卫星定位理论及方法-第14次课-精度评定

卫星定位理论与方法测量与导航工程系导航与定位教研室陈明剑第14次课精度评定上次课内容取接收机某一初值（X0、Y0、Z0），有：其中

e为方向余弦XρSPXj-X当观测有4颗卫星时，j=1~4，有：

当卫星多于4颗时，可以有最小二乘解算采用迭代法求解，一般二次解得误差方程法方程未知参数解未知参数的权逆阵m为伪距观测精度，qii是QX的第i行i列元素其中未知参数精度（中误差）参数精度mX取决于观测精度m和系数阵A，而A只与卫星和接收机几何位置有关，同一类接收机m是不变的，不同地区、不同时间、不同卫星的导航解精度也不同，需有一技术指标衡量导航解的精度观测值等权：协方差矩阵：估值精度有两部分构成：1、观测值等效误差(UERE：userequivalentrangeerror)UERE=URE(UserRangeError)+UEE(UserEquipmentError)SPS:SAon:URER25米SAoff:URER5米2、卫星几何结构有关(GDOP:geometricdilutionofprecision)GPSexhibitsstatisticalaccuracydistributionsbecauseUEREandGDOParecontinuouslyvariable.UERE(UserEquivalentRangeError)isameasureoftheerrorintherangemeasurementtoeachsatelliteasseenbythereceiver.GDOPisameasureoftheerrorcontributedbythegeometricrelationshipofthesatellitesasseenbythereceiver.PositionAccuracyUERE=URE+UEEURE(UserRangeError)istheportionoftheUEREallocatedtotheSpaceandControlsegment.UEE(UserEquipmentError)istheportionoftheUEREallocatedtotheuserequipment.Therefore,receiverpositionaccuracymustbespecifiedforconditionsofDOPandURE.Dynamicpositioningaccuracyrequirementsmusttakeintoaccounttheeffectofvehiclemotionaswell.GeneralDOPconditionsPDOP<6,HDOP<4,VDOP<4.5,andTDOP<2.解的误差协方差阵为：在导航中，经常用到精度衰减因子DOP（DilutionofPrecision）来表示卫星空间图形的贡献。空间精度衰减因子GDOP(GeometricalDOP):

位置精度衰减因子PDOP(PositionDOP):平面精度衰减因子HDOP(HorizontalDOP):垂直精度衰减因子VDOP(VerticalDOP):时间精度衰减因子TDOP(TimeDOP):定义及协方差阵和误差间的关系，有下列关系式：由上面的可知：定位精度若要越高，定位误差越小，DOP值就要越小，即定位精度和DOP值成正比，一般规定GDOP值应小于6。-

Wanttetrahedronaslargeaspossible- WantindexaslowaspossiblePDOP

PositionDilutionofPrecisionGarminsViewofMappingTypicalMappingGradeGPSSettings-PDOP=99-SNR=2-MaskAngle=5ºPDOP=6SNR=6MaskAngle=15ºPDOPof6orLess-GoodDOPof3orLess-GoodPDOP/DOP

PositionDilutionofPrecisionGarminonlyShowsDOPThat’s1/2ofPDOPDilutionofPrecision(DOP)

DOPisafunctionexpressingthemathematicalqualityofsolutionsbasedonthegeometryofthesatellites.Ithasabestcasevalueof1,highernumbersbeingworse.DilutionofPrecision(DOP)3.GPS导航精度评定指标HDOP：水平精度衰减因子VDOP：垂直精度衰减因子PDOP：位置精度衰减因子TDOP：时间精度衰减因子GDOP：几何精度衰减因子六面体的体积越大，所测卫星的空间分布范围也越大，反之越小，GDOP值越大。

DilutionOfPrecision(3)PDOP=PositionDilutionOfPrecision(MostCommonlyUsed)VDOP=VerticalDilutionOfPrecisionGDOP=GeometricDilutionOfPrecisionHDOP=HorizontalDilutionOfPrecisionTDOP=TimeDilutionOfPrecisionQUALITY DOPVeryGood 1-3Good 4-5Fair 6Suspect >6MissionPlanningIsCriticaltoObtainGoodDOPIntuitiveConceptsofXDOP3.GPS导航精度评定指标DilutionOfPrecision(DOP)AMeasureofTheGeometryOfTheVisibleGPSConstellationGoodDOPPoorDOPPoorGDOPResultswhenanglesfromreceivertothesetofSVsusedaresimilarGoodGDOPAnglesfromreceivertoSVsaredifferentGDOP作用：1、衡量卫星几何结构对精度的影响GDOP变化比URER快2、最佳选星GeneralDOPconditionsPDOP<6,HDOP<4,VDOP<4.5,andTDOP<2.Howdoessatellitegeometryinfluenceaccuracy?Atelemetryexample(2D):90oShapeofareawhichmaycontaintransmitter30oShapeofareawhichmaycontaintransmitterReceiverWithoutcorrectingfortheseerrors,wecanachieveabouta5maccuracywithparalleltrackingunits(goodones),or10mwithserialtrackingunits(cheapones).Severalsourcesoferrorareverydifficulttocorrectfor.Fortunately,thelargesterrorsourcescanbecorrectedforusingdifferentialprocessing.Withdifferentialprocessing,wecanachieveaccuraciesof<1m,andevencentimeteraccuracywiththerightreceiver.GPSAccuracyRelationshipPOSITIONERROR=PDOPXUERE-DependsonGeometry-Dependsonsatellitepositionerrors,propagationerrors,andinstrumentationerrorsCodeRangeResultsAutonomousPosition+/-10m(30ft)error(horizontal)+/-15m(45ft)error(vertical)CarrierPhaseResultsMeasuredReducedBaselineorVector(cmprecision)Azimuth=212o42’49.8244”Distance=557.05307mDeltaEle