30:
535:, which makes longitude undefined at these points. Also near the poles the latitude/longitude grid is highly non-linear, and several errors may occur in calculations that are sufficiently accurate on other locations.
738:
When deciding which parameters to use for representing position in a specific application, there are several properties that should be considered. The following table gives a summary of what to consider.
649:-axis in the vertical direction. Hence (three dimensional) position vectors relative to this coordinate frame will have two horizontal and one vertical parameter. The axes are typically selected as
672:
For small areas a local coordinate system can be convenient for relative positioning, but with increasing (horizontal) distances, errors will increase and repositioning of the
550:, and hence specific program code must often be written to handle this. An example of the consequences of omitting such code is the crash of the navigation systems of twelve
454:. There are also several applications where only the horizontal position is of interest, this might e.g. be the case for ships and ground vehicles/cars. It is a type of
869:
716:
712:
707:
470:
389:
527:
However, latitude and longitude should be used with care in mathematical expressions (including calculations in computer programs). The main reason is the
461:
There are several options for horizontal position representations, each with different properties which makes them appropriate for different applications.
211:
379:
347:
357:
921:
485:
726:
UTM is widely used, and the coordinates approximately corresponds to meters north and east. However, as a set of map-projections it has inherent
1028:
862:
North and east directions are undefined at the Poles, and near the Poles these directions may change significantly within the area of interest
337:
524:. The parameters are intuitive and well known, and are thus suited for communicating a position to humans, e.g. using a position plot.
417:
859:
Errors increase with increasing horizontal distance from the tangent point (which may require repositioning of the tangent point)
680:, and near the Poles these directions might have significant errors (here the linearization is valid only in a very small area).
477:
203:
957:
219:
1033:
455:
612:-vector is well-suited for mathematical calculations, e.g. adding, subtracting, interpolating and averaging positions.
842:
645:
at a specified Earth-fixed position. The origin is often selected at the surface of the reference ellipsoid, with the
638:
547:
694:
Instead of one local
Cartesian grid, that needs to be repositioned as the position of interest moves, a fixed set of
998:
182:
730:, and thus most calculations based on UTM will not be exact. The crossing of zones gives additional complexity.
480:, and thus two parameters are sufficient to uniquely describe such a position. However, similarly to the use of
812:
780:
578:
528:
489:
149:
619:-vector is inconvenient for communicating a position directly to humans and before showing a position plot, a
96:
432:
247:
267:
29:
856:
Can only be used for relative positioning (the tangent point must be represented by some other quantity)
689:
410:
327:
77:
972:
926:
662:
642:
590:
539:
501:
317:
287:
227:
177:
103:
1018:
632:
586:
581:
horizontal position representation that can replace latitude and longitude. Geometrically, it is a
139:
87:
666:
601:
59:
936:
784:
677:
597:
532:
446:
159:
144:
1023:
980:
403:
154:
931:
818:
695:
676:
may be required. The alignment along the north and east directions is not possible at the
650:
605:
437:
976:
894:
793:
543:
367:
134:
108:
1012:
904:
849:
Cartesian vectors in meters along the directions of north, east and down are obtained
720:
673:
658:
654:
492:, and thus three parameters are required for the horizontal position to avoid this.
481:
92:
727:
582:
551:
49:
984:
890:
763:
600:. It behaves the same at all Earth positions, and it holds the mathematical
521:
511:
466:
450:(height or depth) separately, and to use some other parameters to represent
128:
54:
802:
759:
715:
is one such system, dividing the Earth into 60 longitude zones (and with
620:
571:
566:
517:
507:
462:
307:
124:
113:
187:
44:
21:
604:
property. The vector formulation makes it possible to use standard 3D
773:
Parameters are easy to recognize by humans (well-suited for plotting)
297:
257:
195:
441:
82:
637:
When carrying out several calculations within a limited area, a
594:
436:
is a set of parameters used to express a position relative to a
384:
277:
897:) gives only approximate answers for most calculations
817:
Efficient in equations/calculations since standard 3D
516:
The most common horizontal position representation is
488:, using only the minimum number of parameters gives
958:"A non-singular horizontal position representation"
831:
Inconvenient for communicating a position to humans
743:Comparison of horizontal position representations
900:Calculations get complex when crossing the zones
473:are common horizontal position representations.
882:One unit corresponds approximately to one meter
708:Universal Transverse Mercator coordinate system
554:fighter aircraft while crossing this meridian.
440:. When representing positions relative to the
411:
8:
444:, it is often most convenient to represent
971:(3). Cambridge University Press: 395–417.
657:, and thus this system can be viewed as a
418:
404:
385:Spatial Reference System Identifier (SRID)
380:International Terrestrial Reference System
17:
999:"Stealth fighters hit by software crash"
741:
948:
922:Rotation formalisms in three dimensions
824:All Earth positions are treated equally
20:
879:Approximate north and east directions
546:longitude, where the longitude has a
7:
486:formalism for representing rotations
243:
698:covering the Earth can be defined.
390:Universal Transverse Mercator (UTM)
352:European Terrestrial Ref. Sys. 1989
262:Ordnance Survey Great Britain 1936
228:Discrete Global Grid and Geocoding
119:Horizontal position representation
14:
621:conversion to latitude/longitude
538:Another problematic area is the
476:The horizontal position has two
178:Global Nav. Sat. Systems (GNSSs)
28:
789:Complex behavior near the Poles
342:N. American Vertical Datum 1988
627:Local flat Earth approximation
372:Internet link to a point 2010
302:Geodetic Reference System 1980
220:Quasi-Zenith Sat. Sys. (QZSS)
1:
1029:Geographic coordinate systems
362:Chinese obfuscated datum 2002
456:geographic coordinate system
312:Geographic point coord. 1983
843:Cartesian coordinate system
639:Cartesian coordinate system
272:Systema Koordinat 1942 goda
1050:
705:
687:
641:might be defined with the
630:
595:Earth centered earth fixed
564:
505:
499:
332:World Geodetic System 1984
985:10.1017/S0373463309990415
965:The Journal of Navigation
322:North American Datum 1983
292:South American Datum 1969
615:Using three parameters,
183:Global Pos. System (GPS)
150:Spatial reference system
585:which is normal to the
433:position representation
956:Gade, Kenneth (2010).
792:Discontinuity at the ±
496:Latitude and longitude
834:Uses three parameters
690:Grid reference system
684:Grid reference system
577:is a three parameter
506:Further information:
78:Geographical distance
927:Geodetic coordinates
502:Geodetic coordinates
252:Sea Level Datum 1929
104:Geodetic coordinates
1034:Geographic position
1001:. 27 February 2007.
977:2010JNav...63..395G
744:
633:Local tangent plane
587:reference ellipsoid
452:horizontal position
282:European Datum 1950
240:Standards (history)
140:Reference ellipsoid
88:Figure of the Earth
742:
478:degrees of freedom
160:Vertical positions
937:Plane coordinates
913:
912:
623:might be needed.
598:coordinate system
447:vertical position
428:
427:
376:
375:
155:Spatial relations
145:Satellite geodesy
100:
1041:
1003:
1002:
995:
989:
988:
962:
953:
745:
589:. The vector is
420:
413:
406:
244:
223:
215:
207:
199:
191:
131:
90:
32:
18:
1049:
1048:
1044:
1043:
1042:
1040:
1039:
1038:
1009:
1008:
1007:
1006:
997:
996:
992:
960:
955:
954:
950:
945:
932:Geodetic system
918:
907:are not covered
736:
710:
704:
696:map projections
692:
686:
651:North-East-Down
635:
629:
569:
563:
514:
504:
498:
438:reference frame
424:
395:
394:
241:
233:
232:
221:
213:
205:
197:
189:
173:
165:
164:
123:
73:
65:
64:
40:
12:
11:
5:
1047:
1045:
1037:
1036:
1031:
1026:
1021:
1011:
1010:
1005:
1004:
990:
947:
946:
944:
941:
940:
939:
934:
929:
924:
917:
914:
911:
910:
909:
908:
901:
898:
895:map projection
885:
884:
883:
880:
877:
872:
866:
865:
864:
863:
860:
857:
852:
851:
850:
845:
838:
837:
836:
835:
832:
827:
826:
825:
822:
819:vector algebra
815:
808:
799:
798:
797:
796:
790:
787:
776:
775:
774:
771:
766:
756:
755:
752:
749:
748:Representation
735:
732:
706:Main article:
703:
700:
688:Main article:
685:
682:
631:Main article:
628:
625:
606:vector algebra
565:Main article:
562:
556:
500:Main article:
497:
494:
426:
425:
423:
422:
415:
408:
400:
397:
396:
393:
392:
387:
382:
374:
373:
370:
364:
363:
360:
354:
353:
350:
344:
343:
340:
334:
333:
330:
324:
323:
320:
314:
313:
310:
304:
303:
300:
294:
293:
290:
284:
283:
280:
274:
273:
270:
264:
263:
260:
254:
253:
250:
242:
239:
238:
235:
234:
231:
230:
225:
217:
209:
201:
193:
185:
180:
174:
171:
170:
167:
166:
163:
162:
157:
152:
147:
142:
137:
135:Map projection
132:
121:
116:
111:
109:Geodetic datum
106:
101:
85:
80:
74:
71:
70:
67:
66:
63:
62:
57:
52:
47:
41:
38:
37:
34:
33:
25:
24:
13:
10:
9:
6:
4:
3:
2:
1046:
1035:
1032:
1030:
1027:
1025:
1022:
1020:
1017:
1016:
1014:
1000:
994:
991:
986:
982:
978:
974:
970:
966:
959:
952:
949:
942:
938:
935:
933:
930:
928:
925:
923:
920:
919:
915:
906:
905:Polar Regions
902:
899:
896:
892:
888:
887:
886:
881:
878:
875:
874:
873:
871:
868:
867:
861:
858:
855:
854:
853:
848:
847:
846:
844:
840:
839:
833:
830:
829:
828:
823:
820:
816:
814:
811:
810:
809:
807:
805:
801:
800:
795:
794:180° meridian
791:
788:
786:
782:
781:Singularities
779:
778:
777:
772:
769:
768:
767:
765:
761:
758:
757:
753:
750:
747:
746:
740:
733:
731:
729:
724:
722:
721:Polar regions
719:covering the
718:
714:
709:
701:
699:
697:
691:
683:
681:
679:
675:
674:tangent point
670:
668:
664:
660:
659:linearization
656:
655:East-North-Up
652:
648:
644:
640:
634:
626:
624:
622:
618:
613:
611:
607:
603:
599:
596:
592:
588:
584:
580:
576:
574:
568:
560:
557:
555:
553:
549:
548:discontinuity
545:
541:
536:
534:
530:
529:singularities
525:
523:
519:
513:
509:
503:
495:
493:
491:
490:singularities
487:
483:
479:
474:
472:
468:
464:
459:
457:
453:
449:
448:
443:
439:
435:
434:
421:
416:
414:
409:
407:
402:
401:
399:
398:
391:
388:
386:
383:
381:
378:
377:
371:
369:
366:
365:
361:
359:
356:
355:
351:
349:
346:
345:
341:
339:
336:
335:
331:
329:
326:
325:
321:
319:
316:
315:
311:
309:
306:
305:
301:
299:
296:
295:
291:
289:
286:
285:
281:
279:
276:
275:
271:
269:
266:
265:
261:
259:
256:
255:
251:
249:
246:
245:
237:
236:
229:
226:
224:
218:
216:
210:
208:
202:
200:
196:BeiDou (BDS)
194:
192:
186:
184:
181:
179:
176:
175:
169:
168:
161:
158:
156:
153:
151:
148:
146:
143:
141:
138:
136:
133:
130:
126:
122:
120:
117:
115:
112:
110:
107:
105:
102:
98:
97:circumference
94:
89:
86:
84:
81:
79:
76:
75:
69:
68:
61:
58:
56:
53:
51:
48:
46:
43:
42:
36:
35:
31:
27:
26:
23:
19:
16:
993:
968:
964:
951:
893:(due to the
803:
737:
725:
711:
693:
671:
646:
636:
616:
614:
609:
579:non-singular
572:
570:
558:
537:
526:
515:
482:Euler angles
475:
460:
451:
445:
431:
429:
172:Technologies
127: /
118:
39:Fundamentals
15:
876:Widely used
821:can be used
813:Nonsingular
770:Widely used
728:distortions
608:, and thus
583:unit vector
552:F-22 Raptor
50:Geodynamics
1019:Navigation
1013:Categories
943:References
891:distortion
734:Comparison
602:one-to-one
591:decomposed
889:Inherent
764:longitude
667:parallels
663:meridians
522:longitude
512:Longitude
467:longitude
129:Longitude
55:Geomatics
916:See also
760:Latitude
567:n-vector
540:meridian
518:latitude
508:Latitude
463:Latitude
308:ISO 6709
206:(Europe)
204:Galileo
190:(Russia)
188:GLONASS
125:Latitude
114:Geodesic
72:Concepts
1024:Geodesy
973:Bibcode
806:-vector
783:at the
661:of the
575:-vector
561:-vector
531:at the
368:Geo URI
338:NAVD 88
248:NGVD 29
222:(Japan)
214:(India)
198:(China)
60:History
45:Geodesy
22:Geodesy
841:Local
643:origin
593:in an
358:GCJ-02
348:ETRS89
328:WGS 84
318:NAD 83
298:GRS 80
258:OSGB36
212:NAVIC
93:radius
961:(PDF)
785:Poles
754:Cons
678:Poles
533:Poles
484:as a
442:Earth
288:SAD69
268:SK-42
83:Geoid
903:The
762:and
751:Pros
665:and
544:180°
542:at ±
520:and
510:and
469:and
278:ED50
95:and
981:doi
870:UTM
723:).
717:UPS
713:UTM
702:UTM
653:or
471:UTM
1015::
979:.
969:63
967:.
963:.
669:.
458:.
430:A
987:.
983::
975::
804:n
647:z
617:n
610:n
573:n
559:n
465:/
419:e
412:t
405:v
99:)
91:(
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