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NAVAL POSTGRADUATE SCHOOL Monterey, California THESIS SECOND ORDER APPROXIMATION FOR VARIANCE OF SEP by Arthur Frederick Brock September 1991 Thesis Advisor: Lyn R. Whitaker Approved for public release; distribution is unlimited T253947 Unclassified SECURITYCLASSIFICATION OFTHIS PAGE FormApproved REPORT DOCUMENTATION PAGE OMB No.0704-0188 1a. REPORTSECURITYCLASSIFICATION 1b. RESTRICTIVE MARKINGS UNCLASSIFIED 2a. SECURITYCLASSIFICATIONAUTHORITY 3. DISTRIBUTION/AVAILABILITYOF REPORT Approved for public release; distribution is unlimited 2b. DECLASSIFICATION/DOWNGRADING SCHEDULE 4. PERFORMING ORGANIZATION REPORTNUMBER(S) 5. MONITORINGORGANIZATION REPORT NUMBER(S) 6a. NAMEOF PERFORMING ORGANIZATION 6b.OFFICESYMBOL!7a. NAMEOFMONITORING ORGANIZATION Naval Postgraduate School OR 6c.ADDRESS(City, State,andZIPCode) 7b.ADDRESS (City, State,andZIPCode) Monterey, CA93943-5000 8a. NAMEOF FUNDING/SPONSORING 8b.OFFICESYMBOL 9. PROCUREMENTINSTRUMENTIDENTIFICATION NUMBER ORGANIZATION 8c.ADDRESS (City,State,andZIPCode) 10. SOURCE OF FUNDING NUMBERS PROGRAM PROJECT TASK WORK UNIT ELEMENTNO. NO. NO. ACCESSION NO 11.TITLE (Including SecurityClassification) SECOND ORDER APPROXIMATION FOR VARIANCE OF SEP 12 PERSONALAUTHOR(S) BROCK, Arthur Frederick 13 TYPEOF REPORT 13b.TIMECOVERED 14. DATEOF REPORT(Year, Month, Day) 15. PageCount Master'sthesis FROM TO 1991, September 100 16.SUPPLEMENTALNOTATION Theviews expressed inthisthesis arethose ofthe authorand do not reflectthe official policy or position ofthe Department of Defense orthe U.S. Government. 17. COSATICODES 18. SUBJECTTERMS (Continueon reverseitnecessaryand identifybyblocknumber) FIELD GROUP SUB-GROUP Spherical Error Probability, SEP, Circular Error Probability, CEP 19.ABSTRACT(Continueon reverseifnecessaryand identifybyblocknumber) A methodforthecomputationofconfidenceintervalsforcircularerrorprobability(CEP) basedonfirstordervariance estimateswasintroduced in 1966. Itwaslaterfoundthat undercertainconditions the resultingconfidence intervals forCEP were smallerthan expected. As a result a second ordervariance estimate method was developed, at the Johns Hopkins University Applied Physics Laboratory, which greatly improved the accuracy of the confidence intervalsforCEP. The purpose ofthisthesis istodevelopandtest proceduresforthe3-dimensional caseto obtain a second order estimateforvariance ofspherical error probability (SEP). 20 DISTRIBUTION/AVAILABILITYOFABSTRACT 1a. REPORTSECURITYCLASSIFICATION |X) UNCLASSIFIED/UNLIMITED SAMEASRPT.n DTIC Unclassified 22a. NAMEOF RESPONSIBLE INDIVIDUAL 22b.TELEPHONE (IncludeArea Code) 22c. OFFICESYMBOL Lyn R. Whitaker (408)646-3482 OR/Wh DD Form 1473, JUN 86 Previouseditionsareobselete. SECURITYCLASSIFICATIONOFTHIS PAGE S/N 0102-LF-014-6603 Unclassified i Approved for public release; distribution is unlimited, Second Order Approximation For Variance of SEP by Arthur F. Brock Lieutenant, United States Navy B.S., Oregon State University, 1986 Submitted in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE IN OPERATIONS RESEARCH from the NAVAL POSTGRADUATE SCHOOL September 1991 . ABSTRACT A method for the computation of confidence intervals for circular error probability (CEP) based on first order variance estimates was introduced in 1966. It was later found that under certain conditions the resulting confidence intervals for CEP were smaller than expected. As a result a second order variance estimate method was developed, at the Johns Hopkins University Applied Physics Laboratory, which greatly improved the accuracy of the confidence intervals for CEP. The purpose of this thesis is to develop and test procedures for the 3-dimensional case to obtain a second order estimate for variance of spherical error probability (SEP) 111 6./ THESIS DISCLAIMER The reader is cautioned that computer programs developed in this research may not have been exercised for all cases of interest. While every effort has been made, within the time available, to ensure that the programs are free of computational and logic errors, they cannot be considered validated. Any application of these programs without additional verification is at the risk of the user. IV