METHOD AND APPARATUS FOR ROAD SURFACE FRICTION ESTIMATION BASED ON THE SELF ALIGNING TORQUE

1 . A method for estimating a road surface friction between a road surface and a tire of a vehicle, comprising the steps of:

computing in a slope estimation step, a slope estimate k_sl for a slope of a linear region of a self aligning torque function, the self aligning torque function being defined by a self aligning torque as a function of a slip angle;

deriving a first estimate μ_sl of a road friction coefficient μ from the slope estimate k_sl;

deciding, in a linearity estimation step, whether a current slope k_op is within the linear region of the self aligning torque function; and

outputting the first estimate μ_sl of the road friction coefficient as a second estimate μ_cont of the road friction coefficient if it is decided in the linearity estimation step that the current slope k_op is within the linear region of the self aligning torque function.

2 . The method according to claim 1 , further comprising the step of halting the computation of the slope estimate k_sl if it is decided in the linearity estimation step that the current slope k_op is not within the linear region of the self aligning torque function.

3 . The method according to claim 1 , wherein the linearity estimation step comprises a computation of a time derivative of the self aligning torque and of the time derivative of the slip angle.

4 . The method according to claim 1 , wherein in the linearity estimation step it is decided that the current slope k_op is within a nonlinear region of the self aligning torque function if k_op falls below a lower threshold k_op_threshold_low and it is decided that the current slope k_op is within the linear region of the self aligning torque function if the current slope k_op rises above an upper threshold k_op_threshold_high, wherein k_op_threshold_low<k_op_threshold_high.

5 . The method according to claim 1 , wherein the slope estimation step comprises a computation of a quotient from the self aligning torque and the slip angle.

6 . The method according to claim 1 , wherein the slope estimation step comprises computing estimates of one or more observation variables by an update formula of a Kalman filter.

7 . The method according to claim 1 , wherein the linearity estimation step comprises computing estimates of one or more observation variables by an update formula of a Kalman filter.

8 . The method according to claim 7 , wherein the one or more observation variables are given by a time derivative of the self aligning torque and the time derivative of the slip angle.

9 . The method according to claim 1 , wherein the slope estimation step and the linearity estimation step are executed as computational threads.

10 . The method according to claim 1 , further comprising the steps of:

comparing the second estimate μ_cont of the road friction coefficient to a lower limit;

comparing the second estimate μ_cont of the road friction coefficient to an upper limit;

outputting as a final estimate μ_SAT of the road friction coefficient the second estimate μ_cont if the second estimate is within a range defined by the upper limit and the lower limit and outputting the lower limit if the second estimate μ_cont is less than the lower limit and outputting the upper limit if the second estimate μ_cont is greater than the upper limit.

11 . The method according to claim 10 , wherein the upper limit is derived from a maximum available road friction μ_max and the lower limit is derived from a minimum available road friction μ_min, a first derivation of the upper limit comprises a computation of a forget function of the maximum available road friction μ_max and a second derivation of the lower limit comprises a computation of the forget function of the minimum available road friction μ_min and the forget function is defined such that a difference between the lower limit and the upper limit increases with time.

12 . A computer readable medium embodying a computer program product, said computer program product comprising:

a program for estimating a road surface friction between a road surface and a tire of a vehicle program, the program configured to:

compute in a slope estimation step, a slope estimate k_sl for a slope of a linear region of a self aligning torque function, the self aligning torque function being defined by a self aligning torque as a function of a slip angle;

derive a first estimate μ sl of a road friction coefficient μ from the slope estimate k_sl;

decide, in a linearity estimation step, whether a current slope k_op is within the linear region of the self aligning torque function; and

output the first estimate μ_sl of the road friction coefficient as a second estimate μ_cont of the road friction coefficient if it is decided in the linearity estimation step that the current slope k_op is within the linear region of the self aligning torque function.

13 . The computer readable medium embodying the computer program product of according to claim 12 , said program further configured to halt the computation of the slope estimate k_sl if it is decided in the linearity estimation step that the current slope k_op is not within the linear region of the self aligning torque function.

14 . The computer readable medium embodying the computer program product of according to claim 12 , wherein the linearity estimation step comprises a computation of a time derivative of the self aligning torque and of the time derivative of the slip angle.

15 . The computer readable medium embodying the computer program product of according to according to claim 12 , wherein in the linearity estimation step it is decided that the current slope k_op is within a nonlinear region of the self aligning torque function if k_op falls below a lower threshold k_op_threshold_low and it is decided that the current slope k_op is within the linear region of the self aligning torque function if the current slope k_op rises above an upper threshold k_op_threshold_high, wherein k_op_threshold_low<k_op_threshold_high.

16 . The computer readable medium embodying the computer program product of according to claim 12 , wherein the slope estimation step comprises a computation of a quotient from the self aligning torque and the slip angle.

17 . The computer readable medium embodying the computer program product of according to according to claim 12 , wherein the slope estimation step comprises computing estimates of one or more observation variables by an update formula of a Kalman filter

18 . The computer readable medium embodying the computer program product of according to according to claim 12 , wherein the linearity estimation step comprises computing estimates of one or more observation variables by an update formula of a Kalman filter.

19 . The computer readable medium embodying the computer program product of according to according to claim 18 , wherein the one or more observation variables are given by a time derivative of the self aligning torque and the time derivative of the slip angle.

20 . The computer readable medium embodying the computer program product of according to according to claim 12 , wherein the slope estimation step and the linearity estimation step are executed as computational threads.

21 . The computer readable medium embodying the computer program product of according to according to claim 12 , the program further configured to:

compare the second estimate μ_cont of the road friction coefficient to a lower limit;

compare the second estimate μ_cont of the road friction coefficient to an upper limit; and

output as a final estimate μ_SAT of the road friction coefficient the second estimate μ_cont if the second estimate is within a range defined by the upper limit and the lower limit and outputting the lower limit if the second estimate μ_cont is less than the lower limit and outputting the upper limit if the second estimate μ_cont is greater than the upper limit.

22 . The computer readable medium embodying the computer program product of according to according to claim 21 , wherein the upper limit is derived from a maximum available road friction μ_max and the lower limit is derived from a minimum available road friction μ_min, a first derivation of the upper limit comprises a computation of a forget function of the maximum available road friction μ_max and a second derivation of the lower limit comprises a computation of the forget function of the minimum available road friction μ_min and the forget function is defined such that a difference between the lower limit and the upper limit increases with time.