Method to determine vehicle longitudinal acceleration measurement error

A method of estimating longitudinal acceleration in a vehicle based on a measured longitudinal acceleration from a sensor of the vehicle, comprising:

• initializing an optimal state vector as
• X
• ^
• ⁢
• (
• 0
• )
• =
• [
• x
• ^
• 1
• (
• 0
• )
• x
• ^
• 2
• (
• 0
• )
• ]
• and an error covariance as
• P
• ⁢
• (
• 0
• )
• =
• [
• 1
• 0
• 0
• 1
• ]
• ;
• predicting a next state vector and a next covariance matrix:
• X
• ^
• ⁢
• (
• k
• )
• =
• [
• x
• ^
• 1
• (
• k
• )
• x
• ^
• 2
• (
• k
• )
• ]
• =
• [
• 1
• 0
• 0
• 1
• ︸
• A
• ]
• [
• x
• ^
• 1
• (
• k
• -
• 1
• )
• x
• ^
• 2
• (
• k
• -
• 1
• )
• ]
• ⁢
• and
• P
• k
• =
• AP
• k
• -
• 1
• ⁢
• A
• T
• +
• Q
• ,
• where Q is a design matrix that represents a process covariance;
• obtaining a vehicle mass value;
• obtaining a longitudinal acceleration measurement from a vehicle sensor;
• determining a measurement vector C=[mameas(k)−m], and a residual covariance:
• S=CPk-1CT+R, where R is a design matrix that represents the measurement covariance;
• determining a Kalman filter gain as K=Pk-1CTS−1;
• determining wheel force (Fx) as a function of wheel size and wheel torque;
• determining total force (Ftotal) as a function of the wheel force, force of gravity, an aerodynamic force, and a rolling resistance force;
• determining a measurement error as ϵ=y−C{circumflex over (X)}(k−1)=FTotal(k)−C{circumflex over (X)}(k−1), where y=FTotal(k);
• updating the error covariance (Pk) and the state vector ({circumflex over (X)}(k)) as Pk=(I−KC)Pk-1, where I is an identity 2×2 matrix, and {circumflex over (X)}(k)={circumflex over (X)}(k−1)+Kϵ;
• and
• subtracting an estimated value of the sensor bias {circumflex over (x)}2(k)=âbias(k) from the longitudinal acceleration measurement from the vehicle sensor.