4Optimal FIR and Limited Memory Filtering
The user of the system naturally tries to minimize the inaccuracies caused by…noise—by filtering.
Brian D. O. Anderson, John B. Moore [9], p. 2.
The state estimator that relates the output to the current time point is also called a filter. As such, it can be designed to have either FIR or IIR. An FIR filter requires data from an FH 
of 
points, from 
to 
, so the length of its impulse response is limited by 
points. In contrast, transients in IIR filters last indefinitely due to internal feedback and decay over time. This important specific feature predetermines two critical properties of FIR estimators: 1) no feedback is required, and thus round‐off errors are not compounded at the output by summed iterations and 2) inherent BIBO stability. Known bottlenecks are that 1) the batch form can cause a computational problem when 
is large and 2) even ...
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