mi> <mi>R</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> <mo>+</mo> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>R</mi> <mi>L</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> <mo>+</mo> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>R</mi> <mi>R</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> </mrow> </mfrac> <msubsup> <mi>V</mi> <mrow> <mi>w</mi> <mi>s</mi> <mi>F</mi> <mi>R</mi> </mrow> <mi>k</mi> </msubsup> <mo>+</mo> <mfrac> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>R</mi> <mi>L</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> <mrow> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>F</mi> <mi>L</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> <mo>+</mo> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>F</mi> <mi>R</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> <mo>+</mo> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>R</mi> <mi>L</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> <mo>+</mo> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>R</mi> <mi>R</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> </mrow> </mfrac> <msubsup> <mi>V</mi> <mrow> <mi>w</mi> <mi>s</mi> <mi>R</mi> <mi>L</mi> </mrow> <mi>k</mi> </msubsup> <mo>+</mo> <mfrac> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>R</mi> <mi>R</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> <mrow> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>F</mi> <mi>L</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> <mo>+</mo> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>F</mi> <mi>R</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> <mo>+</mo> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>R</mi> <mi>L</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> <mo>+</mo> <mfrac> <mn>1</mn> <msubsup> <mi>S</mi> <mrow> <mi>z</mi> <mi>R</mi> <mi>R</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> </mrow> </mfrac> <mrow> <mo>(</mo> <msubsup> <mi>V</mi> <mrow> <mi>w</mi> <mi>s</mi> <mi>R</mi> <mi>R</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <mo>+</mo> <msup> <mi>ax</mi> <mi>k</mi> </msup> <mo>*</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>,</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>i</mi> <mi>f</mi> <mrow> <mo>(</mo> <mo>|</mo> <msubsup> <mi>av</mi> <mrow> <mi>F</mi> <mi>L</mi> </mrow> <mi>k</mi> </msubsup> <mo>-</mo> <msup> <mi>ax</mi> <mi>k</mi> </msup> <mo>|</mo> <mo>&le;</mo> <mi>&Delta;</mi> <mo>,</mo> <mo>|</mo> <msubsup> <mi>av</mi> <mrow> <mi>F</mi> <mi>R</mi> </mrow> <mi>k</mi> </msubsup> <mo>-</mo> <msup> <mi>ax</mi> <mi>k</mi> </msup> <mo>|</mo> <mo>&le;</mo> <mi>&Delta;</mi> <mo>,</mo> <mo>|</mo> <msubsup> <mi>av</mi> <mrow> <mi>R</mi> <mi>L</mi> </mrow> <mi>k</mi> </msubsup> <mo>-</mo> <msup> <mi>ax</mi> <mi>k</mi> </msup> <mo>|</mo> <mo>&le;</mo> <mi>&Delta;</mi> <mo>,</mo> <mo>|</mo> <msubsup> <mi>av</mi> <mrow> <mi>R</mi> <mi>R</mi> </mrow> <mi>k</mi> </msubsup> <mo>-</mo> <msup> <mi>ax</mi> <mi>k</mi> </msup> <mo>|</mo> <mo>></mo> <mi>&Delta;</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced>Wherein,Between the near front wheel wheel speed and speed prediction value that represent the cycle of kth -1 respectively Deviation, the off-front wheel wheel speed in the cycle of kth -1 and speed between deviation, the left rear wheel wheel speed in the cycle of kth -1 and speed prediction value Deviation between the off hind wheel wheel speed and speed prediction value of deviation, the cycle of kth -1 between predicted value,The near front wheel wheel speed in the expression cycle of kth -1, off-front wheel wheel speed, left rear wheel wheel speed, the right side respectively Trailing wheel wheel speed,The near front wheel wheel speed, off-front wheel wheel speed, left rear wheel in kth cycle are represented respectively Wheel speed, off hind wheel wheel speed, VkFor the speed prediction value in kth cycle,The near front wheel wheel acceleration in kth cycle is represented,Table Show the off-front wheel wheel acceleration in kth cycle,The left rear wheel wheel acceleration in kth cycle is represented,Represent the right side in kth cycle Rear wheel rotation acceleration, axkThe longitudinal acceleration of the vehicle in kth cycle is represented, Δ represents wheel acceleration and longitudinal acceleration The threshold value of difference.
- 16. according to the device described in claim any one of 10-14, it is characterised in that the state space vector is with the N The wheel speed of individual wheel is the vector of element, and the state-space model includes:<mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <msubsup> <mi>V</mi> <mrow> <mi>w</mi> <mi>s</mi> </mrow> <mrow> <mi>k</mi> <mo>+</mo> <mn>1</mn> </mrow> </msubsup> <mo>=</mo> <msubsup> <mi>V</mi> <mrow> <mi>w</mi> <mi>s</mi> </mrow> <mrow> <mi>k</mi> <mo>+</mo> <mn>1</mn> </mrow> </msubsup> <mo>,</mo> <mi>i</mi> <mi>f</mi> <mo>|</mo> <msubsup> <mi>V</mi> <mrow> <mi>w</mi> <mi>s</mi> </mrow> <mrow> <mi>k</mi> <mo>+</mo> <mn>1</mn> </mrow> </msubsup> <mo>-</mo> <msubsup> <mi>V</mi> <mrow> <mi>w</mi> <mi>s</mi> </mrow> <mi>k</mi> </msubsup> <mo>|</mo> <mo><</mo> <mi>&Delta;</mi> </mtd> </mtr> <mtr> <mtd> <msubsup> <mi>V</mi> <mrow> <mi>w</mi> <mi>s</mi> </mrow> <mrow> <mi>k</mi> <mo>+</mo> <mn>1</mn> </mrow> </msubsup> <mo>=</mo> <msub> <mi>&lambda;</mi> <mn>1</mn> </msub> <mo>*</mo> <msubsup> <mi>V</mi> <mrow> <mi>w</mi> <mi>s</mi> </mrow> <mi>k</mi> </msubsup> <mo>+</mo> <msub> <mi>&lambda;</mi> <mn>2</mn> </msub> <mo>*</mo> <msubsup> <mi>V</mi> <mrow> <mi>w</mi> <mi>s</mi> </mrow> <mrow> <mi>k</mi> <mo>+</mo> <mn>1</mn> </mrow> </msubsup> <mo>,</mo> <mi>i</mi> <mi>f</mi> <mo>|</mo> <msubsup> <mi>V</mi> <mrow> <mi>w</mi> <mi>s</mi> </mrow> <mrow> <mi>k</mi> <mo>+</mo> <mn>1</mn> </mrow> </msubsup> <mo>-</mo> <msubsup> <mi>V</mi> <mrow> <mi>w</mi> <mi>s</mi> </mrow> <mi>k</mi> </msubsup> <mo>|</mo> <mo>></mo> <mo>=</mo> <mi>&Delta;</mi> </mtd> </mtr> </mtable> </mfenced>Wherein,The cycle of kth+1 and the wheel speed value of any wheel of kth cycle vehicle, λ are represented respectively1、λ2Represent ginseng Numerical value, and meet λ1+λ2=1, Δ represents the deviation threshold of the state space vector in two neighboring cycle.
- 17. device according to claim 13, it is characterised in that the error prediction model includes:xk=xk-1+vk<mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msubsup> <mi>x</mi> <mi>k</mi> <mo>-</mo> </msubsup> <mo>=</mo> <msub> <mover> <mi>x</mi> <mo>^</mo> </mover> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msubsup> <mi>p</mi> <mi>k</mi> <mo>-</mo> </msubsup> <mo>=</mo> <msub> <mover> <mi>p</mi> <mo>^</mo> </mover> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>+</mo> <mi>Q</mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>K</mi> <mi>k</mi> </msub> <mo>=</mo> <msubsup> <mi>p</mi> <mi>k</mi> <mo>-</mo> </msubsup> <msup> <mrow> <mo>(</mo> <msubsup> <mi>p</mi> <mi>k</mi> <mo>-</mo> </msubsup> <mo>+</mo> <mi>R</mi> <mo>)</mo> </mrow> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mover> <mi>x</mi> <mo>^</mo> </mover> <mi>k</mi> </msub> <mo>=</mo> <msubsup> <mi>x</mi> <mi>k</mi> <mo>-</mo> </msubsup> <mo>+</mo> <msub> <mi>K</mi> <mi>k</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>z</mi> <mi>k</mi> </msub> <mo>-</mo> <msubsup> <mi>x</mi> <mi>k</mi> <mo>-</mo> </msubsup> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mover> <mi>p</mi> <mo>^</mo> </mover> <mi>k</mi> </msub> <mo>=</mo> <mrow> <mo>(</mo> <mi>I</mi> <mo>-</mo> <msub> <mi>K</mi> <mi>k</mi> </msub> <mo>)</mo> </mrow> <msubsup> <mi>p</mi> <mi>k</mi> <mo>-</mo> </msubsup> </mrow> </mtd> </mtr> </mtable> </mfenced>Wherein, xkThe error correction values in kth cycle are represented,The predicted value of the error correction values in kth cycle is represented,Represent kth The estimate of the error correction values in cycle, Q represent process noise covariance, zkThe error actual value in kth cycle is represented, R is represented Measurement noise covariance,The evaluated error covariance in kth cycle is represented,Represent the predicting covariance in kth cycle, Kk The kalman gain in kth cycle is represented, I represents unit matrix.
- 18. device according to claim 11, it is characterised in that the filtering algorithm includes:<mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mi>a</mi> <msup> <mi>x</mi> <mi>k</mi> </msup> <mo>=</mo> <mi>a</mi> <msubsup> <mi>x</mi> <mn>1</mn> <mi>k</mi> </msubsup> <mo>,</mo> <mi>i</mi> <mi>f</mi> <mo>|</mo> <mi>a</mi> <msubsup> <mi>x</mi> <mn>1</mn> <mi>k</mi> </msubsup> <mo>-</mo> <mi>a</mi> <msubsup> <mi>x</mi> <mn>1</mn> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <mo>|</mo> <mo><</mo> <msub> <mi>&delta;</mi> <mn>0</mn> </msub> </mtd> </mtr> <mtr> <mtd> <mrow> <msup> <mi>ax</mi> <mi>k</mi> </msup> <mo>=</mo> <msubsup> <mi>ax</mi> <mn>1</mn> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <mo>+</mo> <msub> <mi>&delta;</mi> <mn>0</mn> </msub> <mo>,</mo> <mi>i</mi> <mi>f</mi> <mrow> <mo>(</mo> <msubsup> <mi>ax</mi> <mn>1</mn> <mi>k</mi> </msubsup> <mo>-</mo> <msubsup> <mi>ax</mi> <mn>1</mn> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <mo>)</mo> </mrow> <mo>></mo> <msub> <mi>&delta;</mi> <mn>0</mn> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msup> <mi>ax</mi> <mi>k</mi> </msup> <mo>=</mo> <msubsup> <mi>ax</mi> <mn>1</mn> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <mo>-</mo> <msub> <mi>&delta;</mi> <mn>0</mn> </msub> <mo>,</mo> <mi>i</mi> <mi>f</mi> <mrow> <mo>(</mo> <msubsup> <mi>ax</mi> <mn>1</mn> <mi>k</mi> </msubsup> <mo>-</mo> <msubsup> <mi>ax</mi> <mn>1</mn> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <mo>)</mo> </mrow> <mo><</mo> <mo>-</mo> <msub> <mi>&delta;</mi> <mn>0</mn> </msub> </mrow> </mtd> </mtr> </mtable> </mfenced>Wherein,Kth cycle and the longitudinal acceleration measured value of the vehicle in the cycle of kth -1, ax are represented respectivelyk Represent the longitudinal acceleration value in kth cycle.
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