Optimal filtering of FIR prefiltered data

Given limited computational resources and/or superfluous states in the system model, it is possible to lower computational requirements and/or to diminish the influence of the extra states upon the output of the system by prefiltering the data through a conventional filter before processing them through an optimal filter algorithm. A prefilter-compensated system model is developed which maintains a one-to-one correspondence with the original model which is constructed to represent the system before the prefilter is applied. For the case where the weighting is performed upon the output of a linear shift invariant (LSI) discrete-time system, a system description can be derived which fully characterizes the state and prefiltered measurement, without increasing the dimension of the original system. In the case of a nonlinear system, a compensated system description can be formulated in a similar manner. Thus, state estimates obtained using this model are likely to be significantly improved over those obtained using less accurate models