Resources on Filtering, Prediction and Smoothing

Filtering can essentially be classed into three different problems, namely Estimation, Prediction and Smoothing. These terms are defined based upon the time that the value output by the filter is determined for, relative to the observational data that it has access to. Estimation provides an estimate of the output based upon all data upto the current time. Prediction provides an estimate of what the value ahead of the observed data (i.e. prediction of the final temperature). Smoothing does the opposite, it provides an estimate using observations that are ahead in time of the estimate.

Kalman Filtering is used quite widely, but there are other forms of advanced filtering techniques that can also provide prediction and estimation.

  • Design of Multivariable Cautious Discrete time Wiener Filers: A Probabilistic Approach, PhD Thesis by Kenth Ohrn, Uppsala Uni, Sweden. Chapter 1 is available for download from  and provides a nice introcudtion to uncertain dynamic systems and filtering for state estimation and prediction.
Links to Filtering, Prediction and Smoothing Related Resources