Battery Management System Reference Design

ID 683279
Date 4/02/2016
Document Table of Contents

1.3.3. BMS Reference Design DEKF Technique

In the DEKF technique, the reference design simultaneously executes two cooperating Kalman filters for nonlinear systems: one for the state and the other for the parameters estimation.

Dual estimation, rather than joint estimation, with only one Kalman filter reduces the state matrix dimensions and may improve the estimation robustness. Equation 2 describes the parameter evolution that with the measurement equation 4 builds the first EKF. Equation 3 represents the state evolution that combines to the measurement equation to form the second EKF.

Figure 13. Equation 2
Figure 14. Equation 3
Figure 15. Equation 4
Figure 16. Measurement Equation

The measurement equation is the same for both filters. In the above equations:

  • k is the discrete time
  • p is parameters vector
  • x = [SOC; VRC1] is the battery state vector
  • χ­, ξ and ψ are the parameters, the state and measurement noise, with zero mean and covariance matrix ­ Σχ­, Σξ and Σψ, respectively.
Figure 17. Circuit Equations
Figure 18. DEFK Matrix Equations
Figure 19. Initialization Equation
Figure 20. Prediction Equations
Figure 21. Correction Equation