CN107515374A - A kind of method for adjusting filtering gain applied to AGV cars SOC estimation dynamics - Google Patents

A kind of method for adjusting filtering gain applied to AGV cars SOC estimation dynamics Download PDF

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CN107515374A
CN107515374A CN201710638540.6A CN201710638540A CN107515374A CN 107515374 A CN107515374 A CN 107515374A CN 201710638540 A CN201710638540 A CN 201710638540A CN 107515374 A CN107515374 A CN 107515374A
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吴铁洲
王越洋
邓勇军
王呈
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Hubei University of Technology
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    • G01—MEASURING; TESTING
    • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R31/00—Arrangements for testing electric properties; Arrangements for locating electric faults; Arrangements for electrical testing characterised by what is being tested not provided for elsewhere
    • G01R31/36—Arrangements for testing, measuring or monitoring the electrical condition of accumulators or electric batteries, e.g. capacity or state of charge [SoC]
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Abstract

The present invention relates to a kind of method for adjusting filtering gain applied to AGV cars SOC estimation dynamics, and the filtering gain of extended Kalman filter is improved into dynamic adjustment filtering gain, effectively improves the tracking effect of extended Kalman filter.The present invention fully analyzes the special operating mode of AGV cars, point out current integration method where the reason for estimating its SOC value inaccuracy, it is proposed to estimate its SOC value of battery using extended Kalman filter, the problem of for conventional Extension Kalman filtering method tracking effect difference, it is dynamic change gain to improve its filtering gain, the real-time of estimation SOC value is improved, ensures the accuracy of AGV car SOC values within 5%, solve thes problems, such as that the estimation of AGV cars SOC value is inaccurate in engineering.

Description

A kind of method for adjusting filtering gain applied to AGV cars SOC estimation dynamics
Technical field
The invention belongs to the technical field of AGV cars battery remaining power estimation, and in particular to one kind is applied to AGV cars SOC The method that estimation dynamic adjusts filtering gain.
Background technology
Automatic guide vehicle (AGV) is a kind of haulage equipment of automation, is mainly used in industrial production.AGV cars are general Using battery as power supply, accurately estimation SOC is vital in AGV car EMSs, it is ensured that AGV cars Efficiently and safely run, while can also avoid the service life for ringing AGV car batteries due to overcharging or crossing film playback.But battery Residual capacity it is relevant with several factors, and AGV turner conditions are special, and this, which allows for the estimation of battery SOC value, becomes complicated, accurate Exactness is difficult to be guaranteed.
SOC estimation method mainly has open circuit voltage method, Current integrating method, Kalman filtering method, neural network.AGV cars In commonly use is Current integrating method, but AGV turner conditions are special, and the degree of accuracy of Current integrating method estimation SOC value is unsatisfactory, and And accumulated error can be produced.Although the SOC value of Current integrating method estimation can be proofreaded in practical application in industry, simultaneously The problem of no Current integrating method that fundamentally solves relies on initial value, and accumulated error is larger.Open circuit voltage method can not be real-time online SOC value is estimated, neural network is very big to training method and training data dependence, and there is presently no used well. Kalman filtering method estimates that battery SOC independent of initial value, will not produce error, it is larger to be suitably applied in curent change amplitude In operating mode, comprehensive analysis Kalman filtering method is more suitable for applying in AGV cars SOC estimations.
AGV cars are operated in industrial production line, and its work rhythm is very fast, will not typically reserve the special charging interval, only Have and just charged in the time for waiting process to complete, and charging current is big, and rate of charge can reach 1C-2C, charging Time is short, either tens seconds usually several seconds.And AGV cars electric current in normal work is smaller, usually within 0.5C.Institute It is summarised as that charging current is big, and discharge current is small with the operating mode can of AGV cars, the charging interval is short, and charge frequency is high.Fig. 1 is described AGV cars discharge and recharge situations of change in 12 minutes, discharge current is just, charging current is negative.As can be seen from the figure AGV cars Just charged twice in 10 minutes, and charging current has reached 100A every time, and discharge current only has 5A or so.In this electricity Stream fluctuating range is big, and it is a good problem to study that SOC value how is accurately estimated in the case of charge frequency height.
Current integrating method is the common method for estimating SOC value, but Current integrating method relies on initial value, the measurement essence to electric current Degree requires higher, and AGV cars SOC initial values and current measurement precision under special operation condition are all difficult to be guaranteed, so electric current accumulates The degree of accuracy of point-score estimation AGV car SOC values is not very high.The basic thought of Kalman filtering method is a continuous weighted iteration Process, have two values during whole filtering, be the predicted value of model and the measured value of instrument respectively, then predicted value with Measured value carries out aggregative weighted and has obtained optimal estimation value.And Kalman filtering method will not produce accumulation independent of initial value Error, the accuracy of SOC value under special operation condition can be ensured.But Kalman filtering method relies on battery model, battery model Precision directly affects the precision of SOC value estimation, so accurate establish the base that battery model is Kalman filtering method estimation SOC value Plinth.
The content of the invention
In order to overcome above-mentioned the shortcomings of the prior art, it is an object of the invention to improve extended Kalman filter Tracking effect, devises a kind of method for adjusting filtering gain applied to AGV cars SOC estimation dynamics, and this method effectively improves expansion The tracking effect of Kalman filtering method is opened up, solves the problems, such as that the estimation of AGV cars battery remaining power is inaccurate.
In order to achieve the above object, the technical solution adopted in the present invention is：One kind is applied to AGV cars SOC estimation dynamics The method for adjusting filtering gain, it is characterised in that the filtering gain of extended Kalman filter is improved to dynamic adjustment and filtered Gain, the tracking effect of extended Kalman filter is effectively improved, wherein：
The changing rule of correction function index of coincidence function can be drawn by the fitting of experimental data, make its dynamic corrections Shown in function such as formula (11)：
Gain K after then improving in expanded Kalman filtration algorithmk' as shown in formula (12)：
β is a Dynamic gene in formula (12), and its value is 0-1 number, the parameter can adjust current break it is lasting when Between；It is the amplitude of accommodation factor, the parameter can be with the mutation intensity of tracking system；T is the duration of system sudden change in formula, if t0It is the time that mutation starts, and t ' is the time that mutation terminates, then t=t0-t’；Thus improvement spreading kalman can be calculated In filtering algorithm shown in change in gain such as formula (13)：
After improving EKF gain, filtering gain is expanded to by system when being mutated incipient not to be changed Before enteringTimes, the amendment amplitude of system SOC value becomes big, converges to actual value rapidly；With the end of mutation, filtering gain Taper into, finally revert to Kk；So it is achieved that in expanded Kalman filtration algorithm that filtering gain dynamic adjusts.
Further, the derivation of methods described includes：
Shown in Kalman filtering process such as formula (4)：
Filtering gain after order improves is Kk', then the state of expanded Kalman filtration algorithm is updated as shown in formula (5)：
It can be obtained by formula (5)：
It can be obtained by formula (4)：
It is W (t) to make filtering gain correction function, then can be obtained by formula (6) and formula (7)：
Filtering gain increases when being mutated and starting, and improves amendment amplitude, is gradually reduced with the gain that is filtered of mutation, Recover normal value after mutation terminates, in order to find out this changing rule of filtering gain correction function under special operation condition, choose Then experimental data finds out correction function by data fitting；
The functional relation as shown in formula (9) can be obtained using Matlab least square fittings experimental data：
W (t)=1.011e-0.4909t+0.9998 (9)
Formula (9) abbreviation can be obtained：
W (t)=0.6121t+0.9998 (10)
In Matlab draw experimental data curve figure, mutation just start when correction function cause filtering gain value compared with Greatly, the amendment amplitude to SOC value is also bigger, and filtering gain value recovers normal value after mutation；So filtering gain can Realize that dynamic adjusts according to the situation of mutation, accelerate the tracking velocity of algorithm.
Compared with prior art, the present invention has advantages below：The present invention, which bases oneself upon, solves industrial production practical problem, fully Analyze the special operating mode of AGV cars, it is indicated that current integration method is proposed using expansion where the reason for estimating its SOC value inaccuracy Exhibition Kalman filtering method estimates its SOC value of battery, the problem of for conventional Extension Kalman filtering method tracking effect difference, improves it Filtering gain is dynamic change gain, improves the real-time of estimation SOC value, ensures the accuracy of AGV car SOC values within 5%, Solve the problems, such as that the estimation of AGV cars SOC value is inaccurate in engineering.
Brief description of the drawings
Fig. 1 is the curent change figure under AGV car actual conditions.
Fig. 2 is battery equivalent circuit schematic.
Fig. 3 is filtering gain correction function change curve.
Fig. 4 is that SOC value estimates correlation curve (distinct methods estimation curve).
Fig. 5 is that SOC value estimates correlation curve (error curve).
Fig. 6 is expanded Kalman filtration algorithm tracking effect figure (SOC curves before optimization).
Fig. 7 is expanded Kalman filtration algorithm tracking effect figure (SOC curves after optimization).
Fig. 8 is tracking effect comparison diagram.
Embodiment
For the ease of those of ordinary skill in the art understand and implement the present invention, the present invention is made with reference to embodiment into The detailed description of one step, it will be appreciated that implementation example described herein is merely to illustrate and explain the present invention, and is not used to limit The fixed present invention.
(1) battery model is chosen
The present invention is carried out equivalent using Thevenin models to AGV cars battery.The model can be by lithium ion battery charge and discharge Catastrophe characteristicses and roll-off characteristic in electric process, which are all depicted, to be come, and its equivalent circuit schematic is as shown in Figure 2.Wherein R0Describe The resistance characteristic being mutated during charging and discharging lithium battery, RpAnd CpSimulate the capacitance characteristic of battery gradual change.Battery equivalent circuit mould Parameter in type can be recognized by carrying out intermittent pulse charge-discharge test to battery.By battery in experiment in discharge and recharge During voltage up-down and the parameter such as internal resistance in discharge and recharge time calculation circuit model and electric capacity.
E is cell emf in Fig. 2, R0It is the internal resistance of cell, RpAnd CpIt is polarization resistance and polarization capacity, UocIt is that battery is opened Road voltage, I are battery total currents, IpIt is the electric current for flowing through polarization resistance, UpIt is the voltage at polarization resistance and polarization capacity both ends. Understand to need a quantity of state and an observed quantity during filtering by the principle of Kalman filtering method, and SOC value is not Energy direct measurement obtains, so choosing UpFor state variable, by linearisation and sliding-model control state equation such as formula (1) institute Show.Choose the battery terminal voltage U detectedocIt is shown for observed quantity, the observational equation such as formula (2) of foundation.
U in formula (1)P, kThat represent is k moment UpValue, UP, k-1That represent is k-1 moment UpValue, same SOCkRepresent It is k moment SOC value of battery, SOCk-1What is represented is k-1 moment SOC values, and T is the sampling time of system, w1, k-1And w2, k-1To be System noise.As the matrix such as formula (3) needed for formula (1) and (2) can obtain Kalman filtering：
WhereinAnd UocWith SOC, R0It can be entered with SOC relation by discharge and recharge data Row fitting obtains.
(2) expanded Kalman filtration algorithm estimation AGV car SOC values are improved
Kalman filtering method is that linear system carries out optimal estimation, and expanded Kalman filtration algorithm is to traditional karr The popularization of graceful filtering algorithm, suitable for the optimal estimation of nonlinear system.Battery is typical nonlinear system, so needing Its residual capacity is estimated using extended Kalman filter.State equation and the sight of system have been obtained by the modeling of battery Equation is surveyed, the Kalman filtering process as shown in formula (4) is can be obtained by with reference to the characteristic equation of Kalman filtering method.
The primary condition of filtering equations has：SOC initial value SOC0, CpThe initial voltage U at both endspAnd predictor error (0) Covariance P0。SOC0Obtained by reading last SOC value, Up(0) 0 is generally in initialization, the association side of predictor error Poor initial value P0Suitable value is chosen according to engineering experience.Under normal circumstances, SOC of the degree of accuracy of these initial values to estimation Value influence is not very big, because the Kalman filter initial value poor to accuracy has good robustness, can be received quickly Actual value is held back, if the speed that the reasonable so Kalman filtering of initial value value converges to actual value can be than very fast, if value Unreasonable convergence rate can be relatively slow, it is necessary to successive ignition can just converge to actual value, but it is final can all eliminate it is initial The error that value inaccuracy is brought, here it is basic reason of the extended Kalman filter estimation AGV cars SOC value independent of initial value. Extended Kalman filter estimation battery SOC is exactly to work as k=1, and 2,3 ... carry out loop iteration to formula (4), restrain quantity of state To actual value.
Specific estimation process is as follows：
1) first formula in formula (4), is predicted by battery equivalent model, passes through the state at k-1 moment Amount predicts the quantity of state at k moment；
2) second formula in formula (4), the error co-variance matrix of predicted value is calculated, it is determined that prediction is accurate Degree, carry out weight distribution for back and prepare；
3) the 3rd formula in formula (4) calculates Kalman filtering gain, that is, to measured value and calculating value distribution With weight, and then pass through Kalman filtering gain-boosted op amp quantity of state；
4) the 4th formula in formula (4), the optimal estimation of Kalman is carried out by the formula, is believed using predicted state Inverse observed quantity is ceased, then calculates measured value ZkAnd the difference of inverse value, then carry out aggregative weighted；
5) the 5th formula in formula (4), the formula is exactly that the optimal result calculated is evaluated, and calculates one How is the degree of accuracy of lower optimal result, is prepared also for subsequent time, and guarantee can subsequently circulate down always.
Kalman filtering method estimation SOC value of battery is exactly ceaselessly to be iterated by the step of top five, so that SOC Value converges on actual value, and does not have dependence to initial value during estimating, also in the absence of accumulated error, the SOC value of estimation The degree of accuracy and stability are higher than Current integrating method, but AGV turner conditions are special, and current break frequency is high, expands under actual condition It is poor to open up Kalman filtering method estimation SOC tracking effects in current break, influences the accuracy and real-time of SOC value estimation. So needing to be improved extended Kalman filter, accelerate the predetermined speed of algorithm in current break, improve it in spy The accuracy and real-time of SOC value are estimated under different operating mode.
Accelerating the predetermined speed of algorithm in current break requires algorithm to increase SOC at the current break incipient moment The amendment amplitude of value.Increase filtering gain K is drawn by formula (4)kValue can improve the renewal amplitude of quantity of state, accelerate algorithm Tracking velocity.So the predetermined speed that improve expanded Kalman filtration algorithm under special operation condition just needs to increase when being mutated and starting Big filtering gain, mutation reduces filtering gain later, so as to have the function that dynamic corrections SOC.
Filtering gain after order improves is Kk', then the state renewal of expanded Kalman filtration algorithm is as shown in Equation 5.
It can be obtained by formula (5)：
It can be obtained by formula (4)：
It is W (t) to make filtering gain correction function, then can be obtained by formula (6) and formula (7)：
Filtering gain increases when being mutated and starting, and improves amendment amplitude, is gradually reduced with the gain that is filtered of mutation, Recover normal value after mutation terminates, in order to find out this changing rule of filtering gain correction function under special operation condition, this hair Then bright selection experimental data finds out correction function by data fitting.Experimental data is as shown in table 1.
The correction function of table 1 is fitted experimental data
The functional relation as shown in formula (9) can be obtained using Matlab least square fittings experimental data.
W (t)=1.011e-0.4909t+0.9998 (9)
Formula (9) abbreviation can be obtained：
W (t)=0.6121t+0.9998 (10)
Experimental data curve figure is drawn in Matlab, as shown in Figure 3.In fig. 3 the first it is within 6 seconds the mutation time of electric current, When mutation just starts, correction function make it that filtering gain value is larger, and the amendment amplitude to SOC value is also bigger, and mutation is filtered later Ripple yield value recovers normal value.So filtering gain can according to the situation of mutation realize dynamic adjust, accelerate algorithm with Track speed.
The changing rule of correction function index of coincidence function can be drawn by the fitting of experimental data, make its dynamic corrections Shown in function such as formula (11).
Gain K after then improving in expanded Kalman filtration algorithmk' as shown in formula (12)
β is a Dynamic gene in formula (12), and its value is 0-1 number, the parameter can adjust current break it is lasting when Between, if mutation time continue it is shorter if the parameter value it is smaller, if mutation time duration longer parameter value compared with Greatly, specific value can determine according to Practical Project.It is the amplitude of accommodation factor, the parameter can be with the mutation intensity of tracking system, such as Fruit mutation larger parameter value of intensity is larger, and the mutation smaller value of intensity is smaller.T is the duration of system sudden change in formula, If t0It is the time that mutation starts, and t ' is the time that mutation terminates, then t=t0-t’.Thus improvement extension karr can be calculated In graceful filtering algorithm shown in change in gain such as formula (13).
After improving EKF gain, filtering gain is expanded to by system when being mutated incipient not to be changed Before enteringTimes, the amendment amplitude of system SOC value becomes big, converges to actual value rapidly；With the end of mutation, filtering gain Taper into, finally revert to Kk.So it is achieved that in expanded Kalman filtration algorithm that filtering gain dynamic adjusts, and corrects width Dynamic change is spent, is advantageous to system and quickly converges under catastrophe be really worth, is reduced in expanded Kalman filtration algorithm The influence of observation lagging influence SOC estimation precision, improve the ability of tracking of system.
(3) experiment and analysis
In order to verify the effect of extended Kalman filter estimation AGV car SOC values, while also to verify the extension after improving The tracking effect of Kalman filtering algorithm, the present invention carried out a series of experiment, experimental contrast analysis's spreading kalman filter The difference on effect of ripple method and ampere-hour method estimation AGV car SOC values, comparative analysis expanded Kalman filtration algorithm improve it is front and rear with Track effect.
Under normal operation, the various data of battery record AGV cars in real time, so what the present embodiment used Data are all the field datas of AGV car real time executions.The present invention has write algorithm on the platforms of Visual Studio 2012 and tested Program is demonstrate,proved, the actual condition of AGV cars is simulated by reading the field data of AGV car real time executions, then respectively using electricity Integration method and the SOC value of extended Kalman filter estimation AGV cars are flowed, its comparative analysis curve map is as shown in Figure 4 and Figure 5.
In an experiment in order to ensure the accuracy of ampere-hour method, it is accurate to give its initial value, and Kalman filtering method is first Value has larger error.Understand that ampere-hour method error is larger by experimental result, worst error is more than 7%, and this error range It is caused by the case of initial value is accurate, if its error range of initial value inaccuracy can also further expand.And Kalman filters Ripple method is in the case of initial value inaccuracy, and with the increase of iterations, its estimation result gradually converges to actual value, error model Enclosing can control within 4% substantially, and the degree of accuracy is apparently higher than current integration method.But can also from Comparative result curve Go out extended Kalman filter there is also it is certain the problem of.Two circles have been marked in figure 6, can be with each mark circle Actual value will be lagged behind by finding out the SOC value of Kalman filtering method estimation, cause application condition big, because when AGV cars electricity When stream is undergone mutation, the observation voltage of extended Kalman filter is hysteresis, so as to cause SOC estimation also to lag. In order to solve this problem, extended Kalman filter is improved, i.e., by the adjustment in expanded Kalman filtration algorithm Gain is arranged to dynamic gain, in this experiment β=0.5,Algorithm after improvement is tested, as a result as shown in Figure 7.
The precision for understanding SOC estimations from the experimental result after improvement further improves, compared to the Kalman filtering before improvement Its tracking effect of algorithm is more preferable, can also converge to actual value quickly when electric current is undergone mutation.After further illustrating optimization Kalman filtering algorithm its tracking effect it is more preferable, SOC actual values, improve the SOC value that Kalman filtering method is estimated before improvement The SOC value of Kalman filtering method estimation, which is amplified, afterwards compares, as a result as shown in Figure 8.It can be clear that and change from Fig. 8 Kalman filtering method its tracking effect after entering improves 30% or so compared to no improved Kalman filtering method, so Under the big operating mode of this curent change amplitude of AGV cars, the SOC value of the Kalman filtering method estimation after improvement is more accurate.
The present invention, which bases oneself upon, solves industrial production practical problem, fully analyzes the special operating mode of AGV cars, it is indicated that ampere-hour integrates For method where the reason for estimating its SOC value inaccuracy, proposition estimates its SOC value of battery using extended Kalman filter, for The problem of conventional Extension Kalman filtering method tracking effect difference, it is dynamic change gain to improve its filtering gain, improves estimation SOC The real-time of value, ensure the accuracy of AGV car SOC values within 5%, it is inaccurate to efficiently solve AGV cars SOC value estimation in engineering The problem of true.
It should be appreciated that the part that this specification does not elaborate belongs to prior art.
It should be appreciated that the above-mentioned description for preferred embodiment is more detailed, therefore can not be considered to this The limitation of invention patent protection scope, one of ordinary skill in the art are not departing from power of the present invention under the enlightenment of the present invention Profit is required under protected ambit, can also be made replacement or deformation, be each fallen within protection scope of the present invention, this hair It is bright scope is claimed to be determined by the appended claims.

Claims (2)

  1. A kind of 1. method for adjusting filtering gain applied to AGV cars SOC estimation dynamics, it is characterised in that filter spreading kalman The filtering gain of ripple method is improved to dynamic adjustment filtering gain, effectively improves the tracking effect of extended Kalman filter, wherein：
    The changing rule of correction function index of coincidence function can be drawn by the fitting of experimental data, make its dynamic corrections function As shown in formula (11)：
    Gain K after then improving in expanded Kalman filtration algorithmk' as shown in formula (12)：
    β is a Dynamic gene in formula (12), and its value is 0-1 number, and the parameter can adjust current break duration； It is the amplitude of accommodation factor, the parameter can be with the mutation intensity of tracking system；T is the duration of system sudden change in formula, if t0It is It is mutated the time started, and t ' is the time that mutation terminates, then t=t0-t’；Thus improvement EKF can be calculated In algorithm shown in change in gain such as formula (13)：
    After improving EKF gain, filtering gain is expanded to by system when being mutated incipient do not improve before 'sTimes, the amendment amplitude of system SOC value becomes big, converges to actual value rapidly；As the end of mutation, filtering gain are gradual Diminish, finally revert to Kk；So it is achieved that in expanded Kalman filtration algorithm that filtering gain dynamic adjusts.
  2. 2. a kind of method for adjusting filtering gain applied to AGV cars SOC estimation dynamics as claimed in claim 1, its feature exist In：The derivation of methods described includes：
    Shown in Kalman filtering process such as formula (4)：
    <mrow> <mtable> <mtr> <mtd> <mrow> <msub> <mover> <mi>X</mi> <mo>^</mo> </mover> <mrow> <mi>k</mi> <mo>/</mo> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>=</mo> <msub> <mi>A</mi> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <msub> <mover> <mi>X</mi> <mo>^</mo> </mover> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> <mo>/</mo> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>+</mo> <msub> <mi>B</mi> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <msub> <mi>I</mi> <mi>k</mi> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>P</mi> <mrow> <mi>k</mi> <mo>/</mo> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>=</mo> <msub> <mi>A</mi> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <msub> <mi>P</mi> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> <mo>/</mo> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <msubsup> <mi>A</mi> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> <mi>T</mi> </msubsup> <mo>+</mo> <msub> <mi>Q</mi> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>K</mi> <mi>k</mi> </msub> <mo>=</mo> <msub> <mi>P</mi> <mrow> <mi>k</mi> <mo>/</mo> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <msubsup> <mi>C</mi> <mi>k</mi> <mi>T</mi> </msubsup> <msup> <mrow> <mo>(</mo> <msub> <mi>C</mi> <mi>k</mi> </msub> <msub> <mi>P</mi> <mrow> <mi>k</mi> <mo>/</mo> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <msubsup> <mi>C</mi> <mi>k</mi> <mi>T</mi> </msubsup> <mo>+</mo> <msub> <mi>R</mi> <mi>k</mi> </msub> <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> <mrow> <mi>k</mi> <mo>/</mo> <mi>k</mi> </mrow> </msub> <mo>=</mo> <msub> <mover> <mi>X</mi> <mo>^</mo> </mover> <mrow> <mi>k</mi> <mo>/</mo> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>+</mo> <msub> <mi>K</mi> <mi>k</mi> </msub> <mo>&amp;lsqb;</mo> <msub> <mi>Z</mi> <mi>k</mi> </msub> <mo>-</mo> <msub> <mi>H</mi> <mi>k</mi> </msub> <msub> <mover> <mi>X</mi> <mo>^</mo> </mover> <mrow> <mi>k</mi> <mo>/</mo> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>&amp;rsqb;</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>P</mi> <mrow> <mi>k</mi> <mo>/</mo> <mi>k</mi> </mrow> </msub> <mo>=</mo> <mrow> <mo>(</mo> <mi>I</mi> <mo>-</mo> <msub> <mi>K</mi> <mi>k</mi> </msub> <msub> <mi>C</mi> <mi>k</mi> </msub> <mo>)</mo> </mrow> <msub> <mi>P</mi> <mrow> <mi>k</mi> <mo>/</mo> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> </mrow> </mtd> </mtr> </mtable> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>4</mn> <mo>)</mo> </mrow> </mrow>
    Filtering gain after order improves is Kk', then the state of expanded Kalman filtration algorithm is updated as shown in formula (5)：
    <mrow> <msup> <msub> <mover> <mi>X</mi> <mo>^</mo> </mover> <mrow> <mi>k</mi> <mo>/</mo> <mi>k</mi> </mrow> </msub> <mo>&amp;prime;</mo> </msup> <mo>=</mo> <msup> <msub> <mover> <mi>X</mi> <mo>^</mo> </mover> <mrow> <mi>k</mi> <mo>/</mo> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>&amp;prime;</mo> </msup> <mo>+</mo> <msup> <msub> <mi>K</mi> <mi>k</mi> </msub> <mo>&amp;prime;</mo> </msup> <mo>&amp;lsqb;</mo> <msub> <mi>Z</mi> <mi>k</mi> </msub> <mo>-</mo> <msub> <mi>H</mi> <mi>k</mi> </msub> <msub> <mover> <mi>X</mi> <mo>^</mo> </mover> <mrow> <mi>k</mi> <mo>/</mo> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>&amp;rsqb;</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>5</mn> <mo>)</mo> </mrow> </mrow>
    It can be obtained by formula (5)：
    <mrow> <msup> <msub> <mi>K</mi> <mi>k</mi> </msub> <mo>&amp;prime;</mo> </msup> <mo>&amp;lsqb;</mo> <msub> <mi>Z</mi> <mi>k</mi> </msub> <mo>-</mo> <msub> <mi>H</mi> <mi>k</mi> </msub> <msub> <mover> <mi>X</mi> <mo>^</mo> </mover> <mrow> <mi>k</mi> <mo>/</mo> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>&amp;rsqb;</mo> <mo>=</mo> <msup> <msub> <mover> <mi>X</mi> <mo>^</mo> </mover> <mrow> <mi>k</mi> <mo>/</mo> <mi>k</mi> </mrow> </msub> <mo>&amp;prime;</mo> </msup> <mo>-</mo> <msup> <msub> <mover> <mi>X</mi> <mo>^</mo> </mover> <mrow> <mi>k</mi> <mo>/</mo> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>&amp;prime;</mo> </msup> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>6</mn> <mo>)</mo> </mrow> </mrow>
    It can be obtained by formula (4)：
    <mrow> <msub> <mi>K</mi> <mi>k</mi> </msub> <mo>&amp;lsqb;</mo> <msub> <mi>Z</mi> <mi>k</mi> </msub> <mo>-</mo> <msub> <mi>H</mi> <mi>k</mi> </msub> <msub> <mover> <mi>X</mi> <mo>^</mo> </mover> <mrow> <mi>k</mi> <mo>/</mo> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>&amp;rsqb;</mo> <mo>=</mo> <msub> <mover> <mi>X</mi> <mo>^</mo> </mover> <mrow> <mi>k</mi> <mo>/</mo> <mi>k</mi> </mrow> </msub> <mo>-</mo> <msub> <mover> <mi>X</mi> <mo>^</mo> </mover> <mrow> <mi>k</mi> <mo>/</mo> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>7</mn> <mo>)</mo> </mrow> </mrow>
    It is W (t) to make filtering gain correction function, then can be obtained by formula (6) and formula (7)：
    <mrow> <mtable> <mtr> <mtd> <mrow> <mi>W</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mrow> <msup> <msub> <mi>K</mi> <mi>k</mi> </msub> <mo>&amp;prime;</mo> </msup> <mo>&amp;lsqb;</mo> <msub> <mi>Z</mi> <mi>k</mi> </msub> <mo>-</mo> <msub> <mi>H</mi> <mi>k</mi> </msub> <msub> <mover> <mi>X</mi> <mo>^</mo> </mover> <mrow> <mi>k</mi> <mo>/</mo> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>&amp;rsqb;</mo> </mrow> <mrow> <msub> <mi>K</mi> <mi>k</mi> </msub> <mo>&amp;lsqb;</mo> <msub> <mi>Z</mi> <mi>k</mi> </msub> <mo>-</mo> <msub> <mi>H</mi> <mi>k</mi> </msub> <msub> <mover> <mi>X</mi> <mo>^</mo> </mover> <mrow> <mi>k</mi> <mo>/</mo> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>&amp;rsqb;</mo> </mrow> </mfrac> <mo>=</mo> <mfrac> <mrow> <msup> <msub> <mover> <mi>X</mi> <mo>^</mo> </mover> <mrow> <mi>k</mi> <mo>/</mo> <mi>k</mi> </mrow> </msub> <mo>&amp;prime;</mo> </msup> <mo>-</mo> <msup> <msub> <mover> <mi>X</mi> <mo>^</mo> </mover> <mrow> <mi>k</mi> <mo>/</mo> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>&amp;prime;</mo> </msup> </mrow> <mrow> <msub> <mover> <mi>X</mi> <mo>^</mo> </mover> <mrow> <mi>k</mi> <mo>/</mo> <mi>k</mi> </mrow> </msub> <mo>-</mo> <msub> <mover> <mi>X</mi> <mo>^</mo> </mover> <mrow> <mi>k</mi> <mo>/</mo> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> </mrow> </mfrac> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>=</mo> <mfrac> <mrow> <msup> <msub> <mi>K</mi> <mi>k</mi> </msub> <mo>&amp;prime;</mo> </msup> </mrow> <msub> <mi>K</mi> <mi>k</mi> </msub> </mfrac> <mo>=</mo> <mfrac> <mrow> <msup> <msub> <mover> <mi>X</mi> <mo>^</mo> </mover> <mrow> <mi>k</mi> <mo>/</mo> <mi>k</mi> </mrow> </msub> <mo>&amp;prime;</mo> </msup> <mo>-</mo> <msup> <msub> <mover> <mi>X</mi> <mo>^</mo> </mover> <mrow> <mi>k</mi> <mo>/</mo> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>&amp;prime;</mo> </msup> </mrow> <mrow> <msub> <mover> <mi>X</mi> <mo>^</mo> </mover> <mrow> <mi>k</mi> <mo>/</mo> <mi>k</mi> </mrow> </msub> <mo>-</mo> <msub> <mover> <mi>X</mi> <mo>^</mo> </mover> <mrow> <mi>k</mi> <mo>/</mo> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> </mrow> </mfrac> </mrow> </mtd> </mtr> </mtable> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>8</mn> <mo>)</mo> </mrow> </mrow>
    Filtering gain increases when being mutated and starting, and improves amendment amplitude, is gradually reduced with the gain that is filtered of mutation, prominent Change recovers normal value after terminating, and in order to find out this changing rule of filtering gain correction function under special operation condition, chooses experiment Then data find out correction function by data fitting；
    The functional relation as shown in formula (9) can be obtained using Matlab least square fittings experimental data：
    W (t)=1.011e-0.4909t+0.9998 (9)
    Formula (9) abbreviation can be obtained：
    W (t)=0.6121t+0.9998 (10)
    Experimental data curve figure is drawn in Matlab, correction function make it that filtering gain value is larger when mutation just starts, right The amendment amplitude of SOC value is also bigger, and filtering gain value recovers normal value after mutation；So filtering gain can is according to prominent The situation of change realizes that dynamic adjusts, and accelerates the tracking velocity of algorithm.
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