Method to estimate vehicle mass

A method for estimating vehicle mass, comprising:

• setting an initial vehicle mass estimate {circumflex over (x)}(0)={circumflex over (m)}(0) and setting an initial error variance p(0);
• predicting a next vehicle mass as {circumflex over (x)}(k)=a{circumflex over (x)}(k−1), where the scalar a is equal to 1, and predicting a next error variance as (k)=a2p(k−1)+q, where q is a process variance variable which is a tunable design parameter;
• obtaining or determining a longitudinal acceleration ax(k) of the vehicle;
• obtaining or determining a road slope angle θ(k);
• determining c=ax(k)+fg+gsin(θ(k), where f is the rolling resistance of the vehicle and g is the gravitational acceleration;
• determining a residual variance as s=c2p(k−1)+r;
• where r is a measurement variance variable that is a tunable design parameter;
• determining a Kalman filter gain as
• k
• =
• c
• 2
• ⁢
• p
• ⁡
• (
• k
• -
• 1
• )
• s
• ;
• determining a wheel force as
• F
• x
• =
• τ
• w
• R
• W
• ;
• determining an aerodynamic force as
• F
• a
• =
• 1
• 2
• ⁢
• ρ
• ⁢
• C
• d
• ⁢
• A
• f
• (
• v
• )
• 2
• ,
• where ρ is an air density, Cd is a aerodynamic drag coefficient, Af is a frontal area of the vehicle, and v is the vehicle speed;
• determining a difference between the wheel force and the aerodynamic force as γ;
• determining a measurement residual error as ∈=y−c{circumflex over (x)}(k−1);
• and
• updating the error variance and the vehicle mass, wherein the updated vehicle mass is the estimated vehicle mass.