state of charge estimation for electric vehicle batteries using unscented kalman filtering

Microelectronics Reliability xxx (2013) xxx–xxx

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Microelectronics Reliability

journal homepage: www.elsevier .com/locate /microrel

State of charge estimation for electric vehicle batteries using unscentedkalman filtering

Wei He, Nicholas Williard, Chaochao Chen, Michael Pecht ⇑Center for Advanced Life Cycle Engineering, University of Maryland, College Park, MD 20742, USA

a r t i c l e i n f o a b s t r a c t

Article history:Received 16 June 2012Received in revised form 1 October 2012Accepted 22 November 2012Available online xxxx

0026-2714/$ - see front matter � 2012 Elsevier Ltd. Ahttp://dx.doi.org/10.1016/j.microrel.2012.11.010

⇑ Corresponding author.E-mail address: [email protected] (M. Pecht).

Please cite this article in press as: He W et al. Sta(2013), http://dx.doi.org/10.1016/j.microrel.201

Due to the increasing concern over global warming and fossil fuel depletion, it is expected that electricvehicles powered by lithium batteries will become more common over the next decade. However, thereare still some unresolved challenges, the most notable being state of charge estimation, which alerts driv-ers of their vehicle’s range capability. We developed a model to simulate battery terminal voltage as afunction of state of charge under dynamic loading conditions. The parameters of the model were tailoredon-line in order to estimate uncertainty arising from unit-to-unit variations and loading conditionchanges. We used an unscented Kalman filtering-based method to self-adjust the model parametersand provide state of charge estimation. The performance of the method was demonstrated using data col-lected from LiFePO4 batteries cycled according to the federal driving schedule and dynamic stress testing.

� 2012 Elsevier Ltd. All rights reserved.

1. Introduction

With increasing concerns about global warming and fossil fueldepletion, the automobile industry is facing a transition from inter-nal combustion engines (ICEs) to electric vehicles (EVs). The majorindustrialized nations have outlined their plans for EV develop-ment and production. For example, the US government set a goalof having one million EVs on the road by 2015 [1], and the Chinesegovernment plans to have five million EVs on the road by 2020 [2].

Although EVs will inevitably permeate the market, challengesstill exist. One challenge is the ‘‘range anxiety’’ problem, which re-fers to the driver’s fear of running out of battery power on the road[3]. As of 2011, the driving range of an EV was only 40–100 miles,which is 3–4 times less than ICE vehicles. Adding to the problem isthe current lack of battery charging infrastructure. Therefore, toprevent EVs from running out of charge on the road and leavingpassengers stranded, the ability to predict their residual range isneeded. The first step in residual range prediction is to knowhow much capacity remains in the battery, also known as its stateof charge (SOC).

The most common method for SOC estimation is Coulombcounting [4,5], in which the remaining charge is calculated by inte-grating the current entering or leaving the battery over time. Cou-lomb counting is simple and easy to implement in on-boardapplications. However, it requires knowledge of the starting SOC.In addition, Coulomb counting is an open-loop method, and mea-surement noise and battery aging can cause drift. Another popularmethod for SOC estimation is the voltage-based method, which in-

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te of charge estimation for elect2.11.010

fers SOC by an open circuit voltage (OCV)-SOC look-up table [6].However, OCV measurement requires a long period of rest beforethe terminal voltage converges to the actual OCV. With the useof a battery model, it is possible to infer the battery’s OCV fromits terminal voltage, but this approach can generate large errorsif the model employed is not accurate. A ±0.01 V modeling errorin the OCV could produce a 10% error in SOC estimation for LiFePO4

batteries. Other work has been conducted using computationalintelligence algorithms, such as fuzzy-logic [7], artificial neuralnetworks (NNs) [8–12], and support vector machines (SVMs)[13–15], which do not require detailed expert knowledge of bat-tery systems. A typical example is the SVM-based SOC estimatorfor a large-scale lithium–ion polymer battery pack developed byHansen and Wang [13]. The SVM estimator was tested with US06dynamic operational data from the US Department of Energy’s Hy-brid Electric Vehicle program, and the root-mean-square (RMS) er-ror of the SOC estimation was within 6%. Computationalintelligence methods can be accurate if the training data are suffi-cient to cover the loading conditions of the battery. However, col-lecting training data that provide good coverage of all the loadingconditions can be time consuming.

Recently, effort has been focused on developing model-basedfiltering methods [16–24] aimed at establishing closed-loop esti-mation. The equivalent circuit model and electrochemical modelare used to establish a battery state-space model, where the cur-rent is used as the input, the terminal voltage is the output, andthe SOC is set as the hidden state. Then, a filtering method, suchas the extended Kalman filter (EKF) or particle filter (PF) is utilizedto estimate the hidden state. Plett [16–18] developed an EKFframework for SOC estimation of LiFePO4 batteries, which isclosed-loop in nature. At each time point, the filter proposes a

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voltage based on the measured accumulated current and the sys-tem model. The estimated voltage is then compared to the mea-sured voltage. The difference between the estimated andmeasured voltages is then used to calculate a correction term toadjust the SOC. However, an EKF is just a first or second orderapproximation of a nonlinear model. Large errors can be producedif the state-space model is nonlinear.

To address these problems, we developed an unscented KalmanUKF)-based SOC estimation method with a state-space model. UKFis an improved version of the Kalman filter that applies unscentedtransform, which is a method for calculating the statistics of a ran-dom variable propagating through a nonlinear system. In UKF, thestate distribution is represented by a set of sample points calledsigma points, which capture the mean and covariance of the statedistribution. The posterior mean and covariance of the state distri-bution, when propagated through the nonlinear system, are alsocaptured by the propagated sigma points. UKF has been demon-strated to be better than EKFs in terms of accuracy and robustnessfor nonlinear estimation, and it can be accurate to the third orderfor any nonlinearity [25]. We explored UKF to estimate the modelparameters and SOC in real-time. The developed approach wastested using data from different batteries and different loadingconditions. The paper is organized as follows: Section 2 introducesthe battery model developed in this study, Section 3 illustrates theunscented Kalman filter, Section 4 provides case studies, and Sec-tion 5 presents the conclusions.

2. Battery modeling

To model battery system dynamics, many equivalent circuitmodels have been proposed to represent the electrochemical pro-cess of a battery using electric elements, such as the resistance,capacitor, and inductor. The most straightforward way to modela battery is to model its terminal voltage V as the OCV minus thevoltage drop of the internal resistance R, which is shown in Eq. (1):

V ¼ OCV� I � R ð1Þ

where I is the current.The schematic diagram of this model is shown in Fig. 1, in which

the OCV and R are connected in series. OCV is the terminal voltagewhen no current is put in or drawn out of the battery, and it is afunction of SOC. As the SOC decreases, the OCV will also decrease.The OCV–SOC relationship can be determined using controlledexperiments and stored in a look-up table.

In this research, the experiment for OCV–SOC determinationcontains the following steps [17]:

(1) Discharge the cell at 0.1 A from its fully charged state to itsfully discharged state.

(2) Rest for 2 h.(3) Charge the cell at 0.1 A to its fully charged state.(4) Average the discharge and charge voltages to determine the

OCV.

Fig. 1. A simple battery model.

Please cite this article in press as: He W et al. State of charge estimation for elect(2013), http://dx.doi.org/10.1016/j.microrel.2012.11.010

The low charge/discharge rate minimizes the dynamics excitedinside the battery, and the averaging step reduces the effects ofhysteresis and ohmic resistance.

Five cells were tested with a LiFePO4 cathode and a graphite an-ode. The rated capacity of these cells was 2.3 Ah. The resultantOCV–SOC is shown in Fig. 2. It can be seen that the OCV–SOCs ofthe five cells largely overlap, which means that only one represen-tative OCV–SOC curve is required for cells of the same type.

In order to identify the model parameter R and test the modelperformance, experiments were conducted based on federal driv-ing schedules (FDSs). The current profile was generated by combin-ing the urban dynamometer driving schedule (UDDS) [26] andUS06 [27], which represent city and highway driving conditions,respectively. The purpose of combining these two profiles was toemulate the typical driving cycle of a US driver in 1 day, includingcommuting to and from work in both highway and urban settings.The driving schedule and the corresponding current profile areshown in Fig. 3.

Several cells were tested using the FDS, and the terminal volt-age and current were recorded every second. Based on the col-lected data, the internal resistance R can be estimated by a least-square algorithm. Fig. 4a and b show the fitted result and the errorof the fit for cell #1, respectively. The root mean square (RMS) er-rors and mean errors of the fit are shown in Table 1. The non-zeromean error suggests that there is a small bias in the model, as seenin Fig. 4b. Thus, the model can be improved by adding a constant Cto Eq. (1):

V ¼ OCV� I� Rþ C ð2Þ

The fitted result of Eq. (2) is shown in Fig. 5. The model parameters,as well as the RMS error and mean error, are shown in Table 2. Com-pared with the model in Eq. (1), the RMS error of the model in Eq.(2) is reduced by 1 order, and the mean error is reduced by at least10 orders. Thus, the model is improved.

Eq. (2) is used to infer the OCV from the terminal voltage V andthen, based on the OCV–SOC curve, the SOC is estimated. Fig. 6shows the estimation result for cell #1. The max estimation erroris 28.5%, and the RMS error is 6.12%. The large error is caused bythe flat OCV–SOC curve of LiFeO4 cells. From Fig. 2, the slope ofthe OCV–SOC curve (i.e., dOCV/dSOC) between 30% and 90% SOCis approximately 0.001, which means that an error of 0.01 V inOCV causes about a 10% error in SOC estimation. Therefore, directmodel-based inference requires high accuracy of modeling andmeasurements. In Fig. 6, modeling error is the major cause of the

Fig. 2. OCV–SOC relationship of five cells tested.



Fig. 3. (a) Federal driving schedule and (b) the corresponding current profile.

W. He et al. / Microelectronics Reliability xxx (2013) xxx–xxx 3

estimation error, because the RMS error of the model is 0.0064,which causes approximately a 6% RMS error in SOC estimation.

To improve the estimation accuracy, we developed an un-scented Kalman filter-based approach. Using Eq. (2) and the Cou-lomb counting principle, we can formulate a state-space modelfor UKF estimation. SOC and R are selected as states for the state-space model, since they cannot be directly observed from the mea-surement. The evolution of SOC and R follow the Coulomb countingformula and random walk, respectively. The reason for choosing Ras a state is because it varies among different cells, as shown in Ta-ble 2, while C only varies slightly. In order to address unit-to-unitvariations, R is updated according to specific applications. Themeasurement model is the terminal voltage, which is defined asa function of SOC and R based on Eq. (2). Eq. (3) shows the pro-posed state-space model:

SOCðkþ 1Þ ¼ SOCðkÞ � IðkÞ�DTQmax

þx1

Rðkþ 1Þ ¼ RðkÞ þx2

(VðkÞ ¼ OCV½SOCðkÞ� � IðkÞ � RðkÞ þ C þ e

ð3Þ

where Qmax is the total capacity of the battery, x1 and x2 are pro-cess noises, and e is measurement noise.

3. Unscented Kalman Filter

SOC estimation is a nonlinear problem. The nonlinearity can beseen in the measurement model, where OCV (SOC[k]) is highlynonlinear, as shown in Fig. 2. For the nonlinear state estimationproblem, the extended Kalman filter (EKF) is a standard approach.


The problem with EKF is that it only uses first-order or second-or-der terms of the Taylor series expansion to approximate the non-linear functions. Large errors are produced if the model is highlynonlinear. In this study, we utilized an unscented Kalman filter(UKF), which is accurate to the third order, in the sense of a Taylorseries expansion for any nonlinearity [25]. UKF is a direct applica-tion of the unscented transform (UT), which is a statistical tool. InUT, a Gaussian distribution is represented by a set of carefully cho-sen sample points called sigma points. These sigma points capturethe mean and covariance of the Gaussian random variables (GRVs)when propagated through a nonlinear function. UKF has been ap-plied to system estimation [28,29], anomaly detection [30,31],and prognostics [32,33].

Assume that a Gaussian random variable x (dimension L) hasmean �x and covariance Px. Consider propagating x through thenonlinear function y = g(x). To calculate the statistics of y, we firstfind a matrix v of 2L + 1 sigma vectors vi with correspondingweights Wi, according to the following equations [25]:

v0 ¼ �x i ¼ 0

vi ¼ �xþffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðLþ kÞPx

p� �i i ¼ 1; . . . ; L

vi ¼ �x�ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðLþ kÞPx

p� �i�L i ¼ Lþ 1; . . . ;2L

W ðmÞ0 ¼ k=ðLþ kÞ i ¼ 0

W ðcÞ0 ¼ k=ðLþ kÞ þ 1� a2 þ b

W ðmÞi ¼W ðcÞ

i ¼ 1=f2ðLþ kÞg i ¼ 1; . . . ;2L

8>>>>>>>>>><>>>>>>>>>>:ð4Þ

where k = a2(L + j) � L is a scaling parameter, a determines thespread of the sigma points around �x; j is another scaling parameter



Fig. 4. (a) The fitted result of the model in Eq. (1) and (b) the error of the model fit.

Table 1Parameters and errors of the model in Eq. (1).

Cell #1 Cell #2 Cell #3 Cell #4 Cell #5

R 0.1347 0.2172 0.1636 0.2006 0.1592RMS error 0.0212 0.0218 0.0215 0.0201 0.0210Mean error 0.0180 0.0176 0.0183 0.0169 0.0179


which is set to 3 � L, and b is used to incorporate prior knowledge ofthe distribution of x. For Gaussian distributions, b = 2 is optimal[25].

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðLþ kÞPx

p� �i is the ith column of the matrix square root of

(L + k)Px. Then, each sigma point is propagated through the nonlin-ear function yi = g(vi), i = 0, . . . , 2L. The estimated mean and covari-ance of y are computed by the weighted sample mean andcovariance as follows:

�y ¼X2L

i¼0

W ðmÞi yi ð5Þ

Py ¼X2L

i¼0

W ðcÞi ðyi � �yÞðyi � �yÞT ð6Þ

The UKF is a straightforward application of the UT for state esti-mation. The main steps of UKF are summarized below:

(1) Initialize with bX0 ¼ E½X0� and P0 ¼ E½ðX0 � bX0ÞðX0 � bX0ÞT �(2) For k 2 {1, . . . ,1}, calculate sigma points:

Please(2013

v¼k�1bXk�1

bXk�1 þ cffiffiffiffiffiffiffiffiffiffiPk�1

p bXk�1 � cffiffiffiffiffiffiffiffiffiffiPk�1

ph ið7Þ

cite this article in press as: He W et al. State of charge estimation for elect), http://dx.doi.org/10.1016/j.microrel.2012.11.010

(3) State prediction:a. Propagate the sigma points through the state model:

ric veh

vkjk�1 ¼ H½vkjk�1� ð8Þ

b. Calculate the propagated mean:

X�k ¼X2L

i¼0

W ðmÞi vi;kjk�1 ð9Þ

c. Calculate the propagated covariance:

P�k ¼X2L

i¼0

W ðcÞi vi;kjk�1 � bX�kh i

vi;kjk�1 � bX�kh iTð10Þ

(4) Measurement update:a. Propagate sigma points through the measurement

function:

ykjk�1 ¼ H½vkjk�1� ð11Þ

b. Calculate the propagated mean:

�y�k ¼X2L

i¼0

W ðmÞi yi;kjk�1 ð12Þ

c. Calculate the estimated covariance

icle batte

P�y�k

�y�k¼X2L

i¼0

W ðcÞi yi;kjk�1 � �y�kh i

yi;kjk�1 � �y�kh iT

Pxkyk¼X2L

i¼0

WðcÞi vi;kjk�1 � �x�kh i

yi;kjk�1 � �y�kh iT

ð13Þ

ries using unscented kalman filtering. Microelectron Reliab


Fig. 5. (a) The fitted result of the model in Eq. (2) and (b) the error of the model fit.

Table 2Parameters and errors of model Eq. (2).

Cell #1 Cell #2 Cell #3 Cell #4 Cell #5

R 0.1166 0.1995 0.1453 0.1835 0.1413C �0.0226 �0.0221 �0.0229 �0.0212 �0.0225RMS error 0.0064 0.0092 0.0065 0.0068 0.0063Mean error �6.61e�016 �1.50e�015 1.16e�016 �1.14e�016 8.66e�016

Fig. 6. SOC estimation based on the battery model in Eq. (2).



d. Calculate the Kalman gain K and update the state esti-mation and covariance:

ric veh
icle batter
K ¼ PxkykP�1

�y�k

�y�k

Xk ¼ X�k þ K yk � �y�k� �

Pk ¼ P�k � KP�y�k

�y�k

KT

ð14Þ

The advantages of UKF are: (1) it is robust to noise, because ittakes the measurement and process uncertainties into accountand (2) it has the ability to self-correct. In other words, wheneverthe estimation deviates from the true value, a correction termbased on the Kalman gain will be added to the estimation. The nextsection will present the validation results of the developed methodto show its effectiveness.

4. State of charge estimation case studies

The developed method was tested on data collected in the fed-eral driving schedule, as shown in Fig. 3. The actual initial SOC was

ies using unscented kalman filtering. Microelectron Reliab



80%. The initial SOC guess for UKF estimation was set at 35% fortwo reasons: (1) to simulate the actual field conditions, wherethe exact SOC at the beginning of usage is unknown and (2) to testthe self-correction capability of the UKF. The estimation result isshown in Fig. 7. The blue line is the actual SOC, while the red lineis the UKF estimation. Although the estimation deviates from thereal SOC at the beginning due to the erroneous initial guess, it con-verges to the real SOC as more measurements became available.After it converges, the estimation error is always smaller than 4%.

In order to investigate the effect of different starting SOC condi-tions on the estimation accuracy, the UKF-based method was fur-ther tested by varying the beginning SOC of the battery andallowing the UKF to converge to the SOC. In each case, the initialSOC guesses were set at 35%. Fig. 8 shows the estimation results.The RMS errors of all cases were within 3.1%, and the maximumRMS error occurred when starting from 80% SOC. One reason for

Fig. 7. UKF-based SOC estimation.

Fig. 8. RMS error of SOC estimation when starting from different SOC levels.


this is the flat OCV–SOC slope at 80% SOC, as shown in Fig. 2. There-fore, more data are required for the UKF to track back to the realSOC. As shown in Fig. 8, better accuracy was achieved when theestimation started from a low SOC region, such as 20% SOC, be-cause it is close to the initial guess and the OCV–SOC curve at thisregion is steep. As a result, less data are required for theconvergence.

The method was tested on data collected from a second LiFePO4battery to see whether it can handle unit-to-unit variability. Theparameter settings were the same as those used in the previouscases. As shown in Fig. 9, the maximum RMS error of the SOC esti-mation was less than 4%. The developed UKF method not only up-dates the SOC, but also updates the internal resistance. Therefore, itis able to handle the unit-to-unit variations within batteries.

A good SOC estimation should be able to function effectivelyunder different loading profiles. To examine the applicability ofthe developed method to other profiles, we collected battery dis-

Fig. 9. RMS error of UKF-based SOC estimation for a second EV battery.

Fig. 10. (a) Current profile of the DST and (b) the terminal voltage response of theDST.



Fig. 11. RMS error of UKF-based SOC estimation for DST profile.

Fig. 12. UKF-based SOC estimation for DST profile.


charge data using dynamic stress testing (DST) [34], which is a stepcharge/discharge profile. The current load profile and the corre-sponding terminal voltage response are shown in Fig. 10a and b,respectively. The parameter settings of the UKF, including the ini-tial guess, process, and measurement noise, also remained thesame. The RMS error of the SOC estimation at different startingpoints is shown in Fig. 11. The maximum RMS error was also lessthan 4%. Fig. 12 shows the SOC estimation beginning from 80%. Itcan be seen that the UKF-approach tracks the SOC well.

5. Conclusions

State of charge (SOC) is the actual capacity of a battery ex-pressed as a percentage of the fully-charged capacity. SOC estima-tion is a major function of battery management systems (BMSs).The commonly used Coulomb counting method for SOC estimationrequires knowing the exact initial SOC and suffers from the prob-lem of drift as the error accumulates over time and the batteryages. Additionally, voltage-based estimation methods can producelarge errors when applied to LiFePO4 batteries due to their flatOCV–SOC curves. To solve these problems, we developed an adap-


tive SOC estimation method that combines Coulomb counting anda battery voltage model using the unscented Kalman filter (UKF).The battery voltage model is readily implementable with twoparameters to be determined. One parameter is the internal resis-tance, which is updated on-line as a hidden state to address unit-to-unit variations and loading condition changes. The other param-eter is a compensatory constant term that is identified off-line. Thedynamic SOC model was developed based on the Coulomb count-ing principle. UKF, which is close-looped in nature, was then usedto infer the SOC from the current and voltage measurements.When the SOC estimation drifts, as detected by the deviation be-tween the voltage model output and the voltage measurement,the UKF automatically generates a correction term to rectify the er-ror. As a result, the developed method does not require prior infor-mation of the initial SOC and is robust to measurement noise. Thisfeature is meaningful for EV applications, because when the SOC ofan EV changes due to self-discharge or varying environmental con-ditions, this method self-corrects the SOC. The developed methodwas tested using data from different LiFePO4 batteries and twoloading conditions, namely, the federal driving schedule and dy-namic stress testing. The test results showed that the methodwas able to handle unit-to-unit variations and loading conditionchanges with an RMS error of less than 4%.

This research is significant for two reasons. First, the developedSOC estimation technique can indicate how much charge is left inthe battery while taking into consideration unit-to-unit variationsand loading condition changes. This is meaningful for EVs becauseunit-to-unit variation among the hundreds of cells in an EV batterypack is common due to uncertainties in the manufacturing, assem-bly, and material properties, and also because battery packs expe-rience variant loading profiles as a result of different roadconditions. Second, many battery systems for EVs are over-engi-neered by 25–100% to minimize the risk of premature failurecaused by over-charging and over-discharging. SOC estimationprovides information for the BMS to keep the battery workingwithin a safe operating window. With an accurate SOC estimatorin place, the battery pack can be used to its limit and does not needto be over-engineered, resulting in reduced cost.

Acknowledgments

The authors thank the more than 100 companies and organiza-tions that support research activities at the Center for AdvancedLife Cycle Engineering at the University of Maryland annually.The authors would also like to thank the members of the Prognos-tics and Health Management Consortium at CALCE for their sup-port of this work.

References

[1] One Million Electric Vehicles by 2015: February 2011 Status Report. The USDepartment of Energy, 2011.

[2] F. Yan and J. Wong, China electric vehicles to hit 1 million by 2020: report.<http://www.reuters.com/article/2010/10/16/retire-us-autos-china-idUSTRE69F0J820101016>; October16, 2010 [cited 15.02.12].

[3] Electric vehicles: the future of driving. The Consumer Electronics Association;2010.

[4] Ng KS, Moo C-S, Chen Y-P, Hsieh Y-C. Enhanced coulomb counting method forestimating state-of-charge and state-of-health of lithium-ion batteries. ApplEnergy 2009;86(9):1506–11.

[5] Yan JY, Xu GQ, Qian HH, Xu YS. Robust state of charge estimation for hybridelectric vehicles: framework and algorithms. Energies 2010;3(10):1654–72.

[6] Pop V, Bergveld HJ, Notten PHL, Regtien PPL. State-of-the-art of battery state-of-charge determination. Measur Sci Technol 2005;16(12):R93–R110.

[7] Kozlowski JD. Electrochemical cell prognostics using online impedancemeasurements and model-based data fusion techniques. In: 2003 IEEEaerospace conference proceedings, Big Sky, Montana; 2003.

[8] Shen WX, Chan CC, Lo EWC, Chau KT. A new battery available capacityindicator for electric vehicles using neural network. Energy Convers Manage2002;43(6):817–26.


http://www.reuters.com/article/2010/10/16/retire-us-autos-china-idUSTRE69F0J820101016

http://www.reuters.com/article/2010/10/16/retire-us-autos-china-idUSTRE69F0J820101016



[9] Li IH, Wei-Yen W, Shun-Feng S, Yuang-Shung L. A merged fuzzy neuralnetwork and its applications in battery state-of-charge estimation. IEEE TransEnergy Convers 2007;22(3):697–708.

[10] Lee Y-S, Wang W-Y, Kuo T-Y. Soft computing for battery state-of-charge(BSOC) estimation in battery string systems. IEEE Trans Ind Electron2008;55(1):229–39.

[11] Cheng B, Bai Z, Cao B. State of charge estimation based on evolutionary neuralnetwork. Energy Convers Manage 2008;49(10):2788–94.

[12] Weigert T, Tian Q, Lian K. State-of-charge prediction of batteries and battery-supercapacitor hybrids using artificial neural networks. J Power Sources2011;196(8):4061–6.

[13] Hansen T, Wang C-J. Support vector based battery state of charge estimator. JPower Sources 2005;141(2):351–8.

[14] Shi Q, Zhang C, Cui N. Estimation of battery state-of-charge using v-supportvector regression algorithm. Int J Autom Technol 2008;9(6):759–64.

[15] Pattipati B, Sankavaram C, Pattipati KR. System identification and estimationframework for pivotal automotive battery management systemcharacteristics. IEEE Trans Syst, Man, Cyber, Part C: Appl Rev 2011:1–16.PP(99).

[16] Plett GL. Extended Kalman filtering for battery management systems of LiPB-based HEV battery packs: Part 1. Modeling and identification. J Power Sources2004;134(2):262–76.

[17] Plett GL. Extended Kalman filtering for battery management systems of LiPB-based HEV battery packs: Part 2. Modeling and identification. J Power Sources2004;134(2):262–76.

[18] Plett GL. Extended Kalman filtering for battery management systems of LiPB-based HEV battery packs: Part 3. State and parameter estimation. J PowerSources 2004;134(2):277–92.

[19] Lee J, Nam O, Cho BH. Li-ion battery SOC estimation method based on thereduced order extended Kalman filtering. J Power Sources 2007;174(1):9–15.

[20] Hu C, Youn BD, Chung J. A multiscale framework with extended Kalman filterfor lithium–ion battery SOC and capacity estimation. Appl Energy2012;92:694–704.

[21] He H, Xiong R, Zhang X, Sun F, Fan J. State-of-charge estimation of the lithium–ion battery using an adaptive extended kalman filter based on an improvedthevenin model. IEEE Trans Vehicular Technol 2011;60(4):1461–9.


[22] Chen C, Zhang B, Vachtsevanos G, Orchard M. Machine condition predictionbased on adaptive neuro-fuzzy and high-order particle filtering. IEEE Trans IndElectron 2011;58(9):4353–64.

[23] Chen C, Vachtsevanos G, Orchard M. Machine remaining useful life predictionbased on adaptive neuro-fuzzy and high-order particle filtering. In: Annualconference of the prognostics and health management society, Portland, OR;October 10–16, 2010.

[24] He W, Williard N, Osterman M, Pecht M. Prognostics of lithium–ion batteriesbased on Dempster–Shafer theory and the Bayesian Monte Carlo method. JPower Sources 2011;196(23):10314–21.

[25] Wan EA, Van Der Merwe R. The unscented Kalman filter for nonlinearestimation. in The IEEE adaptive systems for signal processing,communications, and control symposium; 2000.

[26] The EPA Urban Dynamometer Driving Schedule (UDDS), <http://www.epa.gov/otaq/standards/light-duty/udds.htm>; [cited 15.02.12].

[27] EPA US06 or Supplemental Federal Test Procedure (SFTP). <http://www.epa.gov/otaq/standards/light-duty/sc06-sftp.htm>; [cited 15.02.12].

[28] Jafarzadeh S, Lascu C, Fadali MS. State estimation of induction motor drivesusing the unscented Kalman filter. IEEE Trans Ind Electron2012;59(11):4207–16.

[29] He W, Williard N, Chen C, Pecht M. State of charge estimation for electricvehicle batteries under an adaptive filtering framework. In: IEEE conference onprognostics and system health management (PHM), 2012. Beijing; 2012.

[30] Xiong K, Chan CW, Zhang HY. Detection of satellite attitude sensor faults usingthe UKF. IEEE Trans Aerospace Electron Syst 2007;43(2):480–91.

[31] Mirzaee A, Salahshoor K. Fault diagnosis and accommodation of nonlinearsystems based on multiple-model adaptive unscented Kalman filter andswitched MPC and H-infinity loop-shaping controller. J Process Control2012;22(3):626–34.

[32] Wang YL, Wang WH. Failure prognostic of systems with hidden degradationprocess. J Syst Eng Electron 2012;23(2):314–24.

[33] Dai J, Das D, Pecht M. Prognostics-based risk mitigation for telecom equipmentunder free air cooling conditions. Appl Energy 2012;99(0):423–9.

[34] United States Advanced Battery Consortium. Electric vehicle battery testprocedures manual, Revision 2, Southfield, MI; 1996.


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