Minimal formula for bounding the cross correlation between a random forcing function and the state error when this correlation is unknown is used in optimal linear filter theory applications. Use of the bound results in overestimation of the estimation-error covariance

Battin, R. H.

Deckert, J. C.

Fraser, D. C.

Potter, J. E.

English

NASA Technical Reports Server

September 1970	 Brief 70-10427 
NASA TECH BRIEF 
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Method of Statistical Filtering 
.
Application of optimal linear filter theory, to situa-
tions in which the state forcing function is correlated 
with the state in an unknown way, can present serious 
problems. In many instances the cross correlation and 
forcing function must be modeled; if they are ignored, 
the filter gains tend to sink below their optimal levels, 
and useful measurement information is discarded. 
A conservative and minimal formula has been de-
veloped for bounding of the cross correlation between 
a random forcing function and the state error when 
this correlation is unknown. The bound is conservative 
in the sense that its use always results in overestima-
tion of the estimation-error covariance; it is minimal 
in the sense that it is less conservative than any other 
type of conservative bound.
Notes: 
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equipment, as for the oil and chemical industries, 
may be interested. 
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to:
Technology Utilization Officer 
Manned Spacecraft Center, Code BM7 
Houston, Texas 77058 
Reference: TSP70- 10427 
Patent status: 
No patent action is contemplated by NASA. 
Source: James C. Deckert, James E. Potter, 
Richard H. Battin, and Donald C. Fraser of 
Massachusetts Institute of Technology 
under contract to 
Manned Spacecraft Center 
(MSC-13493) 
Category 06 
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Method of statistical filtering

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