Design Case Studies | ![]() ![]() |
Discrete Kalman Filter
The equations of the steady-state Kalman filter for this problem are given as follows.
Given the current estimate , the time update predicts the state value at the next sample
(one-step-ahead predictor). The measurement update then adjusts this prediction based on the new measurement
. The correction term is a function of the innovation, that is, the discrepancy.
between the measured and predicted values of . The innovation gain
is chosen to minimize the steady-state covariance of the estimation error given the noise covariances
You can combine the time and measurement update equations into one state-space model (the Kalman filter).
This filter generates an optimal estimate of
. Note that the filter state is
.
![]() | Kalman Filtering | Steady-State Design | ![]() |