ABSTRACT
The Kalman filter was mentioned as state estimator for the stochastic case. The Kalman filter looks very much like the observer structure. An added feature is optimization, therefore the Kalman filter can be seen as an advanced application of the least squares method in dynamic estimation problems. The only thing that remains is the selection of the gain. For the Kalman filter the approach is totally different and the calculation is done via the least squares method. In order to illustrate this we first will determine the estimation errors and then the variances of the estimation errors. The variances are then located on the main diagonal; the covariances between the different variables are on the other locations. In this chapter the Kalman filter, which can be interpreted as optimal state and parameter estimator in the presence of noise, was discussed. It is a useful tool if one wants to predict otherwise unavailable process information from a limited number of measurements.
