893
PHOTOGRAMMETRIC45075820912867111141183222254291333374402433465478515
ENGINEERING97975820912769109122164191218250263305345
&1338758209136
REMOTE138875820913259101145174201
SENSING16037582091265395121134176215
March502375930785592121153191
2014523875930784181120155
27156317591080356899
A12675860359147
Statistical1475586035914122435844350762270977389710281092
Model26285860359208338469598663
Inspired3351586035970203318449513597727858
by42695860359132237
the4567586035985217347
National13478950359157288373437567700831895
Map23038950359208339470
Accuracy28348950359147269393524608740864972
Standard38668950359141224358491621753837967
F.J.2387149101145067101125
Ariza-López2534149101145586110148197220266314362410449
and3006149101144898146
J.3175149101143457
Rodríguez-Avi32551491011459106154185209259308356394418474513537
Abstract450177101515197137167196241284314
This4501902010760115143183
work6581902010769119154204
proposes887190201075590140195245285330370
a12821902010750
statistical1357190201074070120150178218248276321371400
model17821902010780130185230258
inspired2065190201072984124179207242287342
by2432190201075097
the2554190201073085130
National27091902010770120150178228283450200201075078
Map5532002010780130185
Accuracy7632002010769114159214249299344391
Standard1179200201075585135190245295330385
pass/fail15892002010755105145185220250300328356
philosophy.19702002010755110139167217257307362417464482
The24772002010760115160
model26622002010780130185230258
is450210201072868
formulated543210201073080115195250279329359404459
as1027210201075090
the1142210201073085130
composition1297210201074595175230280320348378406456511
of1833210201075180
a19392102010750
statistical2014210201074069120150178218248276321371400
Binomial2439210201075886141191271300350378
model4502202010780130185230258
on7332202010750105
other863220201075180135180215
statistical1103220201074070120150179219249277322372400
base15282202010751101141186
models17392202010780130185230258298
(parametric2062220201073085135170220300345375410438483
or2570220201075085
nonparametric).268022020107551051604502302010755105140190270315345380408453483508
This9832302010760115144184
formulation1192230201073080115195250278328358387437492
allows1709230201075078106156225265
adapting19992302010750105155210240268323368
of2392230201075080
the2497230201073085130
pass/26522302010755105145185220
fail450240201073080108137
philosophy6122402010755110138166216256306361416463
of1100240201075080
the1205240201073085130
NMAS1360241908556124180224
to1609240201073080
any17142402010750105152
desired18912402010755100140168203248303
statistical2219240201074070120150178218248277322372400
base26442402010750100140185
model,4502502010780130185230258283
tolerance,758250201073080109154189239294339384409
percentage11922502010755100135180225280310360405450
of1667250201075080
points17722502010755105133188218258
in2055250201072984
error,2164250201074580115165200220
and24092502010750105160
risks.2594250201073563103153193218
The28372502010760115160
main4502602010780130158213
contribution688260201074595150180215244294349379407457512
of1225260201075080
this1330260201073085114153
proposal1508260201075590141196246286336364
is1897260201072868
a19902602010750
common2065260201074595175255305360
framework2450260201073065115195240309359394444
for450270201073080115
dealing5902702010755100150178207262307
with922270201076896126181
sampling1128270201074090170225254282337382
and15352702010750105160
risks1720270201073564103154193
with1939270201076896126181
independence2145270201072983138183238283338393438493538583
of2753270201075180
the450280201073085130
underlying6052802010755110165210245273320348403448
base10782802010750100140185
model12882802010780130185230259
(parametric1572280201073085135170220300345375410438483
or2080280201075085
nonparametric).21902802010755105160215265300350430475505540569614644669
The4502902010760115160
use635290201075595140
of800290201075080
nonparametric9052902010755105160215265300350430475505540568613
base15442902010750100140185
models17542902010780130185230258298
is2077290201072868
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and26072902010750105160
exemplified450300201074595140220275303332359387432487
for962300201073080115
the1102300201073085130
1D125730020107501307301908652
case.1384300201074595135180205
For16143002010753103138
2D177730020107511827301908652
and19043002010750105160
3D,20893002010750213930190865221913002010725
the2241300201073085130
Gaussian23963002010765115170210250278328383
base4503102010750100140185
model6603102010780130185230258
has9433102010755105145
been1113310201075196141196
adopted.13343102010750105155210240285340365
The17243102010760115160
Gaussian19093102010765115170210250278328383
models23173102010780130185230258298
allow2640310201075079107157225
the450320201073085130
combining605320201074595175225253308337392437
of1067320201075080
error1172320201074580115165200
components1397320201074595175230280335380435465505
by1927320201075097
means20493202010780125175230270
of2344320201075080
the2449320201073085130
Chi26043202010760115143
Squared4503302010755105160210245290345
and8203302010750105160
the1005330201073085130
Gamma11603302010765115195275325
distributions.1510330201075584123153188217267322352380430485525550
For20853302010754104139
the2249330201073085130
2D240433020107502454331908652
case,2531330201074595135180205
different450340201075583113143188223268323353
situations82834020107406999154204234262312367407
have12603402010755105152197
been1482340201075095140195
considered1702340201074595150190218273318353398453
in2180340201072883
order2288340201075085140185220
to2534340201072980
analyze26393402010750105155450350201072875120165
the640350201073085130
pass/fail7953502010755105145185220250300328357
behavior,1177350201075095150200247275325360380
and15823502010750105160
producer’s1767350201075590140195250295340375400435
and22273502010750105160
user’s2412350201075595140175200235
risks.2672350201073564103154193219
Introduction450376101512470100129174219265308337360405451
The4503892010760115160
positional6353892010755105145175205235285340385415
accuracy1075389201074590135190225270315365
of1465389201075080
geospatial1570389201074590140180235280310340385415
products2010389201075590140195250295325365
has24003892010755100140
always2565389201074575150195245285
been450399201075095140195
of670399201075080
great775399201074580125170200
importance.10003992010730110165215250280325380425470495
This15203992010760115145185
is,173039920107307095
together1850399201073080125170200255300335
with22103992010775105135190
logical2425399201073080125155200245275
consistency,2725399201074595150190220260450409201073075130175225243
the718409201073085130
quality8734092010750105150180210240290
element1188409201074575120200245300330
of1543409201075080
geographic1648409201074590140185220265320375405450
information2123409201073085115165200280325355385435490
most26384092010780130170200
extensively2863409201074595450419201073075130170200250295325375
used850419201075595140195
by10704192010750100
the1195419201073085130
National13504192010770115145175225280325355
Mapping17304192010785130185240270325370
Agencies21254192010770115160215260290335375
(NMA),2525419201073025554209085561241802735419201073055
and28154192010745100155
also450429201074575115165
the640429201073085130
more7954292010780130165210
commonly1030429201074595175255305360390440
evaluated1495429201074595140170225270300345400
quality19204292010750105150180210240290
element2235429201074575120200245300330
option25904292010750105135165215270
(Jakobsson450439201073060105155205255295335385440
and9154392010745100155
Vauglin,10954392010765103158203233263318343
2002).14634392010750100150200230255
Positional17434392010755106145175205235285340385415
accuracy2183439201074590135190225270315365
is2573439201073070
a26684392010745
matter27384392010780125155185230265
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renewed555449201073580135180255300355
interest935449201073085115160195240280310
because1270449201075095140185240280325
of1620449201075080
the1725449201073085130
capabilities1880449201074590145190240270300330360390435475
offered2380449201075080110155190235290
by26954492010750100
the2820449201073085130
Global450459201076595145195240270
Navigation7454592010770115165195240285315345395450
Satellite12204592010755100130175205235265295340
System15854592010755105145175220300
(GNSS)19104592010730194046090855210815219621364592010730
and21914592010745100155
the2371459201073085130
need25264592010755100145200
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a28564592010745
greater450469201074580125170200245280
spatial755469201074095140170200245275
interoperability1055469201073085115160195245300345380425475505535565595645
for1725469201073080115
supporting1865469201074095150205255290320350405450
the2340469201073085130
Spatial24954692010755110155185215260290
Data28104692010765110140185
Infrastructures.450479201073085115150195235265300355400430485520565605630
Different1105479201076595125155200235280335365
positional14954792010755105145175205235285340385415
behaviors1935479201075095150195245275325360400
of2360479201075080
geographic2465479201074590140185220265320375405450
data4504892010755100130175
sets650489201074085115155
mean8304892010780125170225
the1080489201073085130
existence1235489201074595125165195240295340385
of1645489201075080
an17504892010745100
inter-product1875489201073085115160195221276311361416471516546
positional24464892010755105145175205235285340385415
distortion450499201075585125155205240270300350405
and8804992010745100155
a10604992010745
barrier1130499201075095130165195240275
to1430499201073080
interoperation1535499201073085115160195245300345380425455485535590
(Church2150499201073090145200235280335
et2510499201074575
al.,26104992010750782688499201072550
1998).27634992010750100150200230255
This4505092010760115145185
barrier660509201075095130165195240275
exists960509201074595125165195235
not12205092010755105135
only13805092010750105135185
for1590509201073080115
the1730509201073085130
positional18855092010755105145175205235285340385415
and23255092010745100155
geometric2505509201074590140220265295330360405
aspects,450519201074585140185230260300325
but8005192010750105135
also960519201074575115165
for1150519201073080115
thematic1290519201073085130210255285315360
ones16755192010750105150190
which18905192010775130160205260
are2175519201074580125
greatly2325519201074580125170200230280
affected26305192010745751051501952254505292010745100
by5755292010750100
position7005292010755105145175205235285340
(Carmel1065529201073090135170250295325
et1415529201074575
al.,15155292010750781593529201072550
2006).16685292010750100150200230255
For19485292010755105140
these2113529201073085130170215
reasons2353529201073580125165215270310
many26885292010780125180230
NMAS450540908556124180224
are699539201074580125
currently8495392010745100135170215270300330380
involved1254539201073085135185215265310365
in1644539201073085
the1754539201073085130
development19095392010755100150195225275330410455510540
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positional25795392010755105145175205235285340385415
accuracy450549201074590135190225270315365
improvement8405492010730110165200250300345425470525555
programs1420549201075590140185220265345385
(EuroSDR,1830549201073085140175225280345405430
2004).22855492010750100150200230255
In570559201073085
a6805592010745
Spatial7505592010755110155185215260290
Data10655592010765110140185
Set12755592010755100130
(SDS)1430559201073014605609085449614016005592010730
the1655559201073085130
position18105592010755105145175205235285340
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a22805592010745
real2350559201073580125155
world25305592010775125160190245
entity4505692010745100130160190240
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appropriate19755692010745100155190240295330360405435480
coordinate2480569201074595145180235265320365395440
system.450579201074090130160205285310
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accuracy1225579201074590135190225270315365
represents1615579201073580135170215255300355385425
the2065579201073085130
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those2710579201073085135175220
values450589201075095125180225265
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entity’s10005892010745100130160190240265300
“true”1325589201074575110165210255
position16055892010755105145175205235285340
in1970589201073085
that2080589201073085130160
system.2265589201074090130160205285310
The26005892010760115160
positional27855892010755105450599201074070100130180235280310
accuracy785599201074590135190225270315365
requirements1175599201073580130185215250295375420475505545
for1745599201073080115
an18855992010745100
SDS201060090854496140
are2175599201074580125
directly2325599201075585120165210240270320
related2670599201073580110155185230285
to450609201073080
its555609201073060100
intended680609201073085115160215270315370
use(s).1075609201075595140170210240265
Positional13656092010755105145175205235285340385415
accuracy1805609201074590135190225270315365
is2195609201073070
determined22906092010755100130175210290320375420475
by27906092010750100
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a8456192010745
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evaluation1335619201074595140170225270300330380435
of1795619201075080
random1900619201073580135190240320
and22456192010745100155
systematic2425619201074090130160205285330360390435
errors450629201074580115165200240
(DOD,715629201073095165230255
1990)9956292010750100150200230
and12506292010745100155
specified1430629201074095140185215243270315370
by18256292010750100
means19506292010780125170225265
of2240629201075080
the2345629201073085130
Root25006292010760110160190
Mean27156292010785130175230
Squared4506392010755105160205240285340
Error815639201075590125175210
(RMSE)10506392010730108064090854811616020412846392010730
or1339639201075085
by14496392010750100
the1574639201073085130
mean17296392010780125170225
value1979639201075095125180225
of2229639201075080
errors2334639201074580115165200240
(μ)259963920107302636638301204526816392010730
and27366392010745100155
their450649201073085130160195
standard670649201074070115170225270305360
deviation10556492010755100150180225255285335390
(σ).14706492010730150064830120441544649201073055
Comparison16246492010760110190245290325355395445500
with21496492010775105135190
an23646492010745100
independent2489649201073085140185240285340395440495525
source3157181101074090145180225270
of3452181101075080
greater3557181101074580125170200245280
accuracy3862181101074590135190225270315365
is4252181101073070
the4347181101073085130
preferred4502181101075590135165210245280325380
method49071811010780125155210260315
for5247181101073080115
assessing53871811010745851251702102503157191001073085130
positional33121910010755105145175205235285340385415
accuracy3752191001074590135190225270315365
(ANSI,41421910010730100170225255280
1998).44471910010750100150200230255
Since3277201001075585140185230
positional35322010010755105145175205235285340385415
accuracy3972201001074590135190225270315365
is4362201001073070
essential4457201001074585125170225255285330360
in4842201001073085
geospatial4952201001074590140180235280310340385415
production,53922010010755901401952502953157211001073060110165190
all3372211001074575105
NMAS3502212708556124180224
have37512111010755100150195
used3971211101075595140195
statistical4191211101074070115145175215245275320365395
methods46112111010780125155210260315355
for4991211101073080115
its5131211101073060100
control,5256211101074595150180215265295320
which31572211010775130160205260
we34422211010775120
call3587221101074590120150
here37622211010755100135180
Positional39672211010755105145175205235285340385415
Accuracy44072211010770115160215250295340390
Assessment48222211010770110150195235275355400455485
Methodologies5332221101078513016021531572311010750105155185235280310355395
(PAAMs).35772311010730360723270854493149217382523110107407095
Many39452311010785130185235
of4205231101075080
these4310231101073085130170215
have45502311010755100150195
been4770231101075095140195
established4990231101074585115160210240270310365410465
as5480231101074585
national31582411010755100130160210265310340
or3523241101075085
international3633241101073085115160195250295325355405460505535
standards4193241101074070115170225270305360400
and46182411010745100155
can4798241101074590145
be4968241101075095
used5088241101075595140195
for5308241101073080115
specifying54482411010740951401853158251101073060110140195240
spatial3423251101074095140170200245275
data37232511010755100130175
products3923251101075590140195250295325365
but43132511010750105135
also4473251101074575115165
the4663251101073085130
resultant4818251101073580120175205235280335365
positional52082511010755105145175205235285340385415
accuracy3158261101074590135190225270315365
assessment3548261101074585125170210250330375430460
compliance4033261101074595175230260290335390435480
criteria.4538261101074580110140185220250295320
Standards4883261101075585130185240285320375415
should5323261101074095145200230285
be5633261101075095
taken3158271101073075125170225
into3408271101073085115165
account3598271101074590135185240295325
when39482711010775130175230
seeking4203271101074085130180210265310
an45382711010745100
economic4663271101074590140195245325355400
optimization50882711010750105135165245275320365395425475530
of5643271101075080
the3158281001073085130
quality33132810010750105150180210240290
of3628281001075080
geographic3733281001074590140185220265320375405450
information4208281001073085115165200280325355385435490
(Krek4723281001073095130175225
and49732810010745100155
Frank,5153281001075590135190240265
1999):54432810010750100150200230255
with31582910010775105135190
a33732910010745
quality34432910010750105150180210240290
standard3758291001074070115170225270305360
the4143291001073085130
producer4298291001075590140195250295340375
provides4698291001075590140190220275320360
the5083291001073085130
product5238291001075590140195250295325
according3158301001074590135185220275305360405
to3588301001073080
the3693301001073085130
known38483010010750105155230285
specification4158301001074095140185215242270315360390420470525
and47083010010745100155
characteristics,48883010010745100145180225270300345380410450480510555595620
as5533301001074585
defined31583110010755100127155210255310
in3493311001073085
the3603311001073085130
standard.3758311001074070115170225270305360385
This41683110010760115145185
assures4378311001074585125180215260300
a47033110010745
certain4773311001074590125155200230285
level5083311001073075125170200
of5308311001075080
reliability54133110010735801101403158321001074595125155185215265
and34483210010745100155
certainty,3628321001074590125155200230285315365383
allowing4036321001074575105155230260315360
the4421321001073085130
acquirer4576321001074590140195225260305340
to4941321001073080
avoid5046321001074595145175230
excessive5301321001074595140185225265295345390
measuring31583310010780125170210265300330385430
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the3718331001073085130
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the4963331001073085130
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International4243401101073085115160195250295325355405460505535
Standard4803401101075585130185240285320375
also5203401101074575115165
proposes53934011010755901401952452853158411101074585
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Operativa.16907237010770125170205250280310360405430
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Engineering44656657010755110155185240285330365395450495
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Remote50706657010760105185235265310
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Vol.40466765010765108138163
80,42346765010750100125
No.43846765010771121146
3,4555676501075075
March46556765010785130165210265
2014,49456765010750100150200225
pp.51956765010755110135
271–281.53556765010750100150200250300350375
0099-1112/14/8003–271472968730107501001502002302803303804304655155656006507007518018519019511001
©38277001010767
201439197001010750100150200
American41447001010770150195230260305350405
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Photogrammetry50457001010755110160190240285320365445525570600635685
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doi:45347237010755105135160
10.14358/PERS.80.3.271471972370107501001251752252753253754104655205806356607107607858368619119611011
ASPRS553187016183157240330403
MEMBERS9881870161108191299385468558631
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SUBSCRIBERS,1949187016174165251324410499548634717807880911
CLICK2891187016186165214300390
HERE3312187016196179269352
TO3696187016179171
READ3899187016189173256348
THE4278187016180176259
ENTIRE4569187016183175254303393476
ARTICLE5077187016183173252301387466550