Text applies to solution of various optimization problems. Concepts are logically introduced and refinements and complexities for computerized numerical solutions are avoided. Specific topics and essential equivalence of several different approaches to various aspects of the problem are given

Solloway, C. B.

English

NASA Technical Reports Server

November 1971	 Brief 71-10425 
S NASA TECH BRIEF 
NASA Pasadena Office 
NASA Tech Briefs announce new technology derived from the U.S. space program. They are issued to encourage 
commercial application. Tech Briefs are available on a subscription basis from the National Technical Information 
Service, Springfield; Virginia 22151. Requests for individual copies or questions relating to the. Tech Brief program may 
be directed to the Technology Utilization Office, NASA, Code KT, Washington, D.C. 20546. 
Elements of Orbit-Determination Theory: Textbook 
.
A recent textbook presents a lucid, readable, 
comprehensive introduction to the problem of orbit 
determination. Although originally intended as a 
presentation on that subject, the text treats tech-
niques that in fact are applicable to the solution-of 
various optimization problems. As stated in the 
text's introduction, "The concepts are equally appli-
cable to the fields of Optimal Control Theory, Op
-timization Theory, Statistical Estimation, Statistical 
Inference, and Curve Fitting." 
A thorough knowledge of calculus and an acquaint-
ance with matrix algebra and probability theory are 
useful prerequisites to a comprehensive understand-
ing of the text; appendices are included, however, 
as refreshers in these areas. 
The concepts are logically introduced, using a 
simplified model that contains most of the import-
ant features of practical problems but retains the 
possibility of analytical treatment. Refinements and 
complexities for computerized numerical solutions 
are avoided. 
Specific topics include trajectory design and anal-
ysis, variational analysis of the trajectory, orbit 
determination,	 least-squares and weighted-least-
squares analysis of "overdetermined" orbits, maxi-
mum likelihood estimation, properties and relative 
merits of various statistical estimators, minimum 
variance, the combining of statistical estimates, map-
ping of covariance matrices, and dynamic filtering. 
The essential equivalence of several different ap-
proaches to various aspects of the problem is noted. 
Note: 
Requests for further information may be directed 
to:
Technology Utilization Officer 
NASA Pasadena Office 
4800 Oak Grove Drive 
Pasadena, California 91103 
Reference: B71-10425 
Patent status: 
No patent action is contemplated by NASA. 
Source: C.B. Solloway of

Caltech/JPL
under contract to

NASA Pasadena Office

(NPO- l 1466) 
Category 03 
This documefct was prepared under the sponsorship of the National 
Aeronautics and Space Administration. Neither the United States 
Government nor any person acting on behalf of the United States
Government assumes any liability resulting from the use of the 
information contained in this document, or warrants that such use 
will be free from privately owned-rights.
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Elements of orbit-determination theory - Textbook

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