celestial navigation3

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1、celestialnavigationCelestialnavigationfordummies-page4Celestialmechanics-ablueprint(...)Thehatchedtriangleonthetopofthecelestialsphereistheonewewillusetosolvethecelestialnavigationproblem.The3sidesofthetriangleare:col,theco-latitude(90°-latitude);z,thezenithd

2、istance(90°-altitudeh);Delta,thepolardistance(90°-declinationdelta).Theangleofthehttp://www.seamanship.co.uk/deck/navigator/ASNAv/ASNAv%20Site/Text/celnav4.htm(1of4)5/4/20055:00:55PMcelestialnavigationtriangleoppositetothesideziscalledthepolarangleP(180°W-180

3、°E).ThisangleisalsotheangulardistanceQ-Datthecelestialequator:Here:PE=gw-GHA*It'sasphericaltriangle,notaplanetriangle.Weallremember(aren'twe?)theformulatosolveatriangleinplanegeometrybutwhatistheoneincaseofsphericalgeometry?Thetriangleinplanegeometry,foroldti

4、mes'sake.Thecosinusruleforthesphericalgeometryinthegeneralcase.http://www.seamanship.co.uk/deck/navigator/ASNAv/ASNAv%20Site/Text/celnav4.htm(2of4)5/4/20055:00:55PMcelestialnavigationTheapplicationofthegeneralcasetoourproblem.Wefoundamathematicalrelationbetwe

5、enwhatweknow(delta,GHA,h)andwhatwearelookingfor(latitude,longitude).With2observations,wegetasystemof2equationswith2unknownsthatweareabletosolve.Thecelestialnavigationproblemisthusresolved.What?Youdon'tlikemyequation?Well,Iagreethatitsresolutionisnotsosimple..

6、.Foracomputer,theprocessisquitestraightforward:solvingthesystembyaniterativemethodusingtheestimatedlatitudeandlongitudeasstartingvalues.Withmorethan2observations,it'sevenpossibletoimprovethetraditionalmethodandtoperformastatisticalanalysis,inotherwords:●togiv

7、eacertainweighttoeachobservationaccordingtoitsreliabilityinthenormallawmodel;●tocomputeandeliminatethepossiblesystematicerroroftheobserver;●tocorrecttheassumedcourseandspeedifenoughobservationsareprovided(exactlythesamewaytheGPSisabletogivethecourseandspeedof

8、thevesselifenoughsatellitesarevisible).Todothis,ASNAvisusingtheleast-squaremethodwithiterativeweightingadjustmentbytheBiweightfunctiononasystemofequationsgivenbythedifferentialcorrectionm