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Please follow the instructions below to enable JavaScript in your browser. Please enter a display name. Cancel Change Name. Theoretically, the yaw rate can be estimated using wheel speeds, front wheel steering angle, and some vehicle parameters using kinematic relations between these variables.
This approach is called kinematic estimation. Unfortunately, ABS wheel speed signals may sometimes be too noisy to obtain satisfactory yaw rate estimates [ 7 , 8 ]. For this reason, dynamic estimation is used in addition to kinematic estimation for filtering this sensor noise. In the dynamic estimation part, different types of observers can be used.
Observers including Kalman filters for filtering sensor noise have been used in estimation of vehicle parameters [ 2 — 6 , 8 — 15 ] before, and this approach is also used in this paper. The contributions of this work are the introduction of a novel wheel speed-based kinematic estimation algorithm, its combined use with a Kalman filter-based dynamic estimation approach to take care of wheel speed sensor noise, the use of a hardware-in-the-loop setup to develop the estimation algorithms in a lab environment, and road test results to demonstrate the effectiveness of the proposed method in the real world.
This paper concentrates on yaw rate estimation using a virtual sensor based on kinematic and dynamic estimation. In the kinematic estimation part of the virtual sensor design, kinematic relations between yaw rate and wheels speeds are considered. The double-track four wheels geometry of the vehicle chassis is used in the kinematic computations for yaw rate.
Then, kinematic yaw rate estimation is improved by an algorithm which considers wheel longitudinal slips during braking and sudden accelerating skidding.
In the dynamic estimation part, used here for attenuating possible wheel speed sensor noise, a speed-scheduled Kalman filter is introduced and used. The gain matrix of the Kalman filter is scheduled with longitudinal vehicle velocity. The designed virtual sensor for yaw rate is tested first in offline computer simulations, then in hardware-in-the-loop simulations, finally in actual road tests.
In actual road tests, the virtual sensor runs in parallel with the commercial yaw rate sensor such that their outputs could be compared directly. The virtual yaw rate sensor is connected to the ESP electronic control unit instead of the commercial sensor in the tests.
It should be noted that instead of replacing the actual sensor, the virtual yaw rate sensor algorithm can also be used for diagnostic purposes to detect faulty operation of the commercial sensor. The organization of the rest of the paper is as follows. In Section 2 and its subsections, the kinematic and dynamic virtual sensor design is explained.
Simulation results obtained using the virtual sensor are given in Section 3. The hardware-in-the-loop HiL simulator used is introduced in Section 4 where real-time simulation results obtained using that HiL simulator are also presented. The actual road test results are given in Section 5 , and the paper ends with conclusions. Virtual sensor design is realized by combining the kinematic estimation method with the dynamic estimation method.
Figure 1 shows the main structure of the virtual sensor. Firstly, vehicle yaw rate is estimated kinematically using wheel angular speeds, front wheel steering angle, and some vehicle parameters shown in Figure 2. After that, this kinematically estimated yaw rate is used in the dynamic estimation part based on a Kalman filter for attenuating possible wheel speed sensor noise.
Note that a double-track four wheels dynamic vehicle model is not used or needed in the work presented in this paper as the virtual sensor that uses the geometry in Figure 2 is kinematic in nature and does not require a dynamic model.
Basically, yaw rate is estimated for the vehicle geometry seen in Figure 2 from rear wheel angular speeds by using 1 and from the front wheel angular speeds by using 2 [ 10 — 12 ]. Consider the following: where , , , and are the angular speeds of the front left, the front right, the rear left and the rear right wheels, respectively.
Here, denotes the kinematically estimated yaw rate. Previous studies show that the longitudinal slip of the wheels affects the yaw rate estimation [ 7 ]. When considering a front wheel drive vehicle, at sudden acceleration and braking conditions of front wheels and at braking conditions of rear wheels, longitudinal slip occurs at the relevant wheels and this affects the yaw rate estimation adversely.
Kinematic estimation in 1 and 2 should therefore be modified to take this slip into account. Slip ratio is defined as during braking and as during driving [ 16 ]. The vehicle speed reading from the wheel speed sensors is slightly smaller than the true speed of the vehicle as determined by a GPS sensor.
This slight difference did not create any problems in the yaw rate estimation. This paper does not deal with vehicle state estimation. It is assumed that the reference vehicle speed the speed at vehicle center of gravity can be obtained directly.
Vehicle yaw rate can be calculated kinematically based on rear wheels in the case of braking using the slip definition given by 3 and the longitudinal speeds of the rear wheels given by 7 and 8 as follows:. Yaw rate can also be calculated kinematically based on front wheels in the case of braking using the slip definition given by 3 and the longitudinal speeds of the front wheels given by 5 and 6 as follows: and lastly it can be calculated kinematically based on front wheels in the case of vehicle acceleration using the slip definition given by 4 and the longitudinal speeds of the front wheels 5 and 6 as follows: where is the current value of time, is the calculation time interval, and the subscript of shows the th wheel of the vehicle.
The derivation details of 9 — 11 are given in the appendix. Slip ratio of each wheel is computed utilizing slip ratio definitions 3 and 4 and longitudinal speeds of wheels 5 — 8. These slip ratio formulae are given in the following. When braking occurs at the rear wheels,. When braking occurs at the front wheels. When acceleration occurs at the front wheels,. The basic kinematical equations 1 and 2 are utilized together with improved kinematical estimation equations 9 — 11 in forming a general kinematic estimation algorithm in the Matlab environment.
This general kinematic algorithm is embedded into the kinematic estimation part of the virtual yaw rate sensor. Figure 3 shows the flowchart of the rear wheel kinematic estimation algorithm, and Figure 4 shows the flowchart of the front wheel kinematic estimation algorithm. In these flowcharts, represents the kinematically estimated yaw rate. It should be noted that the front wheel and rear wheel angular speed-based calculations lead to similar results with small differences.
Since we are using a front wheel drive vehicle, rear wheel angular speed-based estimation is usually better than front wheel angular speed based estimation. Our overall kinematic estimation algorithm combines information from both rear and front wheels to estimate yaw rate in order to make use of both of these available data.
This combination was realized with the addition of the two estimations from rear and front with the proportion of times the estimated yaw rate from the rear wheels plus times the estimated yaw rate from the front wheels. This ratio was chosen heuristically based on an extensive trial and error procedure applied to simulation and experimental results.
The Kalman filter is an optimal observer that estimates the system states which are hard to measure while filtering the measurement noise [ 17 ].
Note that the Kalman filter-based dynamic virtual sensor is used to filter wheel speed sensor noise here. When there is a change to those standards, the control will make adjustments and corrections to stabilize the vehicle. The Yaw rate sensor measures the rotation rate of the car. This information is then fed into a microcomputer that compares the data with wheel speed, steering angle and accelerator position, and, if the system senses too much yaw, the appropriate braking force is applied.
The lateral acceleration sensor measures the g-force from a turn and sends that information also to the ECU. Lastly, the wheel speed sensors measures the wheel speed. Some quick notes on ESC. First and foremost, the system is not a substitute for safe driving, but is designed to assist the driver recover from dangerous situations. ESC works on virtually any surface, for example, rain slick roads, icy roads and dry pavement.
History A journey of more than 60 years. Annual Report reasons to belive. Whistleblower Channels. Quality Policy. What is WLTP? To ensure this content displays correctly, use one of the following options. Chrome Safari Edge Firefox Opera. Yaw rate sensor The yaw rate sensor determines whether the car is developing a tendency to spin around the vertical axis.
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