Template updating kalman filter
Since that time, due in large part to advances in digital computing, the Kalman filter has been the subject of extensive research and application, particularly in the area of autonomous or assisted navigation. Kalman published his famous paper describing a recursive solution to the discrete-data linear filtering problem [Kalman60].In other words, For more details on the probabilistic origins of the Kalman filter, see [Maybeck79], [Brown92], or [Jacobs93].I will begin this section with a broad overview, covering the "high-level" operation of one form of the discrete Kalman filter (see the previous footnote).
The next step is to actually measure the process to obtain , and then to generate an a posteriori state estimate by incorporating the measurement as in (1.12).
The measurement update equations are responsible for the feedback¯i.e.
for incorporating a new measurement into the a priori estimate to obtain an improved a posteriori estimate.
On the other hand, as the a priori estimate error covariance approaches zero the actual measurement is trusted less and less, while the predicted measurement is trusted more and more.
The justification for (1.7) is rooted in the probability of the a priori estimate conditioned on all prior measurements (Baye's rule).Specifically, On the other hand, as the a priori estimate error covariance approaches zero, the gain K weights the residual less heavily.