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1 Vehicle Velocity Estimation based on Data fusion by Kalman Filtering for ABS Melika Amiri Graduate student in electrical engineering, Islamic Azad uniersity, Science and Research ehran, Iran Bijan Moaeni Assistant Professor, School of Railway Engineering- Electrical Railway, Iran Uniersity of Science echnology ehran, Iran Abstract: During the braking process, because of difference between the wheel elocity and the linear ehicle elocity, the slip occurred and it is made ehicle to lose steering control and the friction force, which stops the ehicle, is greatly reduced. o sole this problem, the Antilock Break System (ABS) was proposed, which monitors the wheel elocity and the ehicle elocity to detect and control the slip. he main stage in slip ealuation is ehicle elocity estimation and there are seeral methods for it, where each one has its adantages and drawbacks. In this paper, an analytical and practical solution to estimate the accurate ehicle elocity estimation based on the data fusion algorithms and during the breaking process is deeloped. Finally, simulation results show the effectieness of the new methodology. Keywords: Antilock Break System, Slip Control, Vehicle Velocity Estimation, Data fusion. I. INRODUCION he main objectie of an Antilock Brake System (ABS) is to preent wheels from locking up and slipping during the braking. Wheel locking up often happens when braking on a wet and slippery road or during a seere braking. During wheel lockup, ehicle loses steering control and reduces the friction force. In normal drie condition, the ehicle elocity is almost same as the wheel elocity. he speedometer calculates and displays the ehicle speed by measuring the wheel rotation elocity and multiplying it with the nominal wheel radius. Howeer, when a wheel becomes locked and slips, the ehicle elocity and the wheel elocity are quite different. In ABS, the wheel slip, λ, is defined to indicate the difference between the wheel elocity and the ehicle elocity. ν r λ = ν (1) where is the actual ehicle elocity oer the ground, is the wheel angular elocity and r is the rolling radius (wheel and tire). In normal driing, ν = r and therefore λ =. In seere braking, it is common to hae = while, thus λ = 1, which is called wheel lockup [1]. he ABS producers companies only utilize the wheel angular speed from the wheel speed sensors and they don t like to use other sensors to measure the ehicle longitudinal speed. So, it is important to estimate the ehicle longitudinal elocity and wheel angular speed using only measured wheel angular speed for the adanced slip control maneuer of ABS. In recent years, many efforts hae been focused on the issue of the ehicle elocity estimation such as linear and nonlinear Adaptie filters, Kalman filer and etc., that each of them hae adantages and drawbacks [1,,3,4,]. In the s, Adaptie filter [1], as a simple and efficient method introduced that the estimation is solely based on the wheel elocity measurements without any additional information on the ehicle acceleration. his adaptie nonlinear filter method based on the characteristics of the wheel elocities and knowledge of the ABS operation and a heuristic assumption is made. his methodology estimates the ehicle longitude elocity by using of the aailable data from wheel speed and the ABS operation. he contributors show that the wheel elocities periodically reflect the actual ehicle elocity. But, since the road surface conditions and the ehicle deceleration are unknown to begin with, the estimation error seems ineitable when the ABS is first applied. Although, in results of nonlinear Adaptie filter experiments mentioned that primer error is ineitable, but as in this article can be seen, this problem is one of the drawbacks of the method and unfortunately, there is a lot of distortions and fluctuations in ehicle elocity estimation [6]. Another main method in elocity estimation of ehicles is Kalman filtering method. Although, this method can proide more accurate estimation and conergent to real elocity, but there is a high transient error [],[6]. In this paper, by studying and analyzing the performance of Kalman filter and nonlinear Adaptie filter to estimate linear elocity, a new solution is presented to reduce fluctuations and distortion, without complex calculations and the problems of the preious methods. In other words, this paper presents proper structure of data fusion with the ability to improe the estimation of ehicle elocity. 149

2 μ II. VEHICLE DYNAMIC BASED ON HE LUGRE MODEL One of the current models on ehicle dynamic, with considering the friction is LuGre model where all researchers and engineers use it as a powerful model in all of the speed estimation methods [7]. he LuGre model can describe the nonlinear friction characteristics, which is required between two leel contacts. Many researchers hae used this model because it has a simple structure to be implemented in the design of the controller and can represent most of the friction characteristics. A quarter-ehicle model with the aerage lumped LuGre dynamic tire friction model was adopted to design the obserer as shown in Fig. 1. F = F ( σ z + σ z σ ν ) x n o 1 r Fr = σν mgν where σo is the normalized rubber longitudinal lumped stiffness, σ1 is the normalized rubber longitudinal lumped damping, σ the normalized iscous relatie damping, Fn is the rolling resistance and σ is rolling resistance coefficient. (3) (4) F x Figure 1. A quarter-ehicle model [] he equations of the quarter-ehicle based on the LuGre model are [8]: σo νr z = νr θ z h( ν r ) J = rfx u m ν = 4Fx Fr h( ν ) = μ + ( μ μ ) e m r c s c ν r νs where z is the LuGre friction internal state, ν r = ν r is the relatie elocity, θ is an unknown parameter of the tire/road condition, which can suitably describe the road characteristics. Also μ s is the normalized static friction coefficient, μ c is the normalized Coulomb friction, ν s is the Stribeck relatie elocity, u is the braking torque, J is the rotational inertia of quarter ehicle mass and m is the ehicle mass. Also, the braking force can be expressed as a follow: F z μ r () III. VELOCIY ESIMAION In this section, we briefly reiew the main methods in ehicle elocity estimation. A. Adaptie Nonlinear filter In this method, the elocity estimation is solely based on the wheel elocity measurements. In normal drie condition, the ehicle elocity is almost same as the wheel elocity and in designing filter, the input of filter is wheel angular speed multiplies with the nominal wheel radius and the output is linear ehicle elocity. Howeer, during the wheel lockup or near lockup situation, this relationship no longer holds. In [1], a nonlinear filter as () was presented. t () = R. signt ( () r()) t g y( t = ) = yo In (), ( t) is the input and t ( ) is the output. R g is an adjustment parameter of filter sensitiity and y o is the initial alue of the speed while braking. he output t ( ) will conerge to the input r ( t) in steady state. he change of t () is limited by R g. When t ( ) represents the actual ehicle elocity, the change of t ( ) reflects the road surface condition. In implementations, the alue of R g, which limits the change of t ( ), is continuously updated. It makes the nonlinear filter adaptie to the road surface changes. An initial alue of the parameter R g, is selected to reflect the maximum ehicle deceleration. () B. Kalman Filter Approach he Kalman Filter (KF) is one of the most widely used methods for tracking and estimation due to its optimality, tractability and robustness. KF is a recursie predicted filter 1496

3 based on state techniques and recurrent algorithms. In fact, this filter is the collection of mathematical equations to estimate effectie state for a dynamic system. he performance of dynamic system can disrupt with some white noises. For a linear noisy system as below XK+ 1 = AKXK + WK ZK+ 1 = HK+ 1XK+ 1+ ν K+ 1 We hae KF equations as (7) [1]. Xˆ = A Xˆ (6) K+ 1 K K K K K+ 1 K = K K+ 1 K K + K+ 1 = K+ 1 K K+ 1( K+ 1 K+ 1 K K K+ 1) P A P A Q K P H H P H R Xˆ ˆ ˆ K + 1 K+ 1 = XK+ 1 K + KK+ 1( ZK+ 1 HK+ 1XK+ 1 K) P = (1 K H ) P K+ 1 K+ 1 K+ 1 K+ 1 K+ 1 K IV. VEHICLE VELOCIY ESIMAION USING DAA FUSION SRAEGY Data fusion is a research area that is growing rapidly due to the fact that it proides means for combining pieces of information coming from different sources/sensors, resulting in ameliorated oerall system performance (improed decision making, increased detection capabilities, diminished number of false alarms, improed reliability in arious situations at hand) with respect to separate sensors/sources[11]. Different data fusion methods hae been deeloped in order to optimize the oerall system output in a ariety of applications. here are a lot of arious methods for multi sensor data fusion that using Kalman filter in the data fusion process [1]. In this section, a new method to estimate the ehicle elocity based on the data fusion are presented. A. Series Fusion In this method, we use the speeds of two wheels of ehicle as the inputs to the data fusion algorithm. In order to, estimated speed from Adaptie filter ( a ) as the initial conditions of ehicle elocity in the first Kalman filter and the estimated speed from the first Kalman filter ( ˆ ν 1 ) as initial conditions of second KF as series is used. Note that the simple block diagram of this method is shown in Figure. First wheel 1 lugre LuGre model LuGre model Kalman filter1 a Adaptie filter ν ˆ1 Kalm an filter (7) ˆ νˆ Figure. Diagram of series fusion method B. he Mean Filter In this method, similar to the preious, we use of two wheels speed to estimate the longitude ehicle elocity. At the first, we employ the wheels speed information with different initial conditions separately ( ν 1, ν ). hen all measured wheels speed, like that series fusion method, are processed. It means that using adaptie filter for each wheel separately, longitude ehicle elocity is estimated and the estimations are used as initial conditions of kalman filter used ( ˆ ν 1, ˆ ν ). At last, with applying the mean filter, the final speed estimation is obtained ( ˆ ν ). Figure 3 shows a simple block diagram of the fusion strategy. First wheel 1 lugre model Kalman filter1 second wheel lugre model Adaptie filter1 Figure 3. Diagram of the Mean filter method Mean filter C. Measurement fusion In this section, the angular speeds of two wheels with measurement fusion are fused. In order to, at the first step the wheels angular speed are brought from wheels ( 1, ) and 1 their ector z = is used in Kalman filter, then the final speed is extracted. We use the simplified structure as equation (8) for measurement fusion: Z = W = 1 + ( 1 1+ ), R R R Z R Z that R 1 is measurement coariance matrix of first wheel and R is measurement coariance matrix of second one. Fig 4 is the block diagram of this method. a Kalman filter Adaptie filter a ˆ 1 ˆ ˆ νˆ (8) Second wheel 1497

4 lugre model lugre model Figure 4. block diagram of measurement fusion V. SIMULAION RESULS In all simulations, LuGre model and following parameters are used [8]: m = kg, r =.33 m, θ = 1. Parameter 1 ABLE I. Value Measurement Fusion Unit VEHICLE PARAMEERS[9] Parameter Value Unit [ ] σ 4 [ 1 m ]. σ [ s m ] μ s.9 [ ] σ.18 [ s m ] ν S 1. [ m s] parameter of Kalman filter are as below[]: W k, V k are Gaussian white noises that added to equations Q= diag([1 1 1 ]), R = 1, υ =., Po = diag ([1 1 1 ]), r =.3 m, x o = o o, r EV [ k ] =, EW [ k ] = [ ]. In simulation of Adaptie filter, we used a quarter-ehicle LuGre model and all parameters as defined in section. Here, the alue of R g = 6 is adjusted. Figure shows the real and estimated speeds during a braking process, while we use of ABS. It is obious that the estimated elocity is conergent to the real speed, but there are a lot of distortions and fluctuations. For more accurate inestigation, Figure 6 shows the estimation error. For Kalman filtering strategy, in the simulation a quarter ehicle LuGre model is considered. Simulation results are shown in figure 7. Figure 8 shows the corresponding estimation error and clearly the alue of error in early moments is much and after a few seconds has a swing around zero. But, in simulation of data fusion, we use the half-ehicle LuGre model. Simulation result of series fusion method is existed on figures 9 and 1. Figure 9, shows the good result of estimation and the estimated elocity conergent to real speed well. Also, ˆ μ c figure 1 shows that the amount of estimation error is too small. In figure 11, the simulation result of mean filter method to estimate the ehicle elocity is demonstrated. he figure shows the conerging estimated to the real speed. as the result and this method to be ok for ehicle elocity estimation without considering the alue of error in early moments. With considering Fig 1, the alue of error in early moments is seen. he error of series in comparison with mean filter error is ery little. he applied calculations in this method are easy and this the main adantage of the mean filter approach, while it has much error than series fusion method. Figure 13 shows the speed estimation of measurement fusion method which conerges to the real speed except of early moments. Figure 14 proe that error in early moments is large. It is worth noting that in the simulation, we consider the different speeds from two wheels. o analyze the simulations result, in table the mean square of estimation errors for all estimation methods are introduced. he results show that the series fusion approach has the best performance. 1 1 adaptie filter - Figure. real speed and estimated speed with Adaptie filter error[m/s] time (Sec) Velocity (m/s) -1. Figure 6. error diagram in Adaptie filter 1498

5 KF with r =.33 elocity(m/s) 1 1 Figure 11. speed estimation with mean filter method Figure 7. cure of real and estimated speed with KF.1 Estimation Error with r =.33.1 error(m/s) [m/s] 1 1 Figure 8. error diagram in KF Figure 9. speed estimation of series fusion method error[m/s] 3 x 1-3 Estimation Error error(m/s) Figure 1. error diagram of mean filter method elocity(m/s) Figure 13. Speed estimation of measurement fusion error(m/s) Figure 14. error diagram of measurement fusion V Figure 1. error diagram of series fusion aerage fuser 1 ABLE II. MEAN SQUARE ERROR (MSE) OF ESIMAION MEHOD Method MSE Series fusion Measurement fusion.8 Mean filter method 1.1 Adaptie filter.17 Kalman filter.3 1 [m/s]

6 VI. CONCLUSION In this paper, we present a new elocity estimation approach based on the data fusion theory. Here, we introduce the three noel structures to access the high accuracy in ehicle elocity estimation. By analyzing and comparing the results, series fusion method has the best operation in all methods. his method soles the the problems like distortion and fluctuations of Adaptie filter and primer error of Kalman filter. REFERENCES [1] Fangjun Jiang, Zhiqiang Gao, An Adaptie Nonlinear Filter Approach to the Vehicle elocity Estimation for ABS IEEE ransaction on Automtic control,pp.49-49,sep.. [] Deng Kun, Li Kaijun, and Xia Qunsheng, Application of Unscented Kalman Filter for the State Estimation of Anti-lock Braking System, IEEE,shinghua Uniersity,Sep. 6. [3] Kazuyuki Kobayashi et al, Estimation of Absolute Vehicle Speed using Fuzzy Logic Rule-Based Kalman Filter, Proceedings of the American Control Conference, Seattle, Washington, June 199, p [4] ianjun zhu, Hongyan Zheng, Aplication ofunscented Kalman Filter to Vehicle State Estimation ISECS International Colloquim on Computing Communiccation,Control and Management,8 [] A.DaiB,U.Kiencke, Estimation of ehicle Speed Fuzzy-Estimation in comparison with Kalman-Filtering,IEEE,Uniersity of Karlsruhe,Institude for zindustrial Information System,199 [6] Amiri melika, designing of optimum filtering structure in order to linear speed estimation of ehicle for ABS thesis of MA, Islamic azad uniersity science and research, 11,p -3 [7] Han Me Kim, Seong Ik Han and Jong Shik Kim, Precision position control of sero systems using adaptie back-stepping and recurrent fuzzy neural networks, Journal of Mechanical Science and echnology 3 (9) 39~37. [8] Jingang Yit, Luis Alarezt, Xaier Claeysf, Roberto Horowitzq and Carlos Canudas de Wit, Emergency Braking Control with an Obserer-based Dynamic ire/road Friction Model and Wheel Angular Velocity information, Proceedings of the American Control Conference Arlington, VA June -7, 1. [9] Carlosc Anudast E Wit, C Dynamic ire Friction Models for Vehicle raction Control, Proceedings of the 38th Conference on Decision & Control Phoenix, Arizona USA December [1] A.H. Jazwinski, Stochastic Processes and Filtering heory Academic Press New York, 197. [11] Dr.IR.Nadaa Milisaljeic, Sensor and Data fusion books in Croatia, fist published February 9 [1] J. R. Raol, Multi-sensor data fusion with MALAB, aylor and Francis, 9. 1