31:
1205:
975:
174:(ENU) Cartesian coordinate system is far more intuitive and practical than ECEF or Geodetic coordinates. The local ENU coordinates are formed from a plane tangent to the Earth's surface fixed to a specific location and hence it is sometimes known as a "Local Tangent" or "local geodetic" plane. By convention the east axis is labeled
720:
369:
The origin of this coordinate system is usually chosen to be a fixed point on the surface of the geoid below the aircraft's center of gravity. When that is the case, the coordinate system is sometimes referred as a "local-North-East-Down
Coordinate System".
474:
970:{\displaystyle R={\begin{bmatrix}-\sin(\phi )\cos(\lambda )&-\sin(\phi )\sin(\lambda )&\cos(\phi )\\-\sin(\lambda )&\cos(\lambda )&0\\-\cos(\phi )\cos(\lambda )&-\cos(\phi )\sin(\lambda )&-\sin(\phi )\end{bmatrix}}}
377:
in that they're
Cartesian, however they can be more convenient due to the relatively small numbers involved, and also because of the intuitive axes. NED and ECEF coordinates can be related with the following formula:
554:
712:
591:
514:
384:
675:
364:
319:
294:
269:
655:
635:
611:
339:
232:
212:
192:
125:
These frames are location dependent. For movements around the globe, like air or sea navigation, the frames are defined as tangent to the lines of
17:
165:
1246:
1270:
1184:
1151:
1118:
1085:
1052:
242:
In an airplane, most objects of interest are below the aircraft, so it is sensible to define down as a positive number. The
519:
680:
559:
482:
85:: one represents the position along the northern axis, one along the local eastern axis, and one represents the
34:
The east north up (ENU) local tangent plane is similar to NED, except for swapping 'down' for 'up' and x for y.
469:{\displaystyle \mathbf {p} _{\mathrm {NED} }=R(\mathbf {p} _{\mathrm {ECEF} }-\mathbf {p} _{\mathrm {Ref} })}
996:
1239:
1220:
110:
246:(NED) coordinates allow this as an alternative to the ENU. By convention, the north axis is labeled
126:
46:
1275:
1232:
1176:
1143:
660:
1011:
1168:
1135:
30:
1001:
640:
141:
8:
344:
299:
274:
249:
1265:
620:
596:
324:
217:
197:
177:
134:
54:
1180:
1169:
1147:
1136:
1114:
1081:
1048:
1016:
86:
1106:
1073:
1040:
986:
1006:
991:
614:
152:
148:
90:
58:
1216:
593:
is the reference ECEF position (where the local tangent plane originates), and
1110:
1105:. Hoboken, NJ, USA: John Wiley & Sons, Inc. 2015-04-11. pp. 129–206.
1259:
50:
366:, etc. in this article we will restrict the local coordinate frame to ENU.
1077:
1044:
82:
1212:
114:
1204:
237:
155:, which does not generally pass through the center of Earth.
374:
159:
166:
Geographic coordinate conversion § From ECEF to ENU
735:
170:
In many targeting and tracking applications the local
723:
683:
663:
643:
623:
599:
562:
522:
485:
387:
347:
327:
302:
277:
252:
220:
200:
180:
1167:Cai, Guowei; Chen, Ben M.; Lee, Tong Heng (2011).
1134:Cai, Guowei; Chen, Ben M.; Lee, Tong Heng (2011).
969:
706:
669:
649:
629:
605:
585:
548:
508:
468:
358:
333:
313:
288:
263:
226:
206:
186:
1257:
617:whose rows are the north, east, and down axes.
1035:Torge, Wolfgang; MĂĽller, JĂĽrgen (2012-05-29).
637:may be defined conveniently from the latitude
549:{\displaystyle \mathbf {p} _{\mathrm {ECEF} }}
1240:
707:{\displaystyle \mathbf {p} _{\mathrm {Ref} }}
586:{\displaystyle \mathbf {p} _{\mathrm {Ref} }}
509:{\displaystyle \mathbf {p} _{\mathrm {NED} }}
71:local vertical, local horizontal coordinates
1034:
109:) coordinates. They serve for representing
1247:
1233:
1166:
1133:
238:Local north, east, down (NED) coordinates
29:
160:Local east, north, up (ENU) coordinates
147:Up–down in the direction normal to the
14:
1258:
1067:
1061:
1199:
1028:
556:is the corresponding ECEF position,
61:of rotation. They are also known as
24:
698:
695:
692:
577:
574:
571:
540:
537:
534:
531:
516:is a 3D position in a NED system,
500:
497:
494:
457:
454:
451:
434:
431:
428:
425:
402:
399:
396:
27:Geographic local coordinate system
25:
1287:
1203:
686:
565:
525:
488:
445:
419:
390:
67:local geodetic coordinate system
373:NED coordinates are similar to
39:Local tangent plane coordinates
1160:
1127:
1094:
956:
950:
936:
930:
921:
915:
901:
895:
886:
880:
859:
853:
842:
836:
820:
814:
803:
797:
788:
782:
768:
762:
753:
747:
463:
414:
13:
1:
1271:Geographic coordinate systems
1068:Seeber, GĂĽnter (2003-06-19).
1022:
321:. To avoid confusion between
18:Topocentric coordinate system
1219:. You can help Knowledge by
997:Horizontal coordinate system
7:
1171:Unmanned Rotorcraft Systems
1138:Unmanned Rotorcraft Systems
980:
10:
1292:
1198:
163:
113:that are commonly used in
1111:10.1002/9781119018612.ch4
670:{\displaystyle \lambda }
127:geographical coordinates
117:and marine cybernetics.
63:local ellipsoidal system
47:spatial reference system
1103:GPS Satellite Surveying
140:North–south tangent to
120:
81:. It consists of three
79:topocentric coordinates
1215:-related article is a
971:
708:
671:
651:
631:
607:
587:
550:
510:
470:
360:
335:
315:
290:
265:
228:
208:
188:
35:
1175:. Springer. pp.
1142:. Springer. pp.
1078:10.1515/9783110200089
1072:. Walter de Gruyter.
1045:10.1515/9783110250008
1012:Grid reference system
972:
709:
672:
652:
650:{\displaystyle \phi }
632:
608:
588:
551:
511:
471:
361:
336:
316:
291:
266:
229:
209:
189:
164:Further information:
133:East–west tangent to
53:defined by the local
33:
1002:Geodetic coordinates
721:
681:
661:
641:
621:
597:
560:
520:
483:
385:
345:
325:
300:
275:
250:
218:
198:
178:
967:
961:
704:
667:
647:
627:
603:
583:
546:
506:
466:
359:{\displaystyle x'}
356:
331:
314:{\displaystyle z'}
311:
289:{\displaystyle y'}
286:
264:{\displaystyle x'}
261:
224:
204:
184:
101:) coordinates and
55:vertical direction
36:
1228:
1227:
1186:978-0-85729-634-4
1153:978-0-85729-634-4
1120:978-1-119-01861-2
1087:978-3-11-017549-3
1070:Satellite Geodesy
1054:978-3-11-020718-7
1017:Local coordinates
677:corresponding to
630:{\displaystyle R}
606:{\displaystyle R}
334:{\displaystyle x}
244:North, East, Down
227:{\displaystyle z}
207:{\displaystyle y}
187:{\displaystyle x}
153:Earth's ellipsoid
103:north, east, down
87:vertical position
16:(Redirected from
1283:
1249:
1242:
1235:
1207:
1200:
1191:
1190:
1174:
1164:
1158:
1157:
1141:
1131:
1125:
1124:
1098:
1092:
1091:
1065:
1059:
1058:
1032:
987:Axes conventions
976:
974:
973:
968:
966:
965:
713:
711:
710:
705:
703:
702:
701:
689:
676:
674:
673:
668:
656:
654:
653:
648:
636:
634:
633:
628:
612:
610:
609:
604:
592:
590:
589:
584:
582:
581:
580:
568:
555:
553:
552:
547:
545:
544:
543:
528:
515:
513:
512:
507:
505:
504:
503:
491:
475:
473:
472:
467:
462:
461:
460:
448:
439:
438:
437:
422:
407:
406:
405:
393:
365:
363:
362:
357:
355:
340:
338:
337:
332:
320:
318:
317:
312:
310:
295:
293:
292:
287:
285:
270:
268:
267:
262:
260:
233:
231:
230:
225:
213:
211:
210:
205:
193:
191:
190:
185:
93:variants exist:
45:) are part of a
21:
1291:
1290:
1286:
1285:
1284:
1282:
1281:
1280:
1256:
1255:
1254:
1253:
1196:
1194:
1187:
1165:
1161:
1154:
1132:
1128:
1121:
1100:
1099:
1095:
1088:
1066:
1062:
1055:
1033:
1029:
1025:
1007:Geodetic system
992:Figure of Earth
983:
960:
959:
939:
904:
868:
867:
862:
845:
824:
823:
806:
771:
731:
730:
722:
719:
718:
691:
690:
685:
684:
682:
679:
678:
662:
659:
658:
642:
639:
638:
622:
619:
618:
615:rotation matrix
598:
595:
594:
570:
569:
564:
563:
561:
558:
557:
530:
529:
524:
523:
521:
518:
517:
493:
492:
487:
486:
484:
481:
480:
450:
449:
444:
443:
424:
423:
418:
417:
395:
394:
389:
388:
386:
383:
382:
348:
346:
343:
342:
326:
323:
322:
303:
301:
298:
297:
278:
276:
273:
272:
253:
251:
248:
247:
240:
219:
216:
215:
199:
196:
195:
179:
176:
175:
172:East, North, Up
168:
162:
149:oblate spheroid
123:
95:east, north, up
28:
23:
22:
15:
12:
11:
5:
1289:
1279:
1278:
1276:Aviation stubs
1273:
1268:
1252:
1251:
1244:
1237:
1229:
1226:
1225:
1208:
1193:
1192:
1185:
1159:
1152:
1126:
1119:
1093:
1086:
1060:
1053:
1039:. DE GRUYTER.
1026:
1024:
1021:
1020:
1019:
1014:
1009:
1004:
999:
994:
989:
982:
979:
978:
977:
964:
958:
955:
952:
949:
946:
943:
940:
938:
935:
932:
929:
926:
923:
920:
917:
914:
911:
908:
905:
903:
900:
897:
894:
891:
888:
885:
882:
879:
876:
873:
870:
869:
866:
863:
861:
858:
855:
852:
849:
846:
844:
841:
838:
835:
832:
829:
826:
825:
822:
819:
816:
813:
810:
807:
805:
802:
799:
796:
793:
790:
787:
784:
781:
778:
775:
772:
770:
767:
764:
761:
758:
755:
752:
749:
746:
743:
740:
737:
736:
734:
729:
726:
700:
697:
694:
688:
666:
657:and longitude
646:
626:
602:
579:
576:
573:
567:
542:
539:
536:
533:
527:
502:
499:
496:
490:
477:
476:
465:
459:
456:
453:
447:
442:
436:
433:
430:
427:
421:
416:
413:
410:
404:
401:
398:
392:
354:
351:
330:
309:
306:
284:
281:
259:
256:
239:
236:
223:
203:
183:
161:
158:
157:
156:
145:
138:
122:
119:
26:
9:
6:
4:
3:
2:
1288:
1277:
1274:
1272:
1269:
1267:
1264:
1263:
1261:
1250:
1245:
1243:
1238:
1236:
1231:
1230:
1224:
1222:
1218:
1214:
1209:
1206:
1202:
1201:
1197:
1188:
1182:
1178:
1173:
1172:
1163:
1155:
1149:
1145:
1140:
1139:
1130:
1122:
1116:
1112:
1108:
1104:
1097:
1089:
1083:
1079:
1075:
1071:
1064:
1056:
1050:
1046:
1042:
1038:
1031:
1027:
1018:
1015:
1013:
1010:
1008:
1005:
1003:
1000:
998:
995:
993:
990:
988:
985:
984:
962:
953:
947:
944:
941:
933:
927:
924:
918:
912:
909:
906:
898:
892:
889:
883:
877:
874:
871:
864:
856:
850:
847:
839:
833:
830:
827:
817:
811:
808:
800:
794:
791:
785:
779:
776:
773:
765:
759:
756:
750:
744:
741:
738:
732:
727:
724:
717:
716:
715:
664:
644:
624:
616:
600:
440:
411:
408:
381:
380:
379:
376:
371:
367:
352:
349:
328:
307:
304:
296:and the down
282:
279:
257:
254:
245:
235:
221:
201:
181:
173:
167:
154:
150:
146:
143:
139:
136:
132:
131:
130:
128:
118:
116:
112:
111:state vectors
108:
104:
100:
96:
92:
88:
84:
80:
76:
72:
68:
64:
60:
56:
52:
51:tangent plane
49:based on the
48:
44:
40:
32:
19:
1221:expanding it
1210:
1195:
1170:
1162:
1137:
1129:
1102:
1096:
1069:
1063:
1036:
1030:
478:
372:
368:
243:
241:
194:, the north
171:
169:
124:
106:
102:
98:
94:
91:right-handed
78:
74:
70:
66:
62:
59:Earth's axis
42:
38:
37:
1101:"Geodesy".
271:, the east
214:and the up
83:coordinates
1260:Categories
1023:References
1266:Aerospace
954:ϕ
948:
942:−
934:λ
928:
919:ϕ
913:
907:−
899:λ
893:
884:ϕ
878:
872:−
857:λ
851:
840:λ
834:
828:−
818:ϕ
812:
801:λ
795:
786:ϕ
780:
774:−
766:λ
760:
751:ϕ
745:
739:−
665:λ
645:ϕ
441:−
142:meridians
135:parallels
1213:aviation
981:See also
353:′
308:′
283:′
258:′
151:used as
115:aviation
89:. Two
57:and the
1037:Geodesy
1183:
1150:
1117:
1084:
1051:
479:where
77:), or
1211:This
613:is a
144:, and
1217:stub
1181:ISBN
1148:ISBN
1115:ISBN
1082:ISBN
1049:ISBN
375:ECEF
341:and
121:Axes
75:LVLH
1107:doi
1074:doi
1041:doi
945:sin
925:sin
910:cos
890:cos
875:cos
848:cos
831:sin
809:cos
792:sin
777:sin
757:cos
742:sin
107:NED
99:ENU
43:LTP
1262::
1179:.
1177:32
1146:.
1144:27
1113:.
1080:.
1047:.
714::
234:.
129::
69:,
65:,
1248:e
1241:t
1234:v
1223:.
1189:.
1156:.
1123:.
1109::
1090:.
1076::
1057:.
1043::
963:]
957:)
951:(
937:)
931:(
922:)
916:(
902:)
896:(
887:)
881:(
865:0
860:)
854:(
843:)
837:(
821:)
815:(
804:)
798:(
789:)
783:(
769:)
763:(
754:)
748:(
733:[
728:=
725:R
699:f
696:e
693:R
687:p
625:R
601:R
578:f
575:e
572:R
566:p
541:F
538:E
535:C
532:E
526:p
501:D
498:E
495:N
489:p
464:)
458:f
455:e
452:R
446:p
435:F
432:E
429:C
426:E
420:p
415:(
412:R
409:=
403:D
400:E
397:N
391:p
350:x
329:x
305:z
280:y
255:x
222:z
202:y
182:x
137:,
105:(
97:(
73:(
41:(
20:)
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
