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

Algorithm 2

Recursive process of MI-CKF.

Nonlinear system:

Step I: initialization

 For , set , , , and .

Step II: computation

 Time update

 Cubature points evaluation

where is calculated by factorizing according to , and

 Cubature points propagation

 State estimation

 Error covariance estimation

Measurement update

 Factorization and cubature points evaluation

 Cubature points propagation

 Measurement estimation:

 Innovation covariance matrix estimation

 Cross-covariance matrix estimation

 Kalman gain calculation

 Innovation value calculation

 Innovation vector and gain vector calculation

 State updating

 Error covariance estimation

Here, is the process noise covariance matrix, is the measurement noise covariance matrix, is the column of , and denotes the dimension of state vector and .