U-.-._ AD-A TWO STOCHASTIC MODE.ING PROBLEMS IN COMMUJNICATIONS AND NAVIG6ATON I/J U) VIRGINIA P0 TECHNIC INS A ND STE BLACKSBURG UNIV

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1 AD-A TWO STOCHASTIC MODE.ING PROBLEMS IN COMMUJNICATIONS AND NAVIG6ATON I/J U) VIRGINIA P0 TECHNIC INS A ND STE BLACKSBURG UNIV U-.-._ W E KO06 ER 12 SEP 83 ARO MA UNCLASSIFED DAAG2V V -C 0065 F/ 12/1 Nt

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3 Unclassified SECURITY CLASSIFICATION OF T,,15 page IPw Dlate Frvto~ed) REPORT DOCUMENTATION PAGE A B3EFORE COMPLETING FORM REPORT NUMBER 2.GOVT ACCESSION NO. 3. RECIPIENT'S CATALOG NUMBER 4TITLE (sidir Subtitle) S. TYPE OF REPORT 6 PERIOD COVEREM Two Stochastic Modeling Problems in Final Report Communications and Navigation 1 July June PERFORMING ORG. REPORT NUMBER 7. AUHOR(. 111 CONTRACT OR GRANT NUMSER(s) Werne E. KhlerDAAG29 79 C PERFORMING ORGANIZATION NAME AND ADDRESS 10. PROGRAM ELEMENT. PROJECT. TASK AREA 6 WORK UNIT NUMBERS Virginia Polytechnic institute & State University Blacksburg, VA ICONTROLLING OFFICE NAME AND ADDRESS 12. REPORT DATE U. S. Army Research Office September 12, 1983 Post Office Box NUMBER OFPAGES Research Triangle Park, NC I.MONITORING AGENCY NAME S ^DDRESS(If different from. Controlling Offie) 1S. SECURITY CLASS. (of this report) 1S DISTRIBUTION STATEMENT (of this Report) Approved for public release; distribution unlimited. Unc lassi fied IS.DECL ASSI PIC ATION! DOWN GRADIN G SCHEDULE D T I C ELECTE 17. DISTRIBUTION STATEMENT (of rho Abstrt entered In Block 20. #1 diff erent fom Report)0 NA D 1S. SUPPLEMENTARY NOTESan/rfdnscotie inti rprtrehsefte The view, opinions, ado idrn otie nti eotaetoeo h author(s) and should not be construed as an official Department of the Army position,,oiicy, or decision, unless so designated by other documentation 19 I. KEY WORDS (Continue an reverse.. sideo necessary and identify by block number) C.. Random Wave Propagation LAU L- 20. AftRACT WCsr~ii 4m rvseoifof newees a" ideqnify, by block nuo,6r) A summary of the problems considered, the principal results obtained and the ensuing research publications is presented. D I r A7) 143 EDITION OF I MOV 65Is OEWLETE UNCLASSIFIED SECUSI TY CLASSIFICATIOPI OF TNIS PAGE (When Dot& Entered)

4 TWO STOCHASTIC MODELING PROBLEMS IN COMMUNICATIONS AND NAVIGATION FINAL REPORT WERNER E. KOHLER SEPTEMBER 12, 1983 U.S. ARMY RESEARCH OFFICE CONTRACT DAAG29 79 C 008' VI R(; I NIA POLYTECHNIC AND STATE UNIVERSITY INSI TUTE " APPROVED FOR PUBLIC RELEASE; NTIS GR&I X DISTRIBUTION UNLIMITED DTIC TAB [1 Unannounced 0 Justificatio By I Distribution/ I; Availnbtlity Codes Avail and/or Dist Special

5 IT THE VIEW, OPINIONS, AND/OR FINDINGS CONTAINED IN THIS REPORT ARE THOSE OF THE AUTHOR(S) AND SHOULD NOT BE CONSTRUED AS AN OFFICIAL DEPARTMENT OF THE ARMY POSITION, POLICY, OR DECISION, UNLESS SO DESIGNATED BY OTHER DOCUMENTATION.

6 - Two problems were studied, the effects of random gravitational fluctuations upon the performance of inertial navigation systems and the effect of random scatterers upon wave propagaticii.. Work on the geodesy problem led to a limiting description of navigational errors as a Gauss Markov process. Such a limitin; process is quite amenable to signal processing techniques. Work on the random wave propagation led to the development of a twofrequetcy stochastic transport theory, new insights into the forward scattering approximation in waveguide propagation and some new results on rough surface scattering. Work on a vector transport theory for electromagnetic propagation through random clouds of scatterers was in it iated and some pre I mi nry results have been obtained; this effort will continue. The following publications were produced: 1) Multiple Scattering and Waves in Random Media, edited by P.L. Chow, W. E. Kohter and G. C. l'apanicolaou, North-Holland Publishing Co., ) Some Applications ot thie Coherent Potential Approximation, W. E.Kohler and G. C. Papanicolaou, in Multiple Scattring and Waves in Random Media, pp ) Two-Frequency Radiative Transfer Equation for a Statistically Inhomogeneous and Anisotropic Absorptive Medium, I. M. Besieris and W. E. Kohler, in Multiple Scattering and Waves in Random Media, pp

7 2 4) Boundary and Interface Problems in Regions with Very Rough Boundaries, W. E. Kohler, G. C. Papanicolauu and S. Varadhan, in Multiple Scattering and Waves in Random Media, pp ) Propagation in a Randomly Perturbed Multimode Matched Waveguide, W. E. Kohler, Wave Motion 4 (1982), pp ) Bounds for the Effective Conductivity of Random lmedia, W. E. Kohler and G. C. Papanicolaou, Macroscopic Properties of Disordered Media, edited by R. Burridge, S. Childress and G. Papanicolaou, Springer- Verlag (1982), pp ) A Transport - Theoretic Analysis of Pulse Propagation through a Random Cloud of Scatterers, I. M. Besicris, W. E. Kohler and A. 1. Tsulakis, ARO Report 83-1, Transactions of the 28th Conference of Army Mathematicians (1982), pp The following Ph.D. Thesis was produced: Asymptotic Stochastic Analysis of a Gravity Model for Inertial Navigation Systems, Mark Torgrimson, Ph.). Thesis, Virginia Polytechnic Institute and State U., The following publications have not yet appeared: 1) Scattering from Two-Scale Surfices for Large Distances, Oleg Yordanov, to appear in Radio Science.

8 3 2) An expanded version of (7), dealing with a transport theoretic description of pulse propagation through discrete scatterers, is being prepared for submittal to Radio Science. Werner E. Kohler was the principal investigator on the contract. Mark TorgrimsOn worked on the geodesy problem for his doctoral dissertation. His thesis is cited above. Oleg Yordanov, a visitor to Virginia Tech from Bulgaria, worked on a rough surface scattering problem. His research will be published in Radio Science. Graduate students Gary Schleuter, Dale McIntyre, Grazyna Slifierz and Helen Zitomer were partially supported by the contract. Schlouter has received his M.S. degree in Mathematics. The others are currently students at Virginia Tech. 1 I