Filtering Theory pp 417-549 | Cite as

# Optimally (suboptimally) input-decoupling filtering under white noise input—*H*_{2} filtering

## Abstract

Chapter 7 considers the exact input-decoupled (EID) filtering problem, whereas Chapters 8 and 9 consider almost input-decoupled (AID) filtering problems. EID filtering seeks perfect performance; i.e., it tries to make the impact of the input on the estimation error signal absolutely zero. AID filtering relaxes this requirement by trying to find conditions under which the impact of the input on the error signal can be made arbitrarily small. In particular, Chapter 8 pertains to AID filtering under white noise input, whereas Chapter 9 pertains to AID filtering without any statistical information on the input. AID filtering under white noise input seeks conditions such that one can render the RMS norm of the error signal as small as *desired*. On the other hand, AID filtering under no statistical information on the input seeks conditions such that one can render the ratio of RMS norm of the error signal to the RMS norm of the input as small as *desired.* In this chapter, we relax the requirement even further by seeking the impact of the input on the error signal be as small as *possible* rather than as small as desired. In particular, we follow here the direction set by AID filtering under white noise input. That is, we assume here that the input to the given system is a white noise of unit intensity and seek to make the RMS norm of the error signal as small as *possible*. The problems we deal with here are called optimally input-decoupling (OID) filtering problems under white noise input. The corresponding filters are of course termed as OID filters under white noise input.

## Keywords

Transfer Matrix Solvability Condition Error Dynamic Auxiliary System Matrix Pair## Preview

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