Digital and HybridComputational AspectsoftheDiscrete Representation Theorem ofNonlinear Estimation
T. Linton · 1973
A nonlinear filtering problem isinvestigated, andthe discrete representation theorem isusedtosynthesize theoptimal filter. Anoptimal filtering algorithm isdescribed, andhybrid tech- niques areemployed toeffect several methods ofimplementing the algorithm onahybrid computer. Theseimplementations arethen compared (viaMonteCarloanalysis) onthebasesofspeedand accuracy. Itisconcluded thathybrid computation techniques canbe usedtoadvantage whenstudying proposed nonlinear optimal esti- mation formulations. IndexTerms-Digital andhybrid simulation, hybrid computer techniques, MonteCarloanalysis, optimal nonlinear filtering, representation theorem. I.INTRODUCTION N THE PASTseveral yearsthere hasbeenacon- siderable amountofresearch intheareaofoptimal nonlinear filtering. Muchofthis workhasbeenofa theoretical nature, whileimplementation efforts have focused on various methodsofobtaining suboptimal nonlinear filters. References (2)-(5) (also seetheref- erences mentioned therein) consider theproblemof digital implementation ofoptimal nonlinear filtering algorithms, andthree recent papers(tO)-(12) discuss hybrid synthesis ofoptimal discrete nonlinear filters. Theselatter three papers should beofinterest toany- onedesiring toobtain anestimate oftherangeofap- plicability ofhybrid methodstoproblems innonlinear filtering. Inthis paper, aparticular nonlinear filtering problem isinvestigated. Thediscrete representation theorem(i) isusedtosynthesize theoptimal filter. Theplant, measurement process, andnoise signals aresimulated withtheaidofadigital computer. Theoptimal filtering algorithm isimplemented bothdigitally andviahybrid techniques. Thehybrid systemusedinthese studies in- cltudes an EAI 680analog computerandan XDS- SIGMA 5 digital computer. Thesevarious filtering implementations aresubjected toaMonteCarloanal- ysis, andarethencompared onthebasesofspeedand accuracy. Theworkdescribed herein wasperformed during the summerof1970, andisarevised andexpanded version of(6), (7), theinitial published worksintheareaof applying hybrid computer techniques tononlinear esti- mationproblems wherein thediscrete representation theorem isemployed.'