Algorithm 8: Functional Flow of Extended Kalman Filter

1. Build A matrix 2. Compute the state time update, (x) 3. Compute the error covariance update, (σ) 4.  Loop (for 1 to 2) a.  Compute the SOC update b.  Build C and D matrix c.  Calculate term s${\phi }_e$and$\Delta \eta$from Non-linear corrections d.  Calculate the predicted output voltage,$(y_{volt,k)}$ e.  If Loop = 2, break f.  Build$\widehat{C}$and$\widehat{D}$ g.  Compute the Kalman Gain matrix (L) h.  Compute the state measurement update, (x) i.  Compute the error covariance measurement update, (σ) 5. End Loop 6.  Create terms needed for MPC formation and constraints a.  Calculate the updated Non-linear φs-e b.  Compute the derivative of OCV at current state/soc c.  Create the C and D matrices for MPC SOC and φs-e output equations 7. End EKF