| Design Case Studies | |
Time-Varying Kalman Filter
The time-varying Kalman filter is a generalization of the steady-state filter for time-varying systems or LTI systems with nonstationary noise covariance. Given the plant state and measurement equations
the time-varying Kalman filter is given by the recursions
with 
and 
as defined in Discrete Kalman Filter, and in the following.
For simplicity, we have dropped the subscripts indicating the time dependence of the state-space matrices.
Given initial conditions 
and 
, you can iterate these equations to perform the filtering. Note that you must update both the state estimates 
and error covariance matrices 
at each time sample.
| | Steady-State Design | Time-Varying Design | |