MATLAB MEX Function Reference |

The measurement (or observation) equation can be written

The transition (or state) equation is denoted as a first-order Markov process of the state vector.

The KALCVF function computes the one-step prediction
and the filtered estimate ,
together with their covariance matrices
and , using forward recursions.
You can obtain the *k*-step prediction and
its covariance matrix with the KALCVF function.
The KALCVS function uses backward recursions to compute the smoothed
estimate and its covariance matrix
when there are *T* observations in the complete data.

The KALDFF function produces one-step prediction of the state and the unobserved random vector as well as their covariance matrices. The KALDFS function computes the smoothed estimate and its covariance matrix .

**See also**

`KALCVF`

performs covariance filtering and prediction

`KALCVS`

performs fixed-interval smoothing

`Getting Started with State Space Models`

`Kalman Filtering Example 1: Likelihood Function Evaluation`

`Kalman Filtering Example 2: Estimating an SSM Using the EM Algorithm`

**References**

[1] Harvey, A.C., *Forecasting, Structural Time Series Models and the Kalman Filter*, Cambridge: Cambridge University Press, 1991.

[2] Anderson, B.D.O., and J.B. Moore, *Optimal Filtering*, Englewood Cliffs, NJ: Prentice-Hall, 1979.

[3] Hamilton, J.D., *Time Series Analysis*, Princeton, 1994.