Prediction and Smoothing

Chapters 9 and 10 consider the filtering problem where a state estimate is obtained at the time of the last measurement. In some applications, measurements are only available until a point before the desired estimation point, and the state must be predicted over an extended period. In other applications, data is available beyond the time where the state estimate is needed. To obtain future state estimates, we use a predictor and for estimates at earlier times we use a smoother. Three types of smoothing are possible: (i) fixed-point smoothing, where additional measurements are collected and progressively used to improve the estimate at a fixed time point, (ii) fixed lag smoothing, where the time point where the estimate is obtained moves at a fixed lag before the current time, and (iii) fixed-interval smoothing, where data is collected over a fixed interval then used to estimate the state at all time points in the interval.