Optimal State Estimation

In a post m o r t e m (after the fact) analysis, it is possible to wait for more observations to accumulate. In that case, the estimate can be improved by smoothing.-Andrew Jazwinski jJaz70, p. 1431 In previous chapters, we discussed how to obtain the optimal a priori and a posteriori state estimates. The a priori state estimate at time k, 2;, is the state estimate at time k based on all the measurements up to (but not including) time k. The a posteriori state estimate at time k, 2:, is the state estimate at time k based on all the measurements up to and including time k: There are often situations in which we want to obtain other types of state estimates. We will define 2 k , j as the estimate of X k given all measurements up to and including time j. With this notation, we see that Now suppose, for example, that we have recorded measurements up to time index 54 and we want to obtain an estimate of the state at time index 33. Our theory in