State of Charge and State of Health Coestimation for Lithium-Ion Capacitor Based on Multi-innovation Filters

Algorithm 3

Recursive process of MI-EKF.

Nonlinear system:

Step I: initialization

 For , set , , , and .

Step II: computation

 Jacobian matrix calculation

 Error covariance prior estimation

 State prior estimation

 Kalman gain calculation

 Innovation value calculation

 Innovation vector and gain vector calculation

 State posterior estimation

 Error covariance posterior estimation

where is the gain vector of MI-EKF, is the covariance matrix, is the process noise covariance matrix, and is the measurement noise covariance matrix.