Kinematic road gradient estimation

1. A vehicle comprising:

a navigation system configured to generate output indicative of a measured vertical displacement of the vehicle;

a controller configured to:

generate output indicative of a kinematic road gradient estimation using an extended Kalman filter having a system input based on a longitudinal acceleration, and a system output based on a predicted vehicle speed, wherein the system output includes a predicted vertical displacement, and

generate output indicative of a kinematic quality factor corresponding to an availability of the kinematic road gradient estimation;

estimate a first state indicative of an acceleration due to gravity based on a difference between the system output and a measured vehicle speed and a difference between the system output and the measured vertical displacement;

estimate a second state indicative of an acceleration due to a vehicle pitch angle based on a difference between the system output and the measured vehicle speed and a difference between the system output and the measured vertical displacement; and

calculate the kinematic road gradient estimation based on the first state and the second state.

2. The vehicle of claim 1 further comprising: an inertial sensor for providing a signal indicative of the longitudinal acceleration.

3. The vehicle of claim 1 wherein the controller is further configured to:

lock the output indicative of the kinematic road gradient estimation when a vehicle speed is less than an exit speed threshold.

4. The vehicle of claim 1 wherein the system input further comprises an acceleration offset corresponding to lateral vehicle dynamics.

5. The vehicle of claim 1 wherein the kinematic road gradient estimation is independent of a vehicle pitch angle.

6. A vehicle system comprising:

a controller configured to:

calculate a vehicle pitch angle based on a suspension damping effect and a suspension stiffness value selected using a phase plane gain scheduling rule; and

generate output indicating a kinematic road gradient estimation using an extended Kalman filter having a system input based on a longitudinal acceleration and an acceleration offset based on the vehicle pitch angle, and a system output based on a predicted vehicle speed.

7. The vehicle system of claim 6 wherein the acceleration offset is based on a lateral velocity, a lateral offset and the vehicle pitch angle, and wherein the controller is further configured to:

evaluate a vehicle turning condition based on input indicative of a yaw rate; and

estimate the lateral velocity based on an integration of input indicative of a lateral acceleration when the vehicle turning condition corresponds to a dynamic driving condition.

8. The vehicle system of claim 6 wherein the acceleration offset is based on a lateral velocity, a lateral offset and the vehicle pitch angle, and wherein the controller is further configured to:

evaluate a vehicle turning condition based on input indicative of a yaw rate; and

derive the lateral velocity from the yaw rate when the vehicle turning condition corresponds to a steady state condition.

9. The vehicle system of claim 6 wherein the acceleration offset is based on a lateral velocity, a lateral offset and the vehicle pitch angle, and wherein the controller is further configured to:

evaluate a vehicle turning condition based on input indicative of a yaw rate;

calculate a body roll angle based on input indicative of a lateral acceleration when the vehicle turning condition corresponds to a dynamic driving condition; and

estimate the lateral offset based on the body roll angle.

10. The vehicle system of claim 6 wherein the acceleration offset is based on a lateral velocity, a lateral offset and the vehicle pitch angle, and wherein the controller is further configured to:

evaluate a vehicle turning condition based on input indicative of a yaw rate;

calculate a body roll angle based on the yaw rate when the vehicle turning condition corresponds to a steady state condition; and

estimate the lateral offset based on the body roll angle.

11. The vehicle system of claim 6 wherein the controller is further configured to:

estimate the vehicle pitch angle using a dynamic pitch compensation based on a vehicle speed and the longitudinal acceleration.

12. The vehicle system of claim 6 wherein the controller is further configured to:

estimate a state indicative of an acceleration due to gravity based on a difference between the system output and a measured vehicle speed;

select the suspension damping effect and the suspension stiffness value from predetermined data based on the state and a derivative of vehicle speed using the phase plane gain scheduling rule; and

calculate the vehicle pitch angle using a transfer function based on the suspension damping effect and the suspension stiffness value.

13. The vehicle system of claim 6 wherein the controller is further configured to:

calculate the vehicle pitch angle based on a vehicle speed, the longitudinal acceleration and a vertical acceleration.

14. The vehicle system of claim 6 wherein the controller is further configured to:

estimate a state indicative of an acceleration due to gravity based on a difference between the system output and a measured vehicle speed; and

calculate the vehicle pitch angle based on a vehicle speed, the longitudinal acceleration, a vertical acceleration and the acceleration due to gravity.

15. A method for operating a vehicle based on an estimated kinematic road gradient comprising:

receiving input indicative of a measured vertical displacement of the vehicle;

generating output indicative of a kinematic road gradient estimation using an extended Kalman filter having a system input based on a longitudinal acceleration, and a system output based on a predicted vehicle speed, wherein the system output comprises a predicted vertical displacement;

generating a kinematic quality factor that corresponds to an availability of the kinematic road gradient estimation;

estimating a first state indicative of an acceleration due to gravity based on a difference between the system output and a measured vehicle speed and a difference between the system output and the measured vertical displacement;

estimating a second state indicative of an acceleration due to a vehicle pitch angle based on a difference between the system output and the measured vehicle speed and a difference between the system output and the measured vertical displacement; and

calculating the kinematic road gradient estimation based on the first state and the second state.

16. The method of claim 15 further comprising:

receiving input indicative of a yaw rate; and

estimating an acceleration offset based on the yaw rate, wherein the acceleration offset includes at least one of a lateral velocity, a lateral offset, and the vehicle pitch angle;

wherein the system input further comprises the acceleration offset.