klomp2014.pdf

Vehicle System Dynamics, 2014

Vol. 52, Supplement, 172–188, http://dx.doi.org/10.1080/00423114.2014.887737

Longitudinal velocity and road slope estimation in hybrid

electric vehicles employing early detection of

excessive wheel slip

Matthijs Klomp

a∗

, Yunlong Gao

b

and Fredrik Bruzelius

a

Vehicle speed is one of the important quantities in vehicle dynamics control. Estimation of the slope

angle is in turn a necessity for correct dead reckoning from vehicle acceleration. In the present work,

estimation of vehicle speed is applied to a hybrid vehicle with an electric motor on the rear axle and

a combustion engine on the front axle. The wheel torque information, provided by electric motor,

is used to early detect excessive wheel slip and improve the accuracy of the estimate. A best-wheel

selection approach is applied as the observation variable of a Kalman filter which reduces the influence

of slipping wheels as well as reducing the computational effort. The performance of the proposed

algorithm is illustrated on a test data recorded at a winter test ground with excellent results, even for

extreme conditions such as when all four wheels are spinning.

Keywords: velocity estimation; Kalman filter; wheel torque; best-wheel speed; slope estimation

and/or impractical for vehicle applications. Therefore, the longitudinal velocity needs to be

estimated from the wheel speed sensors, accelerometers, wheel torque information as well as

other sensors.

These aforementioned sensor sources each have limitations; the wheel speeds become unre-

lated to the vehicle velocity during excessive wheel slip and time integration of the longitudinal

acceleration accumulates sensor bias causing the estimation to drift. Another source of error

is the gravitational component acting in the direction of the road slope contaminating the

acceleration measurement. Hence, estimation of the road slope angle is necessary.

Corresponding author. Email: [email protected]

velocity.

As mentioned, vehicle speed is one of the important quantities in vehicle dynamics control

and estimation of it has consequently drawn substantial attention in both academic research

as well as in the industry. This fact is confirmed by the amount of published work in the field.

Previously reported approaches range from relaying on auxiliary sensors such as microphones

in [1] to optical sensors as in [2]. However, the most common approach in the literature is

based on estimation using primarily the wheel speed sensors. It is typical to combine these with

accelerometers and inertial measurement unit systems in general and other available sensors

in modern vehicles. Simple heuristic approaches of selecting the best candidate, i.e. with the

smallest wheel slip, can be found in for example.[3,4] These heuristic methods have obvious

In this work a similar approach as in [10] is taken, namely using simple kinematic models

in combinations with wheel speed sensors and conventional linear Kalman filers in ordinary

working conditions and using dead reckoning of accelerometers for extreme conditions such as

four excessively spinning wheels. The present work extends the work in [10] with an enhanced

algorithm to more rapidly detecting excessive wheel slip by utilising the force information

from the hybrid electric propulsion system. This rapid detection of excessive wheel slip is

essential to minimise the initial estimation off-set when starting the dead reckoning. A strategy

of using only one best-wheel strategy in the Kalman filer further improves robustness of

the estimation.

This paper is organised as follows. The algorithm is developed in Section 2, and Section 3

best-wheel measurement.

As mentioned in the introduction, the accuracy of this Kalman filter could be improved in two

aspects. One is to find excessive wheel slip in time, the other is the best-wheel speed selection.

Hence, the algorithm in this paper is designed based on these principles. As shown in Figure 1,

this algorithm is composed of five parts. Apart from the Kalman filter for velocity estimation,

the other parts, such as wheel velocity transformation, slope estimation (an additional Kalman

filter), wheel speed selection and excessive slip criteria are other key components in the

overall algorithm.

The general discrete system Kalman filter function consists of two parts; a prediction step

using knowledge about the system behaviour and the inputs to the system and a measurement

k−1|k−1

T

k|k−1

k|k−1

T

k

k|k−1

k

k

k|k−1

,

(1)

k|k

is the post measurement update estimation states vector at the discrete time-step k,

the observation matrix, K

system matrix and input matrices.

For the velocity estimation Kalman filter (index v) we choose

, u

v

x

, z

v

x,BstW

,(2)

where τ is the sample time of the filter. Furthermore, we choose in this work

v

v

to estimate the velocity. These gains are tuning variables and need to be calibrated depending