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1 r - AD A WVERSTY OF SOW RN CALFORNA LOS ANGELES DEPT 0 ETC FG 5F2 A*AAL NTERM SC ENTFC REPORT (U) SEP 78 R S BUCY AFOSR UNCLASSFED AFosR TR m 5 ;9 N t L

2 U L L Lg O P 25 HH 6 MCROCOPY RESOLUT ON TEST CHART NATONAL BUTAJ OF STANDAR OS - %3 A

3 pii r _ SECUR YCL fl A T O N OF T H S P A G E (Thn Data En t e r e d DOCUMENTATON PAGE A CCESSON NO $ 1 ç ( &$! - \ - S 74A* - jrd S7u Y PERFORMNG O R G A N Z A T O N NAME AND ADDRESS University of Southern California Department of Aerospace Engineering Los Angeles, California V p k 14 M O N T O R N G A G E N C Y N A M E 6 AODRESS(1 dilj a rent,izom Cortroll g O U,gc6), 1 i P R O G R A M EL EMENT PROJ EC T, T A S K 611 Air Force Office of Scientific ResearchNM ( j Boiling AFB, Washington, DC 20332, P E R F O R M N G ORG R E P O R T N U M B E R AFOsR 76 3JJ fl C O N T R O L L N G O F F C E N A M E AND ADDRESS J 00 C O V E R E D B C O N T R A C T O R G R A N T N U M B ER ( S ) 7 A U T HO R ( s) 9 T Y P E OF R E P O RT & PE 5 h Ue) ANNUAL NTERM SCENTFC REPORT S,,, j 23 4 Al, - p L J r 1 S E C U R T Y CLASS or t h i s rep UNCLASSFED S DECLASSFCATON DOWNG RADNG SCHEDULE 16 D S T R B U T O N S T A T E M E N T (of this Report) Approved for public release; distribution unlimited 17 D S T R B U T O N S T A T E M E NT (of the abs tr act entered Sn Block 20 iidifferent C) from le S U P P L E M E N T A R Y N OT E S 19 K E Y WORDS (Continue on reverse aide if necessary d identify by block number) Report) 1r w C-, 2O T R A CT (Continue on reverse aid S necessary and identity by bloc k number) n the area of finding performance bounds on the nonlinear filtering problem the information rate between the signal at time t and the observation process up to time t has been evaluated for the general discrete time nonlinear filtering problem t L? DD T T FORM 1 J A N 73 i This information rate allows a general diuinition of s 3ady c j J UNCLASSFED S E C u R T Y C L A S S F C A T O N F THS P A G E (tthn Data Entae T

4 , Abstract continued -_ state new stronger lower bounds for the filtering error are derived n the area of building nonlinear filter the estimate production speed of the two dimensional phase demodulation problem on the Cray 1 is being improved by examining the assembly code generated by the Cray 1 compiler and seeking to improve the running time by changing the Fortran code on the basis of these observations This latter problem has been extensively investigated on the CDC 7600 and the Star 100, which in fact has lead to increased understanding of some of the architectural design constraints inherent in the use of these machines on problems requiring large memories (ie over 200K decimal) -- r jt L L± UNCLASS Fl ED SECURTY CLASS?CAT ON OF THS PAGE(Whn Dta Ent,d), -, - -s-- -

5 - - 2!7 - : O Fi - - : (;:, r Qf TR :::1TTAL TO DD C AFOSR - FR technical report ha been reviewed and is : ved for public release law AFR (7b) tribution is unlimited i echnjcaj nforniatiou Off ia,w ANNUA L NTERM SC ENTF C REPORT Gran t AFOSR September 30, September 29, Richard S Bucy Principal nvesti gator Personne l Supported During the year the following peop le were supported : Tech# ical Typ ist, u se Allott; Graduate Students, Faramarz Ghovanlou and Th as Bleakney ; Secretaries, Virginia Wri ght and Al ice Vaughn; and Princip le nvesti gator R S Bucy Research Summa ry n the area of find i ng performance bounds on the nonl i near filtering prob l em, we have recently (2) evaluated the information rate between the signal at time t and the observation process up to time t for the general discrete time nonlinear filtering prob l em This information rate allows a genera l definition of steady state (i e when it van i shes) for the genera l nonl inea r filtering p rob l em Further in steady state new stronger l ower bounds for the filtering error are derived n the special case of () stronger results are generated n the area of building nonlinear filters, we are currentl y seeking to 1mp rov the estimate production speed of the two dimensional phase demodulation prob l em on the Cray 1 by examining the assemb l y code generated by the C ray 1 compiler and seeking to improve the running time by changing the Fortran code on the basis of these observations We would like to look at the comb i ned phase amp litude prob l em on the Cray, but lack computer time at present This latter problem has been extensivel y investi gated on the 7600 and the Star 100, which in fact has lead to increased understanding of some of the architectural design constraints inherent n the use of these machines on prob l ems requiring large memory requ i rements (ie over 200 K dec imal) These results are reported n (1) and (3) Approved for public releasn distribution unlimited

6 * 4 Papers Appearing (1) R S Bucy, J Pages A Priori Bounds for the Cubic Sensor Prob l em, EEE Trans on Automatic Contro l, Vol AC-23, 1, 1 978, (2) R S Bucy Nonlinear Filtering with Pi peline and Array Processors, Proceeding Conference on Decision and Control, Dec, 1977, F Papers Submitted (1) R S Bucy, K D Senne New Frontiers n Nonlinear Filter ing, M T Lincol n Lab Technical Note, , l-5 i, submitted EEE Trans on Automatic Control (2) R S Bucy nformation and Filtering, submitted nformation Sciences (3) R S Bucy, K D Senne Computational Frontiers in Nonlinear Fi l tering, to appear, Proceeding Conference on Decision and Control, San Diego, a